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Transiting Exoplanets: Characterisation in the Presence of Stellar Activity

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—————————————————— Transiting exoplanets: characterisation in the presence of stellar activity Aude Ekundayo Pauline ALAPINI ODUNLADE —————————————————— Submitted by Mrs Aude Ekundayo Pauline Alapini Odunlade, to the University of Exeter as a thesis for the degree of Doctor of Philosophy in Physics, March 2010. This thesis is available for Library use on the understanding that it is copyright material and that no quo- tation from the thesis may be published without proper acknowledgement. I certify that all material in this thesis which is not my own work has been identified and that no material has previously been submitted and approved for the award of a degree by this or any other University. Mrs Aude E. P. Alapini Odunlade March 2010 This thesis was supervised by Dr. Suzanne Aigrain – University of Exeter, University of Oxford Abstract The combined observations of a planet’s transits and the radial velocity variations of its host star allow the determination of the planet’s orbital parameters, and most inter- estingly of its radius and mass, and hence its mean density. Observed densities provide important constraints to planet structure and evolution models. The uncertainties on the parameters of large exoplanets mainly arise from those on stellar masses and radii. For small exoplanets, the treatment of stellar variability limits the accuracy on the de- rived parameters. The goal of this PhD thesis was to reduce these sources of uncertainty by developing new techniques for stellar variability filtering and for the determination of stellar temperatures, and by robustly fitting the transits taking into account external constraints on the planet’s host star. To this end, I developed the Iterative Reconstruction Filter (IRF), a new post-detection stellar variability filter. By exploiting the prior knowledge of the planet’s orbital period, it simultaneously estimates the transit signal and the stellar variability signal, using a com- bination of moving average and median filters. The IRF was tested on simulated CoRoT light curves, where it significantly improved the estimate of the transit signal, particu- lary in the case of light curves with strong stellar variability. It was then applied to the light curves of the first seven planets discovered by CoRoT, a space mission designed to search for planetary transits, to obtain refined estimates of their parameters. As the IRF preserves all signal at the planet’s orbital period, t can also be used to search for secondary eclipses and orbital phase variations for the most promising cases. This en- abled the detection of the secondary eclipses of CoRoT-1b and CoRoT-2b in the white (300–1000 nm) CoRoT bandpass, as well as a marginal detection of CoRoT-1b’s orbital phase variations. The wide optical bandpass of CoRoT limits the distinction between thermal emission and reflected light contributions to the secondary eclipse. I developed a method to derive precise stellar relative temperatures using equiv- alent width ratios and applied it to the host stars of the first eight CoRoT planets. For stars with temperature within the calibrated range, the derived temperatures are con- sistent with the literature, but have smaller formal uncertainties. I then used a Markov Chain Monte Carlo technique to explore the correlations between planet parameters derived from transits, and the impact of external constraints (e.g. the spectroscopically derived stellar temperature, which is linked to the stellar density). Globally, this PhD thesis highlights, and in part addresses, the complexity of perform- ing detailed characterisation of transit light curves. Many low amplitude effects must be taken into account: residual stellar activity and systematics, stellar limb darkening, and the interplay of all available constraints on transit fitting. Several promising areas for further improvements and applications were identified. Current and future high precision photometry missions will discover increasing numbers of small planets around relatively active stars, and the IRF is expected to be useful in characterising them. Contents 1 Introduction 13 1.1 A brief history on the search for exoplanets . 