UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO
PROGRAMA EN ASTROFÍSICA
INSTITUTO DE ASTRONOMÍA
RAPID RESPONSE SPECTROPHOTOMETRIC
CHARACTERIZATION OF NEAR-EARTH OBJECTS
PARA OPTAR POR EL GRADO DE:
DOCTOR EN CIENCIAS (ASTROFÍSICA)
PRESENTA
SAMUEL AMADEUS JOSSHUA RAMÓN NAVARRO MEZA
DIRECTORES DE TESIS
DR. MAURICIO REYES RUIZ, INSTITUTO DE ASTRONOMÍA,
SEDE ENSENADA, UNAM
DR. DAVID E. TRILLING, DEPARTMENT OF ASTRONOMY AND
PLANETARY SCIENCE, NAU
ENSENADA, BAJA CALIFORNIA, SEPTIEMBRE 2020
 
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Índice
1. Resumen 3
2. Antecedentes 4
2.1. Asteroides . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2. Objetos cercanos a la Tierra (NEOs) . . . . . . . . . . . . . 5
2.3. Sondeos de NEOs . . . . . . . . . . . . . . . . . . . . . . . . 8
3. Introducción 10
3.1. Necesidad de técnicas no estándar . . . . . . . . . . . . . . . 10
3.2. Estudio de 3 métodos diferentes para clasificar NEOs . . . . 12
4. Caracterización de NEOs utilizando fotometría de respues-
ta rápida con RATIR 14
5. Investigando la diversidad taxonómica en familias de aste-
roides utillizando ATLAS 27
6. Taxonomía de NEOs pequeños con RATIR -borrador- 36
7. Discusión 54
8. Conclusiones 58
Apéndice: Trabajos adicionales 59
A. Tránsitos de exoplanetas con múltiples filtros y observatorios 59
B. CMFA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
C. El primer objeto interestelar observado y sus implicaciones
en la formación planetaria . . . . . . . . . . . . . . . . . . . 80
D. Observaciones del efecto YORP . . . . . . . . . . . . . . . . 85
E. Convocatoria CONACYT Ciencia de Frontera 2019 . . . . . 85
F. Divulgación . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
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1. Resumen
Se presentan mediciones de 238 asteroides cercanos a la Tierra y 1612
asteroides del cinturón principal. El objetivo principal del trabajo es utilizar
fotometría para obtener la distribución taxonómica de la muestra, particu-
larmente distinguir entre objetos de tipo rocoso y no rocoso. Para analizar
los datos se utilizan tres métodos computacionales diferentes, incluyendo
una rutina de Machine Learning, y se discute la eficacia de cada uno de
ellos. Los resultados encontrados coinciden con los generados por otros es-
tudios utilizando espectroscopía. Esto representa una ventaja estratégica,
pues muestra que es posible hacer estudios de clasificación de asteroides con
telescopios de menor tamaño o con alta eficiencia con telescopios mayores.
Los asteroides cercanos a la tierra fueron observados con el telescopio de
1.5 m del Observatorio Astronómico Nacional, San Pedro Martir. Los obje-
tos del cinturón principal fueron extraidos del archivo de observaciones del
proyecto Asteroid Terrestrial-impact Last Alert System, que observa con
dos telescopios de 50 cm con una separación de aproximadamente 160 km
entre ellos.
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2. Antecedentes
2.1. Asteroides
Los asteroides son trazadores de las rutas dinámicas y evolutivas del
sistema solar, por lo que el estudiarlos ayuda a entender cómo se formó
y evolucionó, no sólo en estructura sino también en composición. Es claro
que tener un mejor entendimiento de nuestro sistema planetario ayuda a
estudiar otros. Esta idea se ha consolidado aún más con el reciente registro
de dos objetos interestelares (IAU, 2017; Borisov, 2019).
Junto con los cometas, planetas enanos y satélites pequeños, los asteroi-
des forman parte de los llamados ’cuerpos menores’ del sistema solar y se
encuentran en diferentes regiones del mismo: el entorno terrestre, las inme-
diaciones de la órbita de Marte, la órbita de Júpiter, el cinturón principal
de asteroides, la región transneptuniana, la Nube de Oort, etc. Los pla-
netas tienen abundantes procesos internos (e.g. geológicos y atmosféricos),
sin embargo, sus órbitas son estables y su estado general es mayormente
constante. Por otro lado, los cuerpos menores tienden a tener un com-
portamiento opuesto. Estos pueden perder material (e.g. Hartmann et al.,
1987), cambiar su órbita debido a la radiación solar (Opik, 1951; Vokrouh-
lický et al., 2015) o a la influencia de los planetas (Wetherill, 1976; Bottke
et al., 2002), modificar sus superficies (e.g. Miyamoto et al., 2007), coli-
sionar y fragmentarse (Housen, Holsapple, 1990), etc. Las colisiones tienen
un papel importante en la evolución de estos cuerpos, por ejemplo for-
mando ’familias’, las cuales en ocasiones son producto de un asteroide de
mayor tamaño que ha sido fragmentado. Por lo tanto, dada la taxonomía
de un asteroide, se espera que la familia generada a partir de este tenga
una taxonomía mayormente homogénea y similar a la del cuerpo original,
sin embargo es difícil distinguir entre los miembros de la familia y objetos
en el cielo de fondo (Mothé-Diniz et al., 2005). Una de las herramientas
útiles para hacer esta distinción, o distinguir entre diferentes familias son
los colores astronómicos, sean estos definidos como la resta de la magnitud
en dos bandas fotométricas diferentes, u otra combinación lineal de ellas
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(Parker et al., 2008).
Uno de los parámetros más característicos de los asteroides es su ’mag-
nitud absoluta’, comunmente denotada como H o en ocaciones HV. Esta
es la magnitud aparente que un observador mediría si el objeto estuviera
a 1 unidad astronómica del observador, a 1 unidad astronómica del Sol, y
que a su vez el objeto estuviera completamente iluminado. Esta cantidad es
solo una referencia, pues se basa en una configuración imposible, ya que las
dos primeras condiciones requieren una geometría triangular, mientras que
la tercera requiere que la Tierra esté entre el Sol y el objeto (Glo, 2020).
2.2. Objetos cercanos a la Tierra (NEOs)
Los objetos cercanos a la Tierra (NEOs por sus siglas en inglés), son
aquellos que su órbita los mantiene cerca de nuestro planeta y comprenden
una amplia cantidad de parámetros físicos y orbitales (Mommert et al.,
2015). Técnicamente son aquellos objetos con perihelio q menor a 1.3 Uni-
dades Astronómicas (UA), e incluyen tanto asteroides (Near Earth Aste-
roids, NEAs) como cometas (Near Earth Comets, NECs), siendo los pri-
meros los más abundantes. Por sus características orbitales, los NEOs se
dividen principalmente en tres categorías: Amors con semieje mayor, a > 1
UA y 1.017 < q < 1.3 AU; Apollos con a > 1 y q < 1.017 ; Atens con a < 1
UA y afelio Q > 0.983 AU. Un NEA tiene una escala de vida promedio
de 107 años (Morbidelli, Gladman, 1998), la cuál es corta en comparación
con la edad del sistema solar. Por lo tanto, la existencia actual de estos
objetos implica que hay fuentes para su reabastecimiento. Estudios por
medio simulaciones numéricas complementadas con datos observacionales,
han demostrado que el cinturón principal de asteroides es la mayor de estas
fuentes (Bottke et al., 2002; Granvik et al., 2018). En esa región, la inter-
acción gravitacional por medio de resonancias entre los planetas gigantes
provoca que los asteroides alteren su órbita y sean traídos al entorno te-
rrestre, donde pasan la última etapa de su vida, antes de ser engullidos por
el Sol.
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Los primeros estudios de NEOs fueron hechos con fotometría (Groene-
veld, Kuiper, 1954), en ellos se definieron dos grupos taxonómicos princi-
pales, los asteroides de tipo ’C’ que presentan alto contenido orgánico y
los de tipo ’S’ que presentan un alto contenido de silicatos (similar a una
roca común). Tal y como es mencionado por DeMeo et al. (2009), la ca-
pacidad para caracterizar estos objetos ha crecido junto con los avances
en la espectroscopía. Esto debido a que esta técnica permite identificar la
forma general del espectro, que es distintiva entre cada taxonomía, así co-
mo los detalles particulares en el espectro, tal como la firma espectral de
los silicatos en 1 y 2 micras. De esta manera se puede clasificar un objeto
y compararlo con muestras de meteoritos para entender su composición
detallada. No obstante, este proceso solo funciona para NEOs que son lo
suficientemente brillantes para obtener un espectro de alta calidad. Es por
eso que la mayoría de los NEOs pequeños que se descubren cada mes, no
son estudiados en lo absoluto. A partir del estudio de Groeneveld, Kuiper
(1954) se han desarrollado diferentes sistemas taxonómicos para asteroides.
El más completo a la fecha es el sistema Bus-DeMeo (DeMeo et al., 2009),
que utiliza la firma espectral de la región óptica y del cercano infrarojo
para determinar las diferentes clasificaciones.
Se ha observado que los asteroides de tipo C y S predominan en di-
ferentes regiones del sistema solar (Gradie, Tedesco, 1982; DeMeo et al.,
2015; Binzel et al., 2019). Sin embargo, las abundancias específicas de estas
taxonomías varían en cada región, por lo que las proporciones en los NEOs
muestran diferencias con aquellas del cinturón principal (Stuart, Binzel,
2004; Binzel et al., 2019). De manera similar, se observa una posible de-
pendencia de la distribución de composición con el tamaño de los NEOs
(Mommert et al., 2016; Binzel et al., 2019; Devogèle et al., 2019). Cabe
mencionar que los asteroides de tipo C son generalmente considerados pri-
migenios por la poca alteración que han tenido durante la evolución del
sistema solar (Jones et al., 1990), y se caracterizan por tener un albedo ba-
jo1. Por otro lado, los asteroides de tipo S son los más comunes de aquellos
1El albedo es la cantidad de luz reflejada por un objeto no emisor en función de la
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considerados como alterados o evolucionados (Jones et al., 1990; Fornasier
et al., 1999) y cuentan con un albedo mayor.
En el primer párrafo de esta sección se mencionó la motivación general
para el estudio de asteroides, adicionalmente, los NEOs son de particular
interés porque suelen ser fragmentos de asteroides del cinturón principal
traídos a nuestro entorno, ofreciendo entonces una manera indirecta de es-
tudiar objetos del cinturón de asteroides y sus procesos evolutivos, así como
los procesos a los que son sujetos una vez estando en el entorno terrestre.
Además de la curiosidad científica, está el creciente interés en la segu-
ridad planetaria. Actualmente se conoce el ≈ 90% de los NEOs mayores
a 1 km (Mainzer et al., 2011; Trilling et al., 2017) y sus órbitas no repre-
sentan un peligro para la Tierra. Por otro lado, se estima que solo hemos
observado el ≈ 2% de los de menor tamaño (Trilling et al., 2017), y solo
conocemos las propiedades físicas de una pequeña parte de ellos. Estadís-
ticamente este es el tipo de asteroides con más posibilidad de impactar la
Tierra, aunque los objetos que conocemos actualmente y sus respectivas
órbitas no representan un peligro mayor para ella. Sin embargo hay dos
factores a considerar. Primeramente es posible que la órbita de un objeto
cercano a la Tierra cambie o que lleguen nuevos objetos desde el cinturón
principal. En segundo lugar, el evento de Chelyabinsk nos demostró que un
objeto de algunos metros puede causar daños significativos a las comunida-
des en cualquier parte del mundo (Popova et al., 2013; Brown et al., 2013)
y nuestro conocimiento de los objetos de ese tamaño es prácticamente nulo.
Es por esto que el entender las propiedades de los NEOs es fundamental
para planear estrategias preventivas o de mitigación.
Además del gran interés científico y de seguridad, actualmente existen
los fundamentos para la minería espacial, con la Luna y los NEOs como
blanco. Este mercado ha despertado interés por parte de diferentes go-
biernos e individuos, y aún cuando actualmente no hay una misión activa
luz incidente en este.
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al respecto, la intención está claramente definida (Graps, 2019; The Whi-
te House, 2020; Spa, 2020; AMC, 2020; Hein et al., 2020).
2.3. Sondeos de NEOs
La investigación de NEOs fue impulsada por la seguridad planetaria y
la necesidad de identificar los asteroides potencialmente peligrosos (PHAs
por sus siglas en inglés). En la década de 1990, los esfuerzos se centraron en
encontrar los asteroides capaces de ocasionar un daño global (mayores a un
1 km en diámetro). Después de alrededor de 20 años de trabajo, se determi-
nó que los NEOs de mayor tamaño habían sido suficientemente estudiados
en términos de protección planetaria (Harris, 2008; Mainzer et al., 2011).
Por lo que durante la última década, la intención fue encontrar aquellos que
eran más pequeños pero con capacidad de ocasionar un daño severo a nivel
local. Inicialmente se consideró que para este fin había que detectar al me-
nos el 90% de los NEOS >140 m, sin embargo, el evento de Chelyabinsk,
provocado por un objeto de máximo 20 m, sugiere objetos de tan solo unas
decenas de metros pueden causar daños significativos (Brown et al., 2013).
Durante estas tres décadas, ha habido una gran cantidad de sondeos
de NEOs, entre los más destacados por el número de descubrimientos rea-
lizados, están, Catalina Sky Survey (CSS, Larson et al., 1998), Lincoln
Near Earth Asteroid Research (LINEAR, Stokes et al., 2000), Panoramic
Survey Telescope and Rapid Response System (Pan-STARRS, Chambers
et al., 2016) y Asteroid Terrestrial-impact Last Alert System (ATLAS,
Tonry et al., 2018). El propósito de este último va más allá del descu-
brimiento genérico, pues se enfoca en predecir colisiones que representen
una amenaza a nivel local o mundial. Este sistema está actualmente con-
formado por dos telescopios en Hawai y desde su inicio de operaciones ha
descubierto 46 PHAs. Para cumplir su objetivo, los telescopios deben ha-
cer un barrido uniforme del cielo constantemente, lo que produce una gran
cantidad de datos que pueden ser aprovechados por distintas disciplinas de
la astronomía, tal como fuentes de rayos gamma, candidatos a superno-
va y estrellas variables (Stalder et al., 2017; Prentice et al., 2018; Heinze
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et al., 2018). En lo que respecta a asteroides, la astrometría y fotometría
de cada observación realizada son colocadas en el Minor Planet Center, lo
que permite a cualquier astrónomo hacer uso de ellas. La caracterización
de NEOs es una tarea más dificil, lo cuál se explica en la siguiente sección.
A la fecha, entre los sondeos enfocados a la determinación de algún pa-
rámetro físico destacan: EXPLORENEOs (Trilling et al., 2010a), Mission
Accessible Near-Earth Object Survey (MANOS, Devogèle et al., 2019) y
MIT-Hawaii Near-Earth Object Spectroscopic Survey (MITHNEOS, Bin-
zel et al., 2019), los cuáles han brindado información acerca del tamaño,
albedo, emisión térmica y composición. Una discusión más amplia acerca
de sondeos de NEOs puede encontrarse en Stokes et al. (2002) y Jedicke
et al. (2015).
Al día de de hoy, conocemos 901 asteroides mayores a 1 km de diámetro
(NASA, 2020a) de los ∼ 1000 (Mainzer et al., 2011; Trilling et al., 2017)
estimados, y 22,051 (NASA, 2020a) de los ∼ 106 estimados con capacidad
de ocasionar daños (Trilling et al., 2017) . De los menores a un kilómetro,
solo 541 cuentan con algún tipo información física (NASA, 2020b), repre-
sentando ≈ 3% de la muestra observada y ≈ 0.05 de la muestra de interés.
En la década entrante comenzarán a funcionar observatorios de nueva gene-
ración donde los NEOs forman parte de los principales intereses científicos
(e.g. James Web Space Telescope y Vera C. Rubin Observatory: Gardner
et al., 2006; AURA, 2020). Esto nos permitirá estudiar los NEOs en mayor
detalle y cantidad, particularmente los pequeños (e.g. Rivkin et al., 2017).
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3. Introducción
3.1. Necesidad de técnicas no estándar
Los asteroides tienen emisión térmica en el infrarojo que permite su
caracterización física (Allen, 1970; Matson, 1971; Mainzer et al., 2015). Sin
embargo en la región óptica tienden a reflejar poca luz y no emiten. La
superficie reflectiva de un objeto es proporcional a su tamaño, por lo que
los objetos pequeños son aún más difíciles de observar. Los NEOs tienden
a ser descubiertos cuando están más cerca de la Tierra, ya que su superficie
aparente aumenta y por lo tanto su brillo también, pero por lo general su
visibilidad disminuye entre el momento que son descubiertos y cuando es
posible observarlos tras la aprobación de una propuesta de telescopio, pues
es un proceso tardado. Además, muchos NEOs tienen periodos sinódicos
largos, por lo que si se pierde la oportunidad de observarlos después de
su descubrimiento, pueden pasar años hasta que sea posible estudiarlos de
nuevo. Lo anterior ha contribuido fuertemente a que la cantidad de NEOs
pequeños caracterizada sea muy baja. Para abordar este problema utili-
zamos la técnica rapid-response2, que consiste en observar los objetos días
después de su descubrimiento, cuando aún son lo suficientemente brillantes
para estudiarlos. Nos es posible usar esta técnica gracias a la robotización
del telescopio de 1.5 m del Observatorio Astronómico Nacional en San Pe-
dro Martir (OAN-SPM). La de capacidad RATIR (instrumento instalado
en dicho telescopio, Watson et al., 2012) de obtener información en múlti-
ples bandas simultáneamente contribuyó a aumentar la calidad del análisis
en algunos casos. Hemos realizado observaciones utilizando RATIR cada
semestre desde 2014 a 2019.
En los artículos presentados en este documento, utilizamos la técnica
denominada espectrofotometría, que consiste en mediciones fotométricas en
longitudes de onda de particular interés. Se ha demostrado que esta técnica
puede ser suficiente para clasificar asteroides (ver por ejemplo Mommert
et al., 2016, y las referencias ahí citadas), mostrando una ventaja estratégi-
2Utilizada en los artículos 1 y 3
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ca sobre la espectroscopía, ya que colecta la luz en vez de dispersarla, por
lo que permite analizar objetos más pequeños o con telescopios de menor
tamaño.
Sin embargo, es un hecho que la fotometría ofrece menos información
que mediciones espectrales. Por esto, es necesario utilizar técnicas para ana-
lizar los asteroides en base a las características estadísticas de la población.
En años recientes la inteligencia artificial se ha aplicado ampliamente en
diferentes áreas de ciencia y tecnología. La base de esta técnica es que un
algoritmo tome decisiones cognitivas. Una de las grandes ramas de la in-
teligencia artificial es Machine Leaning (e.g. Kubat, 2017), que consiste en
alimentar un algoritmo con una base de datos. Después de que el algoritmo
se ’entrena’ con dichos datos, es capaz de tomar decisiones basadas en lo
que aprendió. Entre las aplicaciones de este mecanismo, está el encontrar
patrones y clasificar objetos con alta eficiencia.
Una de las técnicas que utilizamos ampliamente es el método Monte
Carlo (MC), el cuál es una herramienta muy útil en casos donde es difícil
encontrar una solución de manera analítica y es posible hacer uso de la
estadística. Las bases del método se le asignan a Sanislaw Ulam y John
von Newmann, y tienen su origen en juegos de cartas (Roger, 1987). Su
primera implementación formal fue para estudiar la difusión de neutrones,
que pronto dio origen a investigación en el área de armamento nuclear. Con
el paso del tiempo se han hecho diferentes variaciones e implementaciones
para aplicarlo a diferentes áreas, no solo en investigación científica sino en
cualquier área donde pueda aplicarse la estadística. De manera general, el
método consiste en realizar experimentos aleatorios para aproximar una
solución matemática. En nuestro caso lo utilizamos para dos objetivos dife-
rentes, ambos relacionados con el error de las mediciones. En el primer caso,
MC sirvió para aproximar la función de probabilidad asociada a nuestras
observaciones en el color r-i. La aproximación se construye a partir de una
distribución taxonómica definida, de manera que al encontrar una apro-
ximación que ajusta nuestra función, se encuentra la posible distribución
11
taxonómica de nuestra muestra. En el segundo caso MC se utilizó para
aproximar el valor real en el color de un asteroide a partir del valor medido
y su error correspondiente.
3.2. Estudio de 3 métodos diferentes para clasificar
NEOs
Aún cuando la taxonomía de NEOs no ofrece una composición minera-
lógica detallada, es uno de los primeros pasos para estudiar la distribución
de estos importantes objetos, además de que abre rutas de investigación en
el área. En cuanto a seguridad planetaria, a manera de ejemplo reduccio-
nista, los NEOs tienden a descubrirse cuando están más cerca de la Tierra.
No es imposible que ATLAS o algún otro observador descubra un objeto
que colisionará con la Tierra con solo un par de días de antelación, lo cuál
sería insuficiente para planear una estrategia de mitigación. Sin embargo,
si se estima su taxonomía, se podría calcular el efecto que la atmósfera
tendrá sobre él, y por lo tanto planear medidas pertinentes de prevención
o evacuación. Cabe mencionar que los estudios de taxonomía suponen que
los asteroides tienen una composición homogénea.
Este documento incluye tres artículos en los que se estudia la taxono-
mía de asteroides por medio de análisis fotométrico y técnicas estadísticas
implementadas en algoritmos computacionales. Se presentan diferentes téc-
nicas para clasificación de asteroides que son convenientes dependiendo de
la cantidad de información y recursos que se tengan disponibles. En conjun-
to, los tres artículos brindan información taxonómica de 1850 asteroides,
incluyendo 238 NEOs con diámetro equivalente menor a 1 km. 3
El primer artículo utiliza simulaciones con el método Monte Carlo para
analizar la distribución del color r-i de una muestra de 82 NEOs observa-
3Artículos de caracterización de NEOs presentan típicamente apenas algunas docenas
de ellos.
12
dos con RATIR, encontrando que la fracción de asteroides ricos en material
orgánico es aproximadamente la misma que la de aquellos de tipo rocoso.
Al igual que otros artículos similares, nuestro resultado está sesgado a favor
de los objetos más brillantes, por lo que se espera que la fracción real de as-
teroides rocosos sea menor. Nuestro resultado sugiere una mayor cantidad
de objetos con contenido orgánico que la encontrada en estudios previos,
sin embargo coincide dentro de las barras de error.
En el segundo artículo se clasifican 1612 asteroides del cinturón prin-
cipal, pertenecientes a 5 familias diferentes. Para esto se utilizan datos de
ATLAS en el color c-o y un método de clasificación más simple que en el
artículo anterior. La capacidad de distinguir entre dos clases de asteroides
con un solo color permite estudiar la variación taxonómica en las familias
y establecer un límite para uno de los modelos de formación de la familia
Flora.
El tercer artículo es una continuación del primero, esta vez consideran-
do 5 bandas fotométricas (r, i, Z, Y, J ), lo cuál permite implementar un
sistema de análisis más robusto basado en ML, que ofrece más precisión
y detalle en los resultados. Con este sistema analizamos 87 objetos de la
muestra, encontrando resultados que están más de acuerdo con los de estu-
dios previos. También analizamos 151 objetos con los métodos utilizados en
los primeros artículos, encontrando que el método más simple no es apto
para estudiar la distribución de NEOs. La realización de este último ar-
tículo coincidió con la publicación de la muestra clasificada de NEOs más
grande a la fecha, la cuál utilizamos como muestra control. El contar con
esta base de datos permitió estudiar la eficacia de los diferentes métodos
de clasificación. Por lo tanto, además de ofrecer la taxonomía de los obje-
tos, nuestro estudio explora mecanismos de clasificación no ordinarios en
el área, aspecto de utilidad para los datos que serán generados por los pro-
yectos de gran escala próximos a operar.
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4. Caracterización de NEOs utilizando foto-
metría de respuesta rápida con RATIR
En este artículo se presentan observaciones en las bandas r e i tomadas
en 2014 y 2015. Durante este tiempo la cámara infraroja de RATIR estaba
dañada, por lo que decidimos trabajar exclusivamente con mediciones en el
rango óptico del espectro. Tomando en cuenta las capacidades del telesco-
pio, cada noche se eligen de manera completamente automática los objetos
a observar. Estos se seleccionan de una lista de NEOs recientemente des-
cubiertos, ya que son relativamente más brillantes y por lo tanto es posible
estudiarlos.
El artículo se enfoca en encontrar la cantidad de asteroides ricos en
contenido orgánico en relación a los objetos con alto contenido de silicatos
(expresado como la razón C/S). El análisis de los datos es de tipo estadís-
tico y está basado en el índice de color r-i.
Originalmente, la intención era encontrar las abundancias relativas de
asteroides de tipo C y S por medio de dos ajustes gaussianos, cada uno cen-
trado en el color característico de estos tipos de asteroides. Los resultados
no eran convincentes, por lo que este método solo se utilizó como referencia
y a manera de guía para determinar el límite de error fotométrico de las
observaciones. Para crear un modelo un poco más robusto, se construyó
una función de probabilidad utilizando cada una de las observaciones. Para
extraer el resultado de esta función se realizaron 107 simulaciones Monte
Carlo, considerando asteroides de tipo C, S, X y Q, los cuáles se espera que
sean los mayores componentes de nuestra muestra (Thomas et al., 2011;
Mommert et al., 2016; Binzel et al., 2019). En cada una de las simulaciones
se genera una función de probabilidad asociada a los objetos sintéticos y
se compara con la equivalente de nuestras observaciones por medio de la
prueba del chi cuadrado reducido.
Este artículo proporciona una herramienta útil para aproximar la dis-
14
tribución taxonómica en una población contando con solo un color fotomé-
trico. Cabe destacar la utilidad del color utilizado, ya que está en el rango
visible, mientras que las características espectrales principales que diferen-
cian las distintas taxonomías están en el cercano infrarojo. Encontramos
que nuestra muestra presenta un C/S=1.06.
Mis directores de tesis y mi asesor externo, el Dr. Michael Mommert
sugirieron la metodología a seguir y me brindaron las referencias que deter-
minan los resultados a esperar. También me ayudaron a analizar o incluso
solucionar una situación en etapas cuando no me era claro cómo proceder.
Los otros coautores contribuyeron con la pipa de reducción y/o a planear el
proyecto del cuál mi investigación forma parte. Dicho esto, yo realicé toda
la investigación presentada en este artículo. A continuación se menciona de
manera resumida las actividades que llevé a cabo.
Se esperaba que generar el primer artículo fuera trivial, sin embargo los
datos no eran congruentes. Por mi participación en el proyecto presentado
en la Sección A supuse que RATIR no era apto para estudiar asteroides,
sin embargo el Dr Trilling comentó que debería ser posible extraer resulta-
dos. Por alrededor de un año hice diferentes pruebas, las cuáles incluyeron:
explorar diferentes métodos estadísticos simples para tratar los datos, de
esto derivó la implementación posterior del z-score (puntaje z); estudiar el
desempeño de la pipa de reducción, lo que me permitió identificar y des-
cartar observaciones incorrectas con barras de error pequeñas. Modifiqué
los resultados de la pipa respecto al punto cero y otro parámetro de cali-
bración, lo cuál no tuvo ningún efecto significativo. El estudio de la pipa
sugirió utilizar cada una de las magnitudes observadas durante una visita
en vez de utilizar la suma de ellas hecha por la pipa. A consecuencia de lo
anterior se escribió un pequeño código para organizar las tablas de datos
arrojadas por la pipa. Después de este proceso los datos eran más congruen-
tes, no obstante la distribución de color no era similar a la esperada, por lo
que seguía siendo necesario encontrar una manera de extraer los resultados.
Evalué el uso de un ajuste gaussiano y de la simulación MC. Para esto hi-
15
ce pruebas considerando diferentes combinaciones taxonómicas, límites de
error para las observaciones, etc., analizando en cada caso la congruencia
del resultado obtenido. Escribí todos los códigos para realizar las pruebas,
generar y analizar los resultados.
Algunas de las técnicas estudiadas en este artículo son utilizadas en los
dos siguientes.
16
First Results from the Rapid-response Spectrophotometric Characterization of Near-
Earth Objects Using RATIR
S. Navarro-Meza1,2, M. Mommert2,3 , D. E. Trilling2 , N. Butler4,5 , M. Reyes-Ruiz1, B. Pichardo6 , T. Axelrod7 ,
R. Jedicke8 , and N. Moskovitz3
1 Instituto de Astronomía, Universidad Nacional Autónoma de México, Ensenada B.C. 22860, México; snavarro@astro.unam.mx
2Department of Physics and Astronomy, Northern Arizona University, Flagstaff, AZ 86001, USA
3 Lowell Observatory, Flagstaff, AZ 86001, USA
4 School of Earth and Space exploration, Arizona State University, Tempe, AZ 85287, USA
5 Cosmology Initiative, Arizona State University, Tempe, AZ 85287, USA
6 Instituto de Astronomía, Universidad Nacional Autónoma de México, Ciudad Universitaria, D.F. 04510, México
7 Steward Observatory, University of Arizona, Tucson, AZ 85721, USA
8 Institute for Astronomy, University of Hawaii at Manoa, Honolulu, HI 96822, USA
Received 2018 June 29; revised 2019 March 15; accepted 2019 March 18; published 2019 April 22
Abstract
As part of our multi-observatory, multifilter campaign, we present r–i color observations of 82 near-Earth objects
(NEOs) obtained with the reionization and transients infrared camera (RATIR) instrument on the 1.5 m robotic
telescope at the San Pedro Martir’s National Observatory in Mexico. Our project is particularly focused on rapid-
response observations of small (850 m) NEOs. The rapid response and the use of spectrophotometry allows us to
constrain the taxonomic classification of NEOs with high efficiency. Here we present the methodology of our
observations and our result, suggesting that the ratio of C-type to S-type asteroids in a size range of ∼30–850 m is
1.1, which is in accordance with our previous results. We also find that 10% of all NEOs in our sample are neither
C- nor S-type asteroids
Key words: minor planets, asteroids: individual (near-Earth objects) – surveys
1. Introduction
Solar system minor bodies are tracers of the solar system’s
formation and evolution, and hence can be used as current
samples of the processes that occurred in the early days of the
system and its formation (Delsemme 1991; Malhotra 1997).
Therefore, studies with numerous samples, focused on
analyzing colors, taxonomies, and orbital and physical proper-
ties of asteroids from different populations have been made
(see, for example, Ivezić et al. 2001; Carvano et al. 2010; Carry
et al. 2016).
