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Subsections

Additive Model Components A-M

This and the following sections contain information on specific, installed XSPEC models. The parameters are given as par1, par2, ... and K, which is the normalization. Additive models represent sources of emission.

  
apec

An emission spectrum from collisionally-ionized diffuse gas calculated using the APEC code v1.3.1. More information can be found at http://hea-www.harvard.edu/APEC/ which should be consulted by anyone running this model. By default this model reads atomic physics data from the files apec_v1.3.1_coco.fits and apec_v1.3.1_line.fits in the spectral/xspec/manager file. Different files can be specified by using the command xset set APECROOT. There are three options. APECROOT can be set to a version number (eg 1.2.0). In this case the value of APECROOT will be used to replace 1.3.1 in the name of the standard files and the resulting files will be assumed to be in the spectral/xspec/manager directory. Alternatively, a filename root (eg apec_v1.2.0) can be given. This root will be used as a prefix for the _coco.fits and _line.fits in the manager directory. Finally, if neither of these work then the model will assume that the APECROOT value gives the complete directory path e.g. XSPEC> xset APECROOT /foo/bar/apec_v1.2.0 will use /foo/bar/apec_v1.2.0_coco.fits and /foo/bar/apec_v1.2.0_line.fits as input files.

par1     =  plasma temperature in keV
par2     =  Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Mg, Al, Si, S, Ar, Ca, Fe, Ni. Relative abundances are set by the abund command.
par3     =  redshift, z
K     =  $(10^{-14} / (4 \pi (D_A (1+z))^2)) \int n_e n_H dV$, where DA is the angular size distance to the source (cm), ne and nH are the electron and H densities (cm-3)

  
atable

An additive table model. The filename to be used should be given immediately after atable in the model command. For example





XSPEC>model atable{mymod.mod}




uses mymod.mod as the input for the model. For specifications of the table model file, see the OGIP memo 92-009 on the FITS file format for table model files (available on the WWW or by anonymous ftp from ftp://legacy.gsfc.nasa.gov/caldb/docs/memos. Example additive table model files are mekal.mod and raysmith.mod in $XANADU/spectral/xspec/manager and testpo.mod in $XANADU/src/spectral/session.

  
bbody

A blackbody spectrum.


\begin{displaymath}A(E) = {\tt K}\ 8.0525 E^2 dE /({\tt par1}^4 (\exp (E/{\tt par1})-1))\end{displaymath}

where :

par1     =  temperature kT in keV
K     =  L39/ D102, where L39 is the source luminosity in units of 1039 ergs/sec and D10 is the distance to the source in units of 10 kpc

  
bbodyrad

A blackbody spectrum with normalization proportional to the surface area.


\begin{displaymath}A(E) = {\tt K}\ 1.0344\times 10^{-3} E^2 dE /(\exp (E/{\tt par1})-1)\end{displaymath}

where :

par1     =  temperature kT in keV
K     =  Rkm2/D102, where Rkm is the source radius in km and D10 is the distance to the source in units of 10 kpc

  
bexrav

A broken power-law spectrum multiplied by exponential high-energy cutoff, $\exp[-E\ {\tt par4}]$, and reflected from neutral material. See Magdziarz & Zdziarski 1995, MNRAS, 273, 837 for details. The output spectrum is the sum of an e-folded broken power law and the reflection component. The reflection component alone can be obtained for relrefl < 0. Then the actual reflection normalization is |relrefl|. Note that you need to change then the limits of relrefl excluding zero (as then the direct component appears). If Ec = 0, there is no cutoff in the power law. The metal and iron abundance are variable with respect to those set by a command 'abund'. The opacities are of Balucinska & McCammon (1992, and 1994, private communication). As expected in AGNs, H and He are assumed to be fully ionized. Send questions or comments to aaz@camk.edu.pl.

