Radial-velocity searches for planets around active stars : doctoral thesis accepted by the University of St Andrews, UK

This thesis develops new and powerful methods for identifying planetary signals in the presence of ℓ́ℓnoiseℓ́ℓ generated by stellar activity, and explores the physical origin of stellar intrinsic variability, using unique observations of the Sun seen as a star. In particular, it establishes that the intrinsic stellar radial-velocity variations mainly arise from suppression of photospheric convection by magnetic fields. With the advent of powerful telescopes and instruments we are now on the verge of discovering real Earth twins in orbit around other stars. The intrinsic variability of the host stars themselves, however, currently remains the main obstacle to determining the masses of such small planets. The methods developed here combine Gaussian-process regression for modeling the correlated signals arising from evolving active regions on a rotating star, and Bayesian model selection methods for distinguishing genuine planetary signals from false positives produced by stellar magnetic activity. The findings of this thesis represent a significant step towards determining the masses of potentially habitable planets orbiting Sun-like stars Supervisor’s Foreword 7 Preface 9 Acknowledgements 11 Contents 13 1 Introduction: The Hunt for Extra-Solar Planets 16 References 24 2 Stellar Activity as a Source of Radial-Velocity Variability 27 2.1 Magnetic Activity and Its Manifestations 27 2.1.1 Minutes: Oscillations 29 2.1.2 Minutes: Flares and Coronal Mass Ejections 30 2.1.3 Minutes to Hours: Granulation 30 2.1.4 Days and Longer: Gravitational Redshift 31 2.1.5 Stellar Rotation Period: Spots, Faculae and Plage Regions 32 2.1.6 Decades: Magnetic Cycles 37 2.1.7 Timescales: Summary 39 2.2 Existing Treatments for Activity-Induced RV Variations 39 2.2.1 Spectroscopic Activity Indicators 40 2.2.2 Nightly Offsets Method 42 2.2.3 Harmonic Decomposition 44 2.2.4 Pre-whitening 45 2.2.5 The FF' Method 45 2.2.6 Existing Methods: Summary 46 2.3 RV Target Selection Based on Photometric Variability 47 2.3.1 Preliminary Target Selection Criteria 47 2.3.2 Generalised Lomb--Scargle Periodograms and Autocorrelation Functions 48 2.3.3 Selection Criteria for ``Magnetically Manageable'' Stars 54 2.4 Concluding Note: From Photometric to Radial-Velocity Variations 55 References 55 3 A Toolkit to Detect Planets Around Active Stars 59 3.1 Gaussian Processes 59 3.1.1 Definition 60 3.1.2 Covariance Matrix K 64 3.1.3 Covariance Function k (t, t') 67 3.1.4 Temporal Structure and Covariance 68 3.1.5 Gaussian Processes for Stellar Activity Signals 69 3.1.6 Determining the Hyperparameters θj 70 3.1.7 Constructing the Covariance Matrix K 70 3.1.8 Fitting Existing Data and Making Predictions 71 3.1.9 A Word of Caution 72 3.1.10 Useful References 72 3.2 Monte Carlo Markov Chain (MCMC) 73 3.2.1 Modelling Planets 73 3.2.2 Modelling Stellar Activity 74 3.2.3 Total RV Model 76 3.2.4 Choice of Priors 76 3.2.5 Fitting Procedure 78 3.2.6 Care Instructions 79 3.3 Model Selection with Bayesian Inference 80 3.3.1 Bayes' Factor 81 3.3.2 Posterior Ordinate 81 3.3.3 Marginal Likelihood 82 References 82 4 Application to Observations of Planet-Hosting Stars 84 4.1 CoRoT-7 85 4.1.1 History of the System 85 4.1.2 Observations 88 4.1.3 Preliminary Periodogram Analysis 90 4.1.4 MCMC Analysis 91 4.1.5 Results and Discussion 93 4.1.6 Summary 101 4.2 Kepler-78 102 4.2.1 History of the System 102 4.2.2 Observations 105 4.2.3 MCMC Analysis 106 4.2.4 Results and Discussion 108 4.2.5 Summary 111 4.3 Kepler-10 111 4.3.1 History of the System 111 4.3.2 Observations 113 4.3.3 MCMC Analysis 115 4.3.4 Results and Discussion 116 4.3.5 Summary 120 4.4 Summary and Future Plans 121 4.4.1 Determining the Bulk Densities of Transiting Exoplanets 121 4.4.2 Assessing the Reliability of the Gaussian Process Framework for Exoplanet Mass Determinations 121 4.4.3 Concluding Note 123 References 124 5 An Exploration into the Radial-Velocity Variability of the Sun 125 5.1 Previous Studies on the Intrinsic RV Variability of the Sun 126 5.2 HARPS Observations of Sunlight Scattered Off Vesta 127 5.2.1 HARPS Spectra 127 5.2.2 Solar Rest Frame 128 5.2.3 Relativistic Doppler Effects 128 5.2.4 Sources of Intra-Night RV Variations 130 5.2.5 Time Lag Between Vesta and SDO Observations 132 5.3 Pixel Statistics from SDO/HMI Images 132 5.3.1 Spacecraft Motion 133 5.3.2 Solar Rotation 133 5.3.3 Flattened Continuum Intensity 134 5.3.4 Unsigned Longitudinal Magnetic Field Strength 134 5.3.5 Surface Markers of Magnetic Activity 135 5.4 Reproducing the RV Variations of the Sun 140 5.4.1 Total RV Model 140 5.4.2 Relative Importance of Suppression of Convective Blueshift and Sunspot Flux Deficit 141 5.4.3 Zero Point of HARPS 142 5.5 Towards Better Proxies for RV Observations 142 5.5.1 Disc-Averaged Observed Magnetic Flux |obs| 142 5.5.2 Correlations Between RV and Activity Indicators 143 5.6 Summary 144 References 145 6 Conclusion: Next Steps and Aims for the Future 147 References 150 Index 151 This thesis develops new and powerful methods for identifying planetary signals in the presence of ĺlnoiseĺl generated by stellar activity, and explores the physical origin of stellar intrinsic variability, using unique observations of the Sun seen as a star. In particular, it establishes that the intrinsic stellar radial-velocity variations mainly arise from suppression of photospheric convection by magnetic fields. With the advent of powerful telescopes and instruments we are now on the verge of discovering real Earth twins in orbit around other stars. The intrinsic variability of the host stars themselves, however, currently remains the main obstacle to determining the masses of such small planets. The methods developed here combine Gaussian-process regression for modeling the correlated signals arising from evolving active regions on a rotating star, and Bayesian model selection methods for distinguishing genuine planetary signals from false positives produced by stellar magnetic activity. The findings of this thesis represent a significant step towards determining the masses of potentially habitable planets orbiting Sun-like stars Front Matter....Pages i-xv Introduction: The Hunt for Extra-Solar Planets....Pages 1-11 Stellar Activity as a Source of Radial-Velocity Variability....Pages 13-44 A Toolkit to Detect Planets Around Active Stars....Pages 45-69 Application to Observations of Planet-Hosting Stars....Pages 71-111 An Exploration into the Radial-Velocity Variability of the Sun....Pages 113-134 Conclusion: Next Steps and Aims for the Future....Pages 135-138 Back Matter....Pages 139-140