Near-Earth objects (NEOs) are of particular interest for their
potential to explain the disagreement between the composition
of meteorite falls on Earth and the composition observed in
asteroids (Mommert et al. 2016). Furthermore, the Chelyabinsk
event in 2013 showed us that there exist NEOs with the
potential to cause moderate to devastating damage to our
communities (Brown et al. 2013). It is worth noting that events
like this can happen in any point on the globe. This event has
motivated projects aimed to characterize those asteroids that
could impact the Earth and that have enough energy to
compromise its safety.
Discovery and characterization efforts aimed at NEOs have
significantly increased in the last years. However, due to their
general faintness, characterization of small NEOs lags behind.
The most effective way to constrain NEO compositions is
spectroscopy, which allows for the identification of both the
overall continuum shape and diagnostic band features and
enables their taxonomic classification. However, spectroscopy
is very expensive in terms of telescope time, and is only
possible with relatively bright objects, which generally are the
largest objects. Only few small asteroids (with diameters
smaller than 100 m) get bright enough to be observed
spectroscopically (e.g., Moskovitz et al. 2015). Currently,
DeMeo et al. (2009) offer the most complete taxonomic
classification system.
Photometric measurements at a few key wavelengths—
spectrophotometry—can be sufficient to estimate asteroid
taxonomies (see Mommert et al. 2016, and references therein).
This technique has the advantage of making faint targets
accessible because the light is collected within a broad
bandpass instead of being dispersed as a function of
wavelength. Furthermore, spectrophotometry can be performed
with smaller telescopes than the ones necessary for spectrosc-
opy. Here we present a combination of spectrophotometry and
rapid-response observations, i.e., observations that are obtained
shortly after the discovery of the target, when it is still
relatively bright. This article constitutes the third of a series of
papers oriented to taxonomically classify hundreds of small
NEOs using spectrophotometry.
C (organic rich) and S (siliceous rock) taxonomic types are
the dominant constituents of the distribution of large asteroids
(Stuart & Binzel 2004; Thomas et al. 2011). However, the
compositional distribution of small NEOs appears to be
different from that of Main Belt asteroids, as well as from
large NEOs. Mommert et al. (2016) find S and C+X
complexes9 to be the main components of their sample of
small NEOs. Also as pointed out by them, the compositional
distribution of meteorite falls does not match the observed
NEO distribution, a fact that can yield information on asteroid
strength. This fact needs to be studied with better statistics on
the small asteroid range in order to better understand the threat
to Earth from impactors. It is important to remark that
The Astronomical Journal, 157:190 (10pp), 2019 May https://doi.org/10.3847/1538-3881/ab1138
© 2019. The American Astronomical Society. All rights reserved.
9 Results from Mommert et al. (2016) make no distinction between the C and
the X taxonomic complexes. For comparison purposes the notation C+X will
be used here, which stands for the set of objects corresponding to both the C-
and the X-complexes.
1
according to Thomas et al. (2011, 2014), Q-type asteroids can
be an important component of a magnitude-biased NEO
sample, due to their relatively high albedos. There are other
teams interested in this same topic (see for example Ieva et al.
2018; Popescu et al. 2018).
This study is part of a worldwide systematic survey of NEO
compositions. With the use of the 3.8 m United Kingdom
Infrared Telescope (UKIRT) and KMTNet-SAAO telescope,
we provide detailed information on the compositional distribu-
tion of NEOs with absolute magnitudes up to H∼28, i.e., with
a few meters in diameter. Such rapid response is generally not
feasible through classical observing proposals due to heavily
oversubscribed classically scheduled major research facilities.
Furthermore, this method allows us to classify small NEOs
according to their taxonomy with a higher efficiency than
current spectroscopic methods (see Galache et al. 2015 for a
discussion). Furthermore, photometric studies of the partial
light curves of our objects can lead to the improvement of the
period distribution of asteroids on the smaller range (see
Warner et al. 2009).
In Section 2 we describe the reionization and transients
infrared camera (RATIR), the multiband instrument we use.
Section 3 describes our rapid-response approach and the
planning of our observations. Section 4 addresses our data
selection and analysis. In Section 5 we provide our results and
the corresponding discussion is given in Section 6. Finally in
Section 7 we discuss the conclusions and the future outlook of
this project.
2. Reionization and Transients Infrared Camera
Observations were performed with RATIR (Butler et al.
2012) on the San Pedro Martir (SPM) 1.5 m telescope at the
National Mexican Astronomical Observatory (Observatorio
Astronómico Nacional). This telescope is a Ritchey–Chrétien
type, operated by the Universidad Nacional Autónoma de
México. The instrument is equipped with two optical and two
near-infrared (NIR) detectors, all of them 2048×2048 pixels.
Each of these detectors corresponds to a different channel with
specific filters, as shown in Table 1. RATIR takes four images
of an object in a single shot.10 To minimize dark current and
thermal background effects, the optical detectors are water
cooled, while the NIR detectors are operated in a helium-
cooled cryostat.
RATIR was designed to study gamma-ray bursts (e.g., Butler
et al. 2017a, 2017b, 2017c), but other uses are possible as
Table 1
Channels of the RATIR Instrument
Channel Detector Field size Filters
(arc minute square)
C0 CCD 5.3 SDSS ugr and seven others
C1 CCD 5.3 Fixed SDSS i
C2 H2RG 10 Fixed WFCAM Z and Y
C3 H2RG 10 Fixed MKO J and H
Note. All detectors are 2048×2048 pixels. C0 and C1 channels hold the
visual range filters (observations reported in this paper were taken with the r
and i filters), C2 and C3 channels contain the near-infrared filters, and H2RG
(HAWAII-2RG) are teledyne mercury–cadmium–telluride detectors.
Table 2
Each of the Reported Targets According to Their Number or Designation,
Observation Midtime of the Observing Run, and the Duration of the Run
Object Obs. Midtime Dur. HV r–i Error
(UT) (hr) (mag) (mag) (mag)
2014 MK6 2014 Jul 22 09:30 1.7 21.00 0.29 0.01
2014 MP5 2014 Jul 21 05:25 1.5 21.80 0.27 0.02
2014 OZ337 2014 Aug 04 08:13 0.3 22.50 0.35 0.02
2014 QQ33 2014 Aug 25 10:20 1.3 22.10 0.30 0.02
2014 TT35 2014 Oct 18 03:49 0.1 26.00 0.49 0.01
2014 TZ 2014 Oct 23 05:12 1.1 22.60 0.33 0.01
2014 UT192 2014 Nov 10 09:03 0.2 19.60 0.46 0.03
2014 UZ116 2014 Nov 03 06:41 1.6 20.90 0.36 0.04
2014 WX4 2014 Nov 20 07:16 0.5 26.40 0.40 0.02
2014 WZ4 2014 Nov 20 03:42 0.5 23.50 0.29 0.03
2014 YE35 2015 Jan 15 08:32 0.5 20.30 0.38 0.01
2014 YW34 2015 Jan 15 06:53 1.6 21.60 0.25 0.06
2015 EL7 2015 Apr 05 10:19 0.4 22.70 0.38 0.03
2015 EL7 2015 Apr 09 07:40 0.2 22.70 0.39 0.06
2015 EL7 2015 Apr 11 07:22 0.1 22.70 0.36 0.03
2015 EZ 2015 Mar 15 05:56 0.4 20.30 0.40 0.01
2015 FG120 2015 Apr 10 09:12 1.1 22.90 0.36 0.02
2015 FG120 2015 Apr 11 09:20 0.2 22.90 0.29 0.03
2015 FG120 2015 Apr 12 09:35 1.0 22.90 0.30 0.02
2015 FG120 2015 Apr 13 08:07 0.9 22.90 0.38 0.02
2015 FG120 2015 Apr 17 11:09 0.7 22.90 0.37 0.02
2015 FG37 2015 Apr 15 10:53 1.1 21.70 0.41 0.02
2015 FG37 2015 Apr 22 11:25 0.1 21.70 0.29 0.04
2015 FL290 2015 Apr 09 05:11 1.1 22.20 0.36 0.02
2015 FL290 2015 Apr 10 04:53 1.1 22.20 0.37 0.02
2015 FL290 2015 Apr 11 04:46 1.2 22.20 0.39 0.01
2015 FQ 2015 Mar 29 05:43 0.9 22.30 0.40 0.02
2015 FT118 2015 Apr 20 10:50 0.6 20.40 0.30 0.04
2015 FY284 2015 Apr 02 07:13 0.5 21.60 0.37 0.05
2015 GS13 2015 May 14 09:26 0.4 21.00 0.51 0.03
2015 GS 2015 Apr 15 09:34 1.1 20.60 0.35 0.02
2015 GS 2015 Apr 16 09:53 1.2 20.60 0.33 0.02
2015 GY 2015 Apr 15 05:14 0.6 21.70 0.41 0.01
2015 GY 2015 Apr 19 07:16 0.5 21.70 0.27 0.02
2015 HA1 2015 Apr 25 09:04 0.9 21.20 0.46 0.01
2015 HA1 2015 May 05 07:50 0.5 21.20 0.45 0.01
2015 HP171 2015 May 12 09:32 0.3 20.10 0.34 0.02
2015 HR1 2015 May 06 08:59 0.7 24.30 0.35 0.06
2015 HR1 2015 May 07 09:00 0.4 24.30 0.34 0.06
2015 HR1 2015 May 13 09:39 0.7 24.30 0.26 0.03
2015 HV171 2015 May 08 08:55 0.1 18.10 0.36 0.01
2015 HW11 2015 May 12 07:04 1.1 23.30 0.41 0.02
2015 JQ1 2015 May 18 05:03 1.0 20.30 0.26 0.05
2015 JQ1 2015 May 19 05:45 1.0 20.30 0.28 0.02
2015 KL122 2015 Jun 05 09:19 0.5 22.30 0.47 0.07
2015 KQ120 2015 May 30 10:10 0.1 26.70 0.43 0.04
2015 KQ57 2015 May 26 05:17 0.0 22.20 0.40 0.04
2015 KV18 2015 May 23 09:41 0.8 23.80 0.42 0.03
2015 KV18 2015 May 24 09:28 0.8 23.80 0.37 0.04
2015 KV18 2015 May 25 07:40 0.2 23.80 0.31 0.02
2015 KV18 2015 May 26 07:40 0.1 23.80 0.41 0.03
2015 LA2 2015 Jun 14 06:35 1.0 23.10 0.33 0.01
2015 LG14 2015 Jun 22 06:22 1.0 23.20 0.40 0.03
2015 LG14 2015 Jun 23 06:03 0.8 23.20 0.52 0.04
2015 LG2 2015 Jun 18 07:18 1.0 20.30 0.40 0.03
2015 LG2 2015 Jun 21 08:41 0.8 20.30 0.37 0.02
2015 LJ24 2015 Jun 18 05:11 0.2 20.00 0.42 0.03
2015 LJ 2015 Jul 04 06:43 0.8 24.70 0.45 0.05
2015 LJ 2015 Jul 04 07:50 0.8 24.70 0.33 0.07
2015 LJ 2015 Jul 13 05:21 0.8 24.70 0.27 0.03
2015 LJ 2015 Jul 25 06:54 0.9 24.70 0.29 0.06
2015 LQ21 2015 Jun 21 05:01 0.1 24.50 0.50 0.03
10 See detailed information on RATIR’s web page:http://ratir.astroscu.
unam.mx.
2
The Astronomical Journal, 157:190 (10pp), 2019 May Navarro-Meza et al.
shown here (see also García-Díaz et al. 2014; Tapia et al. 2014;
Ricci et al. 2015). Observations are executed in an automated
queue mode (Watson et al. 2012) if no gamma-ray burst events
are ongoing. The results that we present are the first asteroid
observations made with the instrument.
3. Observations
The observations we present here were taken during 2014
and 2015. During most of 2015 and 2016, RATIR’s channels
C2 and C3 (see Table 1) were not available due to technical
problems. In this work, we analyze the set of optical-only data.
Since the second half of 2016 we are obtaining observations in
all four channels, which will be presented in a future
publication. Table 2 presents the targets analyzed on this
paper, among the main details from their observation.
Our rapid-response approach is the key feature of this
project. We trigger rapid-response spectrophotometric observa-
tions of NEOs within a few days of their discovery when the
objects are generally still bright enough to be observed with a
1.5 m aperture. We can observe and characterize objects as
faint as V∼20. Such rapid response is generally not feasible
through classical observing programs. The first results of NEO
observations made by our team are presented in Mommert et al.
(2016) and Erasmus et al. (2017).
Potential targets are identified and uploaded into the RATIR
queue on a daily basis. Accessible targets are identified among
those NEOs that have been discovered within the last four
weeks; this duration is partially arbitrary,11 but the method
usually leads to a number of well-observable and bright
potential targets. A target is considered accessible if it has a
visible brightness V„20 and an airmass „2.0, as provided by
the JPL Horizons system (Giorgini et al. 1997), for at least the
duration of the estimated RATIR integration time. Potential
targets are manually selected from the list of accessible targets,
prioritizing objects with high absolute magnitudes HV (small
sizes) and large values of HV–V, where V stands for the
apparent magnitude of the target of the upcoming night. A high
value of HV–V ensures that our target is observed when it is
close to the Earth. RATIR queue observing scripts are
automatically created for the selected targets, using the latest
orbital elements of the objects of interest provided by JPL
Horizons. The exposure time of each frame, as well as the total
integration time in each band per visit, are a function of the
object’s brightness. Exposure times usually range between 5
Table 2
(Continued)
Object Obs. Midtime Dur. HV r–i Error
(UT) (hr) (mag) (mag) (mag)
2015 MC 2015 Jun 20 06:18 0.2 24.10 0.45 0.02
2015 MC 2015 Jun 26 06:49 0.9 24.10 0.30 0.04
2015 ME116 2015 Jul 14 04:57 0.3 22.30 0.38 0.06
2015 ME116 2015 Jul 25 04:49 0.4 22.30 0.27 0.04
2015 MQ116 2015 Jul 15 08:09 0.8 23.40 0.35 0.05
2015 MS59 2015 Jul 13 10:15 0.9 21.00 0.25 0.01
2015 MS59 2015 Jul 14 09:26 0.9 21.00 0.49 0.02
2015 MS59 2015 Jul 15 09:25 1.0 21.00 0.41 0.02
2015 MS59 2015 Jul 23 09:48 0.9 21.00 0.37 0.04
2015 MU59 2015 Jul 09 10:01 0.8 20.00 0.31 0.02
2015 MU59 2015 Jul 13 09:15 0.8 20.00 0.44 0.01
2015 MU59 2015 Aug 04 08:44 0.6 20.00 0.39 0.01
2015 MX103 2015 Jul 04 05:13 0.5 24.40 0.46 0.02
2015 MX103 2015 Jul 06 06:16 0.6 24.40 0.38 0.02
2015 MY53 2015 Jul 03 05:59 0.5 25.40 0.39 0.06
2015 MY53 2015 Jul 03 06:49 0.2 25.40 0.52 0.03
2015 NK13 2015 Aug 04 07:07 0.8 21.00 0.40 0.03
2015 NK3 2015 Aug 04 05:56 0.8 21.30 0.26 0.03
2015 NK3 2015 Aug 07 06:57 1.0 21.30 0.28 0.01
2015 NU2 2015 Jul 21 07:10 0.6 20.90 0.28 0.04
2015 NU2 2015 Jul 24 05:15 1.1 20.90 0.35 0.04
2015 OF26 2015 Aug 07 05:37 0.3 21.60 0.32 0.02
2015 OM21 2015 Jul 24 09:55 0.7 22.50 0.38 0.03
2015 OM21 2015 Aug 06 08:00 0.9 22.50 0.45 0.03
2015 OM21 2015 Aug 07 08:05 1.0 22.50 0.48 0.02
2015 PA229 2015 Aug 21 09:39 1.0 21.40 0.41 0.02
2015 PA229 2015 Sep 05 08:55 1.0 21.40 0.39 0.05
2015 PQ56 2015 Sep 03 07:59 0.9 22.60 0.46 0.04
2015 PQ 2015 Sep 07 07:52 0.7 22.70 0.48 0.01
2015 QB 2015 Aug 21 08:32 1.0 24.20 0.39 0.01
2015 QG 2015 Aug 22 05:17 0.3 23.80 0.33 0.02
2015 QM3 2015 Aug 23 04:45 0.4 20.40 0.28 0.05
2015 QN3 2015 Aug 23 04:20 0.4 19.50 0.28 0.01
2015 QN3 2015 Aug 24 04:56 0.4 19.50 0.40 0.01
2015 QO3 2015 Aug 24 07:05 0.6 19.40 0.38 0.01
2015 RH36 2015 Sep 18 09:57 0.5 23.60 0.37 0.06
2015 RO36 2015 Sep 18 05:36 0.3 22.90 0.24 0.03
2015 RQ36 2015 Sep 16 07:25 1.0 24.50 0.36 0.01
2015 RQ36 2015 Sep 19 09:05 0.6 24.50 0.35 0.02
2015 SO2 2015 Sep 26 09:01 0.3 23.90 0.37 0.03
2015 SO2 2015 Sep 27 09:33 0.3 23.90 0.29 0.03
2015 SO2 2015 Sep 28 10:57 0.3 23.90 0.50 0.03
2015 SO2 2015 Oct 02 11:21 0.4 23.90 0.32 0.03
2015 SV2 2015 Sep 29 05:31 0.9 20.80 0.33 0.03
2015 SY 2015 Oct 01 06:35 0.7 23.30 0.44 0.02
2015 SY 2015 Oct 02 06:09 0.8 23.30 0.33 0.03
2015 SZ 2015 Oct 02 05:22 0.4 23.50 0.36 0.01
2015 TE 2015 Oct 08 04:26 0.5 22.50 0.43 0.02
2015 TF 2015 Oct 10 05:15 0.6 22.20 0.39 0.01
2015 TW178 2015 Oct 26 04:18 0.9 21.20 0.28 0.04
2015 TY144 2015 Oct 26 10:14 0.5 21.30 0.48 0.05
2015 TY178 2015 Nov 06 06:52 0.7 21.80 0.32 0.04
2015 UJ51 2015 Oct 27 07:41 0.7 21.40 0.38 0.03
2015 US51 2015 Oct 28 04:54 0.6 22.40 0.44 0.02
2015 US51 2015 Nov 01 05:02 0.8 22.40 0.43 0.01
2015 US51 2015 Nov 02 04:35 0.8 22.40 0.44 0.01
2015 UT52 2015 Nov 05 07:40 0.8 20.90 0.45 0.03
2015 UT52 2015 Nov 11 10:56 0.6 20.90 0.40 0.04
2015 VJ2 2015 Nov 10 09:36 0.4 19.60 0.44 0.02
2015 VJ2 2015 Nov 18 10:50 0.2 19.60 0.37 0.03
2015 VJ2 2015 Nov 19 10:06 0.6 19.60 0.26 0.01
2015 VO66 2015 Nov 14 10:06 0.4 20.60 0.25 0.03
2015 VO66 2015 Nov 19 08:20 0.5 20.60 0.28 0.01
Table 2
(Continued)
Object Obs. Midtime Dur. HV r–i Error
(UT) (hr) (mag) (mag) (mag)
2015 VZ2 2015 Nov 19 04:15 0.9 22.70 0.46 0.04
2014 OT338 2014 Aug 17 11:10 1.4 21.40 0.45 0.02
2014 TX32 2014 Oct 16 05:35 1.1 20.20 0.42 0.01
2015 DE176 2015 Feb 28 06:18 1.0 19.70 0.35 0.03
2015 JV 2015 May 19 07:35 0.8 21.50 0.33 0.01
2015 KJ19 2015 May 24 04:53 0.6 22.50 0.28 0.07
Note. Also presented are the measured color indices (solar colors have been
subtracted) and corresponding uncertainties.
11 After the closest approach, NEOs fade at a rate of typically 0.5 mag within 1
week and 5 mag within 6 weeks (Galache et al. 2015).
3
The Astronomical Journal, 157:190 (10pp), 2019 May Navarro-Meza et al.
and 30 s, while the total integration time per target is usually
less than 1 hr.
Our observations are biased in favor of bright objects. At a
given distance from Earth, for objects of a given diameter,
objects with higher albedo are easier to observe. For targets
close to our limiting magnitude, only those with relatively high
albedos will be observed. Hence, our sample may contain a
higher fraction of S and Q objects than the actual asteroid
population.
4. Data Analysis
4.1. Taxonomic Classification
We use the Bus-DeMeo classification scheme (DeMeo et al.
2009) to classify our sample. This is a widely used taxonomic
scheme that combines the visible and near-infrared ranges,
covering from 0.45 to 2.45 μm. The taxonomy includes 24
classes, most of which correspond to the C-, S-, and
X-complexes that include the majority of the known asteroids
(see DeMeo et al. 2009, and Section 1). For this reason, we
considered these three complexes in our analysis, as well as the
Q-type, which, as described by Thomas et al. (2011, 2014), can
be an important component of a magnitude-biased NEO sample
like ours. Other taxonomic types were not considered, as they
are not expected to be a significant part of the distribution
(perhaps up to 20%; Mommert et al. 2016; Erasmus et al. 2017;
Lin et al. 2018; Perna et al. 2018) and due to the simplicity of
our model. We revisit this assumption below.
We obtain the characteristic color of each taxonomic type
from a sample of measured asteroid spectra.12 For each object
from the sample, its reflectance spectrum is convolved with the
spectral response of each filter of RATIR and the solar
spectrum. Details of the process can be found at Mommert
et al. (2016, their section Section 3. Figure 1 shows these color
indices in the r–i color.
4.2. Photometry
Image reduction and photometry is carried out using a
pipeline developed for gamma-ray burst observations (see, e.g.,
Littlejohns et al. 2015; Becerra et al. 2017). Briefly, the
pipeline reduces, sky-subtracts, and aligns input frames. These
frames are then stacked into a sky image. The stellar point-
spread function (PSF) is determined and fit using custom
Python scripts to determine the photometric zero-point in
comparison with the Sloan Digital Sky Survey (SDSS), Two
Micron All Sky Survey (2MASS), and/or The United States
Naval Observatory (USNO) photometric catalogs. After
finishing the gamma-ray burst pipeline reduction, we create a
source mask using the sky image. By then coadding the frames
in the moving frame of the target, keeping track of the exposure
per pixel, the non-moving sources are removed and we retain
only the signal from the target. The PSF determined from the
sky image is then fit to the moving-target image and the zero-
point from the sky image is applied to normalize the
photometry.
The magnitude of an object as a function of the observing
time is generated by dyadically combining the masked frames,
selecting a sufficiently long time interval for each photometric
epoch as to adequately fill in masked pixels prior to PSF fitting.
In principle, single frame photometry is possible because we
propagate the exposure pixel by pixel; however the accuracy
can depend strongly on the stability of the PSF.
Therefore, the pipeline yields photometry on the original
image, on a set of stacked images, and on the overall visit’s
stacked frame. The stacking creates new images with different
virtual exposure times, which are integer multiples of the real
exposure time. The result of this procedure is available in data
tables and through a graphical display in a private data portal.
In our analysis we use the photometry measured in individual
r-band and i-band images. With this information we measure
the r–i color index. The solar r–i was subtracted from our
measurements in order to make them compatible with the
synthesized colors (see Section 4.1).
4.3. Outlier Rejection
In order to reject photometric outliers we performed a 10σ
clipping on the r–i index for each visit: a weighted mean of the
r–i index was taken, then any measurement further than 10σ
from the mean was rejected and the weighted mean was
calculated again. This process was carried out three times. Each
time the photometric errors from the individual measurements
were propagated to obtain the weights (Taylor 1997).
Figure 1. All r–i indices considered in this work according to the Bus-DeMeo taxonomies. Orange lines are the subtypes that are most distant from the C- and S-type
respectively, thus defining the limits of these complexes. Notice that the C and S subtype are in the middle of their complexes.
12 http://smass.mit.edu/minus.html
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The Astronomical Journal, 157:190 (10pp), 2019 May Navarro-Meza et al.
Therefore, the corresponding error on the r–i index from a visit
is
V =
S
( )
w
1
, 1
k
where
= º
+
( )w
e e e
1 1
, 2
r i
k
k
2 2 2
where ek is associated with the r–i from each of the non-
rejected data points of that visit and er and ei are the
photometric errors from the r- and i-band measurements. The
values of ς are plotted in Figure 2.
4.4. Selection of the Best Observations
We only consider measurements of those objects that passed
through all of our selection criteria, the first of which is a clean
visit-stacked image: a well-defined source and a successful
removal of the non-moving sources (see Section 4.2 for details
on the photometry). Note that we use the visit-stacked image
only to check the quality of the photometry and of the
observation itself, e.g., with respect to background sources
confusion. Also, a limit on the color index’s error due to
photometric uncertainty must be set. The difference in color
index between the C- and S-type asteroids is 0.084, hence it is
convenient that we only consider the objects that have an error
lower than this threshold. Based on the discussion on
Section 6.2, we decide to use 0.075 as an upper error limit
on the color determination. We require a minimum of four
measurements per visit.
The outcome of this selection process is 82 different objects
observed in 131 visits.
4.5. Probability Density
After the selection process described in the previous section,
we have one r–i index and its associated error for each visit in
our clean sample. These indices are shown in Figure 3. In order
to analyze the taxonomic distribution of our sample, we model
it based on the known asteroid colors. We consider every count
in Figure 3 as a normalized Gaussian centered at the r–i value
of that object with the width of the Gaussian equal to the error
on the r–i index (the height is therefore a free parameter). For
objects observed more than once, the Gaussian’s normalization
factor is divided by the number of visits each object has. That
way an object observed in more than one visit will be
represented by different Gaussians, all of which add up an area
of unity. The Gaussians corresponding to all objects were
added up to obtain the probability density function (PDF),
shown in Figure 4.
4.6. Monte Carlo Simulation
In order to measure the compositional distribution from the
PDF, we conducted a Monte Carlo (MC) simulation, which
consists of creating 107 samples of synthetic asteroids, each
sample with the same number of objects as our data sample but
with different taxonomic distributions. In each run the S-, C-,
and X-complexes and the Q-types are considered, and the
number of objects in each taxonomy is set with a pseudo-
random number generator. We call the resulting color index
distribution from each run the random probability density
Figure 2. Error distribution of the color from our sample. The vertical line
shows the upper error limit set for the sample. See Section 4.4 for details on the
selection criteria used.
Figure 3. Color distribution of our sample. Color indices were obtained after
performing the rejection process described in the text. The main subtypes from
the C- and S-complex are shown (see Figure 1).
Figure 4. Probability density function of the color in our sample. Every visit is
considered as a Gaussian centered in the color index obtained. Vertical lines
represent the limits of the C- and S-complexes. See the text for a full
explanation.
5
The Astronomical Journal, 157:190 (10pp), 2019 May Navarro-Meza et al.
function (RPDF) to distinguish it from the PDF from our data.
The process to generate each distribution is the same. The
details of our MC simulation are as follows.
Eighty two synthetic objects were used in each MC run in
order to directly compare the RPDF with the PDF. From
Mommert et al. (2016) and Erasmus et al. (2017), we expect the
C- and S-type asteroids to be the main components of our
sample, and to find a C/S ratio of ∼1. However, we take into
account the possibility that our sample is composed of any
combination of the taxonomic types considered. This is
achieved by using a pseudo-random number generator under
a uniform distribution with equal weights for the three
complexes and the Q-type. The process to obtain the
composition on each of the runs is as follows.
The order in which the number of elements is set for each
complex and the Q-type is randomly sorted. Each of them is
labeled as na, nb, nc, or nd. The assignation of the number of
elements is always in alphabetical order, however the
correspondence between the types and na−d is given by the
pseudo-random number generator. Then na can be assigned
with any number between 0 and 82, the availability for nb is
82-na, and similar for nc and nd.
The main subtypes of the complexes, respectively the
C-type, S-type and X-type, are the most likely to be present
in our sample (Binzel et al. 2015). Therefore, in each of the
random generated samples, half of the elements assigned to
each complex are given to the main subtype, while the other
half is uniformly distributed among the other subtypes (see
Figure 1 for the r–i index of each of the members of these
complexes). The number of elements in the second half will
likely not be an integer multiple of the number of subtypes. For
example, if 36 elements are assigned to the S-complex, 18 will
correspond to the main type, the S-type. The remaining 18 will
correspond to the other 4 subtypes of the complex, but 18 over
4 is not an integer. The procedure is therefore as follows. If the
number of elements assigned to the four subtypes are nS1, nS2,
nS3, and nS4, then nS1=round (18/4)=5; 18−5=13
elements available for the three other subtypes, nS2=round
(13/3)=4; 13−4=9, nS3=round (9/2)=5; and 9
−5=4, nS4=4.
In each run, the correspondence between the nS1−4 and the
four subtypes is randomly sorted, so that over the 107 samples
generated, none of the four subtypes are favored. The same
criteria apply for the C- and the X-complex. The main
processes of the simulation are represented in Figure 5.
After applying all the selection criteria (see Section 4.4),
some of the objects that were observed during different visits
showed a different r–i index. This fact was not considered in
the building of the RPDF. In the simulation, the elements that
are not members of the C- or the S-complex are defined as
pollution.
Once the number of elements of each type in a single run is
determined, it is necessary to add an error to them in order to
emulate the photometric uncertainty. In order to take this into
account, we fitted a Gaussian function to the distribution from
Figure 2 and created a random distribution under that function.
Eighty two errors from that distribution were assigned to the r–i
indices of each of the determined types. This completes our
generated sample. Eighty two elements were randomly selected
following a distribution based on current NEO observations.
Figure 5. Main processes in the Monte Carlo simulation. Particularly the procedure for setting the number of objects of each type in the synthetic sample. Every box
including the word “determine” involves a random process. n is the number of objects of a certain type or complex in a single run; the subindex indicates the referred
taxonomy. Since there are C-, S-, and X-complexes, as well as a C-, S-, and X-types, a super index comp indicates when the variable is associated to the complex. n′ is
the number of objects available for the unassigned taxonomies at a certain point.
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The Astronomical Journal, 157:190 (10pp), 2019 May Navarro-Meza et al.
Each of the elements has an associated error, based on the error
distribution of our observations. Having these, the RPDF was
built up. After creating the 107 samples, the PDF was compared
to each of the 107 RPDFs.
5. Results
In order to extract the results from the simulations, we
calculated the reduced χ2
(c
r
2) between the RPDF and the PDF.
Since we are allowing the simulation to create any possible
combination of the taxonomies considered, the c
r
2 range is
wide as can be seen in Figure 6. We took the first percentile of
simulations in terms of the c
r
2. This is a set of 88 simulations
(∼10−5 from the total). The difference in c
r
2 between the best
and the second-to-best case is minimal. Both present 36
elements of the S-type, the first one suggests 38 C-types, while
the second 39. The main difference is in the number of X- and
Q-type objects. To analyze the behavior of the best cases we
calculated the distribution of the ratio C/S, which is shown in
Figure 7. Our best case corresponds to a value of 1.06 in this
space. Notice that value is well within 1 standard deviation
from the mean, but not in the bin where the mean of the
distribution is. We ascribe this to the fact the histogram is
skewed to the left, which is discussed in the next section.
