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Implementing the Gaia Astrometric Solution

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Implementing the Gaia Astrometric Solution Implementing the Gaia Astrometric Solution William O’Mullane Aquesta tesi doctoral està subjecta a la llicència Reconeixement 3.0. Espanya de Creative Commons. Esta tesis doctoral está sujeta a la licencia Reconocimiento 3.0. España de Creative Commons. This doctoral thesis is licensed under the Creative Commons Attribution 3.0. Spain License. Implementing the Gaia Astrometric Solution prepared by: William O’Mullane supervised by: Xavier Luri, Lennart Lindegren reference: GAIA-C3-CP-ESAC-WOM-007-02 issue: 02 revision: 0 date: 2012-05-15 status: Issued Abstract: An in depth look at the Astrometric Global Iterative Solution (AGIS). This document details the algorithms in AGIS and examines them from several per- spectives. It is argued that they are adequate and probably the best, if not only, approach to making an astrometric solution for Gaia data. Translation of the system of equations to an actual computer infrastructure is a non trivial task. This is the area the author has most experience in and is dealt with in some detail forming the main original content of this thesis. Some initial results us- ing simulation data are presented to demonstrate how the system operates and removes specific effects from the data set within an acceptable time frame. For my pal who ran around the world at my side. My wife, my support, my love Ranpal. Resumen de la tesis: Implementacion´ de AGIS Esta tesis presenta el marco numerico´ y computacional para la solucion´ astrometrica´ Gaia. Tambien´ cubre las consideraciones astrof´ısicas relativas a la solucion´ y los aspec- tos relacionados con la gestion´ de la implementacion´ de un sistema tan complejo. Cada uno de los siguientes apartados es un resumen del correspondiente cap´ıtulo de la tesis. La mision´ Gaia y su procesamiento de datos La astrometr´ıa es uno de los objetivos mas´ antiguos de la ciencia. La medicion´ de las posiciones y subsecuentes movimientos de los cuerpos celestes nos ha ocupado durante milenios. El primer catalogo´ se lo debemos a Hiparco de Nicea (∼ 190 aC - 120 aC) cuyo nombre, por supuesto, se honra en la mision´ Hipparcos (AEE, 1997). Gaia con- tinua´ esta antigua tradicion´ utilizando las tecnicas´ mas´ modernas. En 2013, la AEE lanzara´ el satelite´ Gaia, de unas dos toneladas de peso, en un cohete Soyuz-Fregat. Consta de dos instrumentos astrometricos,´ ademas´ de instrumental fo- tometrico´ y de velocidad radial que le permitiran´ crear un mapa del espacio fasico´ de nuestra galaxia. Se podr´ıa trivializar Gaia afirmando que no es mas´ que una segunda parte de Hipparcos, pero en realidad es mucho mas´ que eso. Hipparcos observo´ con pre- cision´ ciento cuarenta mil fuentes, mientras que Gaia observara´ mas´ de mil millones de fuentes galacticas´ y extragalacticas.´ La exactitud que se espera de Gaia tampoco tiene precedentes: en el rango de microarcosegundos, observara´ fuentes menos luminosas que Hipparcos hasta una magnitud de G=20 (en la que G es la banda pasante del instrumento astrometrico).´ La inclusion´ del espectrografo´ de velocidades radiales subsana una defi- ciencia de la mision´ Hipparcos y permitira´ calcular las velocidades tridimensionales de los objetos. Los potenciales beneficios de Gaia para la ciencia son casi innumerables, sin embargo, la capacidad de procesamiento de datos necesaria para producir el catalogo´ Gaia a partir del que se extraeran´ estos beneficios cient´ıficos no es trivial. Este docu- mento se centra solo´ en la solucion´ astrometrica,´ aunque en las areas´ espectrografica´ y fotometrica´ seran´ necesarias labores de procesamiento igualmente complejas. Gaia se ubicara´ en una orbita´ de tipo Lissajous alrededor del punto de Lagrange L2 en el sistema Sol-Tierra, donde orbitara´ durante al menos cinco anos,˜ observando todo el iii cielo y llevando a cabo un censo de mil millones de fuentes, cada una de las cuales sera´ observada unas ochenta veces en promedio. En la figura 1 la cobertura de cielo estimada para los telescopios astrometricos´ de Gaia, mostrando un m´ınimo de cincuenta transitos´ para la mayor parte del cielo. En el contexto de Gaia, transito´ se refiere a cada vez que una fuente cruza el plano focal. Figure 1: Durante su vida operativa, Gaia escaneara´ el cielo continuamente, aproxi- madamente en grandes c´ırculos, siguiendo una ley de escaneo predefinida y elegida cuidadosamente. Las caracter´ısticas de esta ley, en combinacion´ con la dimension´ AC (across-scan) de los campos astrometricos,´ produce el patron´ que aparece en la ima- gen para a distribucion´ del numero´ predicho de transitos´ en el cielo en coordenadas ecl´ıpticas. (Imagen J. De Bruijne) El autor se ha interesado desde hace mucho tiempo por la solucion´ global de proce- samiento (O’Mullane & Lindegren, 1999) y ha contribuido con una seccion´ al libro blanco de