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Comptonization, Poutanen and Svenson. XSpec model.


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 J., Svensson R., 1996, ApJ, 470, 249 (PS96). The Compton scattering kernel is the exact one as derived by Jones F. C., 1968, Phys. Rev., 167, 1159 (see PS96 for 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 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, Poutanen, 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 ne 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 blackbody (bbodyrad) for Tbb>0 or multicolor disk (diskbb) for Tbb<0. The normalization of the model also follows those models: (1) Tbb>0, 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<0 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.

This is an additive model component.

xscompps Parameters

1 kte electron temperature in keV
2 eleindex electron power-law index [ N(gamma)=gamma^-p ]
3 gmin minimum Lorentz factor gamma
4 gmax maximum Lorentz factor gamma
5 ktbb temperature of soft photons: ktbb>0 = blackbody, ktbb<0 = multicolor disk with inner disk temperature ktbb
6 tauy 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~2 increase MAXTAU to 50 for sphere - tau < 3
7 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')=sim(pi*tau'/tau)/(pi*tau'/tau) where tau' varies between 0 and tau.
8 hrcyl H/R for cylinder geometry only
9 cosincl cosine of inclination angle (if < 0 then only blackbody)
10 cov_frac covering factor of cold clouds; if geom =+/- 4,5 then cov_fac is dummy
11 rel_refl amount of reflection Omega/(2*pi) (if R < 0 then only reflection component)
12 fe_ab_re iron abundance in units of solar
13 me_ab abundance of heavy elements in units of solar
14 xi disk ionization parameter L/(nR^2)
15 tdisk disk temperature for reflection in K
16 betor10 reflection emissivity law (r^beta); if beta=-10 then non-rotating disk; if beta=10 then 1.-sqrt(6./rg))/rg**3
17 rin inner radius of the disk (Schwarzschild units)
18 rout outer radius of the disk
19 redshift redshift, z
20 norm Normalization

XSpec version

This information is taken from the XSpec User's Guide. Version 12.6.0l of the XSpec models is supplied with CIAO 4.3.


For a list of known bugs and issues with the XSPEC models, please visit the XSPEC bugs page.

See Also

atten, bbody, bbodyfreq, beta1d, beta2d, box1d, box2d, bpl1d, const1d, const2d, cos, delta1d, delta2d, dered, devaucouleurs2d, edge, erf, erfc, exp, exp10, gauss1d, gauss2d, hubblereynolds, jdpileup, linebroad, list_model_components, list_models, log, log10, logparabola, lorentz1d, lorentz2d, models, normbeta1d, normgauss1d, poisson, polynom1d, polynom2d, powlaw1d, scale1d, scale2d, schechter, sin, sqrt, stephi1d, steplo1d, tablemodel, tan, xs, xsabsori, xsacisabs, xsapec, xsbapec, xsbbody, xsbbodyrad, xsbexrav, xsbexriv, xsbkn2pow, xsbknpower, xsbmc, xsbremss, xsbvapec, xsc6mekl, xsc6pmekl, xsc6pvmkl, xsc6vmekl, xscabs, xscemekl, xscevmkl, xscflow, xscompbb, xscompls, xscompst, xscomptt, xsconstant, xscutoffpl, xscyclabs, xsdisk, xsdiskbb, xsdiskir, xsdiskline, xsdiskm, xsdisko, xsdiskpbb, xsdiskpn, xsdust, xsedge, xsequil, xsexpabs, xsexpdec, xsexpfac, xsezdiskbb, xsgabs, xsgaussian, xsgnei, xsgrad, xsgrbm, xshighecut, xshrefl, xskerrbb, xskerrd, xskerrdisk, xslaor, xslaor2, xslorentz, xsmeka, xsmekal, xsmkcflow, xsnei, xsnotch, xsnpshock, xsnsa, xsnsagrav, xsnsatmos, xsnsmax, xsnteea, xsnthcomp, xspcfabs, xspegpwrlw, xspexrav, xspexriv, xsphabs, xsplabs, xsplcabs, xsposm, xspowerlaw, xspshock, xspwab, xsraymond, xsredden, xsredge, xsrefsch, xssedov, xssmedge, xsspexpcut, xsspline, xssrcut, xssresc, xssss_ice, xsstep, xsswind1, xstbabs, xstbgrain, xstbvarabs, xsuvred, xsvapec, xsvarabs, xsvbremss, xsvequil, xsvgnei, xsvmcflow, xsvmeka, xsvmekal, xsvnei, xsvnpshock, xsvphabs, xsvpshock, xsvraymond, xsvsedov, xswabs, xswndabs, xsxion, xszbbody, xszbremss, xszdust, xszedge, xszgauss, xszhighect, xszpcfabs, xszphabs, xszpowerlw, xszredden, xszsmdust, xsztbabs, xszvarabs, xszvfeabs, xszvphabs, xszwabs, xszwndabs, xszxipcf

Last modified: December 2010
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