Table 3 shows the percent compositions of the four taxonomic
types considered according to our best case. The errors
correspond to the standard deviation of the individual
distribution of each class within the 1st percentile. Although
we present results on the three complexes and the Q-type, the
scope of this analysis is restricted to suggest a C/S ratio. All of
our targets have a subkilometer diameter. We do not report
subdivisions in size since there was not a clear trend on the
results by doing so.
6. Discussion
6.1. Limitations and Comparison with Previous Studies
The strongest bias in our sample is the one presented by
albedo. Our rapid-response approach is based on optically
discovered objects, hence the sample targets are more likely to
have moderate to high surface albedos. This can lead to an
overestimated fraction of S objects, which means the real
fraction of C/S can be higher than that estimated here. Hence,
our sample is biased, and although debiasing of NEOs had been
carried out (Stuart & Binzel 2004; Hinkle et al. 2015) ,we will
address it in a future work.
Our full sample contains observations in up to six different
bands in the optical and near-infrared range. However, the
results presented here correspond to our control sample using
only the r–i color. Hence, one the main goals of this paper is to
describe the methodology we are using for our observations.
Our future work will include data in all bandpasses.
The distribution in Figure 7 is skewed to the left due to the
feature at r–i∼0.26–0.30 in Figures 3 and 4. It is likely due to
a systematic error in the observations causing a bluer color. The
analysis of the complete sample will allow us to test this idea.
Our full sample is one of the largest for small NEOs. The
analysis of it as well as the work from other teams is needed for
a comprehensive classification of these kinds of objects. (As a
comparison, Ivezić et al. 2001 made a study of the Main Belt
including ∼13,000 objects). The results from other teams on a
similar size range to ours (subkilometer) are compared next.
The fraction of S-type we find is in agreement within the error
bars of the other studies: Ieva et al. (2018), from the analysis 67
NEOs found ∼61% of S-types; Lin et al. (2018), presents 51
subkilometer NEOs. With this sample they found an S fraction
of ∼33%. Perna et al. (2018), for a sample of 146 objects,
found an S fraction of ∼40%. Our team, using different
telescopes and samples than the one presented in this paper,
found ∼40% with 40 NEOs in Mommert et al. (2016), while
Erasmus et al. (2017), with a sample of 45 objects, obtained an
S fraction of ∼43%. Using a sample of 252 objects Stuart &
Binzel (2004) found an S-type fraction of 22%. This number is
a reference for the distribution of NEOs, but is not directly
comparable with our results since they performed bias
Figure 6. c
r
2 from the 107 MC simulations. Vertical line shows the domain of
the first percentile of simulations in terms of the c
r
2.
Figure 7. C/S distribution from the 1st percentile of our MC simulations in
terms of c
r
2. Note that the element in the far right is the 66th best fit, therefore
not considered an issue but still considered in the estimation of the mean and
standard deviation.
Table 3
Compositional Fractions Found in Our Monte Carlo Simulation
Taxonomic Type Percentage
C 46±9
S 44±8
X 8±9
Q 2±8
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The Astronomical Journal, 157:190 (10pp), 2019 May Navarro-Meza et al.
correction, their sample includes Mars crossing asteroids, and
includes objects up to the 10 km scale. Binzel et al. (2019) uses
a sample of 1040 objects, with a median of 0.7 km and finds an
S fraction of ∼50%. The C-type fraction found in these same
papers varies and can be as low as 10% versus the ∼46% we
suggest.
6.2. Gaussian Fit
With the purpose of getting a result independent from the
MC simulation, we performed a Gaussian fit on the PDF, for
which, we considered two components with fixed mean: one
centered on the color index of C-type asteroids (0.335),and the
other one centered on the color index of S-type aster-
oids (0.418).
The result from our fit is overplotted to the PDF and RPDF
in Figure 8. The two components of the fit are equivalent to
48% of S-type objects and 52% of C-type objects yielding C/
S=1.07, which is the same value than in the MC result. The
residual (dashed blue in the figure) does not show a systematic
behavior, and it is similar to the residual of subtracting the
RPDF from the PDF (dashed yellow curve in the figure), so we
assume this is primarily noise.
Fits considering other taxonomic types were made, yielding
a larger residual. Because of this observation we decided only
to consider the C- and S-type in the fitting process.
As can be seen in Figure 9, the width of both the C and S
Gaussian distributions from our fit are wider than that of the
PDF. This does not affect the result since we are using the ratio
of the areas under the fits, but we explore different limits of
integration on the abscissa axis for getting each of the areas:
(a) [−¥,¥]
(b) integrating under the limits of the taxonomic types plus
the maximum error allowed in color (0.075);
(c) and [−¥,midz] for the C Gaussian and [midz,¥] for the
S Gaussian,
where midz is the middle point between the r–i index of the C
and S taxonomic complexes in terms of the z-score.
The three integration limits are shown in Figure 9. They
yield a similar C/S ratio, but, method (b) proved to be more
stable as a function of the pollution in test runs of the MC13
analysis. With the use of this method we made a cut in the tails
of the Gaussians, obtaining more localized components. Notice
from Figure 1 that the main types of the C- and S-complex are
positioned nearly at the center of their corresponding complex
range, making the integration reliable.
We explored the C/S ratio (obtained in Section 4.5) as a
function of the upper error allowed in the clean sample. This
dependence is shown in Figure 10. Excluding the extremes of
the abscissa range on this plot, the C/S ratio does not present a
strong dependence on the error limit. Additionally, more than
70% of the objects that passed our other selection criteria have
an error lower than 0.075 (and most of the asteroids in our full
sample too, see Figure 2).
6.3. Accuracy
The composition of the RPDF is generated during the
simulation, therefore it is known per se. Hence, by applying a
Gaussian fit to the RPDF, such as the one described in
Section 4.5, we can obtain the reliability of the fit in a particular
case with the relative error,
=
-
( )e
f f
f
, 3m k
k
where fk stands for the known compositional fraction of a
certain type in the RPDF, and fm for the fraction measured
through the Gaussian fit. Then we can consider all of the
instances of a fixed k in the 107 runs with
 = ( )e , 4
and the spread of Equation (4) is measured with
s = - ( )e e . 52 2
Equations (3)–(5) are identical for the three complexes and
the Q-type.
As a general trend, ò was larger for the C-complex than for
the S one. This suggests that if objects of the X-complex and
Q-type are present in the data sample, it is more likely for them
to be identified as members of the C-complex than the
S-complex by performing a Gaussian fit. This was also
observed in test runs where only the main type of each
complex was used. In terms of the r–iindex, the Q-type is
closer to the C-complex, while the X-complex is closer to the S
(see Figure 1). It is possible that this behavior is due to the
relative width of the C- and S-complexes and not to the
position of the X-complex itself.
The errors reported in Table 3 were obtained by taking the
standard deviation of each complex/type from the set of 12
best matches from the MC simulation described in previous
subsection.
The Gaussian fit is not as robust as the MC analysis for
obtaining the results, and therefore we can expect lower
accuracy. Having a fit centered on the C and S taxonomic
components, the ratio of the area under the corresponding
Gaussians is directly related to the compositional fraction of the
sample. The fraction of S-type elements obtained through a
Gaussian fit is more reliable than the C-type one. For this
Figure 8. Probability density function (red) of the color in our sample.
Equivalent to Figure 4, this time the best result from our MC simulation is
overplotted (RPDF, orange). A Gaussian fit to the PDF is also overplotted
(blue). Both the RPDF and the fit make a good match with the data, as can be
seen on the residuals (dashed orange and blue). See Sections 5 and 6.2 for
details.
13 We used Equations (3)–(5) presented in Section 6.3 to compare the results.
8
The Astronomical Journal, 157:190 (10pp), 2019 May Navarro-Meza et al.
reason, from the fit we focus on the S-type fraction obtained:
48%, which within the error bars is compatible with our MC
result.
Although in our simulations we allowed for a wide range of
variation in the randomly generated sample, our results
partially rely on the assumptions described in Section 4.6.
7. Conclusions and Future Outlook
With the use of spectrophotometry on a 1.5 m robotic
telescope, we performed rapid-response observations of small
NEOs. Here we present the results from our optical sample.
Measurements were simultaneously made in the r and i band.
After applying selection criteria, our sample consisted on 131
observations of 82 different NEOs within the size range of
∼30–850 m.
For the size range considered, we found that the occurrence
of a C-type asteroid is as frequent as one of an S-type, finding
C/S=1.06. Together, these two asteroid types represent
∼90% of our sample, with the rest likely to be Q- and X-type
asteroids. This compositional fraction is in agreement with the
results of our previous publications (Mommert et al. 2016;
Erasmus et al. 2017), which are based on UKIRT and
KMTNet-SAAO observations.
Observations from our program are ongoing. The facility
used in this study is now observing with the Z, Y, J, and H near-
infrared bands in addition to the optical r and i. By analyzing
the data set presented here, we created the tools to analyze the
observations from the rest of the campaign (2016–present).
Future publications from this study will include observations
from multiple photometric bands, which will improve the
accuracy of the results.
We would like to thank Carlos Román for his help on
scheduling RATIR’s observations. We thank the anonymous
referee for the valuable comments on this work. S.N.M. wants
to dedicate this paper to coauthor, professor, and friend Bárbara
Pichardo, RIP.
The data used in this paper were totally or partially acquired
using the RATIR instrument, funded by the University of
Figure 9. Integration limits considered for the Gaussian components of the fit. The fit is equivalent to the one showed in Figure 8. Vertical dotted shows the position of
the main subtype of the C= and S-complex, thus the center of the Gaussian components. The width of the Gaussians is related to the error of the individual elements,
and the ordinate axis has no practical meaning. See the text for more details.
Figure 10. C-type to S-type ratio found with a Gaussian fit to the PDF after
using different upper error selection criteria. Notice that this figure is a
comparison of different error limits for our sample and it does not represent our
main results.
9
The Astronomical Journal, 157:190 (10pp), 2019 May Navarro-Meza et al.
California (UC) and NASA Goddard Space Flight Center
(GSFC), on the 1.5 m telescope at Observatorio Astronómico
Nacional, San Pedro Martir, operated and maintained by OAN-
SPM and IA-UNAM. This project was supported in part by the
National Aeronautics and Space Administration under the grant
No. NNX15AE90G issued through the SSO Near Earth Object
Observations Program. S.N.M. and M.R.R. also acknowledge
the grant UNAM- DGAPA PAPIIT IN107316.
ORCID iDs
M. Mommert https://orcid.org/0000-0002-8132-778X
D. E. Trilling https://orcid.org/0000-0003-4580-3790
N. Butler https://orcid.org/0000-0002-9110-6673
B. Pichardo https://orcid.org/0000-0002-8195-8493
T. Axelrod https://orcid.org/0000-0002-5722-7199
R. Jedicke https://orcid.org/0000-0001-7830-028X
N. Moskovitz https://orcid.org/0000-0001-6765-6336
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5. Investigando la diversidad taxonómica en
familias de asteroides utillizando ATLAS
Para este artículo se tomaron del archivo del Minor Planet Center las
observaciones de 1612 asteroides realizadas por los telescopios de ATLAS
entre 2015 y 2018.
Determinar si un objeto pertenece a una familia de asteroides no es una
tarea trivial y depende de los elementos orbitales propios (Nesvorný et al.,
2015, hace una discusión al respecto). Para determinar si los objetos de
nuestra muestra son miembros de una familia de asteroides se utilizó un
catálogo creado por Nesvorny (2015), quien basa su análisis en el método
más utilizado para este propósito (Zappala et al., 1990).
Por medio del método Lomb-Scargle (Lomb, 1976; Scargle, 1982) se
calculó el periodo de rotación de cada uno de los objetos estudiados. Es-
te método es ampliamente usado para extraer el periodo de una serie de
datos con un espaciado no uniforme. Solo fueron usadas las mediciones en
el filtro o por tener una frecuencia mayor, sin embargo no se espera que
esto introduzca ningún sesgo. Para obtener el color de un objeto dado se
pusieron en fase las curvas de ambos filtros tomando en cuenta el periodo
obtenido y se le aplicó un ajuste polinomial a la curva del filtro o. Para
poder aplicar el mismo ajuste a la curva del filtro c es necesario aplicar un
offset, dicho offset es por definición color del objeto.
Los objetos de esta muestra corresponden a familias de asteroides que
han sido estudiadas previamente. A excepción de los miembros de la fa-
milia Vesta (con asteroides tipo V) se espera que la gran mayoría de los
objetos sean de tipo C y S como es observado en el cinturón principal. Por
esta razón nuestro análisis supone que toda la muestra está compuesta por
objetos de tipo C y S. De esta manera se clasifica cada uno de los objetos
utilizando el índice de color c-o para los asteroides de estos tipos calculados
a partir de los espectros promedio provistos por DeMeo et al. (2009). Para
27
tomar en cuenta el error en la medición, se utilizó un método similar al del
primer artículo, generando clones de las observaciones por medio de una
simulación Monte Carlo. Se generaron 10,000 clones de cada objeto con
una distribución centrada en el valor medido y con un ancho equivalente
al error en la medición. Posteriormente se clasificó cada uno de los clones
de acuerdo a la distancia respectiva entre su posición en el eje c-o y los
índices de color de los tipos C y S. El promedio de las 10,000 clasificaciones
determina la taxonomía para cada uno de los objetos de la muestra. 16%
de los objetos estudiados fueron clasificados por un estudio independiente
(Warner et al., 2009), por lo que fue posible comparar los resultados. La
clasificación de los objetos coincide en un 85%, mientras que los periodos de
rotación concuerdan en un 89% si se considera una barra de error del 10%.
Aún cuando las familias tienen típicamente la misma taxonomía, exis-
ten diferentes razones para que haya miembros de diferentes clasificaciones
en una familia determinada (ver por ejemplo Cellino et al., 2001; Russell
et al., 2012). Este trabajo identifica la diversidad taxonómica en las fa-
milias Vesta, Nysa-Polana y Flora. Al relacionar los elementos orbitales
propios con dicha diversidad, se observa una posible dependencia, la cuál
es consistente con algunos de los modelos de formación de dichas familias
(ídem), pues uno de los modelos de formación de la familia Flora sugiere
que un asteroide de tipo C colisionó con uno de tipo S. La alta proporción
de objetos de tipo C encontrada en la familia Flora (principalmente de tipo
S), y la dependencia de la misma en el tamaño de los objetos, sugiere un
límite en el tamaño del cuerpo carbonáceo.
Parte de la metodología para clasificar los objetos está basada en el
artículo anterior. El incorporar un meacanismo estadístico para considerar
el error en las mediciones en un m de clasificación simple brindó solidez a
los resultados. También contribuí con la escritura del artículo y discusión
relacionada con trabajos anteriores.
28
Investigating Taxonomic Diversity within Asteroid Families through ATLAS Dual-band
Photometry
N. Erasmus1 , S. Navarro-Meza2,3, A. McNeill3, D. E. Trilling1,3 , A. A. Sickafoose1,4,5 , L. Denneau6 , H. Flewelling6 ,
A. Heinze6 , and J. L. Tonry6
1 South African Astronomical Observatory, Cape Town, 7925, South Africa; nerasmus@saao.ac.za
2 Instituto de Astronomia, Universidad Nacional Autonoma de Mexico, Ensenada B.C. 22860, Mexico
3Department of Astronomy and Planetary Science, Northern Arizona University, Flagstaff, AZ 86001, USA
4Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA
5 Planetary Science Institute, Tucson, AZ 85719-2395, USA
6 Institute for Astronomy, University of Hawaii, Honolulu, HI 9682, USA
Received 2019 July 24; revised 2019 November 13; accepted 2019 November 13; published 2020 February 20
Abstract
We present here the c–o colors for identified Flora, Vesta, Nysa–Polana, Themis, and Koronis family members within
the historic data set (2015–2018) of the Asteroid Terrestrial-impact Last Alert System (ATLAS). The Themis and
Koronis families are known to be relatively pure C- and S-type Bus-DeMeo taxonomic families, respectively, and the
extracted color data from the ATLAS broadband c- and o-filters of these two families are used to demonstrate that the
ATLAS c–o color is a sufficient parameter to distinguish between the C- and S-type taxonomies. The Vesta and Nysa–
Polana families are known to display a mixture of taxonomies possibly due to Vesta’s differentiated parent body origin
and Nysa–Polana actually consisting of two nested families with differing taxonomies. Our data show that the Flora
family also displays a large degree of taxonomic mixing and the data reveal a substantial H-magnitude dependence on
color. We propose and exclude several interpretations for the observed taxonomic mix. Additionally, we extract rotation
periods of all of the targets reported here and find good agreement with targets that have previously reported periods.
Unified Astronomy Thesaurus concepts: Main belt asteroids (2036); Asteroids (72); Broad band photometry (184);
Sky surveys (1464); Minor planets (1065); Small solar system bodies (1469); Lomb-Scargle periodogram (1959);
Period determination (1211); Light curves (918)
Supporting material: figure set, machine-readable table
1. Introduction
Asteroid families are groups of objects where members of the
group display similar proper orbital elements. This suggests a
common collisionally disrupted parent-body source for a family.
Since the identification of asteroid families (Hirayama 1918),
several studies have also shown that for many of the identified
families there is also a strong correlation between taxonomic type
and family membership (Bus 1999). For instance, family members
of the Massalia, Eunomia, and Koronis families all have observed
spectra or colors that are consistent with the Bus-DeMeo S-type
taxonomy (Lazzaro et al. 1999; Masiero et al. 2015; Erasmus et al.
2019). On the other hand, members of the Hygiea, Adeona, and
Themis families all have observed spectra or colors that are
consistent with the Bus-DeMeo C-type taxonomy (Carruba 2013;
Masiero et al. 2015; Erasmus et al. 2019). This leads to the
assumption that the individual parent-body sources of each of these
families must have had a pure composition with either a S-type or
C-type spectral signature (see Figure 1 for spectra in the visible of
the Bus-DeMeo S- and C-type taxonomies).
However, there are several families that display a large
variation in observed spectra or color and therefore potentially
contain a significant mix of two (or more) taxonomies. Some
explanations that have been proposed include: nested families, i.e.,
two overlapping families in orbital space that are actually two
separate families with differing taxonomies (Cellino et al. 2001);
two colliding parents that had completely different mineralogy;
size-dependent space-weathering that modifies the spectral shape
of a subgroup within the family (Brunetto & Strazzulla 2005); a
large differentiated parent body having variations in mineralogy
(Binzel & Xu 1993); or simply incorrectly assigning membership
(sometimes referred to as interlopers).
In this work we present the c–o colors and rotation periods of
1612 (414 Vesta, 494 Flora, 304 Nysa–Polana, 204 Themis, and
197 Koronis) main-belt targets. In Sections 2 and 3 we briefly
summarize the Asteroid Terrestrial-impact Last Alert System
(ATLAS) system and the approach for identifying the relevant
family members within its data set. In Section 4 we explain how
the colors are derived from the data set’s dual-band photometry.
The method for extracting color relies on the determination of
the rotation periods, hence the latter are a convenient byproduct
of our analysis. In Section 5 we discuss how we assign
taxonomies to the targets. Section 6 contains results of validation
tests using previously reported taxonomies and rotation periods.
We also show validation results using the ATLAS c–o colors of
the Themis and Koronis targets that have known and relatively
pure taxonomic distributions. In Sections 7 and 8 we perform a
more in-depth study on the observed taxonomic diversity of the
Vesta, Nysa–Polana, and Flora families and use this to draw
conclusions on the origin of the Flora family by comparing to
the Vesta and Nysa–Polana families that have known reasons for
the observed mixture in the taxonomies present.
2. ATLAS Data
Observations were performed between 2015 and 2018 by
ATLAS.7 Currently consisting of two units both located in
Hawaii, ATLAS is designed to achieve a high survey speed per
The Astrophysical Journal Supplement Series, 247:13 (7pp), 2020 March https://doi.org/10.3847/1538-4365/ab5e88
© 2020. The American Astronomical Society. All rights reserved.
7 http://atlas.fallingstar.com
1
unit cost (Tonry et al. 2018a). Its main purpose is to discover
asteroids with imminent impacts with Earth that are either
regionally or globally threatening in nature. To fulfill this, the
two current ATLAS units scan the complete visible northern
sky every night enabling it to make numerous discoveries in
multiple astronomical disciplines, such as supernovae candi-
date discovery (Prentice et al. 2018), gamma-ray burst
phenomena (Stalder et al. 2017), variable stars (Heinze et al.
2018), and asteroid discovery. Since its inception ATLAS has
found 39 potentially hazardous asteroids among the 370 near-
Earth asteroids that it has discovered. All detected asteroid
astrometry and photometry are posted to the Minor Planet
Center, while the supernova candidates are publicly reported to
the International Astronomical Union Transient Name Server.
The two ATLAS units are 0.5 m telescopes each covering 30
deg2 field-of-view in a single exposure. The main survey mode
mostly utilizes two custom filters, a “cyan” or c-filter with a
bandpass between 420 and 650 nm and an “orange” or o-filter
with a bandpass between 560 and 820 nm (see Figure 1). For
further details on ATLAS, ATLAS photometry, and the
ATLAS All-sky Stellar Reference Catalog see Tonry et al.
(2018a, 2018b) and Heinze et al. (2018).
3. Family Determination
To identify Flora, Vesta, Nysa–Polana, Themis, and Koronis
family members within the ATLAS data set we utilize and
cross-correlate with data from Nesvorny (2015) obtained
through The Planetary Data System8
(PDS) to associate objects
from the ATLAS data set with known collisional families. The
Nesvorny (2015) data set makes use of the Hierarchical
Clustering Method (Zappala et al. 1990) to assign families. The
data set also supplies a “c-parameter” (see Nesvorny 2015 for a
description) that can be used to identify suspected interlopers.
For the ATLAS data set the interloper contamination is low
with a percentage of suspected interlopes for the Flora, Vesta,
Nysa–Polana, Themis, and Koronis of 4.5%, 0.0%, 13.5%,
6.4%, and 5.6% respectively.
4. Rotation Period Extraction and Color Calculation
Rotation periods were extracted from the ATLAS data by
generating a Lomb–Scargle periodogram (Lomb 1976; Scargle
1982) of each target’s o-filter photometric data since this is the
most abundant data out of the two filters used by ATLAS. We
only considered ATLAS targets that had at least 30 photometric
data points in the o-filter and 10 photometric data points in the
c-filter. See the top plots of Figure 2 for example o- and c-filter
photometric data of Flora family member 1785 Wurm (1941
CD), Koronis family member 1809 Prometheus (2522 P-L),
and Vesta family member 2511 Patterson (1980 LM). Targets
that had periodograms containing peaks with a confidence
(Zechmeister & Kürster 2009) larger than 50% were flagged to
have potentially extractable rotation periods. See the middle
plots of Figure 2 for example periodograms that resulted in
high confidence peaks. The final extracted light-curve period is
determined from the strongest periodogram peak, and the
uncertainty of this periodicity is determined by fitting a
Gaussian function to the periodogram peak and using the rms
width (σ) as the uncertainty (see the superimposed black curve
and σ of the fitted function in the periodogram plots in
Figure 2). It has to be noted that because of the ATLAS
observing cadence there is significant alias ambiguity in our
periodograms due to the daily interval between observations.
Therefore, there is the likelihood that some of the periods we
extract are offset from the actual period by a frequency that is a
multiple of a day (24 hr). This is evident by the presence of
multiple peaks in some of our periodograms that have a similar
confidence. The rotation periods (twice the extracted light-
curve period), uncertainty, and confidence in the periods are
recorded in Table 1.
To determine the colors of each ATLAS target we fold both
the c- and o-filter data with the extracted rotation period. A
spline fit in the form of a high-order polynomial is fitted to the
more abundant o-filter data with the fit weighted on the
uncertainty of the photometric values. The same polynomial
that is fitted to the o-filter data, with the inclusion of a
magnitude offset as a variable fit parameter, is fitted to the c-
filter data. The c–o color is assigned as this fitted magnitude
offset. The uncertainty in this color value is derived from the
weighted (by uncertainty of the photometric values) standard
deviation of the residuals of the two filter fits and the respective
filter data. See the bottom plots of Figure 2 for examples of the
results of this procedure with the c–o color values and
uncertainty displayed in bottom left corner of each plot. This
derived color value is not dramatically affected if by chance the
folding is performed using an alias of the rotation period
instead of the actual rotation period.
In a final step we remove photometric outliers and low-
quality data from our data set by discarding targets that have
a c–o color that falls more than 3σ from the median measured
c–o color of the relevant family and targets that had an
uncertainty in measured c–o color larger than 130% of the
median uncertainty of the targets in the relevant family. The
result was that we discarded on average roughly 25% of our
targets for each family. The calculated c–o colors and the
uncertainties are recorded in Table 1.
Figure 1. Transmission curves of the c- and o-filters of ATLAS (Tonry
et al. 2018a) are plotted together with the averaged visible wavelength reflectance
spectra, normalized at 550 nm, of the Bus-DeMeo S- and C-type taxonomies
(DeMeo et al. 2009). The upper and lower bounds of the two taxonomic spectra
provided by DeMeo et al. (2009) are also indicated with shading. The dashed lines
are linear interpolations of the spectra and bounds since no data below 450 nm are
provided.
8 https://pds.nasa.gov/
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The Astrophysical Journal Supplement Series, 247:13 (7pp), 2020 March Erasmus et al.
5. Taxonomic Determination
For this study we limit our target classification to the two
most prominent Bus-DeMeo taxonomic classes, namely, the
silicate-rich S-type and the carbonaceous C-type that make up
roughly 50% and 35% of the main-belt population, respectively
(Bus & Binzel 2002; DeMeo & Carry 2014; Erasmus et al.
2018). Because the Bus-DeMeo S- and V-type spectra are
difficult to distinguish using only two broadband filters in the
visible region we consider those two both as S-type in this
study. To decide which of these two classifications is the most
likely for each of our targets we calculate the expected c–o
ATLAS color for the mean Bus-DeMeo S- and C-type spectra
provided by DeMeo et al. (2009) and compare that to the
target’s measured c–o color. The expected c–o color is
determined by convolving the ATLAS filter responses with
the mean Bus-DeMeo S- and C-type spectra (see Figure 1 for
filter responses and spectra) and use the convolution of the
ATLAS filter responses with the Sun’s spectrum as the zero-
point magnitudes. The same was done for the the upper and
lower bounds of the spectra to determine the uncertainty in the
expected color. The expected c–o color for an S-type asteroid is
-
+0.388 0.012
0.011 and for a C-type is -
+0.249 0.004
0.004 (see the solid blue
and red vertical lines in Figures 3–5 with the upper and lower
bounds indicated in the dashed lines).
To assign the S- or C-type taxonomy to each of our targets
we use a probabilistic approach using a Monte Carlo method
where we generate 10,000 pseudo-measured colors with a
Figure 2. Example ATLAS photometric data (top plots), Lomb-Scargle periodograms of photometric data (middle plots), and phased photometric data (bottom plots)
for (a) Flora family member 1785 Wurm (1941 CD), (b) Koronis family member 1809 Prometheus (2522 P-L), and (c) Vesta family member 2511 Patterson (1980
LM). For the periodograms we also indicate the extracted light-curve period ( )=Pmax
Rot.Period
2
, uncertainty in extracted period (σ), and confidence in extracted period.
Fitted to the phased data are spline fits in the form of a high-order polynomial which are used to determine the color of each target (see Section 4 for detail). The
determined c-o color value and the uncertainty is displayed in the bottom-left of each plot. All 1612 images are available in the Figure Set.
(The complete figure set (1612 images) is available.)
Table 1
ATLAS Colors, Extracted Rotation Periods, and Taxanomic Probabilities
No. Target Name Family H
a
c–o Rotation Period Confidence C-type S-type
(mag) (mag) (hr) % (prob. in %)
0001 158 Koronis Koronis 9.3 0.40±0.09 14.204±0.006 73 18 82
0002 167 Urda Koronis 9.2 0.38±0.06 13.060±0.009 88 14 86
0003 208 Lacrimosa Koronis 9.0 0.42±0.09 14.087±0.010 84 13 87
0004 222 Lucia Themis 9.1 0.22±0.09 9.371±0.005 58 86 14
0005 243 Ida Koronis 9.9 0.39±0.10 4.225±0.001 74 26 74
0006 254 Augusta Flora 12.1 0.42±0.12 5.895±0.002 85 18 82
0007 263 Dresda Koronis 10.2 0.39±0.12 12.450±0.055 72 28 72
0008 277 Elvira Koronis 9.8 0.41±0.04 29.676±0.046 86 1 99
0009 281 Lucretia Flora 12.0 0.44±0.13 4.783±0.001 70 17 83
0010 352 Gisela (A893 AB) Flora 10.0 0.43±0.09 7.480±0.003 82 10 90
Note.
a
H magnitude was obtained from https://ssd.jpl.nasa.gov/horizons.cgi.
(This table is available in its entirety in machine-readable form.)
3
The Astrophysical Journal Supplement Series, 247:13 (7pp), 2020 March Erasmus et al.
Figure 3. Plotted are the c–o colors that could be extracted (see Section 4) from the ATLAS data set of (a) Themis family members and (b) Koronis family members.
The data points are colored depending on the final assigned taxonomy (see Section 5, S-type = red and C-type = blue). The Themis and Koronis families are two
known C- and S-type Bus-DeMeo taxonomic families, respectively, and the color histograms centered at the relevant mean Bus-DeMeo color therefore illustrate that
the ATLAS c–o color is a suitable parameter to distinguish between the C- and S-type taxonomies.
Figure 4. (Top) Plotted are the c–o colors that could be extracted (see Section 4) from the ATLAS data set of (a) Vesta family members and (b) Nysa–Polana family
members. The data points are colored depending on the final assigned taxonomy (see Section 5, S-type = red and C-type = blue). (Middle) Proper orbital elements of
all ATLAS targets with all known family members from Nesvorny (2015) plotted as small black data points in the background (suspected interlopers plotted with a
cross symbol). Also included are the histograms of the taxonomic probabilities (see Section 5) indicating the taxonomic dependence on orbital parameters. (Bottom)
The cumulative probabilities of the two taxonomies with respect to the three orbital parameters: broad red line=S-type and narrow blue line=C-type (see
Section 7).
