Finite Star Factors with Stellar Limb Darkening for Optically Thin Dipole Scattering in Circumstellar Envelopes

A calculation for the finite star correction factors with stellar limb darkening is presented. The application is for dipole scattering, such as free electrons or Rayleigh scattering, in the context of optically thin envelopes that scatter unpolarized starlight. Two previous calculations that presented results with limb darkening employed the wrong geometrical angle. However, the previous approaches did achieve the correct limiting behavior, close to the star and at great distance. The new calculations for finite star correction factors of total scattered light and of depolarization deviate modestly from prior results. Overall, the depolarization factor remains slightly more depolarizing at the crucial distances of a few tenths of a stellar radius above the atmosphere.