compPS: Comptonization, Poutanen & Svensson

Comptonization spectra computed for different geometries using exact numerical solution of the radiative transfer equation. The computational “iterative scattering method” is similar to the standard Lambda-iteration and is described in Poutanen & Svensson (1996, ApJ 470, 249; PS96). The Compton scattering kernel is the exact one as derived by Jones (1968, Phys. Rev. 167, 1159). See PS96 for additional references.

Comptonization spectra depend on the geometry (slab, sphere, hemisphere, cylinder), Thomson optical depth tau, parameters of the electron distribution, spectral distribution of soft seed photons, the way seed soft photons are injected to the electron cloud, and the inclination angle of the observer.

The resulting spectrum is reflected from the cool medium according to the computational method of Magdziarz & Zdziarski (1995) (see reflect, pexrav, pexriv models). $rel_{refl}$ is the solid angle of the cold material visible from the Comptonizing source (in units of $2\pi$), other parameters determine the abundances and ionization state of reflecting material (Fe_ab_re, Me_ab, xi, Tdisk). The reflected spectrum is smeared out by rotation of the disk due to special and general relativistic effects using “diskline”-type kernel (with parameters Betor10, Rin, Rout).

Electron distribution function can be Maxwellian, power-law, cutoff Maxwellian, or hybrid (with low temperature Maxwellian plus a power-law tail).

Possible geometries include plane-parallel slab, cylinder (described by the height-to-radius ratio H/R), sphere, or hemisphere. By default the lower boundary of the “cloud” (not for spherical geometry) is fully absorbive (e.g. cold disk). However, by varying covering factor parameter cov_fac, it may be made transparent for radiation. In that case, photons from the “upper” cloud can also be upscattered in the “lower” cloud below the disk. This geometry is that for an accretion disk with cold cloudlets in the central plane (Zdziarski et al. 1998, MNRAS 301, 435). For cylinder and hemisphere geometries, an approximate solution is obtained by averaging specific intensities over horizontal layers (see PS96). For slab and sphere geometries, no approximation is made.

The seed photons can be injected to the electron cloud either isotropically and homogeneously through out the cloud, or at the bottom of the slab, cylinder, hemisphere or center of the sphere (or from the central plane of the slab if cov_frac is not 1). For the sphere, there exist a possibility (IGEOM=-5) for photon injection according to the eigenfunction of the diffusion equation $\sin(\pi*\tau'/\tau)/(\pi*\tau'/\tau)$, where $\tau'$ is the optical depth measured from the center (see Sunyaev & Titarchuk 1980).

Seed photons can be black body (bbodyrad) for Tbb positive or multicolor disk (diskbb) for Tbb negative. The normalization of the model also follows those models: (1) Tbb positive, K = (RKM)**2 /(D10)**2, where D10 is the distance in units of 10 kpc and RKM is the source radius in km; (2) Tbb negative, K = (RKM)**2 /(D10)**2 cos(theta), where theta is the inclination angle.

Thomson optical depth of the cloud is not always good parameter to fit. Instead the Compton parameter y=4 * tau * Theta (where Theta= Te (keV) / 511 ) can be used. Parameter y is directly related to the spectral index and therefore is much more stable in fitting procedure. The fitting can be done taking 6th parameter negative, and optical depth then can be obtained via tau= y/(4* Te / 511).

The region of parameter space where the numerical method produces reasonable results is constrained as follows : 1) Electron temperature Te >10 keV; 2) Thomson optical depth tau <1.5 for slab geometry and tau <3, for other geometries.

In versions 4.0 and above the Compton reflection is done by a call to the ireflect model code and the relativistic blurring by a call to rdblur. This does introduce some changes in the spectrum from earlier versions. For the case of a neutral reflector (i.e. the ionization parameter is zero) more accurate opacities are calculated. For the case of an ionized reflector the old version assumed that for the purposes of calculating opacities the input spectrum was a power-law (with index based on the 2-10 keV spectrum). The new version uses the actual input spectrum, which is usually not a power law, giving different opacities for a given ionization parameter and disk temperature. The Greens' function integration required for the Compton reflection calculation is performed to an accuracy of 0.01 (i.e. 1%). This can be changed using e.g. xset COMPPS_PRECISION 0.05.

The model parameters are as follows :

par1 Te, electron temperature in keV
par2 p, electron power-law index [ N(gamma)=gamma$^{-\mbox{p}}$]
par3 gmin, minimum Lorentz factor gamma
par4 gmax, maximum Lorentz factor gamma
  • if any of gmin or gmax <1 then Maxwellian electron distribution with parameter Te
  • if Te=0 then power-law electrons with parameters p, gmin, gmax
  • if both gmin,gmax>=1 but gmax<gmin then cutoff Maxwellian with Te, p, gmin (cutoff Lorentz factor) as parameters
  • if Te is non-zero, gmin, gmax >= 1 then hybrid electron distribution with parameters Te, p, gmin, gmax
par5 Tbb, temperature of soft photons. If Tbb is positive then blackbody, if Tbb negative then multicolor disk with inner disk temperature |Tbb|
par6 if >0 : tau, vertical optical depth of the corona; if <0 : y = 4*Theta*tau. limits: for the slab geometry - tau <1, if say tau$\sim$2 increase MAXTAU to 50, for sphere - tau <3
par7 geom, 0 - approximate treatment of radiative transfer using escape probability for a sphere (very fast method); 1 - slab; 2 - cylinder; 3 - hemisphere; 4,5 - sphere input photons at the bottom of the slab, cylinder, hemisphere or center of the sphere (or from the central plane of the slab if cov_fact not 1). if <0 then geometry defined by |geom| and sources of incident photons are isotropic and homogeneous. -5 - sphere with the source of photons distributed according to the eigenfunction of the diffusion equation f(tau')=sin(pi*tau'/tau)/(pi*tau'/tau) where tau' varies between 0 and tau.
par8 H/R for cylinder geometry only
par9 cosIncl, cosine of inclination angle (if <0 then only black body)
par10 cov_fac, covering factor of cold clouds. if geom =+/- 4,5 then cov_fac is dummy
par11 R, amount of reflection Omega/(2*pi) (if R <0 then only reflection component)
par12 FeAb, iron abundance in units of solar
par13 MeAb, abundance of heavy elements in units of solar
par14 xi, disk ionization parameter L/(nR$^2$)
par15 temp, disk temperature for reflection in K
par16 beta, reflection emissivity law (r$^{beta}$, if beta=-10 then non-rotating disk, if beta=10 then 1.-sqrt(6./rg))/rg**3
par17 Rin/Rg, inner radius of the disk (Schwarzschild units)
par18 Rout/Rg, outer radius of the disk
par19 redshift