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Appendix a Radial Velocity

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Appendix a Radial Velocity UNIVERSIDAD DE CHILE FACULTAD DE CIENCIAS FÍSICAS Y MATEMÁTICAS DEPARTAMENTO DE ASTRONOMÍA A HIGH RESOLUTION SPECTROSCOPIC SEARCH FOR THE THERMAL EMISSION OF THE EXTRASOLAR PLANET HD 217107 b TESIS PARA OPTAR AL GRADO DE MAGÍSTER EN CIENCIAS, MENCIÓN ASTRONOMÍA PATRICIO ERNESTO CUBILLOS VALLEJOS PROFESOR GUÍA: PATRICIO ROJO RÜBKE MIEMBROS DE LA COMISIÓN: María Teresa Ruiz González Diego Mardones Pérez John R. Barnes SANTIAGO DE CHILE MAYO 2011 Resumen En este trabajo hemos retomado y afinado un método de correlación para buscar directamente, en alta resolución, el espectro de planetas extrasolares sin tránsito. Nuestro objetivo principal es caracterizar las propiedades físicas de estos objetos, específicamente la inclinación de su órbita, su masa y la proporción de los flujos entre el planeta y su estrella. Esta técnica se vale del efecto Doppler causado por el movimiento orbital del planeta y la estrella en torno al centro de masa del sistema. Para observaciones lo suficientemente extensas, el espectro del planeta se va a desplazar con respecto al de la estrella lo suficiente para que sea detectable en observaciones espectroscópicas de alta resolución. Alineando y sumando los espectros de cada noche construimos un modelo del espectro estelar. Este es substraído a cada espectro, dejando un espectro residual compuesto por la emisión del planeta inmerso en ruido. Dada su baja intensidad, el espectro planetario no es directamente discernible del ruido. Por lo tanto, buscamos la emisión planetaria a través de una función de correlación entre nuestros espectros residuales y modelos de la emisión termal de la atmósfera del planeta. Evaluando para distintos valores de la inclinación de la órbita del modelo, obtenemos una curva de correlación. El valor de esta curva debe ser máximo cuando la inclinación coincida con la inclinación del sistema. Para calcular el valor de la proporción de los flujos entre el planeta y su estrella, recreamos observaciones inyectando espectros sintéticos del planeta con parámetros dados de inclinación y proporción de flujos. Luego, mediante un test de χ2 entre las curvas de correlación, estimamos los parámetros que mejor se ajustan a nuestro resultado. Presentamos resultados en el sistema planetario HD 217107, observado con el espectrógrafo de alta res- olución Phoenix, en una longitud de onda de 2.14 µm. Como resulatado, no logramos detectar el planeta con los datos disponibles, aunque determinamos límites superiores para su emisión termal, siendo menor a 5 10−3 veces la emisión de su estrella, con 3–σ de certeza. × Además, exploramos el escenario ideal de observación para proyectos futuros, y describimos una es- trategia óptima de observación y selección de candidatos que maximice las probabilidades de detección. Finalmente, simulando observaciones realistas para Phoenix, generamos datos sintéticos de observaciones de otros candidatos para demostrar las ventajas de usar nuestra estrategia de observación. Calculamos límites de detectabilidad para este instrumento en los planetas simulados. Nuestra conclusion es que si nos aproxi- mamos al límite de ruido de fotones, si es posible detectar planetas extrasolares con este método. Summary We have revisited and tuned a correlation method to directly search for the high-resolution signature of non-transiting extrasolar planets. The main objective of this work is to characterize the physical properties of non transiting extrasolar planets, aiming to obtain the inclination of the orbit, the mass of the planet, and the planet-to-star flux ratio. The technique is based in the out of phase Doppler-shift effect caused by the wobble of the star and planet around the center of mass of the system. For long enough observing runs, the spectral signals will shift with respect to each other, and thus will be detectable with high resolution spectroscopic observations. By aligning and adding the spectra of each night we construct a stellar template, which we subtract to the data, leaving a residual spectrum consisting of the planetary signal embedded in noise. The planetary spectrum is not readily detectable due to its much fainter signal. Therefore, we search for the planet calculating the correlation between the residual data and thermal emission models of the planet’s atmosphere, assigning different values to the inclination of the orbit of the models, expecting a peak in the correlation when we match the real value of the inclination. To asses the value of the planet-to-star flux ratio, we reproduced the observations using synthetic spectra, injecting a scaled and shifted planetary spectrum according to given flux ratios and inclinations. Then, we determine the best fitting parameters through a χ2 minimization