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The Astrophysical Journal Supplement Series, 247:13 (7pp), 2020 March Erasmus et al.
normal distribution centered on the target’s measured color and
the width of the distribution equal to the uncertainty in the
measured color (see Navarro-Meza et al. 2019 for a similar
approach using r-i colors to classify near-Earth asteroids). Each
pseudo-measured color is classified as either S- or C-type
depending on where it lies relative to the decision line located
at the color value midway between the two expected c–o color
values for an S- and C-type asteroid (i.e., c–o= 0.319; see the
dotted black vertical line in Figures 3–5). The pseudo-
measured classifications are tallied to give the S- and C-type
taxonomic probabilities for each target. The taxonomy with the
highest probability is assigned to the target (data points in
Figures 3–5 are color-coded depending on the final assigned
taxonomy, S-type= red and C-type= blue). We use the
probabilities instead of the discrete classification for all our
analyses in Sections 7 and 8. The taxonomic probabilities for
each target are recorded in Table 1.
6. Validation of Rotation Periods and Taxonomic
Determination
To validate our procedures of extracting rotation periods and
determining taxonomic types, we cross-reference our results
with The Asteroid Light Curve Database (LCDB; Warner et al.
2009, Updated 2019 January 31)9 and find that ∼10% of our
targets are also present in the LCDB. For the 262 targets
present in both data sets we derive the same taxonomy as that
reported in the LCDB for 85% of the targets (for this we
consider V-type and S-type as a match as well as B-type and
C-type as a match) and also match the reported rotation periods
within an error margin of 1% for 76% of our targets and within
an error margin of 10% for 89% of our targets (for this
comparison we also included the two alias periods adjacent to
the main extracted period).
As a second validation test, the Themis and Koronis
families, which are two well-known relatively pure C- and
S-type Bus-DeMeo taxonomic families, are used as bench-
marks for our taxonomic determination. In Figure 3 we plot the
extracted c–o colors of the Themis and Koronis family
members within the ATLAS data set. The data points are
color-coded depending on the final assigned taxonomy,
S-type=red and C-type=blue. Of the 204 Themis targets
we classify 95% as C-type, and the color histogram shown in
Figure 3(a) shows a clear peak centered at the expected mean
Bus-DeMeo C-type color. Of the 197 Koronis targets we
classify 91% as S-type, and the color histogram shown in
Figure 3(b) shows a clear peak centered at the expected mean
Bus-DeMeo S-type color. These two plots demonstrate that the
ATLAS c–o colors that we extract are a sufficient parameter to
distinguish between the C- and S-type taxonomies.
7. Mixture of Taxonomies in the Vesta and Nysa–Polana
Families
The Vesta family, a V-type family, has a spectral signature
similar to the spectral shape of S-type asteroids but with the
distinct S-type absorption feature at 1 μm enhanced in V-types.
The Nysa–Polana family is also a known S-type family.
However, observations have indicated that both contain a
significant number of family members with spectra or color
different from the majority of family members (Erasmus et al.
2019). This could be ascribed to the parent body of the Vesta
family originally consisting of a differentiated object (Russell
et al. 2012) and hence a plausible reason behind the range in
colors observed within the Vesta family. Through albedo
studies the Nysa–Polana family has been identified to consist of
two subgroups overlapping in proper orbital space (Cellino
et al. 2001), i.e., two nested families of which one shows
S-type spectral characteristics and the other B-type spectral
characteristics. The Bus-DeMeo B-type spectrum is similar to
the spectral shape of C-type asteroids, flat and featureless, but
with a slightly bluer slope in the visible. The top set of plots in
Figure 4 are the extracted c–o colors of the Vesta and Nysa–
Polana family members within the ATLAS data set. The two-
taxonomic mix is clearly evident in both families with only
∼70% of Vesta targets having c–o colors in the vicinity of the
expected S(V)-type color while the Nysa–Polana targets have a
1:3 split between c–o colors that match the expected C(B)-type
and S-type colors, respectively.
Figure 5. (Top) Plotted are the c–o colors that could be extracted (see
Section 4) from the ATLAS data set of Flora family members. The data points
are colored depending on the final assigned taxonomy (see Section 5,
S-type = red and C-type = blue). (Middle) Proper orbital elements of all
ATLAS targets with all known family members from Nesvorny (2015) plotted
as small black data points in the background (suspected interlopers plotted with
a cross symbol). Also included are the histograms of the taxonomic
probabilities (see Section 5) indicating the taxonomic dependence on orbital
parameters. (Bottom) The cumulative probabilities of the two taxonomies with
respect to the three orbital parameters: broad red line=S-type and narrow blue
line=C-type (see Section 7)
9 http://www.MinorPlanet.info/lightcurvedatabase.html
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By plotting the distributions of the two taxonomies as a
function of proper orbital space (see the middle set of plots in
Figure 4), the differing causes behind the taxonomic diversity
seen in both of these families can be distinguished from one
another. The assigned taxonomy of Vesta family members has
no dependence on proper orbital space (consistent with a
differentiated parent body origin), while the Nysa–Polana
“B-type subgroup” is positioned at a lower eccentricity (and
to a lesser extent a higher inclination) than the Nysa–Polana
“S-type subgroup” (consistent with two nested families with
slightly differing orbital parameters). This taxonomic depend-
ence (or independence) on orbital parameters is highlighted by
performing Kolmogorov–Smirnov (K-S) tests and plotting the
resultant cumulative probabilities of the two taxonomies with
respect to the three orbital parameters (see the bottom plots
of Figure 4, broad red line= S-type and narrow blue line=
C-type). The two taxonomies in the Vesta family have identical
cumulative probabilities for the three orbital parameters (K-S
statistics for semimajor axis, inclination, and eccentricity of
0.08, 0.04, and 0.01), while the two taxonomies in the Nysa–
Polana family have obvious differing cumulative probabilities
in eccentricity (K-S statistics for semimajor axis, inclination,
and eccentricity of 0.05, 0.12, and 0.15). We use the
cumulative probabilities of these two families as benchmarks
for ascertaining the likely cause of the taxonomic diversity also
seen in the Flora family.
8. Taxonomic Diversity of the Flora Family
The top plot in Figure 5 shows the the extracted c–o colors
of the Flora family members within the ATLAS data set. As is
the case with the Vesta and Nysa–Polana families, the Flora
family also displays a significant taxonomic mix, or at least a
significant range of colors. Roughly 70% of the targets have
c–o colors consistent with the expected S-type color with the
remaining targets displaying bluer C-like colors. This is a
similar proportion to that of the Vesta family. The cumulative
plots of the two colors in the Flora family (see the bottom of
Figure 5) are identical for the three orbital parameters (as is the
case for the Vesta family) as opposed to indicating a nested
family as is the case for the Nysa–Polana family. Therefore, a
nested family is unlikely as the source of the taxonomic mix in
the Flora family.
9. Discussion
There are several possible interpretations for the taxonomic mix
observed for the Flora family. Plotting the moving average of the
colors as a function of H-magnitude (size) reveals a strong color
dependence on size for the Flora family targets (see Figure 5).
Since the smaller bodies are probably younger (more recently
created through collisions) and therefore have fresher surfaces,
one clear possibility is that the older surfaces on the larger bodies
have been reddened through space weathering, whereas the
younger surfaces on smaller bodies are unweathered and therefore
less red. Thomas et al. (2011, 2012) report that small (H≈ 15)
Koronis family objects are bluer than large (H≈ 12) Koronis
family objects and attribute this difference to space weathering.
We also observe a hint of this effect at a similar H-magnitude
range in our Koronis family observations (see Figure 3(b)).
However, this effect is subtle and cannot explain the large color
range we observe for the Flora family (compare color ranges as a
function of H-magnitude for the Koronis and Flora families in
Figures 3(b) and 5)
Another possibility is that, like the Vesta family, the
heterogeneous Flora family may show evidence of a differentiated
parent body. This is in agreement with a differentiated-body
speculation by Gaffey (1984) based on several mineralogic and
petrologic parameters derived for the surface material of asteroid
Flora. Spectral data from the Galileo spacecraft on its flyby
of Flora-family member 951 Gaspra also showed an olivine/
pyroxene ratio that points to Gaspra being a fragment of at least
a partially differentiated parent body (Veverka et al. 1994).
However, various work (Vernazza et al. 2008, 2014; Dunn et al.
2013) has shown that the Flora family is likely the source of the
undifferentiated LL chondrites, making this interpretation poten-
tially problematic.
Alternatively, the C-like asteroids in the Flora family may
simply be interlopers in the family membership list, though this
would imply a relatively high contamination fraction of 28.3%
that is significantly higher than the estimation for our data set of
only 4.5% using the model of Nesvorny (2015).
Finally, two additional possible causes for the C-like colors that
are observed could be due to shocked material and impact melt,
which Kohout et al. (2014) and Reddy et al. (2014) have shown
can make LL chondrite (S-like) spectra appear more C-like, or that
a large member of the original S-type Flora family was simply
impacted by a C-type asteroid that shattered, producing an
embedded family within the Flora family that has a separate
parent body (here we define an embedded family as one that was
created through a collision between a family member and a non-
family member, whereas a nested family occupies similar orbital
element space but has an independent origin). Neither of these
interpretations can be excluded by the taxonomic independence
on orbital parameters we observe. The strong color dependence on
size of our observed Flora family targets can be explained if the
C-type impactor was smaller (H‹ 12) than the original S-type
Flora parent body.
These topics are discussed in further detail in a forthcoming
paper (H. Sun et al. 2020, in preparation).
10. Conclusion
We have reported the c–o colors (and rotation periods) for
identified Flora, Vesta, Nysa–Polana, Themis, and Koronis
family members within the historic data set (2015–2018) of
ATLAS. By using a probabilistic approach we also classify our
targets as either S-type or C-type and compare to previously
reported taxonomies and rotation periods to validate our
methodologies. We use the Themis (a C-type family) and
Koronis (a S-type family) targets in the ATLAS data set to
demonstrate that the ATLAS c–o color is a sufficient parameter
to distinguish between the C- and S-type taxonomies.
We find that the Flora family has a significant mixture of red
(S-like) and blue (C-like) colors and a compelling observed H-
magnitude dependence on the colors and we propose several
possible causes of this range in colors.
This work has made use of data from the Asteroid Terrestrial-
impact Last Alert System (ATLAS) project. ATLAS is primarily
funded to search for near earth asteroids through NASA grants
NN12AR55G, 80NSSC18K0284, and 80NSSC18K1575; bypro-
ducts of the NEO search include images and catalogs from the
survey area. The ATLAS science products have been made
possible through the contributions of the University of Hawaii
6
The Astrophysical Journal Supplement Series, 247:13 (7pp), 2020 March Erasmus et al.
Institute for Astronomy, the Queen’s University Belfast, the Space
Telescope Science Institute, and the South African Astronomical
Observatory.
This work is partially supported by the South African National
Research Foundation (NRF), the Arizona Board of Regents’
Regents Innovation Fund, the National Aeronautics and Space
Administration (NASA), and by a grant from NASA’s Office of
the Chief Technologist.
ORCID iDs
N. Erasmus https://orcid.org/0000-0002-9986-3898
D. E. Trilling https://orcid.org/0000-0003-4580-3790
A. A. Sickafoose https://orcid.org/0000-0002-9468-7477
L. Denneau https://orcid.org/0000-0002-7034-148X
H. Flewelling https://orcid.org/0000-0002-1050-4056
A. Heinze https://orcid.org/0000-0003-3313-4921
J. L. Tonry https://orcid.org/0000-0003-2858-9657
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6. Taxonomía de NEOs pequeños con RATIR
-borrador-
En este artículo se analizan las observaciones realizadas por nuestro
equipo con el instrumento RATIR de 2014 a 2018. Las mediciones de 2016
a 2018 incluyen información en bandas del rango óptico (r e i) y cercano
infrarojo (Z, Y, J y H ), sin embargo la calidad de la medición en cada ban-
da no es uniforme, porque ninguno de los objetos cuenta con mediciones
en todas las bandas con calidad suficiente. Particularmente no fue posible
utilizar mediciones en la banda H. Por lo anterior fue necesario utilizar
diferentes modelos para analizar la muestra.
Considerando el color formado por dos filtros fotométricos arbitrarios,
todos los objetos de cierta taxonomía tienen un color similar. En los dos
artículos anteriores se demostró cómo un solo color puede ser de gran utili-
dad para estudiar la distribución taxonómica de una muestra de asteroides.
Al contar con información de diferentes filtros, el objetivo es construir un
método de análisis con la mayor cantidad de dimensiones (colores) posible
para tener un resultado más exacto. Sin embargo el rango efectivo de nues-
tra muestra, así como de la muestra control no es uniforme en función de la
longitud de onda, por lo que empleamos distintas combinaciones de filtros
que tuviesen suficiente información en ambas muestras, y que el algoritmo
de clasificación (resumido en el siguiente párrafo) ofreciera una exactitud
confiable.
El análisis se centra en una técnica de Machine Learning conocida co-
mo k-NN (k-Nearest Neighbors). Este algoritmo identifica las zonas de cada
clase en un espacio N-dimensional, en este caso las clases son las taxonomías
de los asteroides y cada color una dimensión. Dado que todos los objetos
de una misma taxonomía tienen colores similares, el algoritmo determina
cuáles son los límites entre una taxonomía y otra en el espacio de colores.
Se consideraron todas las taxonomías que cuentan con más de 5 espectros
en la muestra control y que por lo tanto se espera que representen una
36
parte significativa de la muestra, esto incluye a los complejos taxonómicos
C (formado por los tipos C, B y Ch), X (tipos X, Xn, Xk, Xe), S (tipos S,
Sw, Sr, Srq, Sqw) Q (tipos Q y Sq) y los tipos D, V y L.
Para cada conjunto de filtros a utilizar, el algoritmo determina las zonas
de cada taxonomía por medio de la muestra control, por lo que al introducir
los objetos observados el algoritmo regresa su clasificación. Para tomar en
cuenta el error en la observación se procedió de manera similar a los ar-
tículos anteriores, generando 1000 copias Monte Carlo de cada observación
bajo una distribución gaussiana. Se encontró la clasificación para cada una
de las copias y se determinó como cierta aquella con mayor peso estadístico.
Basado en esto, presentaremos tablas con la probabilidad de cada objeto
de pertenecer a las diferentes taxonomías.
87 objetos fueron tratados con Machine Learning y 151 con simulaciones
Monte Carlo, con la metodología del primer artículo. Diferentes estudios
acerca de la taxonomía de asteroides han considerado distintas taxonomías
en su análisis, así como distintos rangos de tamaño, lo cuál afecta las pro-
porciones reportadas por cada autor. Para comparar nuestros resultados
con otros estudios decidimos utilizar el cociente entre objetos primitivos
y evolucionados: C+D+X
A+K+L+O+Q+R+S+T+V
. El análisis de resultados está en
curso, sin embargo, los resultados preliminares concuerdan con los obteni-
dos en el trabajo más reciente de taxonomía de NEOs menores a 1 Km
(Devogèle et al., 2019) y los del mayor estudio a la fecha del mismo tipo
de objetos (Binzel et al., 2019). Por lo tanto -potencialmente-, al estudiar
la distribución taxonómica, la combinación de mediciones fotométricas y
herramientas de cómputo pueden ofrecer la misma calidad que la espec-
troscopía, pero de manera más eficiente.
Para este artículo seguí la metodología usada por uno de mis asesores
en un trabajo similar con datos del telescopio UKIRT (Mommert et al.,
2016), sin embargo yo escribí mis propios códigos. De manera similar al
primer artículo, yo realicé la investigación asociada a este. Como trabajo
37
preliminar, escribí una rutina para organizar y limpiar los espectros de la
muestra control. Esto incluyó eliminar mediciones repetidas o nulas, descar-
tar los Mars Crossers y organizar cada espectro de acuerdo a la taxonomía
reportada por el equipo de MITHNEOS (Binzel et al., 2019). Escribí una
rutina adicional para recortar los espectros de la muestra control en los
casos donde su cobertura no fuera suficiente en comparación con los filtros
de RATIR. Esto para que la convolución no arrojara colores característicos
falsos. Exploré el uso de Principal Component Analysis para encontrar los
colores que brindan más información acerca de la clasificación de asteroi-
des, no obstante decidí utilizar todos los colores con los que contaba en los
casos donde fuera posible.
38
Draft version September 4, 2020
Typeset using LATEX preprint2 style in AASTeX62
Taxonomy of Sub-kilometer NEOs from multiwavelength photometry with RATIR
S. Navarro-Meza,1, 2 M. Mommert,3, 2 D.E. Trilling,2 N. Butler,4, 5 and M. Reyes-Ruiz1
1Instituto de Astronomia, Universidad Nacional Autónoma de México, Ensenada B.C. 22860, México.
2Department of Astronomy and Planetary Science, Northern Arizona University, Flagstaff, AZ 86011, USA
3Lowell Observatory, Flagstaff, AZ 86001, USA
4School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287, USA
5Cosmology Initiative, Arizona State University, Tempe, AZ 85287, USA
ABSTRACT
As part of our multi-observatory, multi-filter campaign, we present results from obser-
vations of 238 near-Earth Objects (NEOs) obtained with the RATIR instrument on the
1.5 m robotic telescope at the San Pedro Martir’s National Observatory in Mexico. Our
project is focused on rapid response photometric observations of NEOs with absolute
magnitudes in the range 20-25. Data with coverage in the near infrared and optical
range was analyzed with Machine Learning techniques, while optical-only data was
analyzed via Monte Carlo simulations. The rapid response and the use of spectropho-
tometry allows us to obtain taxonomic classification of sub-kilometer objects with small
telescopes, representing a convenient characterization strategy. We present taxonomic
classification of the 87 objects observed in the optical and near infra-red. The ratio of
primitive to non-primitive objects is estimated for all objects, finding values of ≈ 0.7
and ≈ 0.9 in our sample.
Keywords: asteroids: individual (near-Earth objects) — minor planets — surveys
1. INTRODUCTION
Solar System minor bodies are tracers of the
System’s formation and evolution and they can
be used as current samples of such processes
(Delsemme 1991; Malhotra 1997). In order to
understand the processes occurring in our Sys-
tem, studies with numerous samples focused
on analyzing colors, taxonomies, orbital and
physical properties of asteroids from different
populations have been made (see for example
Ivezić et al. 2001; Carvano et al. 2010; Carry
Corresponding author: S. Navarro-Meza
snavarro@astro.unam.mx
et al. 2016). Near-Earth Objects (NEOs), the
minor bodies closest to us, originate from the
asteroid Main Belt (MB) between the orbits
of Mars and Jupiter. Hence our surrounding
objects and inform us about the physical prop-
erties in the region of the gas giants (Bottke et
al. 2002; Granvik et al. 2018) and enable us to
take a closer look to the processes that occur in
the Solar System.
It is well known that an asteroid of a few
dozens of meters in diameter can cause serious
damage when impacting (see for example Brown
et al. 2013). Given that there exist nearly a mil-
lion objects (Trilling et al. 2017) of that size or
2
larger, their discovery and characterization has
become a high priority.
We report spectrophotometric observations of
asteroids within a H magnitude range of 18.1
to 27.1, with median in 21.8. Using the av-
erage albedo for NEOS (Thomas et al. 2011),
this is equivalent to a diameter range from di-
ameters from approximately 10 to 600 meters.
We acquired them using RATIR, a mult-imager
with 4 channels, available to observe in the
visible and near infrared wavelengths at the
same time. Spectrophotometry consists of pho-
tometric measurements at a few key spectral
bands, hence collecting the light within a broad
bandpass instead of dispersing it as in spec-
troscopy. It has been shown that spectropho-
tometry can be sufficient to classify asteroids
according to their main compositional features,
via a taxonomic scheme (Tholen 1984; Hahn,
& Lagerkvist 1988; Ivezić et al. 2001, etc.).
Where objects of a given taxonomy cluster in
a color diagram, generally creating different
zones for each taxonomy. Different taxonomies
are defined by distinctive spectral features of
the objects. Spectrophotometry also has the
advantage of being less expensive than spec-
troscopy in terms of telescope time and can be
performed with smaller telescopes.
Recent observations of asteroids in near Earth
space (Devogèle et al. 2019; Binzel et al. 2019;
Navarro-Meza et al. 2019; Lin et al. 2018; Perna
et al. 2018; Ieva et al. 2018; Erasmus et al. 2017;
Mommert et al. 2016), have shown that the tax-
onomy of NEOs is size dependent and different
from the objects in the MB. Currently we are
unable to observe subkilometer objects in the
MB, so a comparison between these and small
NEOs is not possible. These studies agree that
S- and Q-types (unweathered version of the for-
mer), together with the primitive types C and
X, constitute the majority of the small NEOs.
However, the percentage of each taxonomy in
the distribution reported by each study can dif-
fer by a factor larger than 3: Devogèle et al.
(2019) report 17% of S-types, while Ieva et al.
(2018) estimates 61%. Several factors affect for
the different estimations: the size range consid-
ered is not exactly the same; the small size of
the sample in most of the studies; observational
biases; some studies don’t consider Q-types; the
quality of the data; the methodology followed,
etc. To help with this discrepancy, it is needed
to increase the fraction of characterized NEOs.
During the process it would be helpful to make
studies with larger samples (a few hundreds
of objects) using an homogeneous classification
method.
Here we present a combination of spectropho-
tometry and rapid-response observations, i.e.,
observations that are obtained shortly after the
discovery of the target, when it is still relatively
bright. This study is part of a worldwide sys-
tematic survey of NEO compositions (See Mom-
mert et al. 2016; Erasmus et al. 2017; Navarro-
Meza et al. 2019, for our previous results),
aimed to increase the number of small NEOs
with physical information. Which is of interest
for science, industry and planetary safety. The
rapid response approach is generally not feasi-
ble through classical observing proposals due to
heavily oversubscribed classically scheduled ma-
jor research facilities. Furthermore, this method
allows us to classify small NEOs according to
their taxonomy with a higher efficiency than
current spectroscopic methods (see Galache et
al. 2015 for a discussion).
Section 2 describes our rapid response ap-
proach and the instrument we used. Section 3
addresses our data selection and analysis. In
Section 4 we provide our results and the cor-
responding discussion is given in 5. Finally in
3
Section 6 we present our conclusions.
2. OBSERVATIONS
We present data taken from 2014 to 2018.
Observations were performed with the Reioniza-
tion And Transients InfraRed camera (RATIR,
Butler et al. 2012), on the San Pedro Martir
(SPM) 1.5 m telescope at the National Mex-
ican Astronomical Observatory (Observatorio
Astronómico Nacional). The instrument is
equipped with two optical and two near-infrared
(NIR) detectors, all of them 2048x2048 pixels.
Each of these detectors correspond to a different
channel with specific filters in the optical and
NIR, as shown in Table 1. RATIR takes four
images of an object in a single shot, enabling
us to observe with f 6 different filters at a time1.
Potential targets are identified and uploaded
into the RATIR queue on a daily automated
basis. Accessible targets are identified among
those NEOs that have been discovered within
the last four weeks; this duration is partially
arbitrary2, but the method usually leads to a
number of well-observable and bright potential
targets. A target is considered accessible if it
has a visible brightness V ≤ 20 and an air-mass
≤ 2.0, as provided by the JPL Horizons system
(Giorgini et al. 1997), for at least the duration
of the estimated RATIR integration time.
Potential targets are manually selected from
the list of accessible targets, prioritizing objects
with high absolute magnitudes HV (small sizes)
and large values of HV -V, where V stands for
the apparent magnitude of the target of the up-
coming night. A high value of HV -V ensures
1 See detailed information in RATIR’s web page: http:
//ratir.astroscu.unam.mx
2 After the closest approach, NEOs fade at a rate of
typically 0.5 mag within one week and 5 mag within 6
weeks (Galache et al. 2015).
that our target is observed when it is close to
the Earth. RATIR queue observing scripts are
automatically created for the selected targets,
using the latest orbital elements of the objects
of interest provided by JPL Horizons. The ex-
posure time of each frame, as well as the total
integration time in each band per visit are a
function of the object’s brightness. Exposure
times usually ranges between 5 and 30 seconds,
while the total integration time per target is
usually less than 1 hour. A visit is defined as
an observational run. One object can have one
single visit during our campaign or different
ones, made during different days or all in one
night. The maximum number of visits of a tar-
get reported here is 4.
Our rapid response approach is the key feature
of this project. We trigger rapid response spec-
trophotometric observations of NEOs within a
few days of their discovery when the objects are
generally still bright. We can observe and char-
acterize objects as faint as Hmag ≈ 27 (equiva-
lent to a dozen of meters). Such rapid response
is generally not feasible through classical ob-
serving programs.
Image reduction and photometry is carried
out using a pipeline developed for Gamma Ray
Burst observations (see, e.g. Littlejohns et al.
2015; Becerra et al. 2017). The pipeline was
adapted for working with asteroids: it removes
sidereal sources to extract the NEO from the
image and coadds in the moving frame of the
target. The PSF determined from the sky image
is then fit to the moving-target image and the
zero point from the sky image is applied to nor-
malize the photometry (see Navarro-Meza et al.
(2019) for details). We obtain from the pipeline
the magnitude and error of the observed object
in each of the 6 broadbands used, which enables
us to have 15 different pair wise astronomical
colors. The error associated to each color is ob-
4
Channel Detector Field size Filters
(arc minute square)
C0 CCD 5.3 SDSS ugr and seven others
C1 CCD 5.3 Fixed SDSS i
C2 H2RG 10 Fixed WFCAM Z and Y
C3 H2RG 10 Fixed MKO J and H
Table 1. Channels of the RATIR instrument. All detectors are 2048x2048 pixels. C0 and C1 channels hold
the visual range filters. C2 and C3 channels contain the near infrared filters; H2RG (HAWAII-2RG) are
Teledyne mercury-cadmium-telluride detectors. We report observations using the r, i, Z, Y, J and H filters.
For more details, see http://ratir.astroscu.unam.mx/public/wiki
tained by adding in cuadrature the errors from
each of the corresponding bands.
The colors reported in this article were esti-
mated in the Vega system and the solar com-
ponent has been subtracted.
2.1. Outlier rejection
Our observations were planned in order to
observe faint objects within our facility’s capa-
bilities. However, the weather or other factors
might interfere during our automated observa-
tions. Hence, we use several criteria in order
to identify and reject photometric outliers. In
next section we describe the different methods
we used to analyze our data. One of them
makes use of multiple colors to classify each ob-
ject, while the other one makes the classification
using only one color. The rejection method is
very similar for all the data, however the mul-
tidimensional approach is more accurate, hence
we imposed more relaxed limits on the selection
of the data analyzed with such method.
For all targets, we visually confirm the per-
formance of the pipeline by verifying that the
image resulting from the coaddition is clean: a
well defined source and a successful removal of
the background sources is required. The next
lines describe the selection process of the objects
analyzed with the multi-dimensional approach.
We use a 10 − σ clipping algorithm applied to
the measured colors: for all the objects of the
sample under analysis, we estimated the vari-
ance of each color, and used the largest of them
as the standard deviation for the σ clipping. If
any of the colors of an object is not within the
10−σ limit, all measurements from that object
are removed. The later is to keep the set of ob-
servations “complete”, concept that will be ex-
plained in the next Section. The 10−σ clipping
was carried out 3 times. Each time the photo-
metric errors from the individual measurements
were propagated to obtain the weights for the
average. Notice that this step is conservative
since it uses the color with the largest, not the
smallest variance. However, using the shortest
could clip many good measurements in other
colors. The rejection process has an additional
stage in which we exclude those objects outside
the limits of the expected distribution of colors.
The expected range is the color distribution(s)
of the sample with measured spectra that we
use as a reference plus a flexibility of 0.3∆,
where ∆ is the range of a given color in the
training sample. We reject observations with
an error in color larger than 0.13 We tested this
upper limit by giving it values between .07 and
0.13, finding no direct correlation between this
value and the accuracy on the taxonomy proba-
bility for objects in Set 1 (Table 4). For objects
5
from Set 2, the accuracy in the classification is
negatively correlated to the photometric error.
However for Set 2, even objects with high error
can be classified as primitive or evolved. For
example, object 2016 FB (see Table 4) has a
Z − Y error of 0.127, but the probability of it
being a non-primitive object is 85%.
The procedure applied to objects classified
with the 1-dimensional approach is as follows:
A limit on the color index’s error due to photo-
metric uncertainty of 0.07 was set. The differ-
ence in color index between the C- and S-type
asteroids is 0.091, hence it is convenient that
we only consider the objects that have an error
lower than this threshold. As explained bellow,
the 1-D analysis is made with a fit considering
the average colors from each of the considered
types in the training sample. Objects with a
measured color larger than the largest average
value (plus the 0.07 error limit) and smaller
than the smallest average value (minus 0.7) are
excluded. We require a minimum of 4 measure-
ments per visit.
The outcome of this selection process is 87
different for the multidimensional analysis, and
151 objects observed for the 1-D analisis. Mak-
ing a total of 238 objects.
3. DATA ANALYSIS
We use the MITHNEOS database as a refer-
ence for the asteroid’s colors. This is hitherto
the largest sample of measured NEO spectra3.
To obtain the characteristic color of each tax-
onomic type, its reflectance spectrum is con-
volved with the spectral response of each of
RATIR’s filters and the solar spectrum. Details
of the process are discussed by Mommert et al.
(2016), Section 3. Hereafter, we refer to this
3 http://smass.mit.edu/minus.html
database as ’Control Sample’. When reffering
to all the objects we observed with RATIR we’ll
do it as ’Observed Sample’.
In an ideal case, the Control Sample would
cover the same wavelengths as RATIR’s broad-
band filters. However not all the objects in the
control sample have observations in the same
wavelength range, and not all the objects from
the observed sample have valid measurements in
all of the considered bands.To address this, we
only consider those objects that have at least
half of the coverage in wavelength of a given
RATIR’s filter.
3.1. Taxonomic classification
We use the Bus-DeMeo scheme (DeMeo et al.
2009) to classify our sample. This is a widely
used taxonomic scheme that combines the visi-
ble and near infrared ranges, covering from 0.45
to 2.45 µm. The taxonomy includes 24 classes,
most of which are sub-types of the C-, S- and
X-complexes, which include the majority of the
known asteroids (see DeMeo et al. 2009).
The control sample includes objects of most
of the classes in the Bus-DeMeo scheme. We
train our Machine Learning algorithm on the
characteristic colors of each type (see next sub-
section), we only considered taxonomies that
have at least 5 spectra to pr/ovide sufficient
training data. Based on this constraint and
Machine Learning test runs, we decided to use
the S, C, X and Q4 taxonomic complexes. but
not to make a distinction between their individ-
ual classes; we also considered the D- and the
4 We group the Sq-types with the Q-types, forming the
’Q complex’. In our previous paper we included the Sq-
types in the S complex, however in this study we found
that the colors of such class are clearly more similar to
the ones of the Q- rather than the S-types. Sq-types
also tend to be clustered in a 2-dimensional color space.
However, the Sqw-types have colors more similar to the
S-complex and they are scattered rather than clustered.
6
V-type objects.