Gaia sobre el tema (ESA-SCI(2000)4). El sistema de procesamiento de Gaia difiere del de otras misiones astronomicas´ por el propio diseno˜ de la mision;´ es decir, porque proporciona astrometr´ıa global absoluta. Para conseguir la exactitud en microar- cosegundos de arco necesaria para obtener la recompensa cient´ıfica que se esboza en (ESA-SCI(2000)4) es necesario llevar a cabo un procesamiento de los datos bastante complicado, tal y como se describe en el cap´ıtulo 2. Principios de la astrometr´ıa Gaia El catalogo´ Hipparcos (ESA, 1997, Volumen 3 Cap´ıtulo 23) formula el principio gene- ral de una mision´ de astrometr´ıa global de manera sucinta en el siguiente problema de minimizacion:´ iv William O’Mullane min obs calc a,nkg − g (a,n)kM (1) Aqu´ı a es el vector de incognitas´ que describe el movimiento baricentrico´ de una es- trella. Estos parametros´ se extraen a partir de un numero´ de observaciones de una es- trella. Las observaciones de una estrella se expresan en las coordenadas del detector denominadas G y H. Por lo tanto, la observacion´ en el tiempo tk se representa mediante 0 obs el vector de mediciones gk = (Gk,Hk) y sus estad´ısticas asociadas. g representa el vector de todas las mediciones y gCALC representa el vector de coordenadas de detector calculadas a partir de los parametros´ astrometricos.´ n es un vector de los parametros´ 1 que no resultan de interes´ para el problema astronomico,´ pero necesarios para dar forma a los datos de manera realista. La norma se calcula en una metrica´ M definida por las estad´ısticas de los datos, lo que se denomina comunmente´ ponderacion´ de errores. En el cap´ıtulo 2 se analizan los detalles matematicos´ de la solucion´ iterativa por bloques para este problema en el caso de Gaia. Implementacion´ de AGIS La implementacion´ eficaz en algun´ tipo de codigo´ de la solucion´ iterativa por bloques resulta todo un reto y durante el procesamiento de datos de Hipparcos se abandono´ un primer intento de alcanzar dicha solucion.´ En (O’Mullane & Lindegren, 1999). se presento´ una prueba basica´ del concepto, mas´ bien una pseudoimplementacion,´ en la que se utilizaron de nuevo los datos y el sistema de gestion´ de base de datos de Hipparcos. Se realizo´ un gran esfuerzo para adaptarlo a las dimensiones de Gaia hasta que el grupo ESAC (O’Mullane et al., 2006) lo consiguio.´ Este ultimo´ marco de trabajo es el que se presenta en el cap´ıtulo 3. AGIS no es sino una de las muchas partes que componen el sistema de procesamiento de datos de Gaia, sin duda una parte fundamental, pero tan solo una parte. En la Fig. 2 se presenta una descripcion´ general aunque simplificada de AGIS. Cada uno de los componentes de la imagen puede ejecutarse en cualquier maquina´ independiente, salvo el Attitude Update Server que requiere un poco mas´ de memoria. El DataTrain, como mediador, se puede observar en el centro del cuadro de la izquierda. Los algoritmos y compiladores se describen en la seccion´ 5 del cap´ıtulo 3. El sistema AGIS se despliega en una maquina´ multiprocesador local dedicada a Gaia. El marco utiliza funciones de lenguaje Java como RMI (Remote Method Invocation, Invocacion´ Remota de Metodos).´ Por supuesto, el acceso a los datos es uno de los principales problemas para AGIS y en la seccion´ 2 del cap´ıtulo 3 se analiza con bastante detalle. Se trata de un sistema de software unico,´ disenado˜ y optimizado para realizar la reduccion´ de datos astrometricos´ de Gaia y constituye la principal contribucion´ original del autor. 1 Llamados parametros´ de perturbacion.´ Implementing the Gaia Astrometric Solution v Convergence Data Source Monitor Servers Collector Data Servers Run Source Whiteboard Manager Updater Global Up. Server Source Up. Manager Data Train Data Global. Up. Servers Client Object Object Calib. Up. Factory Calib. Up. Server Client Attitude Up. GaiaTable Store Client Data Servers Attitude Up. Server DB distribution layer Algorithm Processes Database GIS DB Figure 2: Este diagrama simplificado pretende mostrar una perspectiva de la logica´ general de AGIS. AGIS ejecuta el mismo numero´ de procesos en muchas maquinas,´ que no se muestran aqu´ı. El cuadro grande de la izquierda representa el tren de datos, aunque puede haber un gran numero´ de ellos ejecutandose.´ A la derecha se encuentran los servidores de actualizacion,´ de los que puede haber solo uno ejecutandose´ en todo el sistema. Todos estos procesos estan´ basados en una base de datos. vi William O’Mullane Consideraciones astrof´ısicas En el cap´ıtulo 4 se tratan algunos de los fenomenos´ f´ısicos y astrof´ısicos sobre los que AGIS debe rendir cuenta. Lo que aqu´ı se presenta, por supuesto, es solo un subconjunto de esos fenomenos.´ En efecto, se trata de un amplio rango de efectos cuya descripcion´ en el catalogo´ final ocupara,´ sin duda, varios volumenes.´ El propio AGIS solo se ocupa de una parte de todos los fenomenos´ conocidos que tienen efecto en el ambito´ de µas.
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