between the data and the synthetic results. We present the results of this technique on the planetary system HD 217107, observed with the high resolution spectrograph Phoenix, at 2.14 µm. We could not detect the planet with our current data, but we present an upper limit to its thermal emission determined with a Monte Carlo Bootstrap method. With a confidence level of 3–σ we constrain the HD 217107 planet-to-star flux ratio to be no more than 5 10−3. × Furthermore, we explore the ideal observing scenario for future projects, and outline an optimized obser- vational and selection strategy to increase future probabilities of success by considering the best conditions to observe and the best candidates using this method. Finally, using realistic data sets for the Phoenix instrument we carried out simulations on other planet can- didates to demonstrate the improvements achieved when we use our optimal observing strategy. Detectability limit of the method using this instrument and the simulated planets are given. We conclude that with our same number of observations, it is possible to detect extrasolar planets with planet-to-star flux ratios of the order of 10−4 if we approach to the photon noise limit. Agradecimientos Primero quiero agradecer a Patricio Rojo, mi profesor guía, por toda su ayuda y compromiso con este tra- bajo. Tanto su ayuda, guía, y experiencia, como constante apoyo anímico y paciencia fueron fundamentales para llevar a cabo este trabajo, y de gran ayuda para mi futuro desarrollo como investigador. A mi familia le agradezco toda la confianza depositada en mi, dandome libre oportunidad de tomar mis propias decisiones, sin cuestionar, al momento de definir mi futuro. Gracias a ellos es que he tenido la oportunidad de llegar hasta donde estoy. También quiero agraceder especialmente a mi polola, Elisa Carrillo, quien estuvo constantemente apoyan- dome y acompañandome hacia el final del proceso, gracias por ser tan espectacular conmigo, por saber que decir para darme ánimos y poder terminar esta tesis. No podría estar mas feliz de tenerte a mi lado. Merecen mención también los profesores de la Universidad de Chile, tanto de Licenciatura como de Magíster, gracias por su disposición. De ellos adquirido un enorme conocimiento tanto en astronomía como en las ciencias relacionadas. El nivel en dominio de la materia y capacidad de enseñar de la mayoría de ellos ha sido de lo mas alto, siendo un ejemplo a seguir. Finalmente le agradezco a mis compañeros y amigos que he encotrado en mi recorrido a lo largo de estos años como estudiante de la Universidad de Chile, haciendo que los buenos momentos hayan sido realmente espectaculares y dando apoyo en los momentos mas críticos. Fue un agrado realmente compartir aquellos años de Licenciatura con Luis Gutiérrez, Eduardo Godoi, Ricardo Ordenes, entre muchos otros más. Tam- bién a todos mis compañeros en Cerro Calán, Cinthya Herrera, Sergio Hoyer, Maria Fernanda Durán, Matias Jones, Viviana Guzmán, Felipe Murgas, Andrés Guzmán, Matias Vidal, entre tantos otros, han sido la mejor compañía tanto como para pasar un buen momento como de ayuda en mis cursos y trabajo. Contents 1 Introduction 1 2 The Planetary System HD 217107 3 2.1 BackgroundInformation ............................... ..... 3 2.2 Radial Velocity . 4 2.3 Flux Estimate . 7 3 Observations and Data Reduction 11 3.1 TheData........................................... 11 3.2 Reduction.......................................... 12 3.3 Wavelength calibration . 14 4 Data Analysis and Results 17 4.1 Stellar Light Removal . 17 4.2 Planet’s Atmospheric Model . 20 4.3 Correlation ......................................... 23 4.4 DataResults......................................... 25 4.5 Planet-to-Star Flux Ratio Fitting . 25 4.6 False Alarm Probability . 29 4.7 Data Results Discussion . 29 5 The Optimal Acquisition of Data 30 5.1 TargetSelection..................................... 30 5.2 Optimal Observing Strategy . 31 I 5.3 HD 179949 b Simulation . 33 5.4 Tau Boo b and HD 73256 b Simulations . 38 6 Discussion and Conclusions 42 Appendices 44 A Radial velocity 45 B Error Propagation 47 B.1 Equilibrium Temperature . 47 B.2 DataReduction ....................................... 47 C Observing Log of HD 179949 50 II List of Tables 2.1 HD217107Parameters ................................. .... 3 3.1 Gemini South Telescope Characteristics . ...... 11 3.2 Observinglog....................................... 12 3.3 InfraredLinesCatalog ................................ ..... 14 4.1 Theoretical Atmospheric Models. ..... 22 5.1 Favorable targets for Gemini South . ..... 31 5.2 Parameters ......................................... 33 C.1 ObservationLog ..................................... 50 III List of Figures 2.1 Detection Methods. ... 4 2.2 HD 217107’s radial velocity . ..... 6 2.3 HD 217107’s
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