3.2. Machine Learning
We base our analysis on the k-Nearest Neigh-
bors (k-NN), a supervised classification/regression
algorithm implemented in Python via Scik-
itlearn (Pedregosa et al. 2011). We train
the algorithm on the training data set, which
allows it to classify new data by itself based
on what it learned. Then the algorithm is able
to work by itself on new data based on what
it learned. Our training sample is the MITH-
NEOS database (Binzel et al. 2019, data avail-
able at: http://smass.mit.edu/minus.html) and
the algorithm learns the regions of each taxo-
nomic class in an N-dimensional space, where
N depends on the number of bands that con-
stitute a particular Complete Set. Once the
algorithm is trained, it is fed with a Complete
Set and the classification of each of its objects
is returned according to their position on the
N-dimensional color space.
We recall that not all of the observed objects
have valid measurements in the same number
of bands. Particularly the colors involving the
H band don’t meet the criteria explained in
Section 2.1, hence we decided not to use such
band. We use k-NN and cross validation via
GridSearchCV from Scikitlearn to study the
training sample and determine which combina-
tion of bands is more convenient for classifying
the objects. With the use of GridSearchCV (Pe-
dregosa et al. 2011), our ML algorithm uses
80% of the control sample to train itself and
20% to evaluate the training by re-classifying
the objects, keeping track of its success on do-
ing so. This is made iteratively, mixing the
sample and taking every time different specific
objects. The average of the success of assigning
the correct classification is the so-called ’test
accuracy’. We judge the different filter combi-
nations options by considering the outputs from
GridSearchCV and the number of observed ob-
jects with valid measurements on each of the
combinations. Table 2 shows the 3 combina-
tions selected and their structure: photometric
bands, number of objects, k, training sample ac-
curacy and test sample accuracy. We call each
of these combinations ’Complete Sets’. For each
of the Sets we obtain an equivalent one from the
Control Sample to train our algorithm. Next
we extract from the observed sample the ob-
jects with valid measurements in such bands.
The objects that don’t fulfil the selection crite-
ria for Set 1 are returned to the poll of observed
data to be considered by Set 2. Equivalently
those not suitable for Set 2 are considered for
Set 3. This last one is constituted by the r-i
color and its analysis is described in Section
3.3.1. All the objects from the observed sample
that meet the selection criteria from Section 2.1
belong to a Complete Set.
We exemplify the procedure described above
for the case of the first Set: we extract 185 ob-
jects with 10 different colors from the control
sample to train our code with the use of 10-NN.
As a result, we obtained a 10-dimensional space,
in which each of the taxonomies considered oc-
cupies a characteristic region. Then we fed the
code with our observed 1st Complete Set and
the algorithm determines the classification of
each member according to its position on this
10-dimensional space. Data was scaled prior to
the k-NN analysis by using the StandardScaler
from Scikitlearn, which normalizes the mean
and scales the variance to one. The results from
GridSearchCV applied on the training sample,
also determine the best parameters to use in
each Set for classifying the observed objects.
3.2.1. Monte Carlo clones
The true a−b color from one of our objects for
any a,b bands is expected to be in the interval
[α − ς, α + ς] in a 1-σ confidence level, where
7
Complete Set Bands No. of k Training accuracy Test accuracy
classified objects
1 r,i,Z,Y,J 64 4 0.884 0.828
2 i,Z,Y 23 9 0.761 0.671
3 r,i 151 - - -
Table 2. For its analysis, our data is splitted in three independent Sets. By combining two different bands
(out of r, i, Z, Y, J ) in a non-commutative way, Set 1 is constituted by 10 different colors, producing a
10-dimensional model (10-D). Similarly, Set 2 makes a 6-D model and Set 3 a 1-D one. Set 1 and 2 are
analyzed with a Machine Learning approach using a k-Nearest Neighbors algorithm (see Section 3.2). The
third Set is analyzed with a Monte Carlo approach (see Section 3.3.1)
α is the measured value of a − b and ς is the
photometric error derived by the pipeline. In
order to account for the uncertainty in our clas-
sification scheme, 10,000 copies of each Com-
plete Set were generated and classified. From
this we can obtain the likelihood of an object
to be assigned to different taxonomies, as well
as the error in the taxonomy distribution of the
Set. The 10,000 copies of each object in the
Set were generated under a Gaussian distribu-
tion with a mean equal to the measured value
of each color and a standard deviation equal
to ς. For objects with multiple visits a simi-
lar procedure is done: a Gaussian distribution
is formed with each visit, centered in the color
measured and with a width equal to the error
in the measurement. Then, the Gaussians are
added and a Gaussian fit is made to them, its
mean is taken as the color of the object and its
standard deviation as the error. For members of
Set 1 with multiple visits, we obtained the tax-
onomy of each visit independently finding the
same classification in the great majority of the
objects.
3.3. 1-Dimensional analysis
3.3.1. Monte Carlo simulations with synthetic
objects
We consider every object from the third Com-
plete Set as a normalized Gaussian centered at
the r-i value and with its width equal to the
error on the r-i index. To account for objects
observed in different telescope visits, the Gaus-
sian’s normalization factor is divided by the
number of visits each object has. The Gaus-
sians from all the objects are added up to build
a probability density function (PDF). To obtain
the compositional distribution from the PDF,
we performed a Monte Carlo (MC) simulation
consisting of 107 samples of synthetic asteroids.
each sample with the same number of objects
as in Set 3 but with different taxonomic distri-
butions. The types considered for the synthetic
population were selected according to the fol-
lowing criteria. From all the objects reported
in the Control Sample’s chart (Binzel et al.
2019), those NEOs with H > 17 are exctracted,
which correspond to subkilometer objects con-
sidering an average albedo of 0.28 (Thomas
et al. 2011). From these, we use those types
that have a representation of more than 1%
of the training sample and that belong to one
of the taxonomy complexes (we consider Q as
a complex), namely: B, C, X, S, Sr, Sk, Sw,
Q, Sq. Considering more types could overdue
the simplicity of model. The number of ob-
jects belonging to these taxonomies is set with
8
a pseudo-random number generator. First it is
assigned the amount of objects in the S, Q and
“C+X” complexes.
A Monte Carlo simulation requires a distri-
bution with information from the system. For
this we use three Gaussian distributions cen-
tered on the expected values of the complexes
used, which are derived from the Control Sam-
ple: The percentage of spectra classified as each
of the complexes is scaled to the sum of all the
complexes (≈ 90%). This is equivalent to our
model’s assumption that all the objects are
members from a complex. We give room for
testing other distributions by means of the stan-
dard deviation of the Gaussians. In terms of the
C+X
S+Q
space, our simulations are centered on 0.35
and cover the range C+X
S+Q
≈ [0.06, 0.85], consid-
ering one standard deviation from the mean of
the distributions, thus the actual tested range
over 107 simulations is wider.
The resulting color index distribution from
each run is added up as described at the begin-
ing of this section. We call the result Random
Probability Density Function, RPDF, to dis-
tinguish it from the PDF from our data. The
process is repeated 107 times and the reduced
χ2 (χ2
r ) between the distributions is calculated.
This 1-D analysis is based on the approach
taken in P1 were more details from the process
are given.
3.3.2. 1 Nearest Neighbor
We explore the use of the method used in
Erasmus et al. (2020) to distinguish between
C- and S-type objects. The method can be
understood as a simplification of the MC ap-
proach previously explained. 10,000 clones are
generated under a Gaussian distribution cen-
tered in the measured color and with an error
equivalent to the propagated photometric error
corresponding to the r-i color. The taxonomy
of each synthetic object is determined depend-
ing on its relative distance to the characteristic
color of the C- and S-types. The classification of
each of the observed objects is estimated from
the highest probability, based on the classifica-
tion of each of the clones.
In order to obtain an accuracy value simi-
lar to the ’testing accuracy’ but for the 1-D
algorithms, we use the Control Sample as an
input on each of them and measured the ac-
curacy of the reclasification. We derive the
colors of the color sample from spectra, hence
to make this procedure it was needed to ap-
proximate the error in the color by propagating
the uncertainty from the observations. Both
1-D algorithms over-estimated approximated
the value of fraction from the Control Sample.
The Monte Carlo presented a relative error of
1.02, while the 1-Nearest Neighbor presented a
relative error of 2.51. The higher discrepancy
using 1-NN is due to the characteristic color
of the Q-complex. Q- and Sq-types have char-
acteristic colors between those of the X- and
S-complex. Hence, in a binary5 1-NN approach,
the classification of members of the Q-complex
will be splitted between X- and S-types while
due their features they are more similar to the
S-types. 1-NN tests were made including the
possibility of an object being classified as a Q-
type, however the accuracy didn’t improve.
4. RESULTS
We present independently the results obtained
with the multi-dimensional Machine Learning
approach on the objects with data in the optical
and NIR range, and the ones obtained with a
one-dimensional approach on the objects with
optical-only data. Different authors have taken
different approaches and considerations while
5 The only possible classifications are X or S
9
studying small NEOs. Among the factors with
a larger effect on the results (ergo the compar-
ison between different ones) is the taxonomies
that are considered. For this reason we present
the individual classification of each asteroid
and the taxonomic distribution when possible,
but we also present the results as the ratio of
primitive to non-primitive asteroids, roughly
equivalent to ’carbonaceous’ to ’rocky’ type:
fraction = C+D+X
A+K+L+O+Q+R+S+T+V
. Where, C,
X, Q and S correspond to the complexes and all
types within them. Taxonomies not considered
under a particular model have a value equal to
zero. Notice that primitive objects tend to have
low albedo and a relatively similar color among
them, while non-primitive tend to be brighter,
with similar colors among them as well.
Table 3 shows the taxonomic distribution
found in the 87 objects analyzed with the
Machine Learning algorithm, equivalent to a
fraction = 0.64 ± 0.12. Figure 1 compares
our results by taxonomic type in comparison
with the latest study of subkilometer NEOs
(Devogèle et al. 2019) and to largest study up
to date of this kind (Binzel et al. 2019). Fig-
ure 2 compares the value we find for fraction
with the corresponding one of such studies, as
well as the fraction we find for the 151 objects
analyzed with the Monte Carlo (MC) method.
Table 4 shows some of the objects classified
with this method -full table available online-.
This table displays the probability of an object
to be assigned to each of the main taxonomies,
the highest of them is denoted in bold. The
last column refers to the Complete Set that was
used to estimate the probabilities: 1 is the 10-D
model, 2 is the 6-D model, while 3 is the 1-D
model, all of them defined in Table 2.
For the objects with only the r-i color avail-
able, we estimate the result from the 7 best
matching cases out of the 107 runs in the MC
C+X S Q D V L
Taxonomy
0
5
10
15
20
25
30
35
40
%
 o
f N
EO
s
MITHNEOs
MITHNEOs
recalculated*
MANOS
RATIR
Figure 1. Taxonomic fractions found in our sam-
ple analyzed with Machine Learning in compari-
son with those found by the MITHNEOS survey
(Binzel et al. 2019), the MANOS survey (Devogèle
et al. 2019) and the MITHNEOS’ as re-calculated
in Devogèle et al. (2019). We remark that the
MITHNEOS and MANOS teams also considered
other taxonomies, here we only plot the intersection
with the classes we considered, which constitute the
majority of the population.
simulation. These 7 cases show the lowest χ2
values and converge on the number of objects
from the S complex. The average of these
7 cases produces a fraction = 0.87 ± 0.29.
Considering the relative error obtained for the
MC simulations in Section 3.3, the sample
could have a fraction as low as 0.43, produc-
ing the asymmetric bars shown in Figure 2
The analysis using the 1-NN algorithm yields a
C
S
= 1.34± 0.24.
5. DISCUSSION
5 broad band filters (10 colors) are enough
to build a robust model able to distinguish be-
tween C, X, Q, S, D, V and L types. The accu-
racy or detail in the classification can be affected
by two main factors. When the training and
the observed sample don’t match completely in
the wavelength range covered, or when a lower
amount of bands is available. We find that a
model with 5 bands is robust enough to allow for
high photometric errors without affecting the
general quality of the results.
10
Taxonomy Percentage
C+X 31.9 ±6.0
S 32.5 ±6.2
Q 18.0 ±4.5
D 8.3 ±3.0
V 6.3 ±2.8
L 2.9 ±3.4
Table 3. Taxonomic distribution found in the 87 objects analyzed with the Machine Learning algorithm.
Object Ob. Midtime Dur. Hv P(C) P(X) P(Q) P(S) P(D) P(V) Set
2014 MP5 2014-07-21 04:55 0.5 21 0.00 0.00 0.00 98.40 1.60 0.00 1
2014 MK6 2014-07-22 08:54 0.5 21 71.70 28.20 0.00 0.10 0.00 0.00 1
2014 PT59 2014-08-17 07:32 0.1 20 69.00 15.10 4.90 11.00 0.00 0.00 1
2014 QQ33 2014-08-25 10:04 0.8 22 0.00 7.30 0.00 10.40 82.30 0.00 1
2016 DZ 2016-02-28 06:16 0.6 22 46.40 28.20 6.00 19.40 0.00 0.00 1
2016 DZ 2016-03-02 05:52 0.3 - - - - - - - -
2016 FB 2016-03-19 06:25 0.2 23 9.20 5.60 30.10 46.80 0.70 7.60 2
Table 4. Observed targets. Observation Midtime, duration of the observing run and absolute magnitude is
presented for all objects. For objects classified with Machine Learning in a multidimensional space, it is also
shown the probability of an object to be assigned to each of the main taxonomies. In bold the highest of
these probabilities. The last column refers to the Complete Set that was used to estimate the probabilities
(see Table 2) -full table available online-.
5.1. Efficiency of each method and
observational errors
The test accuracy for Set 2 is low (67%, see
Table 2), however by using Monte Carlo copies
of the objects to ’spread’ the error around the
color measurement, we are able to obtain highly
reliable classifications for some objects. We ob-
served that the dependence of the result on
the observational error shallows by increasing
the dimensions of the model. For the Machine
Learning algorithm we measure this dependence
by counting the amount of objects with a tax-
onomic probability higher than 60% and 90%
as a function of the maximum error on the
color allowed for the objects. The proportions
from Set 1 (10-D) were not significantly affected
while ranging the error limit from 0.07 to 0.13.
For Set 2 (6-D), adding objects with an error in
color higher than 0.07, will likely produce a less
reliable classification. This is not always the
case, since the object could have a large error
in the filter with least sensitivity but smaller
errors in the rest.
The values presented in table 3 are obtained
by adding up the probability of every object
to belong to each taxonomy. This is equivalent
11
0.4 0.6 0.8 1.0 1.2
primitive/evolved
MANOS
MITHNEOS
RATIR (ML)
RATIR (MC)
Primitive to evolved ratio for subkilometer NEOs
Figure 2. Comparison of the ratio of primitive
to non-primitive objects (see text) found in the 87
objects analyzed with Machine Learning (ML) and
in the 151 objects analyzed with the Monte Carlo
approach (MC). Also shown the equivalent values
from MANOS (Devogèle et al. 2019) and MITH-
NEOS (Binzel et al. 2019). The value from MITH-
NEOS as re-calculated by (Devogèle et al. 2019) is
shown with a water mark .
to adding the probability columns in Table 3
and dividing by the number of objects. This
procedure is statistically more correct, since it
yields the distribution of the sample as a whole
instead of using the result of each individual
object to build it. The difference in the per-
centage of each taxonomy obtained by the two
different procedures is lower than 2% and the
value of fraction differs only by ∼ 5%. The low
difference between these values suggests robust-
ness in our model, despite the fact that some of
the objects in Table 3 have large uncertainty in
the classification.
5.2. Limitations and comparison with other
studies
Our observations are biased in favor of bright
objects. At a given distance from Earth, for
objects of a given diameter, those with higher
albedo are easier to observe. For targets close
to our limiting magnitude, only those with rela-
tively high albedos will be observed. Hence, our
sample may contain a higher fraction of S and Q
objects than in the actual asteroid population.
A similar bias is imposed by the Minimum Orbit
Intersection Distance (MOID) as remarked by
Devogèle et al. (2019). For small objects, only
those that get close to Earth (small MOID) will
be visible with a ground-based small telescope.
The close encounter with Earth of an asteroid
can cause the rejuvenation of its surface by tidal
forces, reducing the effects of space-weathering.
This phenomenon could increase the real pro-
portion of Q-types observed from Earth (the
’nearest Earth objects’), but not necessarily in
the whole NEO population.
While using different methodologies on biased
and relatively small samples, it is not expected
to find exact matches between results of the
taxonomic distribution from different studies.
Devogèle et al. (2019) finds that even the same
sample analyzed with different methods can
yield results that do not agree within 1-σ Pois-
son error bars. The results presented in Table 3
and Figure 1 are in better agreement with the
ones from the MITHNEOS team presented in
Binzel et al. (2019). If we restrict our multi-
dimensional analysis to the 74 objects in the
range 20 ≤ HV ≥ 25 and compare them to the
objects from MITHNEOS in the same range,
both distributions agree with the only excep-
tion of the D-types objects (see Bottom panel
from Figure 3). Perhaps our model is clas-
sifying a small amount of S objects as D, or
possibly objects of taxonomies not considered
by our model are being classified as D-types.
This and the other small percentual differences
increases the value of fraction we derive for this
magnitude range, however, as can be seen in
the upper panel from Figure 3, our value still
agrees with all the other cited studies.
Given the high amount of Q-type objects
present in the NEO population, we do not con-
sider the 1-NN model to be appropriate for
analyzing this population, due to its high rate
of classifying members of the Q complex as C
12
C+X S Q D V L
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
MANOS
MITHNEOS
RATIR (ML)
UKIRT
KMTNET
Figure 3. Top: Taxonomic distribution found
in our sample analyzed with Machine Learning.
Only objects with 20 ≤ HV ≥ 25 are considered.
The distribution found by the MITHNEOS (Binzel
et al. 2019) team in the same range is shown in
comparison. Bottom: Comparison of the fraction
of primitive to non-primitive objects for the same
HV range. Values from (MANOS Devogèle et al.
2019), (UKIRT Mommert et al. 2016) and (KMT-
NET Erasmus et al. 2017) are also included .
types. Having the MITHNEOS sample (Binzel
et al. 2019) allowed us to refine our Monte Carlo
model with respect to our previous publication
(Navarro-Meza et al. 2019). The 1-D analysis
performed here includes the objects reported
in such work, hence although the results agree
within the error bars, we consider the one pre-
sented here to be more correct.
While analyzing size dependency in the sub-
kilometer NEO population, authors have split
the sample in absolute magnitudes bins of
HV < 20, 20 ≤ HV < 25 and HV ≥ 25,
or analyzed the sample by mass fraction (see
Mommert et al. 2016; Erasmus et al. 2017;
Binzel et al. 2019). Our observations are fo-
cused on targets of magnitudes in the range
20 ≤ HV ≥ 25 , hence we have very few objects
in the other ranges to make a similar size de-
pendence analysis. We find no variations within
the 20 ≤ HV < 25 range. The value of fraction
we find for this bin agrees within 1-σ with all
the works cited.
5.3. Implications for large scale projects
The methodologies explored in this article
allow for smaller telescopes to study the taxon-
omy of subkilometer NEOs. They also offer an
efficient way to analyze data for large telescopes.
Our Machine Learning analysis classified effec-
tively objects with an error in color as large as
0.13 (equivalent to 0.091 magnitude error per
band). With high precision photometric mea-
surements, this machinery can classify hundreds
of objects in minutes with high accuracy. For
example, the Rubin Observatory (Brough et al.
2020) will count with the filters u, g, r, i, Z,
Y, four of which we studied here. As a first
stage, it would be recommendable to expand
the MITHNEOS (Binzel et al. 2019) catalog,
since it lacks on observations on the visible
range. This would improve the accuracy of the
method and likely enable it to distinguish be-
tween the classes that compose the taxonomic
complexes.
6. CONCLUSIONS
We present a taxonomic study of 238 sub-
kilometer NEOs taken with a 1.5 m robotic tele-
scope over the course of 4 years. We obtain our
results using 2 different models. The first one
is a Machine Learning approach that uses the
database from the MITHNEOS survey (Binzel
et al. 2019) to classify the objects using mul-
tiple photometric color combinations. The sec-
ond one is a Monte Carlo approach to obtain the
taxonomic distribution from the objects in our
sample with measurements in only one color.
The taxonomic distribution found for the ob-
jects analyzed via Machine Learning in the ab-
solute magnitude range that our observations
are focused: 20 ≤ HV ≥ 25 match the ones
obtained by Binzel et al. (2019) from spectral
analysis. In order to compare our results from
the different methods and with respect to previ-
ous studies which consider different taxonomies,
13
we also present our results in terms of the ra-
tio of primitive to non-primitive objects. Such
value, denoted as fraction agrees within the er-
ror bars with different previous studies for our
main magnitude range. The fraction value ob-
tained for all our sample is in better agreement
with the equivalent value from Devogèle et al.
(2019). The Monte Carlo method offers an ap-
proximation that matches within the error bars,
however its use is suggested for cases when only
two photometric bands are available. In all
cases, we find that the primitive asteroids, often
denoted as carbonaceous, are a little less com-
mon than siliceous objects for the sub-kilometer
-biased- population of NEOs.
7. ACKNOWLEDGMENTS
We would like to thank Carlos Román-Zúñiga
and Diego Butriago for their help on scheduling
RATIR's observations.
The data used in this paper were totally or
partially acquired using the RATIR instrument,
funded by the University of California (UC) and
NASA Goddard Space Flight Center (GSFC),
on the 1.5 meter telescope at Observatorio As-
tronómico Nacional, San Pedro Martir, oper-
ated and maintained by OAN-SPM and IA-
UNAM. This project was supported in part by
the National Aeronautics and Space Admin-
istration under the Grant No.NNX15AE90G
issued through the SSO Near Earth Object Ob-
servations Program. SNM also acknowledges
the grant UNAM- DGAPA PAPIIT IN107316.
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All Authors and Affiliations
S. Navarro-Meza,1, 2 M. Mommert,3, 2 D.E. Trilling,2 N. Butler,4, 5 and M. Reyes-Ruiz1
1Instituto de Astronomia, Universidad Nacional Autónoma de México, Ensenada B.C. 22860, México.
2Department of Astronomy and Planetary Science, Northern Arizona University, Flagstaff, AZ 86011, USA
3Lowell Observatory, Flagstaff, AZ 86001, USA
4School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287, USA
5Cosmology Initiative, Arizona State University, Tempe, AZ 85287, USA
7. Discusión
Presentamos métodos para determinar la taxonomía de asteroides que
son más eficientes en términos de tiempo y recursos que los típicamente
utilizados. Esto es conveniente ya que por razones de seguridad planetaria,
es apremiante tener información física de los NEOs de menor tamaño, dado
que la fracción de ellos que tenemos caracterizada es muy pequeña y son
los que presentan mayor posibilidad de impactar la Tierra.
Utilizamos 3 tipos diferentes de clasificación que son recomendables de-
pendiendo de la calidad y cantidad de información que se tenga a partir
de las observaciones. En nuestro caso, la mayoría de los NEOs solo tenía
mediciones válidas en los filtros del espectro visible r e i. La complejidad de
cada modelo es diferente, por lo tanto cada uno considera diferentes clases
de asteroides. Para comparar los resultados entre nuestros modelos, así co-
mo con otros estudios, dividimos los asteroides en primitivos (generalmente
no rocosos) y evolucionados (generalmente rocosos). En el primer grupo se
incluyen los asteroides de los complejos C, X y el tipo D, mientras que en
el segundo los complejos S, Q y los tipos A, K, L, O, R, T y V.
Nuestro primer modelo se basa en el análisis de dos bandas del espectro
visible, r e i, y utiliza una simulación Monte Carlo para generar objetos
sintéticos que buscan aproximar la distribución taxonómica de la muestra.
El método distingue entre los dos principales tipos de asteroides, C y S,
así como los tipos X y Q, teniendo mayor precisión en la determinación
de la fracción de tipo S. En este algoritmo hay dos tipos de variables, la
distribución taxonómica de objetos sintéticos y los errores de cada uno de
ellos. La convergencia del resultado podría darse por medio de los erro-
res, arrojando una distribución incorrecta. Por esta razón generamos 107
simulaciones y el resultado se obtiene promediando las distribuciones de
los mejores casos. La distribución taxonómica obtenida es en proporción al
total de la muestra.
El segundo método es también unidimensional y más sencillo de imple-
54
mentar. La clasificación de un objeto se determina basándose en la taxono-
mía más próxima en el espacio unidimensional utilizado. Con este modelo
sólo distinguimos entre asteroides de tipo C y S, sin embargo el modelo
ofrece una ventaja sobre el primero en el sentido que brinda la clasificación
específica de cada objeto observado. Concluimos que no es conveniente uti-
lizar este esquema en poblaciones de asteroides donde es posible que haya
objetos de tipo Q o Sq, tal como es el caso de los NEOs, ya que los colores
r-i característicos de estos tipos están entre los índices de los tipos C y
S, provocando que algunos del complejo Q sean clasificados como C, sobre
estimando así la proporción de objetos primitivos.
El tercer método utiliza diferentes filtros para hacer la clasificación y
está basado en técnicas de inteligencia artificial. El método determina los
límites entre cada clase de asteroide en un espacio multidimencional, por lo
que es capaz de hacer una clasificación más detallada de la muestra obser-
vada, diferenciando entre las taxonomías C, X, S, Q, D, V y L para cada
objeto observado.
El modelo de inteligencia artificial fue aplicado a dos conjuntos de da-
tos, uno con las bandas fotométricas r, i, Z, Y, J, que genera un espacio
de 10 dimensiones y otro con las bandas i, Z, Y, que produce un espa-
cio en 6-D. Utilizando mediciones de 87 objetos, los resultados de estos
dos conjuntos, sugieren una fracción: primitivos
evolucionados
= 0.64 ± 0.12. Mientras
que con el método Monte Carlo empleado sobre 151 objetos obtenemos
primitivos
evolucionados
= 0.87 + 0.29,−0.43. Estos valores concuerdan con los resul-
tados obtenidos por otros autores con muestras y metodologías distintas,
particularmente con el de Devogèle et al. (2019) que encuentran un valor
de 0.58 para esta fracción. Sin lugar a dudas el método que utiliza inte-
ligencia artificial es el más robusto en términos de precisión y del detalle
taxonómico ofrecido, siendo además capaz de clasificar objetos que poseen
errores observacionales grandes.
Por otro lado hicimos un estudio de asteroides miembros del cinturón
55
principal utilizando datos archivados del proyecto de protección planetaria
ATLAS. Encontramos que un color en la región óptica del espectro es sufi-
ciente para estudiar la diversidad taxonómica de una familia de asteroides.
La efectividad del método depende de la posible distribución taxonómica
de la familia a estudiar y de los índices de color característicos de esas
clases. Sin embargo, típicamente las familias están dominadas por objetos
de tipo C y S, cuyos colores característicos son notablemente distintos. En-
contramos la clasificación taxonómica y los periodos de rotación de 1612
asteroides, pertenecientes a las familias Flora, Nysa-Polana, Vesta, Themis
y Korionis. Estudiando la familia Flora se relacionó la abundancia de aste-
roides de tipo C con los parámetros orbitales propios de tales objetos. Una
de las interpretaciones de este análisis es que el objeto que posiblemente
dio origen a la familia Flora como producto de una colisión, era menor a 2
km de diámetro.
La exploración de métodos computacionales es inminente, ya que en
la década entrante operará la nueva generación de telescopios espaciales y
terrestres que producirán una gran cantidad de descubrimientos serendí-
picos en adición al tiempo de observación ya asignado a cuerpos menores
del sistema solar. Particularmente podemos mencionar el Observatorio Ru-
bin (Ivezić et al., 2019; AURA, 2020). Este telescopio, que se espera que
entre en funcionamiento total en 2023, contará con los filtros u, g, r, i, Z,
Y, cuatro de ellos utilizados en nuestro análisis. La calidad de las medi-
ciones realizadas por este telescopio con primario de 8.4 metros serán de
una calidad incomparable a las analizadas en nuestro estudio. Por lo tanto
cualquiera de los métodos analizados aquí sería suficiente para estimar la
razón entre objetos primitivos y evolucionados en una muestra de obje-
tos observada con tal telescopio. Para un análisis más detallado se podría
utilizar el modelo multidimencional aquí analizado con las siguientes consi-
deraciones. Nuestra muestra control (necesaria para el funcionamiento del
modelo) cuenta con pocos objetos con mediciones en la región óptica del
espectro. Una opción sería enriquecer la muestra control con mediciones
que incluyan pero no estén limitadas al rango visible, esto sería lo más
56
recomendable, ya que al contar con más objetos control sería posible dis-
tinguir entre las subclases que forman cada complejo taxonómico. Cabe
destacar que para este caso la muestra control debe ser construida con la
misma metodología, ya que Devogèle et al. (2019) encuentran que la misma
muestra de espectros puede generar distribuciones diferentes dependiendo
de las herramientas de análisis. Otra opción es extrapolar cuidadosamente
el espectro de los objetos en la muestra control, algo que no se hizo en
nuestro estudio por limitaciones de tiempo. La tercera opción es utilizar
solo las bandas i, Z, Y, tal y como hicimos para analizar una fracción de
la muestra, sin embargo un menor número de filtros tiende a implicar una
menor precisión y/o detalle en la clasificación.
57
8. Conclusiones
Después de analizar una muestra de 238 objetos cercanos a la Tierra
(NEOs) concordamos con estudios recientes en que se observan ligeramente
menos NEOs pequeños de tipo primitivo que de tipo rocoso, sin embargo la
distribución taxonómica no concuerda con la encontrada en los meteoritos.
Además de brindar la clasificación de los objetos, una parte fundamental
de este trabajo fue utilizar tres métodos diferentes para estudiar asteroides
utilizando fotometría.
El método más robusto utilizado consiste en utilizar técnicas de inteli-
gencia artificial para analizar mediciones fotométricas en múltiples bandas.
En términos de taxonomía, este método puede ser tan útil como la espec-
troscopía, lo cuál representa una ventaja en términos de recursos. También
encontramos que este modelo permite trabajar con errores fotométricos
grandes sin comprometer la calidad de la clasificación. El método con simu-
laciones Monte Carlo ofrece una aproximación a la distribución taxonómica
en casos donde solo se cuenta con dos bandas fotométricas. El tercer méto-
do, basado en la distancia relativa en el espacio de color, permite clasificar
de manera simple objetos en poblaciones dominadas por dos tipos de as-
teroides con colores característicos distintos. En poblaciones más variadas
la efectividad de este método se reduce, por lo tanto se considera efectivo
para analizar familias de asteroides en el cinturón principal, pero no para
el entorno terrestre.
58
Apéndice: Trabajos adicionales
En esta sección se presentan trabajos en los que participé y que se con-
cluyeron o llevaron a cabo durante el transcurso de mi doctorado. En cada
uno se menciona mi nivel de participación.
