The limb darkening via transit modeling and bayesian inference

Space missions to search for exoplanets by photometry have been improved in terms of precision and require a more accurate and efficient treatment of limb darkening coefficients, and this seems to be a bottleneck in modeling the transits of discovered planets. Limb darkening coefficients often have subtle effects on light curves and are therefore often degenerate with other modeling parameters. In this work, we study the K0-type star KIC 5357901 (Kepler-425), with effective temperature of $5170K$, from light curve obtained by NASA’s Kepler satellite. We drove photometric modeling of the Kepler-425b exoplanet and we applied a Bayesian inference method to obtain a credible interval based on a Monte Carlo Markov chain (MCMC) algorithm. We obtained the Kepler-425 limb darkening coefficients values of $u_1={0.559}_{-0.070}^{+0.071}$ and $u_2={0.104}_{-0.117}^{+0.120}$ according to the quadratic law. These determinations are consistent with values obtained previously with different parameterization. Our result based on a smaller number of iterations per chain presents similar accuracy, of about ${10}^{-2}$ for u₁. In addition, we explored in a more focused way the region of the parameter of interest.

Keywords:
Exoplanets; Limb Darkening; Planetary Transit Method; Photometry