Beaming of polarized radiation in subcritical X-ray pulsars

Abstract

Radiation of X-ray pulsars is powered by accretion on the neutron star surface from a binary companion under the influence of a strong magnetic field. We study beaming of this radiation in the case of subcritical X-ray pulsars, where it is formed in the accretion channel close to the neutron star surface. We solve equations of the hydrodynamics and radiative transfer of two coupled polarization modes in the accretion channel numerically, taking into account resonant Compton scattering and vacuum polarization. The beaming patterns are obtained for different accretion rates, photon energies and polarizations, and for different models of the neutron star surface radiation. The calculated beaming patterns are converted into light curves for both the intensity and polarization, taking into account the effects of General Relativity. These beaming patterns and light curves are found to be strongly affected by the resonant Compton scattering for photon energies comparable with the electron cyclotron energy. In particular, the angular redistribution of radiation near the cyclotron resonance may reduce the light-curve modulation amplitude, which is consistent with observational indications of a suppressed pulsed fraction at these energies.

Figures (10)

• Figure S1: Dependence of the normalized radiant intensity $Q_E$ on the polar angle $\theta$ (left panels) and corresponding beam pattern (right panel) at accretion rate $\dot{M} = 10^{15}$ g s$^{-1}$ for photon energies $E = 0.2E_\mathrm{cyc}$ (dotted orange lines), $0.4E_\mathrm{cyc}$ (solid red lines), $E_\mathrm{cyc}$ (dashed green lines) and $1.5E_\mathrm{cyc}$ (dot-dashed blue lines). The specific intensity $I_E(\theta)$ at the surface is assumed constant (parameter $b=0$). Each curve is normalized to its maximum.
• Figure S2: Same as in \ref{['fig:gen10']} but for $\dot{M} = 2.5\times10^{15}$ g s$^{-1}$.
• Figure S3: Same as in \ref{['fig:gen10', 'fig:gen25']} but for $\dot{M} = 5\times10^{15}$ g s$^{-1}$.
• Figure S4: Polar diagram of outgoing radiation at $\dot{M}=2.5\times10^{15}$ g s$^{-1}$ (as in \ref{['fig:gen25']}) for separate polarizations of NS surface radiation: incoming X-mode (left panel) and incoming O-mode (right panel).
• Figure S5: Polar diagram of beaming of outgoing radiation at $\dot{M}=2.5\times10^{15}$ g s$^{-1}$ for the unpolarized NS surface radiation, suppressed near the normal to the surface according to \ref{['I_E_b']} with parameter $b=-1$ (left panel) or $b=-0.75$ (right panel).