A. Tránsitos de exoplanetas con múltiples filtros y ob-
servatorios
El proyecto consistió en realizar un seguimiento a lo largo de 2 años
de más de una docena de exoplanetas con el objetivo principal de encon-
trar variaciones en el periodo orbital y explorar la posible dependencia de
la estimación del radio planetario en el filtro fotométrico utilizado para la
observación.
Realicé o ayudé a realizar y planear un gran número de las observaciones
tomadas con el telescopio de 84 cm del OAN-SPM. Para esto tomé junto
con otros un curso informal de observación con el Dr. Raúl Michel, ya que
mi maestría tuvo un enfoque 100% numérico. Contribuí menormente en la
extracción de resultados y análisis. Durante loa huecos de observación en
el tiempo asignado a este proyecto realicé mis primeras observaciones de
asteroides.
59
Multi-filter Transit Observations of HAT-P-3b and TrES-3b with Multiple
Northern Hemisphere Telescopes
D. Ricci1,2,3, P. V. Sada4, S. Navarro-Meza3, R. López-Valdivia5, R. Michel3, L. Fox Machado3, F. G. Ramón-Fox6,
C. Ayala-Loera3,15, S. Brown Sevilla7, M. Reyes-Ruiz3, A. La Camera8, C. Righi9,10, L. Cabona9,10, S. Tosi11,12, N. Truant1,2,13,
S. W. Peterson14, J. Prieto-Arranz1,2, S. Velasco1,2, E. Pallé1,2, and H. Deeg1,2
1 Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife, Spain; davide.ricci82@gmail.com
2Universidad de La Laguna, Departamento de Astrofísica, E-38206 La Laguna, Tenerife, Spain
3Observatorio Astronómico Nacional, Instituto de Astronomía—Universidad Nacional Autónoma de México, Ap. P. 877, Ensenada, BC 22860, México
4Departamento de Física y Matemáticas—Universidad de Monterrey, Avenida Ignacio Morones Prieto 4500 Pte., Jesús M. Garza,
66238 San Pedro Garza García, N.L., México
5 Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro 1, Tonantzintla, Puebla 72840 México
6 SUPA, School of Physics and Astronomy, University of St. Andrews, North Haugh, KY16 9SS, Scotland, UK
7 Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y 18 Sur, 72570 Puebla, México
8 Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi (DIBRIS), Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy
9Università degli Studi dell’Insubria, via Valleggio 11, 22100 Como, Italy
10 INAF-Osservatorio Astronomico di Brera, via Bianchi 46, 23807 Merate (LC), Italy
11Dipartimento di Fisica—Università degli studi di Genova, Via Dodecaneso 33, 16146 Genova, Italy
12 Istituto Nazionale di Fisica Nucleare—Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
13 Dipartimento di Fisica—Università degli Studi di Trieste, Via Alfonso Valerio, 2, 34127 Trieste, Italy
14Kitt Peak National Observatory, National Optical Astronomy Observatory, 950 N Cherry Avenue, Tucson, AZ, 85719, USA
15Observatório Nacional MCTIC, Rua Geral José Cristino 77, Rio de Janeiro, RJ, 20921-400, Brasil
Received 2017 March 6; accepted 2017 April 4; published 2017 May 4
Abstract
We present a photometric follow-up of transiting exoplanets HAT-P-3b and TrES-3b, observed by using several
optical and near-infrared filters, with four small-class telescopes (D= 36–152 cm) in the Northern Hemisphere.
Two of the facilities present their first scientific results. New 10 HAT-P-3b light curves and new 26 TrES-3b light
curves are reduced and combined by filter to improve the quality of the photometry. Combined light curves fitting
is carried out independently by using two different analysis packages, allowing the corroboration of the orbital and
physical parameters in the literature. Results find no differences in the relative radius with the observing filter. In
particular, we report for HAT-P-3b a first estimation of the planet-to-star radius R R 0.1112p 0.0026
0.0025
*
= -
+ in the B
band which is coherent with values found in the VRIz′JH filters. Concerning TrES-3b, we derive a value for the
orbital period of P=1.3061862±0.0000001 days which shows no linear variations over nine years of
photometric observations.
Key words: planets and satellites: fundamental parameters – (stars:) planetary systems
1. Introduction
The literature of exoplanetary transit observations started
with the works of Charbonneau et al. (2000) and Henry et al.
(2000), who separately confirmed radial velocity shifts of the
star HD 209458 (Vogt et al. 1994; Baranne et al. 1996) due to
the presence of its companion HD 209458 b. Since then, big
efforts have been made to build up ground-based survey
projects such as WASP (Pollacco et al. 2006); HAT (Bakos
et al. 2004) and its implementation HATSouth in the Southern
Hemisphere (Bakos 2011; Penev et al. 2011); TrES (Alonso
et al. 2007); XO (McCullough et al. 2005); KELT (Pepper
et al. 2007); and the recent NGTS (Wheatley et al. 2013).
Among the current and forthcoming dedicated space-based
programs, we mention Kepler (Borucki et al. 2010), PLATO
(Rauer et al. 2014), and TESS (Ricker et al. 2010), as well as
the European CHEOPS mission (Fortier et al. 2014), which
will help to infer and characterize the exoplanetary population,
and which also has the ambition to detect exomoons (Simon
et al. 2015) and other interesting features. Such a huge amount
of data can benefit from useful online databases such as ETD
(Poddaný et al. 2010)16 and exoplanets.eu
17
(Schneider
et al. 2011) to help astronomers in programming their
observations or defining the best candidates for an independent
follow-up.
In this framework, we have recently shown (Ricci et al.
2015) the adequacy of the San Pedro Mártir—Observatorio
Publications of the Astronomical Society of the Pacific, 129:064401 (8pp), 2017 June https://doi.org/10.1088/1538-3873/aa6b54
© 2017. The Astronomical Society of the Pacific. All rights reserved. Printed in the U.S.A.
16 See, for example, the observations provided by Phil Evans and flagged
with a quality of “2” and “3” at http://var2.astro.cz/ETD/etd.php?
STARNAME=WASP-39&PLANET=b, used to complement Ricci et al.
(2015) data.
17 http://exoplanets.eu
1
Astronómico Nacional (OAN-SPM) facilities, located in north-
west Mexico, as a valid resource in the Northern Hemisphere for
the follow-up of exoplanetary transits, particularly that of hot
Jupiters. The survey, which started in 2014 (Ricci et al. 2014) and
is still ongoing, has allowed, to date, the observation of a total of
30 transiting exoplanetary systems18, mainly with the 84 cm
telescope, achieving good quality light curves in several filters,
most of them through the Johnson’s VRI filters.
In this paper, we focus on two objects: the Jupiter-
sized HAT-P-3b and the grazing transiting planet TrES-3b,
which we present in Sections 2.1 and 2.2, respectively.
Moreover, we will present data from other sites by using not
only OAN-SPM survey data, but also light curves obtained
from the following facilities: the Observatorio de la
Universidad de Monterrey (UDEM) in the state of Nuevo
Léon, Mexico; the Telescopio Carlos Sánchez (TCS) at the
Observatorio del Teide (OT) in Tenerife, Spain, provided with
WIDE-FASTCAM, a new concept of fast camera with a wide
field of view (FoV); and the Osservatorio Astronomico
Regionale Parco Antola, comune di Fascia (OARPAF) in
northern Italy. All of the telescopes and the relative instruments
involved in our observations are described in Section 3.1. In
particular, WIDE-FASTCAM is a new instrument, and OARPAF
is a new facility, and we present their first scientific results. In
Sections 3.2 and 4 we focus on observations and data reduction
of HAT-P-3b and TrES-3b. Conclusions are described in
Section 5.
2. Targets
2.1. HAT-P-3
In the framework of the HATNet survey, Torres et al. (2007)
discovered HAT-P-3b, a Jupiter-size planet with a period of
2.899703±0.000054 days, which was the smallest of the 18
transiting extrasolar planets known at that time, with a planet
radius Rp=0.890±0.046 RJ, where RJ stands for the radius
of Jupiter. HAT-P-3b immediately appeared to be metal-rich,
with a content representing 75 Earth masses M⊕, (or, in Jupiter
masses, 0.24 MJ). Radial velocity measurements allowed
authors to estimate a planetary mass of Mp=0.599±0.026
MJ, and found a distance between planet and parent star of
0.03894±0.00070 au, assuming no orbital eccentricity.
System parameters with an improved precision were then
updated by Gibson et al. (2010) by fitting seven light curves
obtained after performing aperture photometry on short-
exposure (4–5 s), wide-band filter (500–700 nm) Liverpool
Telescope data. Particular attention was given to possible
Earth-mass planets in the inner and outer 2:1 orbital resonance,
but the lack of evidence of transit timing variations (TTVs)
excluded this hypothesis. Furthermore, Nascimbeni et al.
(2011, 2012) refined the orbital parameters and ephemerides
with a timing accuracy of 11 s, demonstrating the potential of
the observing and reduction strategy of the TASTE19 survey.
The anomalous radius of HAT-P-3b, smaller than a pure
hydrogen-helium planet suggested the presence of a heavy-
element core estimated to be 100M⊕. This was the subject of
the investigation of Chan et al. (2011, 2012), who observed the
target in the i and z′ bands, again finding no deviations in the
timing of eclipses. Chan et al. (2011) found a period of
P=2.8997360±0.0000020 days, a planet-to-star radius ratio
of Rp/R*=0.1063±0.0020, an orbital inclination of i=
87.07±0°.55, and a scaled semimajor axis of a/R*=
10.39±0.49, adopting a circular orbit. An additional follow-
up at Kitt Peak National Observatory was carried out by Sada
et al. (2012), while Southworth (2012) conducted a homo-
geneous study of more than 30 extrasolar planets including
HAT-P-3b, based on all available data sets in the literature. The
author found a larger stellar radius ( M0.947 J0.027
0.015
-
+ ) and pointed
out that further photometric monitoring was needed to get rid of
the discrepancy between the data sets of Torres et al. (2007);
Gibson et al. (2010); Nascimbeni et al. (2011), and Chan et al.
(2011). Finally, a space-based investigation of secondary
eclipses in 3.6–4.5 μm spectral bands of the Spitzer Space
Telescope was carried out by Todorov et al. (2013), finding
inefficiencies in heat redistribution, but letting the scenario open
about thermal inversion in the atmosphere. Moreover, Todorov
et al. (2013) found the eccentricity of HAT-P-3b consistent
with zero.
2.2. TrES-3b
TrES-3b is a massive transiting hot Jupiter discovered by
O’Donovan et al. (2007) and confirmed by radial velocity
measurements. The authors derived a period of P=
1.30619±0.00001 days, a semimajor axis of a=0.0226±
0.0013 au and a near-grazing inclination value of i=82.15±
0°.21. The mass of the planet is estimated to be Mp=1.92±
0.23MJ in front of a stellar mass of M=0.9±0.15M☉, while
the planet radius is Rp=1.295±0.081 RJ. de Mooij &
Snellen (2009) reported a temperature of the planet of
T=2040±185 K by measuring the thermal emission in the
K band using secondary eclipse observations which were
carried out with the William Hershel Telescope, which
complemented the space-based observations of the Spitzer
Telescope.
The same value was found by de Mooij & Snellen (2011). de
Mooij & Snellen (2009) also suggest that the planet is in a non-
circular orbit. Measurements of the radius of the planet in the K
band do not significantly differ from the results obtained with
optical observations.
Many follow-ups were carried out by several groups in
optical and ultraviolet (UV) bands (Turner et al. 2011;
18 http://www.astrosen.unam.mx/~indy/spm-transits/ 19 The Asiago Search for Transit timing variations of Exoplanets.
2
Publications of the Astronomical Society of the Pacific, 129:064401 (8pp), 2017 June Ricci et al.
Jones et al. 2012; Smith et al. 2012; Vaňko et al. 2012; Walker-
LaFollette et al. 2012). In particular, Turner et al. (2013) did
not detect any early ingress in UV as predicted by Vidotto et al.
(2011), resulting in an abnormally small strength of the
magnetic field. The observations in the near-infrared by de
Mooij & Snellen (2009), and the near-UV by Turner et al.
(2013), do not show differences in the value of the radius of the
planet.
An attempt to calculate TTVs was made for the first time by
Thakur et al. (2013), using 32 transits in the existing literature,
and five new transits. Authors use dynamic models to suggest
the presence of an additional outer planet close to the 1:2
resonance with an estimated mass in terms of Earth masses,
≈100M⊕. The result contradicts that found by Kundurthy et al.
(2013), which observed an additional set of 11 transits in the
framework of the Apache Point Survey of Transit Lightcurves
of Exoplanets (APOSTLE), excluding the possibility of other
planets and confirming the system’s parameters but with
reduced error bars. Finally, transit times of TrES-3b were
updated by Maciejewski et al. (2013), whose results also
support no TTVs.
3. Observations
3.1. Facilities
Observations presented in this paper were carried out by using
four different telescopes located in the Northern Hemisphere. A
summary of their characteristics is shown in Table 1.
• The first telescope is the OAN-SPM 84 cm. It provides a
set of instruments that can be mounted according to the
observational needs, among which MEXMAN, a wide-field
imager already successfully tested for the observation and
characterization of exoplanets using the transit method
(Ricci et al. 2015).
• The second telescope is the UDEM 36 cm, a LX200GPS
college telescope located close to the city of Monterrey,
Mexico, and classed with a minor planet center code of
720. It is available for student training and has been active
for almost 10 years in the field of exoplanetary transit
observations Ramón-Fox & Sada (2013); Sada & Ramón-
Fox (2016).
• The third telescope, the TCS, is a 152 cm equatorial
Cassegrain telescope20 located at the OT and managed by
the Astrophysics Institute of Canary Islands (IAC), Spain.
This telescope is provided with different instruments. One
of them, FASTCAM, allows quasi-diffraction limited real-
time observations using the Lucky Imaging technique, the
implementation of the instrument being targeted to high
temporal resolution up to tens of images per second (Oscoz
et al. 2008). Despite these advantages, FASTCAM is limited
(Murga et al. 2010) by its 20″×20″ FoV.
For this reason, an implementation of the FASTCAM
detector with a wider FoV was carried out: WIDE-FASTCAM
offers a 1024×1024 px EMCCD array and an optical design
(Murga et al. 2014) to provide observers with an ≈8×8′
FoV. We used WIDE-FASTCAM for our observations to test
its small readout time and low electronic noise. Linearity tests
on the camera on flat-field images show that the instrument
works in the linear regime between 1700 and 4000 counts
(Velasco et al. 2016, 2017). During the observations, we took
care to tune the exposure time accordingly.
• The fourth telescope is the alt-azimuthal21 OARPAF
80 cm, located near Mt.Antola in Northern Italy, and
whose scientific activity is managed by the physics
department (DIFI) of the University of Genova, Italy.
The telescope was designed by the Astelco company22 to
foresee a double focal station: the first, provided with a
field derotator, is dedicated to scientific observations and is
currently equipped with an air-cooled SBIG STL 11000M
camera and a standard UBVRI Johnson filter wheel
(Federici et al. 2012); the second is dedicated to ocular
observations by amateurs.
Table 1
Main Characteristics of Observing Facilities and their Photometric Instruments and Altitude on the Map on the Right
20 http://www.iac.es/telescopes/pages/es/inicio/telescopios/tcs.php
21 https://www.difi.unige.it/it/ricerca/altri-progetti/osservatorio-monte-
antola
22 http://www.astelco.com
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Publications of the Astronomical Society of the Pacific, 129:064401 (8pp), 2017 June Ricci et al.
Pointing and positioning of the secondary mirror are
controlled using the proprietary AstelOS software,
provided by the constructor, on a dedicated Linux machine,
while the image data capture is managed by the MaxIm
software. The time stamp is obtained via a global
positioning system (GPS) device. The instrument was
recently fully characterized with standard stars observa-
tions in all available filters for zero-point determination and
extinction coefficient determination. Concerning the CCD
commissioning, deep tests allowed calculation of: gain,
Read Out Noise, dark current, plate scale, and linearity
regime (Righi 2016).
3.2. Targets
We carried out four observations of HAT-P-3b at OAN-SPM
in nearly full-moon conditions in 2014 over a period spanning
five months and using three filters: two with the R filter, one
with the I filter, and the final one with the V filter. Except for
the first R observation, we were able to follow the target for
roughly five hours. We also obtained six transits from UDEM
taken with the Ic filter between 2009 and 2013. Moreover, we
also aggregated four already published observations from Sada
et al. (2012): two light curves from the Kitt Peak National
Observatory (KPNO) 200 cm telescope observed with the JH
filter, and one light curve from the KPNO Visitor Center
Telescope (KPNO-VCT) 51 cm telescope with the B filter and
one curve from the same telescope with the Sloan z′ filter. A
log of HAT-P-3b observations is shown in Table 2.
Concerning TrES-3b, we obtained three complete light
curves in the R band at OAN-SPM, and two in the I band.
Except for the first I light curve, we used the defocused
photometry method described in detail by Southworth et al.
(2014) and in previous papers of the series. We also present 18
UDEM transits: six with the V filter, five with the Rc filter, six
in the Ic band, and finally one in the z′ band. Additional z′ data
come from KPNO (two curves). An additional curve in the z′
band comes from the KPNO-VCT operator Steven Peterson
(StPr) using his private observatory, and located close to the
KPNO facilities. TCS also observed the target one night by
using WIDE-FASTCAM and short-exposure images of 1 s each,
in the R band. Finally, one observation with the R filter was
carried out at OARPAF. We carefully checked that the targets
and reference stars were not relaying too close to hot or bad
pixels or bad lines of devices, nor at the edge of their FoV. We
also used a 2×2 binning for our observations in OAN-SPM,
UDEM and OARPAF, windowing the devices in order to
minimize the readout time. OAN-SPM, UDEM, and OARPAF
telescopes were also slightly defocused in order to spread the
point spread function over a large number of pixels, allowing
longer exposure times, a shorter total readout time, and
reducing errors due to pixel response or flat-field correction
problems. A log of TrES-3b observations is shown in Table 3.
Table 2
Log of HAT-P-3b Observations
Date (UT) Filter Exp. time Observatory
2009-01-19 Ic 60 s UDEM
2009-04-22 Ic 60 s UDEM
2009-05-15 JH 30 s KPNOa
2009-05-15 z′ 60 s KPNO-VCTa
2009-05-21 Ic 60 s UDEM
2010-05-27 JH 20 s KPNOa
2010-05-27 B 45 s KPNO-VCTa
2012-04-22 Ic 60 s UDEM
2012-05-24 Ic 60 s UDEM
2013-06-02 Ic 60 s UDEM
2014-04-01 R 120 s OAN-SPM
2014-03-13 R 120 s OAN-SPM
2014-03-16 I 120 s OAN-SPM
2014-05-13 V 90 s OAN-SPM
Note.
a Published in Sada et al. (2012).
Table 3
Log of TrES-3b Observations
Date (UT) Filter Exp. time Observatory
2007-07-23 Ic 120 s UDEM
2007-08-09 Ic 120 s UDEM
2008-07-11 Ic 60 s UDEM
2008-07-15 V 90 s UDEM
2008-10-04 V 90 s UDEM
2009-05-06 z′ 45 s KPNO-VCT
2009-05-10 z′ 120 s KPNO-VCT
2009-05-31 Ic 120 s UDEM
2009-07-17 z′ 120 s UDEM
2010-04-04 z′ 40 s StPr
2010-04-25 V 90 s UDEM
2010-06-19 V 90 s UDEM
2010-07-19 V 90 s UDEM
2010-08-05 Ic 90 s UDEM
2011-04-27 Ic 90 s UDEM
2011-06-08 Rc 60 s UDEM
2011-08-24 Rc 60 s UDEM
2012-08-12 Rc 60 s UDEM
2013-08-14 Rc 60 s UDEM
2013-10-08 V 90 s UDEM
2014-06-13 Rc 60 s UDEM
2015-07-17 R 120 s TCSa
2015-08-03 R 120 s OARPAF
2015-08-22 R 120 s OAN-SPM
2016-04-09 R 120 s OAN-SPM
2016-04-13 R 120 s OAN-SPM
2016-05-30 I 60 s OAN-SPMb
2016-06-03 I 60 s OAN-SPM
Notes.
a Binning 120 individual frames of 1 s each.
b Binning 6 individual frames of 10 s each.
4
Publications of the Astronomical Society of the Pacific, 129:064401 (8pp), 2017 June Ricci et al.
4. Data Analysis
Images of both targets were debiased and flat-field corrected.
We used the aperture photometry technique to obtain light
curves. In particular, we used the defot routine (Southworth
et al. 2010) written in the IDL language that we modified to
work with FITS headers generated by the OAN-SPM, TCS,
and OARPAF telescopes, while UDEM data were reduced
using independent custom IDL routines. OAN-SPM and
OARPAF images were not aligned, as we decided to calculate
and follow, for each image, the centroid of the target and that of
the reference stars, by using a cross-correlation method that we
re-implemented in defot. For the OARPAF data coming from
an Alt-Az telescope, we set up a rotation tracking subroutine to
correct for the residual rotation of the field due to eventual
errors in the alignment between the optical axis, the derotator,
and the CCD center.
Several field stars were tested to find a reference from which
performing differential photometry, and for both HAT-P-3b
and TrES-3b we chose a number between two and eight non-
saturated reference stars with count values as close as possible
to those of the target, also taking into account sky conditions
and availability.
A first-order trend in light curves was removed with the
technique described by Ramón-Fox & Sada (2013) to get rid of
airmass effects. Timestamps of the light curve points were
converted to the dynamical time-based system (BJDTDB),
applying the transformation given by Eastman et al. (2010).
Data were then combined by using the procedure described
by Sada & Ramón-Fox (2016). Using this procedure, we
obtained a total of seven combined curves for HAT-P-3b for
each one of the following filters: B (one curve from KPNO-
VCT), V (one curve from OAN-SPM), R (two curves from
OAN-SPM), I (one curve from OAN-SPM), Ic (six curves from
UDEM), z′ (one curve from KPNO-VCT), and JH (two curve
from KPNO).
The same technique was applied to TrES-3b data and we
obtained a total of six combined curves in the different filters as
follows: V (six curves from UDEM), R (three curves from
OAN-SPM, one from TCS, and one from OARPAF), Rc (five
curves from UDEM), I (two curves from OAN-SPM), Ic (six
curves from UDEM), z′ (two curves from KPNO, one from
StPr, and one from UDEM).
Light curves were fitted with EXOFAST (Eastman et al.
2012, 2013). A value of the inclination i, of the semimajor axis
in terms of the host star radius a/R*, of the mid-time Tmid, and
of the radius of the planet in terms of the host star radius Rp/R*
were fitted for each combined curve. An independent light
curve fitting was performed by using the IDL software Transit
Analysis Package (TAP) implemented by Gazak et al. (2011).
Both software use a Markov Chain Monte Carlo (MCMC)
method to find best fit parameters for the Mandel & Agol
(2002) model.
Differing from EXOFAST, TAP allows fitting together, or
separately, a set of parameters linking their value with a lock
matrix. Thus, it was possible to simultaneously fit a unique
value of the inclination i and of the scaled semimajor axis a/R*
for all combined curves, a different Mid-time Tmid value for
each light curve, and a scaled planet radius Rp/R* value for
each of the different observing filter.
4.1. HAT-P-3b
In fitting procedures, we fixed the period: P=2.8997382
days (Sada et al. 2012), and we supposed a circular orbit
(eccentricity e= 0, argument of periastron ω=0). Concerning
limb darkening, for EXOFAST fitting we used interpolated
values from Claret (2000) with the following parameters:
T*=5224±69 K, glog 4.58 0.03
*
=  , and [Fe/H]*=
0.41±0.08 (Torres et al. 2007, 2012); while for TAP fitting,
we used an online tool (Eastman et al. 2012, 2013) that
interpolates atmosphere models of Claret & Bloemen (2011).
Figure 1. Combined light curves of HAT-P-3b and fit models. Models are
slightly shifted in flux for better visualization. The lower panel shows the
residuals.
5
Publications of the Astronomical Society of the Pacific, 129:064401 (8pp), 2017 June Ricci et al.
Fit results obtained with EXOFAST are shown in Figure 1 and
in Table 4. In particular, weighted means obtained with EXOFAST
are consistent with those of Nascimbeni et al. (2011): EXOFAST
obtain i 86.73 0.11
0.11= -
+ against 86.75 0.10
0.10
-
+ of Nascimbeni et al.
(2011); a R 10.13 0.11
0.11
*
= -
+ against 10.12 ;0.32
0.32
-
+ and R Rp *
=
0.1093 0.0005
0.0005
-
+ against 0.1094 0.0011
0.0011
-
+ . TAP calculates a unique
value for the first two parameters: the inclination i 86.27 0.18
0.28= -
+
and the scaled semimajor axis a R 9.65 0.18
0.28
*
= -
+ , which are
slightly different from EXOFAST and Nascimbeni et al. (2011)
results, but in agreement within 3σ. A visual comparison
between EXOFAST and TAP fit values of the scaled planet radius
Rp/R* is shown in Figure 2.
Figure 2 also show additional TAP fit solutions obtained by
fixing i and a/R* found by Chan et al. (2011) and Nascimbeni
et al. (2011), and fitting only a separate value of Rp/R* for each
observing filter. The figure gives evidence of the fact that we
find no significant radius variation with the observing filter.
Figure 3 shows the calculated mid-times.
4.2. TrES-3b
We used the same technique applied for HAT-P-3b fitting for
what concerns TrES-3b limb darkening with following parameters:
log(g*)=4.571±0.006 (Southworth 2011), T*=5650±75K,
and [Fe/H]*=−0.19±0.08 (Sozzetti et al. 2009).
EXOFAST fit results of TrES-3b are shown in Figure 4 and in
Table 5.
While performing the TAP fit, we fitted a unique value of i
and a/R* for all combined curves, and we fitted separately a
value of Rp/R* for each considered filter. TAP results show
good agreement with the EXOFAST weighted averages of i and
a/R*: i 81.70 0.22
0.17= -
+ of TAP against 81.63 0.23
0.20
-
+ of EXOFAST,
and a R 5.885 0.080
0.068
*
= -
+ of TAP against 5.903±0.062 of
EXOFAST. Results are slightly lower than, but in agreement
with, the values provided by Kundurthy et al. (2013):
i 81.86 0.26
0.08= -
+ and a R 5.91 0.05
0.04
*
= -
+ . Concerning Rp/R*, we
have differences between the two fit procedures which are
within −2σ (for the V filter) and +1σ (for the I filter).
Comparisons of Rp/R* between different filters show a
maximum absolute variation of 2.9σ between R and V curves
in EXOFAST results, which are not confirmed by TAP results
(0.04σ). We then assume no Rp/R* variations with the
observing filters, and we consider average results finding good
agreement between fit procedures: R R 0.1665p 0.0050
0.0081
*
= -
+ for
EXOFAST and 0.1667 0.0035
0.0047
-
+ for TAP, against the value of
0.1649±0.0015 provided by Kundurthy et al. (2013) in the
r′ band (see Figure 5).
Figure 5 also shows additional TAP fit solutions obtained by
fixing i and a/R* found by Kundurthy et al. (2013) and (Turner
et al. 2013), and fitting only a separate value of Rp/R* for each
observing filter.
Mid-times fit linearly a period of P=1.3061862±
0.0000001 days (see Figure 6). Scatter of calculated values
of Tmid corresponds to variations of ≈4 minutes peak-to-valley,
Table 4
EXOFAST Fit Results for HAT-P-3b
Filter Obs. i a/R* Rp/R*
B KPNO-VCT 86.78 0.27
0.29
-
+ 10.17 0.34
0.37
-
+ 0.1112 0.0026
0.0025
-
+
V OAN-SPM 86.57 0.26
0.27
-
+ 10.19 0.32
0.34
-
+ 0.1111 0.0018
0.0018
-
+
R OAN-SPM 86.83 0.39
0.36
-
+ 10.12 0.36
0.34
-
+ 0.1079 0.0012
0.0014
-
+
I OAN-SPM 86.71 0.27
0.29
-
+ 10.18 0.31
0.32
-
+ 0.1083 0.0015
0.0015
-
+
Ic UDEM 86.74 0.29
0.31
-
+ 10.18 0.30
0.32
-
+ 0.1094 0.0012
0.0012
-
+
z′ KPNO-VCT 88.96 0.90
0.71
-
+ 10.04 0.21
0.16
-
+ 0.1129 0.0015
0.0015
-
+
JH KPNO 86.60 0.24
0.25
-
+ 10.16 0.28
0.29
-
+ 0.1084 0.0008
0.0008
-
+
Figure 2. Rp/R* values of HAT-P-3b for each observing filter resulting from
EXOFAST and TAP fit procedures. Arrows show weighted means. Large light
circles show TAP results obtained by fixing i and a/R* with values provided by
Chan et al. (2011) and Nascimbeni et al. (2011). Small bold circles show values
provided in the literature: V+R (Gibson et al. 2010), R (Nascimbeni
et al. 2011), I (Torres et al. 2007), z′ (Chan et al. 2011), and JH (Sada
et al. 2012).
Figure 3. Observed minus calculated mid-times values for HAT-P-3b
observations presented in this work.
6
Publications of the Astronomical Society of the Pacific, 129:064401 (8pp), 2017 June Ricci et al.
mostly ruled by UDEM data, which is reduced to ≈1 minute
peak-to-valley while considering OAN-SPM, OARPAF, and
TCS data. Calculated mid-times show no significant linear
variation of the period with the time and our sampling does not
allow us to search for periodic variations in the 1:2 resonance
as in the work of Thakur et al. (2013).
5. Conclusions
We obtained 10 new exoplanetary transit observations
of HAT-P-3b in the BVRIz′JH bands, and 26 new observations
of TrES-3b in the VRIz′ bands, which confirmed the potential
adequacy of small-size telescopes (36–152 cm) for this research
topic. In particular, the new OARPAF observatory and the new
instrument WIDE-FASTCAM at TCS can provide reliable
photometric observations in the framework of ground-based
exoplanetary transit follow-ups.
The simultaneous fit of light curves, carried out in multiple
observing bands by several telescopes, allowed us to achieve
orbital and physical parameters which corroborate results of
Nascimbeni et al. (2011) for what concerns HAT-P-3b, and of
Kundurthy et al. (2013) for what concerns TrES-3b.
We also report specific values of Rp/R* in multiple optical
and near-infrared bands, and a first estimation of this parameter
in the B band for HAT-P-3b which is coherent with our values
provided by using other filters.
Figure 4. Light curves of TrES-3b and fit. The lower panel shows the residuals.
