Integrating polarized light over a planetary disk applied to starlight reflected by extrasolar planets

We present an efficient numerical method for integrating planetary radiation over a planetary disk, which is especially interesting for simulating signals of extrasolar planets. Our integration method is applicable to calculating the full flux vector of the disk-integrated planetary radiation, i.e. not only its observed flux ( irradiance), but also its state of polarization ( linear and circular). Including polarization is important for simulations of the light reflected by a planet, in particular, because this will generally be polarized. Our integration method is based on the expansion of the radiation field of a spherical, horizontally homogeneous planet into generalized spherical functions. With the expansion coefficients, the flux vector of the disk-integrated, reflected starlight can be obtained rapidly for arbitrary planetary phase angles. We describe the theory behind the disk-integration algorithm and results of accuracy tests. In addition, we give some illustrative examples of the application of the algorithm to extrasolar planets.