par1     =  Gamma1, first power law photon index
par2     =  Ebreak, break energy (keV)
par3     =  Gamma2, second power law photon index
par4     =  Ec, the e-folding energy in keV (if Ec=0 there is no cutoff)
par5     =  relrefl, reflection scaling factor (1 for isotropic source above disk)
par6     =  redshift, z
par7     =  abundance of elements heavier than He relative to the solar abundances
par8     =  iron abundance relative to the above
par9     =  cosine of inclination angle
K     =  photon flux at 1 keV of the cutoff broken power-law only (no reflection) in the observed frame.

  
bexriv

Broken power-law spectrum multiplied by exponential high-energy cutoff, $\exp[-E/{\tt par4}]$, and reflected from ionized material. See Magdziarz & Zdziarski 1995, MNRAS, 273, 837 for details. Ionization and opacities of the reflecting medium is computed as in the procedure absori. The output spectrum is the sum of an e-folded broken power law and the reflection component. The reflection component alone can be obtained for relrefl < 0. Then the actual reflection normalization is |relrefl|. Note that you need to change then the limits of relreflexcluding zero (as then the direct component appears). If Ec = 0,there is no cutoff in the power law. The metal and iron abundances are variable with respect to those set by a command 'abund'. Send questions or comments to aaz@camk.edu.pl.

par1     =  Gamma1, first power law photon index
par2     =  Ebreak, break energy (keV)
par3     =  Gamma2, second power law photon index
par4     =  Ec, the e-folding energy in keV (if Ec=0 there is no cutoff)
par5     =  relrefl, reflection scaling factor (1 for isotropic source above disk)
par6     =  redshift, z
par7     =  abundance of elements heavier than He relative to the solar abundances
par8     =  iron abundance relative to the above
par9     =  cosine of inclination angle
par10     =  disk temperature in K
par11     =  disk ionization parameter, $\xi = 4\pi F_{ion}/n,$ where Fion is the 5 eV - 20 keV irradiating flux, n is the density of the reflector; see Done et al., 1992, ApJ, 395, 275
K     =  photon flux at 1 keV of the cutoff broken power-law only (no reflection) in the observed frame.

  
bknpower

A broken power law.


\begin{displaymath}\begin{array}{lcll}
A(E) & = & {\tt K}\ (E/1 {\rm keV})^{-{\t...
...)^{-{\tt par3}} & {\rm for\ } E \geq
{\tt par2}\\
\end{array}\end{displaymath}

where :

par1     =  power law photon index for E < break energy
par2     =  break point for the energy in keV
par3     =  power law photon index for E > break energy
K     =  photons/keV/cm2/s at 1 keV

  
bkn2pow

A three-segment broken power law (ie with two break energies).


\begin{displaymath}\begin{array}{lcll}
A(E) & = & {\tt K}\ (E/1 {\rm keV})^{-{\t...
...)^{-{\tt par5}} & {\rm for\ } E \geq
{\tt par4}\\
\end{array}\end{displaymath}

where :

par1     =  power law photon index for E < first break energy
par2     =  first break point for the energy in keV
par3     =  power law photon index for E between two break energies
par4     =  second break point for the energy in keV
par5     =  power law photon index for E > second break energy
K     =  photons/keV/cm2/s at 1 keV

  
bmc

This is an analytic model describing Comptonization of soft photons by matter undergoing relativistic bulk-motion. The typical scenario involves thermal X-rays from the inner region of an accretion disk in a black-hole binary illuminating in-falling matter in close proximity to the black-hole event horizon. For a detailed description of the model, refer to Titarchuk, Mastichiadis & Kylafis 1997, ApJ, 487, 834; Titarchuk & Zannias, 1998, ApJ, 493, 863; Laurent & Titarchuk 1999, ApJ, 511, 289; Zannias, Borozdin, Revnivtsev., Trudolyubov, Shrader, & Titarchuk, 1999, ApJ, 517, 367; or Shrader & Titarchuk 1999, ApJ 521, L21. The model parameters are the characteristic black-body temperature of the soft photon source, a spectral (energy) index, and an illumination parameter characterizing the fractional illumination of the bulk-motion flow by the thermal photon source. It must be emphasized that this model is not an additive combination of power law and thermal sources, rather it represents a self-consistent convolution. The bulk-motion up-scattering and Compton recoil combine to produce the hard spectral tail, which combined with the thermal source results in the canonical high-soft-state spectrum of black hole accretion. The position of the sharp high energy cutoff (due to recoil) can be determined using the theta function $\Theta(E_c-E)$. The model can also be used for the general Comptonization case when the energy range is limited from above by the plasma temperature (see compTT and compST).

