Statistical methods using hydrodynamic simulations of stellar atmospheres for detecting exoplanets in radial velocity data

When the noise affecting time series is colored with unknown statistics, a difficulty for periodic signal detection is to control the true significance level at which the detection tests are conducted. This thesis investigates the possibility of using training datasets of the noise to improve this control. Specifically, for the case of regularly sampled observations, we analyze the performances of various detectors applied to periodograms standardized using the noise training datasets. Emphasis is put on sparse detection in the Fourier domain and on the limitation posed by the necessary finite size of the training sets available in practice. We study the resulting false alarm and detection rates and show that the proposed standardization leads, in some cases, to powerful constant false alarm rate tests. Although analytical results are derived in an asymptotic regime, numerical results show that the theory accurately describes the tests? behavior for moderately large sample sizes. In the case of irregularly sampled observations, while analytical expressions for the false alarm rate are out of reach, we show that it is possible to combine the proposed periodogram standardization and bootstrap techniques to consistently estimate the false alarm rate. We also show that the procedure can be improved by using generalized extreme value distributions. Throughout the study, we focus on the particular problem of extrasolar planet detection in radial velocity (RV) data. With the instrumental precision of the recent spectrographs, the main barrier to detect Earth-mass planets comes from the host star activity: e.g. spots and plages, convection, and stellar oscillations. This activity affects the RV as a colored noise, which can mimic or hide the planet’s signatures. While external chromospheric indicators can (partially)deal to avoid the (quasi-) periodic noise source due to the magnetic activity (e.g. the rotation-ally modulated starspots this thesis focuses on the contribution of convective process, which induced a permanent stellar ?jitter? leading to correlated RV variations with magnitude at the level of the smallest planet signatures. In parallel, reliable (ab initio) hydrodynamic simulations of the stellar surface convection activity have recently been developed during the last decade and we aim to prove that they can statistically improve the control of the significance assigned to the detection of exoplanets. In this spirit, a comparison of RV solar observations and simulations will be presented at the end of this thesis to confirm the reliability of these simulations. In this context, the proposed periodogram standardization and detection tests investigated in the theoretical part of the thesis open several interesting applications in the field of exoplanet detection in RV data.