Wavelength-dependent limb darkeningin the analysis oftransit spectroscopy of exoplanets

Abstract: Limb darkening, an optical effect characteristic of stars, where the limb (edge) seemsto be darker than the centre of the stellar body; plays an important role in our under-standing of exoplanetary transits, as it is fundamental for developing light curve modelsthat can help to undercover extrasolar companions. To recover atmospheric featuresfrom exoplanets, a principal component analysis method is typically used. The Aronsonmethod proposes an alternative, less model-dependent, approach to uncover exoplanetaryspectrum from the stellar and the telluric spectra. The limb darkening coefficient, ratiobetween the intensity in the limb and any other point of the star, can be approximatedin several ways. In this project, we present an algorithm for the analytical calculationof the four polynomial coefficients of a non-linear approximation of the limb darkeningcoefficient. These coefficients are obtained from a 1D MARCS model atmosphere of theM-dwarf star LTT1445A. The analytical calculation is coded in Python and consists oftwo parts, reading the data and using linear algebra for the calculation of the non-linearcoefficients. As a result, we obtain the limb darkening coefficient for near infra-red wave-lengths. Polynomial regressions, of order from 0 to 4, have been fitted. The coefficientsdid not show a clear linear tendency. Outliers are detected and co-related to the presenceof spectral absorption lines derived from the synthetic spectrum. The results will be usedto uncover planetary atmospheres in extrasolar systems.1