Monte Carlo radiative-transfer solutions for cool stellar photospheres

Numerical evaluations of the exact solution for the uniformly emitting, Rayleigh scattering, conservative, plane-parallel, finite atmosphere are presented for optical thicknesses i = 0.20, 1.00, and 2.00, and are used to evaluate the precision of solutions made with the adjoint Monte Carlo method. The inadequacy of the single-scattering approximation is shown for optical thicknesses T1 0.2. This method is employed to calculate the limb darkening and polarization produced by Rayleigh scattering in an M-star model atmosphere, at four wavelengths. The result of Chandrasekhar lies between those obtained for AA4560 and 5520. Subject headings: atmospheres, stellar - late-type stars - polarization - radiative transfer