par1     =  Temperature of thermal photon source in keV.
par2     =  Energy spectral index alpha.
par3     =  Log of the A parameter. Note that f in Borozdin et al 1999 and Shrader & Titarchuk 1999 is 10par(3).
K     =  AN defined in in Borozdin et al 1999 and Shrader & Titarchuk (1999)

  
bremss

A thermal bremsstrahlung spectrum based on the Kellogg, Baldwin & Koch (ApJ 199, 299) polynomial fits to the Karzas & Latter (ApJSuppl 6, 167) numerical values. A routine from Kurucz (priv. comm.) is used in at low temperature end. The He abundance is assumed to be 8.5% of H by number.

par1     =  plasma temperature in keV
K     =  $(3.02\times 10^{-15} / (4 \pi D^2) \int n_e n_I dV$, where D is the distance to the source (cm) and ne, nI are the electron and ion densities (cm-3)

  
c6mekl

A multi-temperature mekal model using sixth-order Chebyshev polynomial for the differential emission measure. The DEM is not constrained to be positive. The abundance is relative to the Solar abundances set by the abund command. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate. The reference for this model is Singh et al.(1996, ApJ, 456, 766).

par1-6     =  Chebyshev polynomial coefficients
par7     =  H density (cm-3)
par8     =  abundance wrt to Solar
par9     =  Redshift
par10     =  0 $\Rightarrow$ calculate, 1 $\Rightarrow$ interpolate
K     =  $(10^{-14}/(4 \pi (D_A (1+z))^2) \int n_e n_H dV$, where DA is the angular size distance to the source (cm), ne is the electron density (cm-3), and nH is the hydrogen density (cm-3)

  
c6pmekl

A multi-temperature mekal model using the exponential of a sixth-order Chebyshev polynomial for the differential emission measure. (see e.g. Lemen et al. ApJ 341, 474, 1989). The abundance is relative to the Solar abundances set by the abund command. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate. The reference for this model is Singh et al.(1996, ApJ, 456, 766).

par1-6     =  Chebyshev polynomial coefficients
par7     =  H density (cm-3)
par8     =  abundance wrt to Solar
par9     =  Redshift
par10     =  0 $\Rightarrow$ calculate, 1 $\Rightarrow$ interpolate
K     =  $(10^{-14}/(4 \pi (D_A (1+z))^2) \int n_e n_H dV$, where DA is the angular size distance to the source (cm), ne is the electron density (cm-3), and nH is the hydrogen density (cm-3)

  
c6pvmkl

A multi-temperature, variable abundance mekal model using the exponential of a sixth order Chebyshev polynomial for the differential emission measure (eg Lemen etal. ApJ 341, 474, 1989). The abundances are relative to the Solar abundances set by the abund command. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate. The reference for this model is Singh et al.(1996, ApJ, 456, 766).

par1-6     =  Chebyshev polynomial coefficients
par7     =  H density (cm-3)
par8 - par21     =  Abundances of He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni wrt Solar (defined by the abund command)
par22     =  Redshift
par23     =  0 $\Rightarrow$ calculate, 1 $\Rightarrow$ interpolate
K     =  $(10^{-14}/(4 \pi (D_A (1+z))^2) \int n_e n_H dV$, where DA is the angular size distance to the source (cm), ne is the electron density (cm-3), and nH is the hydrogen density (cm-3)

  
c6vmekl

A multi-temperature, variable-abundance mekal model using the sixth-order Chebyshev polynomial for the differential emission measure. The DEM is not constrained to be positive. The abundances are relative to the Solar abundances set by the abund command. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate. The reference for this model is Singh et al.(1996, ApJ, 456, 766).

