Modelling Light and Velocity Curves of Exoplanet Hosts
Research in extrasolar-planet science is data-driven. With the advent of radial-velocity instruments like HARPS and HARPS-N, and transit space missions like Kepler, our ability to discover and characterise extrasolar planets is no longer limited by instrumental precision but by our ability to model the data accurately. This chapter presents the models that describe radial-velocity measurements and transit light curves. I begin by deriving the solution of the two-body problem and from there, the equations describing the radial velocity of a planet-host star and the distance between star and planet centres, necessary to model transit light curves. Stochastic models are then presented and I delineate how they are used to model complex physical phenomena affecting the exoplanet data sets, such as stellar activity. Finally, I give a brief overview of the processes of Bayesian inference, focussing on the construction of likelihood functions and prior probability distributions. In particular, I describe different methods to specify ignorance priors.
The author thanks the organisers of the IVth Azores International Advanced School in Space Sciences and acknowledges the participants—both lecturers and students—for the quality of their work. The preparation of this lecture was carried out within the frame of the Swiss National Centre for Competence in Research “PlanetS” funded by the Swiss National Science Foundation (SNSF). The author acknowledges support by the Argentinian National Council for Research and Technology (CONICET).
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