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sttorus: X-ray polarized reflection from a torus

This additive model (version 2.0) computes the $0.1$–$100$ keV spectral and polarization (Stokes $I$, $Q$, $U$) properties of a power-law X-ray source of arbitrary incident polarization that is reprocessed by an optically thick, axially symmetric elliptical or circular torus – representing, e.g., an opaque AGN torus, a broad-line region, or a super-Eddington accretion funnel around an accreting stellar-mass black hole or neutron star. The local reflection was precomputed with the STOKES code for partially ionized, fully neutral, or fully ionized (Chandrasekhar electron-scattering) surfaces and is interpolated from FITS tables. No relativistic effects are included and all components are static.

As with the other polarization models, the Stokes selector (par12) set to $-1$ returns, for each spectrum, the quantity named by its Stokes XFLT keyword (“Stokes:0”$\,=I$, “Stokes:1”$\,=Q$, “Stokes:2”$\,=U$); this is the mode used for joint $I,Q,U$ fitting with the chistokes statistic. Setting par12 to 0–$10$ returns a single quantity ($I$, $Q$, $U$, $V$, polarization degree or angle, or a normalized ratio); when par12 is $5$–$10$ the normalization (par13) should be frozen at unity.

Caution. The public tables have low resolution in the reprocessing parameters. beta (par6) must be held at one of $-2$, $2$, $6$ and not fitted, and one should not switch between those discrete values, between the xi0 regimes ($<0$, 0–$5$, $\ge5$), between rhorhoin $=-1$ and $1$–$2$, or between pol_deg $=-1$ and 0–$1$ within a single XSPEC session, as new tables are accumulated in memory at each switch.

After a fit the xset command reports the derived quantities Theta_degrees (true half-opening angle), inc_degrees (inclination) and RF (reflection fraction); and, given the XSET inputs NORMVAL, D_MPC, NH0 and MASS, the $2$–$10$ keV luminosity L and the inner-torus distance rho_in_pc / rho_in_r_g. The reflection tables (stokes-*-torus.fits, stokes-*-ctorus.fits) and the visibility files (visibility_line*.txt) are installed in the standard model-data directory.

References: Podgorný et al. 2022, MNRAS 510, 4723; Podgorný et al. 2024, MNRAS 530, 2608; Podgorný 2025, A&A 702, A43.

The parameters are :

par1 PhoIndex, photon index of the primary power law
par2 cos_incl, cosine of the observer inclination ($1=$pole, $0=$disc)
par3 trTheta, transformed torus half-opening angle (0–$1$)
par4 rhorhoin, inner-wall skew $\rho/\rho_{\rm in}$ ($1$–$2$ elliptical; $-1$ circular, freeze)
par5 xi0, ionization parameter at the inner edge (erg cm s$^{-1}$; $\ge5$ ionized, 0–$5$ neutral, $<0$ fully ionized)
par6 beta, ionization-profile power-law index (use only $-2$, $2$, $6$; freeze)
par7 N_p, primary switch ($1=$reflection$+$primary, $0=$reflection only)
par8 pol_deg, primary polarization degree (0–$1$; $-1=$slab-corona anisotropy prescription)
par9 chi, intrinsic polarization angle of the primary (degrees, $-90$ to $90$)
par10 pos_ang, position angle of the system (degrees, $-90$ to $90$)
par11 zshift, overall redshift
par12 Stokes, output selector ($-1=$per-spectrum via XFLT; 0–$10=I$/$Q$/$U$/$V$/PD/PA/ratios)
par13 norm
next up previous contents
Next: step: step function convolved Up: Additive Model Components Previous: stdisc: X-ray polarized reflection   Contents