par1-6     =  Chebyshev polynomial coefficients
par7     =  H density (cm-3)
par8- par21     =  Abundances of He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni wrt Solar (defined by the abund command)
par22     =  Redshift
par23     =  0 $\Rightarrow$ calculate, 1 $\Rightarrow$ interpolate
K     =  $(10^{-14}/(4 \pi (D_A (1+z))^2) \int n_e n_H dV$, where DA is the angular size distance to the source (cm), ne is the electron density (cm-3), and nH is the hydrogen density (cm-3)

  
cemekl

A multi-temperature plasma emission model built from the mekal code. Emission measures follow a power-law in temperature (ie emission measure from temperature T is proportional to $(T/{\tt par2})^{\tt par1}$. The abundance ratios are set by the abund command. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate.

par1     =  index for power-law emissivity function
par2     =  maximum temperature
par3     =  nH (cm-3)
par4     =  Abundance relative Solar
par5     =  Redshift
par6     =  0 $\Rightarrow$ calculate, 1 $\Rightarrow$ interpolate
K     =  Normalization

  
cevmkl

A multi-temperature plasma emission model built from the mekal code. Emission measures follow a power-law in temperature (ie emission measure from temperature T is proportional to $(T/{\tt par2})^{\tt par1}$. The abundances are relative to the Solar abundances set by the abund command. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate.

par1     =  index for power-law emissivity function
par2     =  maximum temperature
par3     =  nH (cm-3)
par4- par17     =  Abundances for He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni wrt Solar (defined by the abund command)
par18     =  Redshift
par19     =  0 $\Rightarrow$ calculate, 1 $\Rightarrow$ interpolate
K     =  Normalization

  
cflow

A cooling flow model after Mushotzky & Szymkowiak (``Cooling Flows in Clusters and Galaxies," ed. Fabian, 1988). An index of zero for the power-law emissivity function corresponds to emission measure weighted by the inverse of the bolometric luminosity at that temperature. The model assumes H0 = 50 and q0 = 0. The abundance ratios are set by the abund command. There are two versions of this model available. xset cflow_version 1 gives the original (11.2.0 and earlier) version which has an error in the calculation of the emission measure distribution at the ends of the temperature range. The default is xset cflow_version 2 which uses a number of emission measure steps that can be set by xset cflow_ntemps <number>

par1     =  index for power-law emissivity function
par2     =  low temperature (keV)
par3     =  high temperature (keV)
par4     =  abundance relative Solar
par5     =  redshift
K     =  Mass accretion rate (solar mass/yr)

  
compbb

A comptonized blackbody model after Nishimura et al., 1986, PASJ, 38, 819.

par1     =  blackbody temperature (keV)
par2     =  electron temperature of the hot plasma (keV)
par3     =  optical depth of the plasma
K     =  L392/D102, where L39 is the source luminosity in units of 1039 ergs/sec and D10 is the distance to the source in units of 10 kpc (the same definition as for the bbodyrad model)

  
compLS

A Comptonization spectrum after Lamb and Sanford, 1979, M.N.R.A.S, 288, 555. This model calculates the self-Comptonization of a bremsstrahlung emission from an optically-thick spherical plasma cloud with a given optical depth and temperature. It was popular for Sco X-1.

par1     =  temperature in keV
par2     =  optical depth
K     =  Normalization

  
compST

A Comptonization spectrum after Sunyaev and Titarchuk 1980, A&A, 86, 121. This model is the Comptonization of cool photons on hot electrons.

par1     =  temperature in keV
par2     =  optical depth
K     =  $(N f)/(4\pi d^2)$, where N is the total number of photons from the source, d is the distance to the source, and f is the factor $z(z+3)y^z/\Gamma(2z+4)/\Gamma(z)$, where z is the spectral index, y is the injected photon energy in units of the temperature, and $\Gamma$ is the incomplete gamma function.

