Polarized radiative transfer: two Monte Carlo codes versus integral equations

While modelling astronomical objects in general, and dust envelopes of cool stars in particular, only numerical solutions of radiative transfer equation (RTE) can give correct physical pictures of real, asymmetric objects. Naturally Monte Carlo method is the most frequently used technique for radiative transfer modelling, and there exist many various Monte Carlo radiative transfer codes within the astronomical community.

We created our own Monte Carlo code for polarized radiative transfer modelling. Besides, we created computer code solving exact Fredholm integral equations for polarized source functions in homogeneous sphere with Rayleigh scattering and concentric spherical star inside it. We compared the modelled image of outcoming radiation (intensity, polarization degree and position angle) for three codes: our Monte Carlo code, RADMC3D by C.Dullemond et al., and the code based on integral equations.

For optical radius of the scattering sphere being up to about 10, all three codes give similar results for single scattering albedo being in the interval from 0.466 to 1.0. The differences between codes slowly grow with growing optical radius. For single scattering albedo being very close to unity and optical radius equal to 10, statistical noise of polarization degree enhances in the central region of the observable disk, due to very small values of the polarization itself.

If the optical radius of the scattering sphere exceeds 10 then the statistical noise of our code becomes too large for realistic total number of photon packages (about 10^9) and the corresponding computing time on our computer system. In such cases RADMC3D uses code acceleration through the diffusion approximation.