Table 5
EXOFAST Fit Results for TrES-3b
Filter Obs. i a/R* Rp/R*
V UDEM 81.34 0.25
0.23
-
+ 5.903 0.066
0.066
-
+ 0.1598 0.0045
0.0059
-
+
R a 81.80 0.17
0.15
-
+ 5.899 0.056
0.054
-
+ 0.1715 0.0030
0.0040
-
+
Rc UDEM 81.59 0.14
0.15
-
+ 5.913 0.059
0.060
-
+ 0.1616 0.0019
0.0018
-
+
I OAN-SPM 81.77 0.16
0.14
-
+ 5.895 0.061
0.061
-
+ 0.1610 0.0015
0.0024
-
+
Ic UDEM 81.83 0.22
0.19
-
+ 5.902 0.064
0.063
-
+ 0.1667 0.0050
0.0070
-
+
z′ b 81.46 0.37
0.28
-
+ 5.906 0.066
0.067
-
+ 0.1787 0.0095
0.0170
-
+
Notes.
a Combining OAN-SPM, OARPAF, and TCS data.
b Combining UDEM, KPNO, and StPr data.
Figure 5. Rp/R* values of TrES-3b for each observing filter resulting from
EXOFAST and TAP fit procedures. Arrows show weighted means. Large light
circles show TAP results obtained by fixing i and a/R* with values provided by
Kundurthy et al. (2013) and (Turner et al. 2013). Small bold circles show
values provided in the literature: V and Rc (Turner et al. 2013), R (Kundurthy
et al. 2013), and z′ (O’Donovan et al. 2007).
Figure 6. Observed minus calculated mid-times values for TrES-3b
observations presented in this work. Data are consistent with a
P=1.3061862±0.0000001.
7
Publications of the Astronomical Society of the Pacific, 129:064401 (8pp), 2017 June Ricci et al.
We find that observing filters do not significantly influence the
determination of the relative radius of HAT-P-3b and TrES-3b.
This result confirms the relative radius of HAT-P-3b estimated by
near-infrared band observations (de Mooij & Snellen 2009), and
the relative radius of TrES-3b estimated by UV observations
(Turner et al. 2013) in the literature.
Mid-times of TrES-3b fit a P=1.3061862±0.0000001
days, finding no significant linear variations of the period over
≈9 years of photometric observations. Further observations are
planned to discriminate eventual Rp/R* variations with the
observing filter and to extend Tmid information to estimate TTVs.
The authors acknowledge the following financial support: D.R.
from the Spanish Ministry of Economy and Competitiveness
(MINECO) under the 2011 Severo Ochoa Program MINECO
SEV-2011-0187; L.F.M. and R.M. from the UNAM under grant
PAPIIT IN 105115; D.R. and F.G.R.F. from the CONACYT
scholarship for postgraduate studies in Mexico. Research was
carried out thanks to the support of UNAM-DGAPA-PAPIIT
project IN115413. S.N. thanks H.Navarro-Meza for assistance
during OAN-SPM observations in 2016/06. D.R. thanks Claudia
Molina and Katie Marley for language editing and the
anonymous referee for suggestions and remarks. We also
acknowledge the OAN staff for daily support. The 1.5 m Carlos
Sánchez Telescope is operated on the island of Tenerife by the
Instituto de Astrofísica de Canarias in the Spanish Observatorio
del Teide.
Facilities: OAN-SPM 84 cm (MEXMAN), UDEM 80 cm,
TCS 152 cm (WIDE-FASTCAM), OARPAF 80 cm.
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Publications of the Astronomical Society of the Pacific, 129:064401 (8pp), 2017 June Ricci et al.
B. CMFA
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ferentes instituciones y observatorios para observar coordinadamente aste-
roides específicos. Cabe mencionar que el estudio de cuerpos menores del
sistema solar es una rama joven en México, siendo que es uno de los prin-
cipales temas de investigación actual en la astronomía internacional. Este
proyecto ayudó a fomentar el interés en esta rama. En su primera etapa, la
CMFA se enfocó en calcular los periodos de rotación utilizando mediciones
en diferentes filtros. En algunos casos se reporta la primera estimación del
periodo, se confirman mediciones previas o se aclaran discrepancias entre
distintos reportes. También se observó variabilidad en la curva de luz du-
rante nuestras observaciones para un objeto.
Realicé las observaciones del OAN-SPM incluidas en el primer reporte
y algunas del segundo; instruí a uno de los observadores y participé en las
discusiones desde la planeación de la campaña.
68
154 
 Minor Planet Bulletin 43 (2016) 
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RESULTS OF THE 2015 MEXICAN ASTEROID 
PHOTOMETRY CAMPAIGN 
Pedro V. Sada 
Departamento de F’sica y Matem‡ticas 
Universidad de Monterrey 
Av. I. Morones Prieto 4500 Pte. 
Garza Garc’a, N.L., 66238 
MƒXICO 
pedro.valdes@udem.edu 
Samuel Navarro-Meza & Mauricio Reyes-Ruiz 
Instituto de Astronom’a 
Universidad Nacional Aut—noma de MŽxico 
Ensenada, Baja California, MƒXICO 
Lorenzo L. Olgu’n, Julio C. Saucedo & Pablo Loera-Gonz‡lez 
Depto. de Investigaci—n en F’sica 
Universidad de Sonora 
Hermosillo, MƒXICO 
 (Received: 2016 January 9) 
The 2015 Mexican Asteroid Photometry Campaign was 
organized at the 2nd National Planetary Astrophysics 
Workshop held in 2015 March at the Universidad 
Aut—noma de Nuevo Le—n in Monterrey, MŽxico. Three 
asteroids were selected for coordinated observations 
from several Mexican observatories. We report full 
lightcurves for the main-belt asteroid 1084 Tamariwa (P 
= 6.195 ± 0.001 h) and near-Earth asteroid (NEA) 4055 
Magellan (P = 7.479 ± 0.001 h). Asteroid 1466 
Mundleria was also observed on eight nights but no 
lightcurve was obtained because of its faintness, a 
crowded field-of-view, and low amplitude (<0.03 mag).  
Planetary astronomy in general is becoming a more popular field 
of scientific study in Mexico, in part due to the recent 
establishment of the Mexican Space Agency 
(http://www.aem.gob.mx/). As a consequence, the Universidad 
Aut—noma de Nuevo Le—n, in the city of Monterrey, organized a 
series of National Planetary Astrophysics Workshops. The first 
was in 2013 and the second in 2015 (http://tasp.fcfm.uanl.mx/). 
 155 
 Minor Planet Bulletin 43 (2016) 
Astronomers from all over MŽxico were invited to present their 
research and encouraged to cooperate and plan projects related to 
the study of Solar System objects or extrasolar planets. 
One of the results from the latest meeting was the organization of 
the 2015 Mexican Asteroid Photometry Campaign 
(http://www.astro.uson.mx/~lorenzo/CMFA2015/CMFA2015). The 
objective of this first campaign was to organize, coordinate, and 
share photometric observations of asteroids between interested 
parties at various national observatories and university research 
centers. Because asteroid photometry is not a common activity 
amongst Mexican astronomers, it was decided as a first effort to 
form individual observing groups that would start to develop their 
own expertise in the matter by observing relatively simple targets.  
Three asteroids were chosen: the C-class main-belt asteroid 1084 
Tamariwa has a well-defined period, large amplitude, and is 
relatively bright. 1466 Mundleria, another C-class inner-belt 
asteroid, is a smaller and dimmer target with an unknown rotation 
period. 4055 Magellan was also selected since the V-type Amor 
asteroid would have a favorable opposition during 2015. 
We present the results of this first Mexican Asteroid Photometry 
Campaign. In all we collected 18 nights of observations from three 
different observatories and managed to reconstruct full lightcurves 
for 1084 Tamariwa and 4055 Magellan. 1466 Mundleria turned out 
to be a more difficult target to observe and analyze since it was 
dim, in a crowded field of stars, and apparently exhibits a very 
small brightness amplitude variation.  
At the Universidad de Monterrey (UdeM) Observatory (MPC 720) 
we observed all three asteroids on 10 different nights using a 
Meade 0.36-m f/8 LX-600GPS telescope and an SBIG STL-1301E 
CCD. The camera contains a 1280&1024-16µm KAF-1301E/LE 
chip which covers a ~26.3&21.1 arcminute field-of-view (FOV) 
with an image scale of about 1.25 arseconds/pixel. All asteroids 
were observed unfiltered and exposures were set for each target as 
follows: 40 seconds for fast-moving 4055 Magellan, 60 seconds 
for 1084 Tamariwa, and 120 seconds for dim 1466 Mundleria. The 
CCD images were read in 2&2 binned format for faster download 
time and improved observing efficiency. The FOV was maintained 
fixed in the chip by using a guide star at all times. 
Two observing runs were scheduled with the 0.84-m f/15 Ritchey-
Chretien telescope at the Observatorio Nacional de San Pedro 
M‡rtir (SPM; MPC 679) in Baja California for this program. This 
telescope uses a 2048&2048&13.5 µm Spectral Instruments CCD 
for regular imaging. This combination yields a FOV of ~6.3&6.3 
arcminutes with an approximate image scale of 0.185 
arcsecond/pixel. 1084 Tamariwa was observed for only one night 
on the first observing run in May, while 4055 Magellan was 
observed for three nights and 1466 Mundleria for two nights on the 
second observing run in August. All images were obtained using 
an off-axis guide star for stability (although the field drifted a bit 
during the observing sessions) and were also unfiltered and binned 
2&2 for efficiency. Exposure times varied for each target: 30 and 
45 seconds for 4055 Magellan, 90 and 120 seconds for 1466 
Mundleria, and 60 seconds for 1084 Tamariwa.  
One observing night for 1084 Tamariwa and two for 1466 
Mundleria were recorded at the Carl Sagan Observatory belonging 
to the Universidad de Sonora in Hermosillo. The observatory 
operates a Meade LX-200 0.41-m f/10 telescope equipped with a 
2499&2499&12 µm Apogee Alta F9000 CCD for imaging. This 
yields a 25.4&25.4 arcminute FOV with an image scale of ~0.61 
arcsecond/pixel. The images at this site were obtained unguided, 
unfiltered and Ð in this case Ð unbinned. Exposure times were 20 
seconds for 1084 Tamariwa and 50 seconds for 1466 Mundleria. 
All the data were concentrated at the Universidad de Monterrey 
Observatory where the photometric analysis was performed using 
MPO Canopus (version 9.5.0.14). Images were also processed in 
the standard manner using nightly dark current and flat-field files 
from each site.  
1084 Tamariwa. This asteroid was observed at the Carl Sagan 
Observatory (2015 April 22), Universidad de Monterrey 
Observatory (2015 April 28-30), and San Pedro M‡rtir Observatoy 
(2015 May 13). During analysis, the April 22 observations from 
Carl Sagan Observatory were treated as two separate sessions due 
to re-centering the FOV during the night. 
The asteroid was previously observed and reported by Behrend et 
al. (2007), Stecher et al. (2008), and Sada (2008). Our 
observations confirm the period of 6.195 ± 0.001 h, amplitude 
~0.30 magnitudes, and general lightcurve shape presented in Sada 
(2008).  
The similarity of both lightcurves obtained at different opposition 
dates (2007 August 19 and 2015 April 21) would suggest a 
rotational axis alignment perpendicular to the ecliptic, although too 
few complete lightcurves are available for a full polar orientation 
and shape analysis. We note in particular that the main minimum 
(without the ÒhumpÓ) exhibits a large scatter in both the 2007 and 
2015 lightcurves. We are uncertain as to its origin but it might be 
associated with topographical features sensitive to slight variations 
in phase angle illumination. 
 
As an aside, initial analysis of the April 28 observations at the 
Universidad de Monterrey Observatory found the intended 
comparison star, GSC 5553-0670 (magnitude ~13.4), to be 
variable. It was discarded for the asteroid measurements but 
follow-up analysis found a sinusoidal lightcurve of short period. 
We plan to obtain more data and report the results to the AAVSO. 
This serves both as a warning to make sure comparison stars are 
not variable and a reminder that asteroid images can be data mined 
for other objects. 
1466 Mundleria. This asteroid was observed for four nights at the 
Universidad de Monterrey Observatory (2015 July 25 and 27 and 
August 6-7), two nights at the San Pedro M‡rtir Observatory (2015 
August 20-21), and two nights at the Carl Sagan Observatory 
(2015 June 15-16). Despite being the most observed asteroid in the 
156 
 Minor Planet Bulletin 43 (2016) 
set, no conclusive brightness variations larger than 0.03 
magnitudes could be detected over a single observing session. 
Therefore, no rotational period could be derived. This small (~22 
km.) asteroid was the faintest in our set and, at the time, was also 
crossing a dense star field in Ophiuchus. These circumstances 
combined to make the data reduction difficult,  even with the star 
eliminating option in MPO Canopus, and yielded relatively large 
scatter for the smaller UdeM and Carl Sagan Observatory 
telescopes. The SPM data were of much better quality but sparser. 
Nevertheless, it was useful to set our magnitude variation upper 
limit. No other reports for this asteroid were found. A larger 
aperture instrument and more patience are required to derive a 
lightcurve for this asteroid. 
4055 Magellan. This NEA was observed for three nights at the 
Universidad de Monterrey Observatory (2015 August 14, 18-19) 
and three more nights at the San Pedro M‡rtir Observatory (2015 
August 19, 22-23). The derived lightcurve exhibits similar maxima 
and minima with a period of 7.479 ± 0.001 hours and a relatively 
large amplitude of ~0.45 magnitudes. The August 19 data were 
acquired independently at both the UdeM and SPM observatories. 
The August 22 SPM data were analyzed as two separate sessions 
because of recentering of the FOV due to the asteroidÕs fast sky 
motion.  
Our August 18 UdeM data show large scatter due to weather but 
assure full lightcurve phase coverage. The August 14 UdeM data 
exhibited even larger scatter and were omitted from the period and 
lightcurve shape calculations even though its general outline does 
corroborate our derived final lightcurve.  
This asteroid has been observed several times. Warner (2014) 
suggests a period of ~6.384 hours from sparse 2004 data over a 
7.475-hour period initially proposed by Pravec et al. (2000). 
However, older observations reported in Waszczak et al. (2015) 
and observations from the current 2015 opposition by Warner 
(2015) and Behrend et al. (2015) favor the later ~7.5-hour period. 
Our results are consistent with this period estimate, amplitude and 
general lightcurve shape. 
 
Future Mexican Asteroid Photometry Campaigns are being 
planned with an increasing number of proposed targets (main-belt 
asteroids and NEAs) and participation from other Mexican 
observatories. We are also working on standardizing the observing 
sequences and data reduction and analysis techniques to make the 
data easier to share and publish.  
Acknowledgments 
The results presented in this report were partially based on 
observations acquired at the Observatorio Astron—mico Nacional 
in the Sierra San Pedro M‡rtir (OAN-SPM), Baja California, 
MŽxico. We also would like to thank Ricardo L—pez-Valdivia for 
his aid during the OAN-SPM August observations. 
References 
Behrend, R. (2007, 2015). ÒAsteroids and Comets Rotation 
Curves, CdR.Ó http://obswww.unige.ch/~behrend/page_cou.html 
Pravec, P., Wolf, M. Sarounova, L. (2000). ÒOndrejov Asteroid 
Photometry Project.Ó  
http://www.asu.cas.cz/~ppravec/neo.htm 
Sada, P.V. (2008). ÒLightcurve Analysis of 1084 Tamariwa.Ó 
Minor Planet Bulletin 35, 50. 
Stecher, G., Ford, L., Lorenzen, K., Ulrich, S. (2008). 
ÒPhotometric Measurements of 1084 Tamariwa at Hobbs 
Observatory.Ó Minor Planet Bulletin 35, 76-77. 
Warner, B.D. (2014). ÒNear-Earth Asteroid Lightcurve Analysis at 
CS3-Palmer Divide Station: 2014 January-March.Ó Minor Planet 
Bulletin 41, 157-168. 
Warner, B.D. (2015). ÒNear-Earth Asteroid Lightcurve Analysis at 
CS3-Palmer Divide Station: 2015 March-June.Ó Minor Planet 
Bulletin 42, 256-266. 
Waszczak,  A.,  Chang,  C.-K.,  Ofek,  E.O.,  Laher,  R.,  Masci,  
F., Levitan,  D.,  Surace,  J.,  Cheng,  Y.-C.,  Ip,  W.-H.,  Kinoshita,  
D., Helou, G., Prince, T.A., Kulkarni, S. (2015). ÒAsteroid 
Lightcurves from the Palomar Transient Factory Survey:  Rotation 
Periods and Phase Functions from Sparse Photometry.Ó Astron. J. 
150, id. 75. 
 
PHOTOMETRY OF ASTEROIDS  
2014 EK14 AND 2015 FS332  
AT THE TERSKOL OBSERVATORY   
Vira Godunova, Volodymyr Reshetnyk, Maxim Andreev 
ICAMER Observatory of NASU (MPC B18) 
27 Acad Zabolotnoho Str. 
Kyiv 03680 UKRAINE 
V_Godunova@bigmir.net 
Andrii Simon, Volodymyr Vasylenko 
Taras Shevchenko National University of Kyiv 
Kyiv, UKRAINE 
(Received: 2016 January 15)  
We report photometric observations of two near-Earth 
asteroids that were obtained with the Zeiss-600 telescope 
at the Terskol Observatory in 2015. Based on our data, 
we were able to estimate the rotation properties of these 
asteroids. 
Starting in 2003, the facilities of the Terskol Observatory in the 
Northern Caucasus (43¡16'29" N, 42¡30'03" E, 3120 m ASL) have 
 1 
Minor Planet Bulletin xx (xxxx) 
RESULTS OF THE 2016 MEXICAN ASTEROID 
PHOTOMETRY CAMPAIGN 
Pedro V. Sada 
Departamento de Física y Matemáticas 
Universidad de Monterrey 
 Av. I. Morones Prieto 4500 Pte. 
San Pedro Garza García, N.L. 66238 
MÉXICO  
pedro.valdes@udem.edu 
Lorenzo Olguín, Julio C. Saucedo & Pablo Loera-González 
Departamento de Investigación en Física 
 Universidad de Sonora 
Hermosillo, Sonora, MÉXICO  
Laura Cantú-Sánchez, Jaime R. Garza, Sandra A. Ayala-Gómez 
Andrés Avilés & Eduardo Pérez-Tijerina 
Facultad de Ciencias Físico-Matemáticas 
Facultad de Ingeniería Mecánica y Eléctrica 
 Universidad Autónoma de Nuevo León 
Monterrey, Nuevo León, MÉXICO  
Samuel Navarro-Meza, J. S. Silva & Mauricio Reyes-Ruiz 
Instituto de Astronomía 
 Universidad Nacional Autónoma de México 
Ensenada, Baja California, MÉXICO  
Juan Segura-Sosa 
Facultad de Ciencias Físico-Matemáticas 
 Universidad Autónoma de Coahuila 
Saltillo, Coahuila, MÉXICO  
Ricardo López-Valdivia 
Área de Astrofísica 
 Instituto Nacional de Astrofísica, Óptica y Electrónica 
Tonantzintla, Puebla, MÉXICO  
F. Álvarez-Santana 
Área de Astrofísica 
 Universidad Autónoma de Baja California 
Ensenada, Baja California, MÉXICO  
(Received:     Revised:  ) 
We report the results of the 2016 Mexican Asteroid 
Photometry Campaign. This year observers from seven 
different research institutions carried out 34 nights of 
observations at three Mexican observatories. An 
uncertain, but long, period of ~115.108±0.014h was 
estimated for 703 Noëmi from sparse data. A nearly-
complete lightcurve was obtained for 1305 Pongola (P = 
8.0585±0.0003h). Asteroid 2535 Hämeenlinna turned out 
to be a binary system where the primary exhibits a 
rotation period of 3.2311±0.0001h and the secondary 
shows an orbital period of 21.20±0.004h. Asteroid 4775 
Hansen (P = 3.1186±0.0001h) was well observed and 
showed variations of its lightcurve between two sets of 
observations separated by about 6 weeks. 
After the successful start of the Mexican Asteroid Photometry 
Campaign in 2015 with the coordinated observation of three 
asteroids from three different Mexican observatories (Sada et al. 
2016), it was decided to continue and seek to increase the 
collaboration during 2016. The eventual goal of this effort is to 
develop teams of coordinated observers in México capable of 
characterizing not only main belt asteroids, but NEOs as well. We 
report here the results of the 2016 Mexican Asteroid Photometry 
Campaign. 
On this occasion, we collected 34 nights of observations from three 
different observatories by researchers from seven different 
institutions. On three of those nights the observing session was 
carried out simultaneously from two separate observatories, 
providing a basis for photometric comparison between them and 
prolonging the observing period for the target since the 
observatories were separated by more than 10º in longitude. 
At the Universidad de Monterrey (UdeM) Observatory (MPC 720) 
we observed four asteroids on 17 different nights using a Meade 
0.36-m f/8 LX-600GPS telescope and an SBIG STL-1301E CCD. 
The camera uses a 1280×1024-16µm KAF-1301E/LE chip which 
covers a ~26.3×21.1arcmin field-of-view (FOV) with an image 
scale of about 1.24arcsec/pix. All asteroids were observed 
unfiltered for maximum throughput, and the CCD images were read 
in 2×2 binned format for faster download time and improved 
observing efficiency. The FOV was maintained fixed on the chip by 
using an on-axis guide star at all times. Exposure times varied 
between 60s and 210s for each night depending on the target’s 
brightness, and sometimes a slight defocus was applied to the 
telescope to spread the images over a few binned pixels allowing 
for slightly longer exposure times. 
Three one-week observing runs were scheduled throughout the year 
with the 0.84-m f/15 Ritchey-Chretien telescope at the Observatorio 
Astronómico Nacional on the Sierra de San Pedro Mártir (OAN-
SPM; MPC 679) in Baja California for this program. On top of that, 
a few additional partial nights of observations were attained on an 
availability basis from other observing runs. This telescope uses a 
2048×2048-13.4µm Spectral Instruments CCD for regular imaging. 
This combination yields a FOV of ~6.3×6.3arcmin with an 
approximate image scale of 0.185arcsec/pix. All images were 
obtained using an off-axis guide star for stability (although the field 
drifted a little during the observing sessions due to telescope sag), 
were obtained unfiltered, and were also binned 2×2 for efficiency. 
Exposure times also varied for each asteroid, between 20s and 480s, 
depending on the target brightness.  
Five observing nights were also recorded at the Carl Sagan 
Observatory belonging to the Universidad de Sonora (UNISON) in 
Hermosillo. This observatory operates a Meade LX-200GPS 0.41-
m f/10 telescope equipped with a 3056×3056×12µm Apogee Alta 
F9000 CCD for imaging. The image frame was trimmed to a 
subframe of 2000×2000 pixels and then binned 2×2 yielding an 
effective ~20×20arcmin FOV with an image scale of about 
1.2arcsec/pix. The images at this site were obtained unguided and 
unfiltered. Exposure times varied between 70s and 240s. 
Images from these observatories were processed in the standard 
manner using nightly dark current and flat-field files. Photometric 
measurements and lightcurve analysis were performed using MPO 
Canopus (version 10.7.3.0). Although all observations were 
unfiltered, differential magnitudes were calculated based on R-band 
stellar magnitudes. 
703 Noëmi. Was discovered by Johann Palisa on 1910 October 3 
and named for Baroness Valentine Noémi von Rothschild 
(Schmadel, 2003). This S-class asteroid from the Flora Family was 
observed on five nights from the OAN-SPM Observatory (2016 Oct 
13, 16, 20 & Nov 10, 11), four nights from the UDEM Observatory 
(2016 Nov 1, 28 & Dec 1, 7) and two nights at the UNISON 
Observatory (2016 Oct 30 & Nov 2). The 2016 Oct 16 observations 
were treated as three separate sessions because of differences in 
exposure times. The 2016 Oct 30 observations were treated as two 
2 
 Minor Planet Bulletin xx (xxxx) 
separate sessions because the FOV was slightly rotated partway 
through the night. Initial results showed that the asteroid brightness 
varied a small amount during each night, suggesting either a long 
rotation period and/or low amplitude. We derived a tentative long 
rotation period of 115.108±0.014h by matching the observations 
from 2016 Nov 2 and Dec 1 in the phased lightcurve, because they 
exhibited almost identical behavior, and then looking for other 
possible matches using whole fractions of that time-span and 
assuming a simple two-maxima and two minima lightcurve. The 
fact that differential photometry was performed on the unfiltered 
images, which meant that we could also shift the nightly 
observations in the brightness axis, added too many degrees of 
freedom in the search of a solution. Thus, we can only state that the 
rotation period for this asteroid is long, in the realm of tens of hours, 
and that our derived tentative value is only one possible solution. 
Our sparse observations are insufficient to cover an entire 
lightcurve. No other reports of the rotation period were found in the 
literature for this asteroid. However, A. Noschese reports in the 
Collaborative Asteroid Lightcurve Link (CALL) website 
(http://www.minorplanet.info/call.html) a larger set of observations 
from his group that indicates a longer period of ~201.9±0.8h, also 
with larger amplitude. Most of our observations predate his earliest 
observing date and there is little overlap, so this would be a good 
opportunity to join both data sets in an effort to obtain a more 
reliable solution to the rotation period of 703 Noëmi. 
 
1305 Pongola. Was discovered on 1928 July 19 by H. E. Wood at 
Johannesburg and named for a river in South Africa (Schmadel, 
2003). This C-class outer main-belt asteroid was observed at the 
UdeM Observatory on three nights (2016 Apr 4, 5 & May 7) and at 
OAN-SPM Observatory on five (2016 April 4, 11, 13, 14 & May 
13). During analysis, the 2016 April 4 observations were treated as 
three separate sessions because of differences in exposure times of 
the image sets and because they were obtained at two separate 
observatories. The April 11, 13 and 14 observing sessions were 
short, obtained during time gaps of other assigned projects, but still 
provided useful data to complement the lightcurve. A total of 457 
data points was used to find a period of 8.0585±0.0003h with an 
amplitude of ~0.19mag. Initial rotation period determinations were 
made by Binzel (1987), 8.03±0.10h; and Ditteon et al. (2012), 
8.06±0.02h. More recently, Waszczak et al. (2015) reported a 
rotation period of 8.0586±0.0015h with an amplitude of 0.17mag, 
while Mansego et al. (2016) reported a period of 8.335±0.002h with 
an amplitude of 0.16mag. Our resulting period and amplitude are in 
better agreement with those obtained by Waszczak et al. (2015). 
 
 
2535 Hämeenlinna. Was discovered in 1939 February 17 by Y. 
Väisälä at Turku and named for an old town in the province of 
Häme (Schmadel, 2003). This S-class asteroid from the Flora 
Family was observed at the UdeM Observatory on eight nights 
(2016 Feb 10, 11, 12, 16, 29 & Mar 3, 4, 13). On two of these nights 
2016 Feb 11 & Mar 3) the asteroid was also observed from the 
UNISON Observatory, extending the nightly observing period 
because of its location further west. For the final analysis, the night 
of 2016 Mar 13 was not included as it was much noisier than the 
rest. From the onset, this asteroid exhibited a clear ~3.23h period. 
However, each night the asteroid also exhibited a different overall 
trend in the data with each successive period not quite matching the 
previous ones. This was particularly evident in the two extended 
observing sessions from both observatories. The asteroid was thus 
suspected as having two periods and further observations were 
programmed until it was too faint to follow. The following figure 
below shows the best-fit single period obtained for the data. It 
confirms a 3.2311±0.0001h rotation period, but also exhibits larger 
than usual scatter.  
 
It was decided to use the dual period option included in MPO 
Canopus to attempt and disentangle the possibility of the existence 
of two periods. The results are shown in the following two figures. 
Our initial short rotation period of 3.2311±0.0001h with an 
amplitude of 0.11mag was maintained and the scatter was 
considerably reduced. An additional period of 21.20±0.004h with 
an amplitude of 0.11mag is also extracted from the data. This 
 3 
Minor Planet Bulletin xx (xxxx) 
second ligtcurve exhibits what appear to be primary and secondary 
dimmings due to the possible presence of a small companion 
orbiting the asteroid. The secondary dimming was well sampled by 
our data, but not the primary. This renders the derived possible 
orbital period of the companion as tentative since other nearby 
periods could also fit the data, which has an overall scatter similar 
to the derived amplitude. The only other report about 2535 
Hämeenlinna found in the literature is from Benishek et al. (2016) 
in which they report that this asteroid is a binary system where the 
primary exhibits a rotation period of 3.23106±0.00006h, the 
secondary shows a synchronous orbital period of 21.23±0.01h, and 
the reported lightcurve amplitude is 0.10mag. They also register 
eclipse/occultation events with depths of 0.05-0.10mag. Our data 
independently confirms this preliminary report from Benishek et al. 
(2016). 
 
 
4775 Hansen. Was discovered in 1927 Oct 3 by Maximilian Franz 
Wolf at Heidelberg and named after the German astronomer Peter 
Andreas Hansen (Schmadel, 2003). This is a C-class asteroid that 
crosses the orbit of Mars. It was observed on six nights at the OAN-
SPM Observatory (2016 Aug 17, 18, 19, 22, 23 & Oct 10) and two 
nights at the UDEM Observatory (2016 Oct 5, 7). During analysis, 
the 2016 Aug 22 and 23 observations were treated as two separate 
sessions. From all this data combined, we derive a period of 
3.1186±0.0001h with an amplitude of 0.15mag. This is in general  
agreement with the results of P = 3.1185±0.0001h and amplitude of 
0.18mag obtained by Pravec et al. (2016web), but in slight 
disagreement with the results of P = 3.124±0.001h and amplitude 
of 0.12mag obtained by Warner (2017). We note that the lightcurve 
did show some variation in shape and amplitude between the 
observations performed the third week of August vs those 
performed the first week of October. The October data exhibits a 
noticeable decrease in amplitude, from 0.16mag to 0.13mag, 
suggesting a more pole-on view, as outlined by Warner (2017) from 
his 2016 November observations. 
 
 
Acknowledgements 
The results presented in this report were partially based on 
observations acquired at the Observatorio Astronómico Nacional 
on the Sierra de San Pedro Mártir, Baja California, México. Laura 
Cantú-Sanchez is working on her Master’s Degree at the Planetary 
Astrophysics Program of the Universidad Autónoma de Nuevo 
León. 
References 
Benishek, V., Pray, D., Pravec, P., Kusnirak, P., Hornoch, K., 
Kucakova, H., Vrastil, J., Pollock, J., Groom, R., Stranger, K., 
Carbognani, A., Montaigut, R., Leroy, A., Reichart, D., Haislip, J. 
(2016). CBET 4262. 
Binzel, R.P. (1987). “A Photoelectric Survey of 130 Asteroids.” 
Icarus 72, 135-208. 