    =   

  
compTT

This is an analytic model describing Comptonization of soft photons in a hot plasma, developed by L. Titarchuk (see ApJ, 434, 313). This replaces the Sunyaev-Titarchuk Comptonization model in the sense that the theory is extended to include relativistic effects. Also, the approximations used in the model work well for both the optically thin and thick regimes. The Comptonized spectrum is determined completely by the plasma temperature and the so-called $\beta$ parameter which is independent of geometry. The optical depth is then determined as a function of $\beta$ for a given geometry. Thus par5 switches between spherical and disk geometries so that $\beta$ is not a direct input here. This parameter MUST be frozen. If ${\tt par5} > 0$, $\beta$ is obtained from the optical depth using analytic approximation (e.g. Titarchuk 1994). If ${\tt par5} < 0$ and $0.1 < \tau
< 10$, $\beta$ is obtained by interpolation from a set of accurately calculated pairs of $\beta$ and $\tau$ from Sunyaev & Titarchuk 1985 (A&A 143, 374).

In this incarnation of the model, the soft photon input spectrum is a Wien law [ $x^2\ e^{-x}$ photons] because this lends itself to a particularly simple analytical form of the model. For present X-ray detectors this should be adequate. Note that in energy flux space the peak of the Wien law occurs at 3kT as opposed to 2.8kT for a blackbody.

The plasma temperature may range from 2-500 keV, but the model is not valid for simultaneously low temperatures and low optical depth, or for high temperatures and high optical depth. The user is strongly urged to read the following references (esp. HT95 Fig 7) before and after using this model in order to fully understand and appreciate the physical assumptions made: Titarchuk, L., 1994, ApJ, 434, 313; Hua, X-M., Titarchuk, L., 1995, ApJ, 449, 188; Titarchuk, L., Lyubarskij, Y., 1995, ApJ, 450, 876.

par1     =  Redshift.
par2     =  Input soft photon (Wien) temperature (keV).
par3     =  Plasma temperature (keV).
par4     =  Plasma optical depth.
par5     =  Geometry switch. ABS( par5) <=1 : disk, >1: sphere. ${\tt par5} >= 0$ : use analytic approx for $\beta$ vs. $\tau$. ${\tt par5} < 0$ : Get beta vs. tau from interpolation.
K     =  Normalization

  
cutoffpl

A power law with high energy exponential rolloff.


\begin{displaymath}A(E) = {\tt K}(E/1 {\rm keV})^{-{\tt par1}} \exp(-E/{\tt par2})\end{displaymath}

where :

par1     =  power law photon index
par2     =  e-folding energy of exponential rolloff (in keV)
K     =  photons/keV/cm2/s at 1 keV

  
disk

The spectrum from an accretion disk, where the opacities are dominated by free-free absorption, i.e., the so-called blackbody disk model. Not correct for a disk around a neutron star.

par1     =  accretion rate in Eddington Luminosities
par2     =  central mass in solar mass units
par3     =  inner disk radius in gravitational (= 3 Schwarzschild) radii
par4     =  distance in kpc
K     =  $2\cos i/d^2$, where i is the inclination of the disk and d is the distance in units of 10 kpc

  
diskbb

The spectrum from an accretion disk consisting of multiple blackbody components. For example, see Mitsuda et al., PASJ, 36, 741, (1984), Makishima et al., ApJ 308, 635, (1986).

par1     =  temperature at inner disk radius (keV)
K     =  ((Rin/km)/(D/10kpc))2 $\cos{\theta}$, where Rin is the inner disk radius, D the distance to the source, and $\theta$ the angle of the disk

  
diskline

A line emission from a relativistic accretion disk. See Fabian et al., MNRAS 238, 729. Setting par2 to 10 is the special case of the accretion disk emissivity law ( $(1-\sqrt{6/R})/R^3$).