13 1.2 The detection of exoplanets . 15 1.2.1 The methods . 15 1.2.2 Properties of the exoplanets discovered to date . 17 1.3 Characterising exoplanets . 20 1.3.1 Analytic equations to derive the planet parameters from the transit light curve . 20 1.3.2 Analytic equations for the radial velocity variations of a star due to an orbiting planet . 28 1.3.3 Planetary atmospheres . 30 1.4 Challenges for the detection and characterisation of exoplanets . 32 1.4.1 Stellar systems mimicking planetary transits . 32 1.4.2 Systematics . 33 1.4.3 Stellar activity . 33 1.4.4 Uncertainties on the planet parameters . 35 1.5 Instruments for the detection and characterisation of transiting exoplanets 37 1.5.1 Current . 37 1.5.2 Future of the transiting exoplanet search and characterisation . 39 1.6 This thesis . 40 1.6.1 Motivations . 40 1.6.2 Structure . 40 2 Transit signal reconstruction 42 2.1 Motivation . 42 2.2 Data set . 43 2.2.1 BT2 light curves . 43 2.2.2 Reference light curve sample . 44 2.3 Quantifying transit deformation with the Non-linear Iterative Filter . 45 2.3.1 Definition of the NIF . 46 2.3.2 NIF quantitative impact on transit parameters . 47 3 CONTENTS 4 2.4 A new stellar variability filter: the Iterative Reconstruction Filter . 49 2.4.1 Definition of the IRF . 49 2.4.2 Comparison with the Trend Filtering Algorithm (TFA) . 52 2.4.3 Performance of the IRF on the BT2 transits . 52 2.5 Discussion on the IRF performance . 54 2.5.1 Star-planet parameters . 54 2.5.2 Application to orbital signal reconstruction . 57 2.5.3 Potential application to transit detection . 57 2.6 Conclusion . 58 2.7 Appendix . 60 2.7.1 Best-fit parameters to BT2 transits . 60 2.7.2 Full BT2 light curve sample . 60 3 IRF applied to the transit of CoRoT planets 67 3.1 Description of the CoRoT data . 67 3.1.1 Instrument . 67 3.1.2 Light curve generation . 68 3.1.3 Additional light curve pre-processing . 70 3.1.4 Planetary transit detection and confirmation . 71 3.2 Primary transit parameters with the IRF-filtering . 71 3.2.1 Method . 71 3.2.2 CoRoT-1b . 75 3.2.3 CoRoT-2b . 77 3.2.4 CoRoT-3b . 79 3.2.5 CoRoT-4b . 81 3.2.6 CoRoT-5b . 83 3.2.7 CoRoT-6b . 85 3.2.8 CoRoT-7b . 87 3.2.9 Discussion . 89 3.3 IRF performance on CoRoT space data . 90 3.3.1 Limitations . 90 3.3.2 Future work . 90 4 Detecting photons from the CoRoT planets 92 4.1 Theory of the secondary eclipse and orbital phase variations . 93 4.1.1 Planet’s emission . 93 4.1.2 Secondary eclipse . 94 4.1.3 Planet’s equilibrium temperature . 94 4.1.4 Variations of secondary eclipse’s depth with Rp=R?, a=R?, AB and f 96 4.1.5 Expected depth and phase for the secondary eclipse of CoRoT planets . 100 CONTENTS 5 4.2 Method . 102 4.2.1 The IRF as a reconstruction tool . 102 4.2.2 Light curve processing . 103 4.2.3 Search for secondary eclipses and orbital phase variations . 104 4.2.4 Optimising the parameters of the IRF . 109 4.3 Application to CoRoT planets . 113 4.3.1 CoRoT-1b . 113 4.3.2 CoRoT-2b . 119 4.4 Discussion . 123 4.4.1 Comparison with the literature . 123 4.4.2 Performance of the IRF . 124 4.4.3 Limitations . 125 4.4.4 Future work . 126 4.5 Conclusions . 127 5 Stellar temperatures using equivalent width line-ratios 128 5.1 Teff calibration of equivalent width line-ratios . 129 5.1.1 Choosing the line ratios . 130 5.1.2 Calibrating the line ratios with temperature . 131 5.1.3 Using the calibration to derive stellar temperatures . 134 5.1.4 Testing the calibration . 136 5.1.5 Discussion . 139 5.2 Comparison to the calibration of Sousa et al. (2009) . 141 5.3 Applying the calibration to the host stars of CoRoT planets . 143 5.3.1 Spectra and equivalent width measurements . 143 5.3.2 Deriving the effective temperatures . 144 5.3.3 Discussion . 146 5.4 Conclusion . 147 5.5 Appendix . 148 5.5.1 Line list . 148 5.5.2 List of the calibration stars . 149 5.5.3 Plot of the line ratio and their calibration . 150 5.5.4 List of the line ratios and their calibration coefficients . 157 6 Joint modelling of transit and stellar temperature using an MCMC approach 161 6.1 Markov Chain Monte Carlo . 162 6.1.1 MCMC implementation . ..
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