4 
 Minor Planet Bulletin xx (xxxx) 
Ditteon, R., Horn, L., Kamperman, A., Vorjohan, B., Kirkpatrick, 
E. (2012). “Asteroid Lightcuve Analysis at the Oakley Souther Sky 
Observatory: 2011 April-May.” Minor Planet Bulletin 39, 26-28. 
Harris, A.W., Young, J.W., Scaltriti, F., Zappala, V. (1984). 
“Lightcurves and phase relations of the asteroids 82 Alkmene and 
444 Gyptis.” Icarus 57, 251-258. 
Mansego, E.A., Rodriguez, P.B., de Haro, J.L., Chiner, O.R., Silva, 
A.F., Porta, D.H., Martinez, V.M., Silva, G.F., Garcerán, A.C. 
(2016). “Eighteen Asteroids Lightcurves at Asteroides Observers 
(OBAS) – MPPD: 2016 March-May.” Minor Planet Bulletin 43, 
332-336. 
Pravec, P., Wolf, M., Sarounova, L. (2016). “Photometric Survey 
for Asynchronous Binary Asteroids.” 
http://www.asu.cas.cz/~asteroid/binastphotsurvey.htm. 
Sada, P.V., Navarro-Meza, S., Reyes-Ruiz, M., Olguín, L.L., 
Saucedo, J.C., Loera-González, P. (2016). “Results of the 2015 
Mexican Asteroid Photometry Campaign.” Minor Planet Bulletin 
43, 154-156. 
Schmadel, L.D. (2003). Dictionary of Minor Planet Names, pp. 
107, 171, 260, 328, 628. Springer, New York. 
Warner, B.D., Harris, A.W., Pravec, P. (2009). “The Asteroid 
Lightcurve Database.” Icarus 202, 134-146. Updated 2016 Sep. 
http://www.minorplanet.info/lightcurvedatabase.html. 
Warner, B.D. (2017). “Asteroid Lightcurve Analysis at CS3-Palmer 
Divide Station: 2016 October-December.” Minor Planet Bulletin 
44, 116-120. 
Waszczak, A., Chang, C.-.K., Ofeck, E.O., Laher, R., Masci, F., 
Levitan, D., Surace, J., Cheng, Y.-C., Ip, W.-H., Kinoshita, D., 
Helou, G., Prince, T.A., Kulkarni, S. (2016). “Asteroid Light 
Curves from the Palomar Transient Factory Survey: Rotation 
Periods and Phase Functions from Sparse Photometry.” A. J. 150, 
A75. 
 
Number Name 2016 mm/dd Pts Phase LPAB BPAB Period(h) P.E. Amp A.E. Grp 
 703 Noemi 10/13-12/07 1104 18.4,15.0  50 -1 115.108 0.014 0.28 0.05 FLO 
 1305 Pongola 04/04-05/13 457  3.2,12.4 202  2 8.0585 0.0003 0.19 0.02 MBO 
  2535 Hämeenlinna 02/10-03/04 940  1.9,12.3 143 -2 2.2311 0.0001 0.11 0.02 FLO 
 4775 Hansen 08/17-08/23 1511 19.5,16.4 342 -1 3.1187 0.0001 0.16 0.02 MC 
 4775 Hansen 10/05-10/10 507 16.7,18.8  5 12 3.1182 0.0002 0.13 0.02 MC 
Table I. Observing circumstances and results. Pts is the number of data points. The phase angle is given for the first and last date. LPAB and 
BPAB are the approximate phase angle bisector longitude and latitude at mid-date range (see Harris et al., 1984). Grp is the asteroid 
family/group (Warner et al., 2009). 
Astronomy in Focus, Volume 1
XXIXth IAU General Assembly, August 2015
Piero Benvenuti, ed.
c© 2018 International Astronomical Union
DOI: 00.0000/X000000000000000X
The Mexican Asteroid Photometry
Campaigns: Aiming for Asteroids’ Rotation
Periods
W. J. Schuster1, S. A. Ayala-Gómez2, A. Avilés2, M. E. Contreras3,
S. A. R. Haro-Corzo4, P. A. Loera-Gonzlez3, S. Navarro-Meza1, L.
Olgúın3, E. Pérez-Tijerina2, M. Reyes1, J.C. Saucedo3, J.
Segura-Sosa5, P. A. Valdés-Sada6, I. L. Fuentes-Carrera7, C.
Chávez-Pech2, M. Rodŕıguez-Mart́ınez4, & R. Vázquez1
1 IAEnsenada, Universidad Nacional Autónoma de México,
Km 107 Carretera Tijuana-Ensenada, Ensneada, B.C., Mexico
email: schuster@astrosen.unam.mx
2FCFM−Universidad Autónoma de Nuevo León, 3DIF−Universidad de Sonora,
4ENES−Universidad Nacional Autónoma de México, 5FCFM−Universidad Autónoma de
Coahuila, 6DFM−Universidad de Monterrey, 7ESFM−Instituto Politécnico Nacional.
Abstract. Thousands of new asteroids are discovered every year and the rate of discovery is by
far larger than the determination rate of their physical properties. In 2015 a group of researchers
and students of several Mexican institutions, have established an observational program to study
asteroids photometrically. The program, named Mexican Asteroid Photometry Campaign, is
aiming to derive rotation periods of asteroids based on optical photometric observations. Since
then four campaigns have been carried out. The results obtained throughout these campaigns,
as well as future work, are presented.
Keywords. Solar system: general, minor planets, asteroids, techniques: photometry
1. Overview
Currently, more than 760,000 asteroids are known and every year thousands of new
ones are discovered. Nevertheless, most of their physical parameters: size, shape, albedo,
rotation, taxonomical classification, etc. are unknown. Thus, we need to make a greater
effort to increase our knowledge about these objects. Some asteroid properties, such as
their rotation period, can be derived from their lightcurve. However, according to the
Asteroid Lightcurve Photometry Database (ALCDEF), only a few thousand (∼6000)
asteroids have reliable rotation periods. These periods are important because they are
related to the cohesion strength of the material from which an asteroid has been made.
Figure 1 shows the relation between the asteroid rotation frequency and its size. We can
see that fast rotators have sizes smaller than ∼300 m. In addition, 3D asteroid shapes
can be inferred from lightcurves obtained at different epochs, since objects are observed
from different viewing angles.
In order to contribute to asteroid characterization, in 2015 a group of researchers
and students of several Mexican institutions, have established an observational program
to study asteroids photometrically. The program, named Mexican Asteroid Photometry
Campaign (CMFA, from the Spanish), is aiming to derive rotation periods of asteroids
based on optical photometric observations. This program has been established at an
introductory stage to generate the abilities and basic knowledge related to asteroids,
1
2 W. J. Schuster et al.
Figure 1. Relation between the asteroid rotation frequency and its size. Figure taken from the
ALCDEF web site.
allowing us to carry out broader and deeper studies in the near future. The first campaign
started during the second half of 2015. Since then, three campaigns have been completed
and the fourth is ongoing.
2. Observations, data reduction, analysis and results
The observatories and telescopes involved in the campaigns are the following: i) 0.84-m
telescope at the Observatorio Astronómico Nacional at Sierra San Pedro Mártir (OAN-
SPM), operated by Universidad Nacional Autónoma de México, at Baja California,
ii) 0.40-m telescope at Observatorio Astronómico Carl Sagan (OACS), Universidad de
Sonora, Hermosillo, Sonora, and iii) 0.36-m telescope of the Universidad de Monterrey
Astronomical Observatory, Monterrey, Nuevo León.
Typically, to obtain complete lightcurves, five to ten nights of observation are dedicated
to each asteroid. Exposure times for individual images are in the range of 30 to 240
seconds, depending on asteroid’s visual magnitude. Generally, a few hundred images per
object are taken during each observing night.
Basic steps in data reduction are performed using IRAF or MaximDL software. For
lightcurve extractions and period determinations, MPO Canopus software is used. For
crowded stellar fields, first DAOPHOT (Stetson 1987) is used to obtain the photometry
and then MPO Canopus is used for deriving the lightcurve and rotation period. Figure 2
shows examples of lightcurves derived using these procedures.
The asteroid sample has been obtained from the Collaborative Asteroids Lightcurve
Link (CALL). In general, asteroids with poorly, or unknown, rotation periods were cho-
sen. Only those with declinations > −30o were observed. In three years more than fifty
objects have been observed in four campaigns from which a dozen lightcurves and rota-
tion periods have been published (Sada et al. 2016; Sada et al. 2017; Sada et al. 2018;
Haro-Corzo et al. 2018). Some data are still under analyses. A sample of derived rotation
periods and relevant information are presented in Table 1. Near Earth Asteroids’ (NEAs’)
information is not included because it has been presented in a separate contribution by
J.C. Saucedo et al. at this same IAU Focus Meeting.
JD 11. The Mexican Asteroid Photometry Campaigns 3
Figure 2. Examples of asteroids’ phased lightcurves.
Table 1. Asteroids with reliable period determinations.
Name Period Error Amplitude Nights Group
(h) (h) (mag)
703 Noemi 11.108 0.014 0.28 11 Flora
1084 Tamariwa 6.195 0.001 0.30 5 Outer Main Belt
1218 Aster 3.1581 0.0002 0.35 7 Flora
1305 Pongola 4.349 0.0003 0.19 8 Outer Main Belt
1491 Balduinus 15.3044 0.0057 0.45 4 Outer Main Belt
1856 Ruzena 5.957 0.001 0.68 11 Main Belt
2022 West 14.1385 0.0031 0.54 7 Outer Main Belt
2535 Hameenlinna 3.2311 0.0001 0.11 10 Flora
2733 Hamina 93.23 0.02 0.36 13 Inner Main Belt
3394 Banno 7.3249 0.0008 0.21 5 Main Belt
3887 Braes 5.81 0.01 0.60 6 Main Belt
4775 Hansen 3.1186 0.0001 0.15 Mars Crossing
8433 Svecica 20.9905 0.0015 0.65 10 Outer Main Belt
18301 Konyukhov 2.6667 0.0003 0.15 6 Outer Main Belt
3. Concluding remarks and future work
After three years we have refined observational and analysis methods to derive reliable
asteroids’ lightcurves. The pace at which we are obtaining and processing photometric
data is increasing. However, due to the shortage of trained people, we are reaching our
maximum rate of studied objects to about 12 objects per year. Therefore, we are planning
to coach a new generation of students and researchers in the observation and analysis
techniques. Besides, we plan to improve and increase our observation facilities. In the
meantime, we will fulfill the following tasks: i) carry out infrared observations to estimate
precise asteroid sizes and albedos, ii) start taxonomical classification of bright objects
(V<15), and iii) undertake theoretical studies of asteroids’ dynamical behavior.
4 W. J. Schuster et al.
4. Acknowledgments
WJS gratefully acknowledges financial support from the Universidad Nacional Autónoma
de México, grant DGAPA-PAPIIT, project IN100918. M.E.C. acknowledges financial sup-
port from CONACyT (México). IRAF is distributed by the National Optical Astronomy
Observatory, which is operated by the Association of Universities for Research in Astron-
omy (AURA) under a cooperative agreement with the National Science Foundation. Col-
laborative Asteroids Lightcurve Link (CALL) can be accessed at www.minorplanet.info/
call.html. Asteroid Lightcurve Photometry Database (ALCDEF) can be accessed at
alcdef.org.
References
Haro-Corzo, S. A. R., Villegas, L. A., Olgúın, L., Saucedo, J. C., Contreras, M. E., Sada, P. V.,
Ayala, S. A., Garza, J. R., Segura-Sosa, J., & Beńıitez-Beńıitez, C. P. 2018, MPBu, 45, 233
Sada, P. V., Navarro-Meza, S., Reyes-Ruiz, M., Olgúın, L., Saucedo, J. C., & Loera-González,
P. 2016, MPBu, 43, 154
Sada, P. V., Olgúın, L., Saucedo, J. C., Loera-González, P., Cantú-Sánchez, L., Garza, J. R.,
Ayala-Gómez, S. A., Avilés, A., Pérez-Tijerina, E., Navarro-Meza, S., Silva, J.S., Reyes-
Ruiz, M., Segura-Sosa, J., López-Valdivia, R., & Álvarez-Santana, F. 2017, MPBu, 44,
239
Sada, P., Loera-González, P., Olgúın, L., Saucedo-Morales, J. C., Ayala, S. A., & Garza, J. R.
2018, MPBu, 45, 122
Stetson, P. 1987, PASP, 99, 191
C. El primer objeto interestelar observado y sus im-
plicaciones en la formación planetaria
’Oumuamua es el primer objeto interestelar observado. Utilizando una
aproximación geométrica simple, este artículo calcula la probabilidad de
que un observador en la Tierra detecte objetos como este. Se concluye que
es posible detectarlos si las estrellas vecinas eyectan una masa de su disco
protoplanetario comparable a la que se calcula que se eyectó durante la
formación del nuestro.
Me integré al trabajo cuando el modelo ya estaba bosquejado. Participé
en la discusión de qué suposiciones era razonable considerar en el modelo
y en la discusión de los resultados.
80
Implications for Planetary System Formation from Interstellar Object
1I/2017 U1 (‘Oumuamua)
David E. Trilling1 , Tyler Robinson1 , Alissa Roegge1, Colin Orion Chandler1 , Nathan Smith1, Mark Loeffler1, Chad Trujillo1,
Samuel Navarro-Meza1,2, and Lori M. Glaspie1
1Department of Physics and Astronomy, Northern Arizona University, P.O. Box 6010, Flagstaff, AZ 86011, USA; david.trilling@nau.edu
2 Instituto de Astronomía Universidad Nacional Autónoma de México, Ensendada B.C. 22860, México
Received 2017 November 3; revised 2017 November 8; accepted 2017 November 8; published 2017 November 30
Abstract
The recently discovered minor body 1I/2017 U1 (‘Oumuamua) is the first known object in our solar system that is
not bound by the Sun’s gravity. Its hyperbolic orbit (eccentricity greater than unity) strongly suggests that it
originated outside our solar system; its red color is consistent with substantial space weathering experienced over a
long interstellar journey. We carry out a simple calculation of the probability of detecting such an object. We find
that the observed detection rate of 1I-like objects can be satisfied if the average mass of ejected material from
nearby stars during the process of planetary formation is ∼20Earth masses, similar to the expected value for our
solar system. The current detection rate of such interstellar interlopers is estimated to be0.2 yr−1, and the expected
number of detections over the past few years is almost exactly one. When the Large Synoptic Survey Telescope
begins its wide, fast, deep all-sky survey, the detection rate will increase to1 yr−1. Those expected detections will
provide further constraints on nearby planetary system formation through a better estimate of the number and
properties of interstellar objects.
Key words: comets: individual (1I/2017 U1 (‘Oumuamua)) – local interstellar matter – minor planets, asteroids:
individual (1I/2017 U1 (‘Oumuamua)) – planetary systems – protoplanetary disks – solar neighborhood
1. Introduction
On 2017 October 18, the minor body C/2017-UT
(PANSTARRS), which would become known as A/2017U1
and later 1I/2017 U1 (‘Oumuamua)—hereafter, 1I—was
discovered by the Panoramic Survey Telescope And Rapid
Response System (Pan-STARRS) survey (Chambers et al.
2016). In a matter of days, it became clear that this object was
on an unbound (hyperbolic) trajectory, with eccentricity
e≈1.2 (Williams 2017). In addition to its high eccentricity,
1I’s orbit is inclined to the solar system plane at an angle
i≈123°, so it is very unlikely to have encountered any
massive objects within our solar system (other than the Sun).
With no gravitational perturbations to explain its anomalously
high eccentricity, the most likely explanation is that this object
originated outside of our solar system and happened to pass
close to the Earth during its journey through interstellar space.
This implies that 1I formed in another planetary system and
was ejected, presumably through dynamical interactions in its
natal planetary system. Consequently, we refer to 1I and similar
bodies as “ejectoids.”
The theoretical existence of ejectoids has been long proposed
(e.g., Sekanina 1976), with various authors using nondetections to
place upper limits on the population (McGlynn & Chapman 1989;
Sen & Rama 1993; Engelhardt et al. 2017). Jewitt (2003) and
Francis (2005) suggested that PanSTARRS could detect an
interstellar object, if the number density was great enough. In the
two weeks since the discovery of 1I and its identification as an
interstellar object, we have learned about its optical spectrum
(Masiero 2017; Ye et al. 2017), its light curve (Knight
et al. 2017), its orbit (de la Fuente Marcos & de la Fuente
Marcos 2017), and its potential origin scenarios (Gaidos
et al. 2017; Laughlin & Batygin 2017; Mamajek 2017).
Here we use a simple calculation to estimate the probability
of detecting such an object and explore the implications for the
prevalence and properties of planetary systems that are implied
by the existence and properties of 1I.
2. Ejectoid Encounters and Ejected Mass Constraints
Gravitational microlensing results have shown that, on
average, every star in the Milky Way is accompanied by at
least one bound planet (Cassan et al. 2012), which implies that
planet formation is a near-universal process. We assume here
that the formation of a typical planetary system results in a
mass m of ejectoids with a typical size of re and mass density
ρe. The number of ejectoids per star is therefore
p r
( )
m
r
. 1
4
3 e
3
e
We can write the number density of stars (in, e.g., stars per
cubic parsec) ns in terms of a characteristic stellar spacing, R, as
p
= ( )n
R
1
. 2s 4
3
3
This enables us to express the number density of ejectoids
(number/volume) as
p r p
=
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟ ( )n
m
r R
1
. 3e 4
3 e
3
e
4
3
3
We next wish to determine the number of ejectoids that we
expect to have encountered. We assume that telescopic
searches for 1I-like objects have swept out a cylindrical
volume of interstellar space given by
p= D D ( )V r v t, 4obs obs
2
where robs is the geocentric distance out to which we are
sensitive to 1I-like objects, Δve is the Sun’s velocity through
The Astrophysical Journal Letters, 850:L38 (4pp), 2017 December 1 https://doi.org/10.3847/2041-8213/aa9989
© 2017. The American Astronomical Society. All rights reserved.
1
the solar neighborhood (and the presumed cloud of ejectoids),
and Δt is the time interval over which observational surveys
have been capable of discovering 1I-like objects. Using this
volume and the number density of ejectoids, we find that the
number of detections of 1I-like objects is
p r p
p= = D D
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟ ( ) ( )N n V
m
r R
r v t
1
, 5e obs 4
3 e
3
e
4
3
3
obs
2
which simplifies to
p r
=
D D
( )N
mr v t
r R
9
16
. 6obs
2
e e
3 3
We can now use 1I to constrain the characteristic mass in
ejectoids for a forming planetary system. With N=1, we can
rearrange Equation (6) to write that
p r
=
D D
( )m
r R
r v t
16
9
. 7e e
3 3
obs
2
The absolute magnitude of 1I is given in the Minor Planet
Center catalog as22.1 (as of 2017 November 2), which
corresponds to a radius re of around 100meters, assuming a
moderate-to-dark albedo.
The range of densities for cometary and asteroidal material
that may be relevant is around 500to 3000kg m−3
(Davidsson
& Gutíerrez 2006; Davidsson et al. 2007; Richardson et al.
2007; Carry 2012). While 1I’s highly eccentric orbit would
typically be associated with a comet, and theoretical predictions
suggest that most ejectoids should be more comet-like
(Raymond et al. 2011), there are no signs of activity from 1I
(Knight et al. 2017; Ye et al. 2017). Thus, here, we assume that
1I may be more asteroidal than cometary and adopt a density of
2000 kg m−3.
There are 357stars within 10parsecs of the Sun.3 This gives
an average distance between adjacent stars R of 1.4pc. The
average discovery distance of near-Earth objects in the minor
planet center robs is 0.3au.
The velocity of the Sun relative to nearby stars is around
20km s−1
(Schönrich et al. 2010). 1I has been found4 to have
an interstellar speed (velocity at infinity) of 26km s−1, while
Mamajek (2017) reports that an object entering the solar system
with median velocity of the local stellar population would have
a speed of around 22.5km s−1. The fact that the Sun’s relative
velocity is comparable to the velocity of 1I confirms our
assumption that the population of interstellar ejectoids has zero
mean velocity (due to the fact that both the source planetary
systems and ejection trajectories are assumed to be isotropic).
Based on these three estimates, we set Δve to be 25km s−1.
In recent years, improvements on detector size and field of
view at the Catalina Sky Survey and Pan-STARRS (the two
major NEO surveys) have enhanced the ability to detect 1I-like
objects, so we estimate Δt to be 5years.
Our characteristic values, when inserted in Equation (7),
yield a typical mass in ejected 1I-like objects of 1026kg, or
20M⊕. This is in remarkably good agreement with values
derived for mass loss during the formation of our solar system.
For example, Weidenschilling (1977) and Bottke et al. (2005)
derive 1–5M⊕ of material lost from the asteroid belt. Kuiper
(1951), Kenyon & Luu (1999), and Morbidelli (2005) find
12–30M⊕ lost from the Kuiper Belt. Together, these imply a
total mass lost from our solar system of close to 20M⊕.
Identifying the characteristic size and density of ejectoids as
being the most uncertain terms in our analysis, and inserting the
parameter values adopted above, we can write
r
= Å -
⎜ ⎟
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎞
⎠
( )m M
r
20
2000 kg m 100 m
. 8e e
3
3
This relationship is shown in Figure 1. The plausible range
of ejection masses is roughly 1–100M⊕. We note that in
principle the radius of 1I, which we take to be characteristic of
ejectoids, will be determined through our forthcoming thermal
infrared observations of 1I with the Spitzer Space Telescope
(observations scheduled for late 2017 November). There is no
direct way to constrain the density of 1I, though indirect
constraints may be possible from the rotation period.
Alternatively, if we adopt the ∼20M⊕ in ejectoids lost
during the formation of the solar system as a characteristic
number, we can use Equation (6) to derive the number of 1I-
like objects expected over five years. We find that N is very
close to unity—exactly matching the observations. The
detection rate (N/Δt) is therefore 0.21I-like objects per year,
or one 1I-like object every five years. The number density of
ejectoids is, from Equation (3), around 0.1/au3, which is
around 1015/pc3.
3. Caveats and Uncertainties
We do not claim that this is the only mechanism for
producing 1I-like objects or delivering such objects to the
detectable space near the Earth, as the above calculation
admittedly contains a number of assumptions. However, this
does give a plausible explanation for 1I that in turn has several
interesting implications that are discussed below.
The radius and density of 1I are unknown, though the values
above are unlikely to be in error by more than a factor of two.
Similarly, the geometry arguments (average stellar distance,
solar velocity, and observational distance) are likely within a
factor of two, while the time interval is approximately correct.
We ignore gravitational focusing here. The largest overall
uncertainty is simply the unknown statistical likelihood of
detecting this ejectoid and our extrapolation from a single
object. 1I may be part of a constant stream of interstellar
objects moving through our solar system (as implied here), or a
very unlikely occurrence, in which case the arguments made
here are less applicable.
In addition, the true population of ejected extrasolar material
must follow some size distribution, and will not consist of only
100m 1I-like objects. Small objects are presumably more
numerous in any planet formation scenario, but larger objects
will be preferentially detected by our surveys. We must simply
take 1I to be representative.
In the above calculation, we have assumed that a steady-state
population of 1I-like objects is ejected from all planetary
systems. However, we might instead assume that the majority
of ejectoids are produced during the earliest phases of planetary
system formation, in a single pulse of material. The nearest star
formation regions are some 100parsec away, with typical ages
of 1–10Myr (Andrews et al. 2009; Currie & Sicilia-
Aguilar 2011; Esplin & Luhman 2017). If we take the escape
velocity from those systems to be on the order of 10km s−1
then material from one of these nearby star formation regions
3 http://www.recons.org
4 https://projectpluto.com/temp/2017u1.htm
2
The Astrophysical Journal Letters, 850:L38 (4pp), 2017 December 1 Trilling et al.
would reach the Earth in a few million years, and we would
therefore be moving through a cloud of ejected 1I-like objects.
However, the rest of the assumptions still apply, and the
expected value does not change significantly. A more
complicated model (perhaps not warranted, given this single
detection) could account for the total number of stars contained
in the Milky Way, integrated over its history, as even stars that
no longer exist could have contributed ejectoids to an
interstellar stream of material.
Finally, we note that the above calculation implies a typical
ejected mass of 20M⊕, but that need not imply that every
stellar or planetary system ejects mass, or that amount of
material. For example, while planet–planet scattering among
gas giant planets is likely to produce a pulse of ejected
planetesimals (Raymond et al. 2011; Marzari 2014), and while
systems with gas giants on stable orbits can eject planetesimals
on longer timescales (Raymond et al. 2011; Barclay
et al. 2017), systems without gas giants rarely eject
planetesimals because in that case escape velocity cannot
readily be achieved by planetesimals. Thus, if the fraction of
nearby stars with gas giants is (for example) 50%, then the
average mass ejected by those systems must be a factor of∼2
greater than our nominal value in order to produce the
necessary interstellar density of ejectoids.
4. Implications
The 520–950nm reflectance spectrum of 1I, albeit noisy,
indicates no absorption features and a red spectral slope
(Masiero 2017; Ye et al. 2017), making compositional
characterization difficult. However, we note that a red spectral
slope over this range is not unexpected and is characteristic of
many primitive objects in our solar system (Cruikshank
et al. 1998; Jewitt & Luu 1998; Bus & Binzel 2002;
Sheppard 2010; Carry et al. 2016). Whether this slope is
something intrinsic to the bulk properties of 1I or a consequence
of its surface being altered via energetic processing is unclear.
Given the presence of cosmic rays in the interstellar medium and
other forms of ionizing radiation that would have been present in
1I’s natal stellar environment, 1I’s red spectral slope is entirely
consistent with formation elsewhere and a long journey to our
solar system. This implies that the surface of 1I may have
different properties than its bulk material.
1I’s trajectory makes it very unlikely that it experienced a
gravitational encounter with any of the proposed as-yet unknown
planets in the outermost part of our solar system (Trujillo &
Sheppard 2014; Brown & Batygin 2016; Volk & Malhotra
2017). Another possibility is that 1I was a member of our solar
system’s Oort Cloud and was perturbed inbound onto an
unbound orbit by a passing star. We do not comment on these
scenarios; in this work, we have assumed that 1I is an interstellar
interloper that originated in a different plantary system.
The Large Synoptic Survey Telescope (LSST; Ivezić
et al. 2008) will commence its 10-year all-sky survey in
2022. One of the driving science cases for LSST is the
detection of moving objects. Most moving objects detected by
LSST will be “unremarkable” asteroids in the main belt, but
this very large and deep survey (20,000 deg2 surveyed to
rmagnitude 24.5 repeatedly over 10 years) naturally has the
possibility to discover unusual objects in all areas of
astrophysics. Several authors have studied the detectability of
interstellar interlopers in LSST data (Moro-Martín et al. 2009;
Cook et al. 2016; Engelhardt et al. 2017).
LSST will help constrain nearby planetary system formation
by measuring the number of 1I-like objects. LSST will be
sensitive to fainter and therefore smaller and/or more distant
objects, and is therefore likely to have a greater detection rate
than the current rate. The possibility of LSST detecting
interstellar comets increases by an order(s) of magnitude when
Figure 1. Characteristic ejection mass (colors and contours, in Earth masses) required to produce the observed rate of 1I-like objects as a function of the primary
unknown parameters in our analysis: 1I’s density (ρe) and radius (re). For nominal values of 2000kg m−3 and 100m, respectively, the required average ejection mass
per star in the solar neighborhood is 20M⊕ (black star), remarkably close to various calculations of the mass lost from our solar system during the era of planet
formation. Our upcoming observations of 1I with the Spitzer Space Telescope in late 2017 November should place a constraint on 1I’s radius.
3
The Astrophysical Journal Letters, 850:L38 (4pp), 2017 December 1 Trilling et al.
considering cometary outbursting (Cook et al. 2016), which
makes objects brighter, although 1I has shown no signs of
activity so far in its observational record.
As described above, with our current detection sensitivities,
the detection rate for 1I-like objects is0.2 yr−1. The LSST
detection limit will be around three magnitudes deeper than
Pan-STARRS’ typical limiting magnitude of V∼21.5; this
translates to a factor of three smaller in size. The only measured
size distribution in this size range in our solar system is for the
near-Earth object population; a factor of three in size
corresponds roughly to a factor of five in number of objects
(Trilling et al. 2017). Thus, the expected detection rate of
interstellar objects for LSST is around1 yr−1. The LSST
discovery rate of ejectoids will help us constrain the frequency
and properties of planetary system formation in our nearby
galaxy.
We thank an anonymous referee for a very prompt and
thoughtful review that has improved this paper. This research
has made use of data and services provided by the International
Astronomical Union’s Minor Planet Center. We have used
information from the RECONS program, retrieved from http://
www.recons.org. The discussions that led to this paper began at
an NAU Astrocookies gathering.
ORCID iDs
David E. Trilling https://orcid.org/0000-0003-4580-3790
Tyler Robinson https://orcid.org/0000-0002-3196-414X
Colin Orion Chandler https://orcid.org/0000-0001-7335-1715
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D. Observaciones del efecto YORP
El efecto YORP es una interacción no dinámica que afecta el compor-
tamiento de los asteroides, particularmente su efecto de rotación. La escala
de tiempo para este efecto es del orden de mega años, sin embargo estudios
recientes sugieren que el efecto puede observarse en una escala de tiempo
medible para nosotros y que además altera los asteroides de otras maneras,
como en su forma.
Sometí dos propuestas de observación para estudiar este efecto durante
el 2018, las cuales fueron aceptadas por la CATT del OAN. Este traba-
jo lo estoy haciendo junto con el Dr. Sergio Silva y otros colaboradores.
La generación de resultados está en curso por parte del Dr. Silva y sus
estudiantes.
E. Convocatoria CONACYT Ciencia de Frontera 2019
Junto con mis asesores, los Dres Mauricio Reyes, Joel Castro y un equi-
po de colaboradores elaboramos una propuesta para dicha convocatoria
orientada al estudio de NEOs. Proporcioné referencias para familiarizar a
los miembros del equipo ajenos al área, participé activamente en la discu-
sión de los objetivos del proyecto y contribuí a la escritura y edición de la
propuesta. Estamos en espera de los resultados.
F. Divulgación
Contribuí con un artículo para la Gaceta Ensenada, 33a edición (p.10
y 11). El artículo se basa en un proyecto en curso titulado ’Para qué te
sirve la astronomía?’ que estoy realizando con la estudiante de doctorado
Valeria Ramírez y la diseñadora Paulina Lazcano.
En agosto de 2018 participé en el Día de la juventud, dentro del marco
de la Feria de la Nación Navajo en Window Rock, Arizona. Junto con otros
voluntarios realizamos observaciones solares, hicimos brazaletes que brillan
85
tras iluminarse con la luz UV del Sol y explicamos un poco de mecánica
rotacional por medio de un juego.
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