Chaotically magnetized atmosphere with dust

ABSTRACT We consider the influence of absorbing dust particles on the intensity and polarization of radiation in chaotically magnetized atmospheres. The Milne problem is considered. It is known that the existence of absorbing dust particles leads to more elongated intensity distribution along the normal to the atmosphere and increasing of polarization degree near the direction perpendicular to the normal. The chaotic Faraday rotations practically do not change the intensity distribution, but they decrease the polarization degree. How looks the picture when the atmosphere is chaotically magnetized and contains the absorbing dust particles? Usually one assumes that such atmospheres exist in active galactic nuclei in Seyfert galaxies, both in accretion discs and gas–dusty toruses. In particular, we establish when both mechanisms cancel one another and the resulting polarization is near to ordinary atmosphere without the magnetic field fluctuations and absorbing particles. Of course, the angular distribution mostly corresponds to the level of existing dust particles, because it is practically independent of polarization.

Regularity of Milne problem with geometric correction in 3D

Consider the Milne problem with geometric correction in a 3D convex domain. Via bootstrapping arguments, we establish [Formula: see text]-regularity for its solutions. Combined with a uniform [Formula: see text]-estimate, such regularity leads to the validity of diffusive expansion for the neutron transport equation with diffusive boundary conditions.