Polarization properties of thermal accretion disk emission. I. Direct radiation

Abstract

The X-ray polarimetric observing window re-opening is shedding new light on our current understanding of compact accreting sources. This is true, in particular, for stellar-mass black hole sources observed in the thermally-dominated state, for which the polarization signal is expected to depend on the accretion disk inclination and the black hole spin. Two main effects determine the polarization properties of the accretion disk emission: the absorption and scattering processes occurring before the radiation leaves the disk atmosphere, and the relativistic effects influencing its propagation towards the observer at infinity. In this work, we investigate these effects together considering only the contribution of direct radiation. We analyze how the ionization state of the disk atmosphere, approximated with a constant-density surface layer assumed to be either in collisional ionization equilibrium or photoionization equilibrium, can influence the spectro-polarimetric properties of the radiation at the emitting disk surface. Subsequently we study how these are modified by the propagation in a strong gravitational field.

Figures (8)

• Figure 1: Top row: Spectra of radiation emerging from a partially ionized slab observed at $75^\circ$ relative to the slab normal for $n_\mathrm{H}=10^{17}$ (dash-dotted), $10^{19}$ (solid) and $10^{21}\,\mathrm{cm^{-3}}$ (dotted), and for $T=0.3$ (cyan) and $1.0\,\mathrm{keV}$ (orange). The slab is either in CIE (left column) or in PIE (right column). Middle and bottom rows: Polarization degree of the emerging radiation for slabs with a seed blackbody temperature of $0.3$ keV (middle row) or $1$ keV (bottom row).
• Figure 2: Simulated spectrum and polarization degree in the high-ionization regime under PIE (solid lines), viewed at an inclination angle of $75^\circ$ relative to the slab normal. Results are shown for different temperatures of the blackbody radiation, $T_\mathrm{BB} = 0.32$ (cyan), $0.56$ (orange), $1.0$ (green) and $1.78\,\mathrm{keV}$ (red), with the slab density adjusted to maintain a constant ionization parameter of $\log \xi \sim 6$ (see equation \ref{['eq:IonPIE']}). Dotted lines represent simulations for the same values of the parameters but with all interactions except scattering processes have been artificially turned off in STOKES.
• Figure 3: Spectrum and polarization degree for radiation emerging at an inclination angle $75^\circ$ for different optical depths, $\tau=0.67$ (cyan), $1$ (red), and $3.33$ (brown). The blackbody temperature is fixed at $T_\mathrm{BB} = 1\,\mathrm{keV}$, with a slab density $n_\mathrm{H} = 10^{19}$ cm$^{-3}$. Solid (dotted) lines depict the results for a slab in the PIE (CIE) configuration. The horizontal black line marks the value predicted by Cha60 computations for a $75^\circ$ inclination angle.
• Figure 4: Radial profiles of the disk surface temperature (left) and density (right) used in CLOUDY computations (see equation \ref{['eq:Tprofile']} and equations (A1)--(A3) in Tav21) for a non-rotating BH (cyan) and a maximally rotating BH (orange), and for two values of the mass accretion rate, $\dot{M}=0.1$ (solid) and $0.3\,\dot{M}_\mathrm{Edd}$ (dashed). In both cases a BH mass of $10 \ \mathrm{M_\odot}$ and a hardening factor $f_\mathrm{col}=1.8$ have been considered. The vertical dotted lines indicate the location of the ISCO for the two spin values.
• Figure 5: Spectra (top row) and polarization degree (bottom row) of the disk radiation at the emission at different inclinations with respect to the disk normal, $\theta=13^\circ$ (cyan), $39^\circ$ (orange), $55^\circ$ (green), $68^\circ$ (red) and $80^\circ$ (purple), considering two values of the BH spin, $a = 0$ (left column) and $0.998$ (right column). A BH mass $M=10 \ \mathrm{M_\odot}$ and accretion rate $0.1\,\dot{M}_\mathrm{Edd}$ were set, with a hardening factor $f_\mathrm{col} = 1.8$ and stop column density of $N_\mathrm{H} = 10^{24}\,\mathrm{cm}^{-2}$. The disk medium is modeled either in the CIE (dotted lines) or PIE (solid lines) regimes. The Stokes parameters for radiation emitted from each radial bin are weighted according to the temperature and area of each bin (see Equations \ref{['eq:StokesMean']}).