Scattering of light in thin magnetized envelopes

Abstract

ABSTRACT We consider optically thin spherical stellar envelopes with dipole magnetic field. The source of magnetic dipole field is assumed a star with radius Rs and magnetic moment $\boldsymbol{ M}$. We also assume that a star emits the non-polarized radiation. The general formulas for the Stokes parameters of single scattered radiation are given for both small and large parameters $x=\omega _B/\omega =0.93\times 10^{-8}\lambda (\mu \rm{m})\, \mathit{ B}(\rm{G})$. The particular calculations are related with circular polarization of scattered radiation on the condition x ≪ 1 for the following electron number densities: Ne(r) = N0(Rs/r)n with n = 0, 1, and 2. It is shown that observed circular polarization is $p_\mathit{ V}\simeq 31\, x(R_\mathrm{ s})\, N_0\sigma _\mathrm{ T} R_\mathrm{ s}\, \cos \vartheta _\mathrm{ m}\, (1-\eta ^{n+2})/(n+2){{\ \rm per\ cent}}$, where σT is the Thomson cross-section, parameter x(Rs) corresponds to that at the star surface, and ϑm is the angle between the magnetic dipole $\boldsymbol{M}$ and the direction to a telescope. The value η = Rs/R0, where R0 is the radius of envelope.