Polarized radiation transfer in neutron star surface layers

Abstract

The study of polarized radiation transfer in the highly-magnetized surface locales of neutron stars is of great interest to the understanding of accreting X-ray pulsars, rotation-powered pulsars and magnetars. This paper explores scattering transport in the classical magnetic Thomson domain that is of broad applicability to these neutron star classes. The development of a Monte Carlo simulation for the polarized radiative transfer is detailed: it employs an electric field vector formalism to enable a breadth of utility in relating linear, circular and elliptical polarizations. The simulation can be applied to any neutron star surface locale, and is adaptable to accretion column and magnetospheric problems. Validation of the code for both intensity and Stokes parameter determination is illustrated in a variety of ways. Representative results for emergent polarization signals from surface layers are presented for both polar and equatorial magnetic locales, exhibiting contrasting signatures between the two regions. There is also a strong dependence of these characteristics on the ratio of the frequency ω of a photon to the cyclotron frequency ωB =eB/mc. Polarization signatures for high opacity domains are presented, highlighting compact analytic approximations for the Stokes parameters and anisotropy relative to the local field direction for an extended range of frequencies. These are very useful in defining injection conditions deep in the simulation slab geometries, expediting the generation of emission signals from highly opaque stellar atmospheres. The results are interpreted throughout using the polarization characteristics of the magnetic Thomson differential cross section.

Intensity and Polarization Characteristics of Extended Neutron Star Surface Regions

“…To render the simulation more accurate and efficient for moderate opacities, the anisotropy and polarization distributions of the photons injected at the base of the slab need to represent those appropriate for conditions deeper down in the atmosphere than MAGTHOMSCATT actually simulates. To achieve this, Barchas, Hu & Baring (2021) presented a high opacity photon simulation configuration, which captured the angular and the polarization information for photons fully processed by magnetic Thomson scatterings. This implementation described the asymptotic state of the scattering system regardless of photons' spatial displacements or boundary conditions.…”

“…The Stokes Q that describes linear polarization is always negative and strongest along the horizon; this corresponds to a dominance of the ⊥ mode, always possessing a larger cross section than the mode ( Q = +1 ) when ω > ω B -see Fig. B1 of Barchas, Hu & Baring (2021). The polarization signatures are considerably diminished at non-polar magnetic colatitudes θ B due to the integration over local azimuth: this convolution mixes the particular Stokes parameter information that is tied to the field direction and is summarized in Figs.…”

“…The full expression for dσ/dΩ f in terms of the wave fields and directions can be found in Eq. ( 48) of Barchas, Hu & Baring (2021). It is routinely integrated over solid angles Ω f for the scattered wave to yield the total cross section:…”

“…This Section summarizes the basic structure of the magnetic Thomson scattering simulation MAGTHOMSCATT, whose design was detailed at length in Barchas, Hu & Baring (2021). Our results provide a more sophisticated understanding of neutron star atmospheres, yielding refinements for predictions of phase-resolved polarization signals from extended neutron star surfaces that are of great interest for soft X-ray polarimetry missions like IXPE, and planned future missions such as the enhanced X-ray Timing and Polarimetry mission 2 (eXTP) (Zhang et al 2016) and the X-ray Polarization Probe (XPP) (Jahoda et al 2019).…”

“…The complex electric field vector captures the complete polarization information (linear, circular and elliptical) of a photon, thus it suitably represents photon polarization near the cyclotron resonance where there is a strong interplay between circular and linear polarizations due to the induced electron gyration. The magnetic scattering formalism in our E vector formalism is summarized in Appendix A, and detailed in Barchas, Hu & Baring (2021). This field vector approach can also be extended to treat dispersive transport in plasma or the magnetized quantum vacuum, especially near the so-called vacuum resonance where the contribution of plasma and vacuum dispersion are in strong competition with each other (e.g., see Mészáros 1992;Lai & Ho 2003).…”