par1     =  line energy
par2     =  power law depend. of emissivity. If this parameter is 10 or greater then the accretion disk emissivity law $(1-\sqrt{6/R})/R^3$ is used. Otherwise the emissivity scales as $R^{{\tt par2}}$.
par3     =  inner radius (units of GM/c2)
par4     =  outer radius (units of GM/c2)
par5     =  inclination (degrees)
K     =  photons/cm2/s in the spectrum

  
diskm

A disk model with gas pressure viscosity. The spectrum from an accretion disk where the viscosity scales as the gas pressure. From Stella and Rosner 1984, ApJ, 277, 312.

par1     =  accretion rate in Eddington luminosities
par2     =  central mass in units of solar mass
par3     =  inner disk radius in gravitational ( = 3 Schwarzschild) radii
par4     =  viscosity
K     =  cos(i)/d2, where i is the inclination of the disk and d is the distance in units of 10 kpc

  
disko

A modified blackbody disk model. The spectrum from the inner region of an accretion disk where the viscosity is dominated by radiation pressure.

par1     =  accretion rate in Eddington luminosities
par2     =  central mass in units of solar mass
par3     =  inner disk radius in gravitational ( = 3 Schwarzschild) radii
par4     =  viscosity
K     =  cos(i)/d2, where i is the inclination of the disk and d is the distance in units of 10 kpc

  
diskpn

Blackbody spectrum of an accretion disk. This is an extention of diskbb model, including corrections for temperature distribution near the black hole. The temperature distribution was calculated in Paczynski-Wiita pseudo-Newtonian potential. An accretion rate can be computed from the maximum temperature found. For details see Gierlinski et al., 1999, MNRAS, 309, 496. Please note that the inner disk radius (par2) can be a free parameter only close to ${\tt par2} = 6;$otherwise par2 is strongly correlated with K.

par1     =  maximum temperature in the disk (keV)
par2     =  inner disk radius in Rg = GM / c2 units, 6 <= par2 <= 1000
K     =  $(M^2 \cos i ) / (D^2 \beta^4)$ - normalization, where M - central mass in solar masses, D - distance to the source (kpc), i - inclination of the disk, $\beta$ - color/effective temperature ratio.

  
equil

Ionization equilibrium collisional plasma model. This is the equilibrium version of Kazik Borkowski's NEI models. Several versions are available. To switch between them use the xset neivers command. xset neivers 1.0 gives the version from xspec v11.1, xset neivers 1.1 uses updated calculations of ionization fractions using dielectronic recombination rates from Mazzotta et al (1988), and xset neivers 2.0 uses the same ionization fractions as 1.1 but uses APED to calculate the resulting spectrum. Note that versions 1.x have no emission from Ar. The default is version 1.1.

par1     =  plasma temperature (keV)
par2     =  Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni. Abundances are given by the Anders & Grevesse mixture.
par3     =  redshift z
K     =  $(10^{-14} / (4 \pi (D_A (1+z))^2)) \int n_e n_H dV$, where DA is the angular size distance to the source (cm), ne and nH are the electron and H densities (cm-3)

The references for this model are as follows :

  
expdec

An exponential decay.


\begin{displaymath}A(E) = \exp(-{\tt par1} * E)\end{displaymath}

where:

par1     =  exponential factor

  
gaussian

A simple gaussian line profile. If the width is $\leq 0$, then it is treated as a delta function.


\begin{displaymath}A(E) = {\tt K}\ (1./{\tt par2}\sqrt(2\pi)) \exp(-0.5((E-{\tt par1})/{\tt par2})^2) \end{displaymath}

where :

par1     =  line energy in keV
par2     =  line width ($\sigma$) in keV
K     =  total photons/cm2/s in the line

  
gnei

Non-equilibrium ionization collisional plasma model. This is a generalization of the nei model where the temperature is allowed to have been different in the past ie the ionization timescale averaged temperature is not necessarily equal to the current temperature. For example, in a standard Sedov model with equal electron and ion temperatures, the ionization timescale averaged temperature is always higher than the current temperature for each fluid element. The references for this model can be found under the description of the equil model. Several versions are available. To switch between them use the xset neivers command. xset neivers 1.0 gives the version from xspec v11.1, xset neivers 1.1 uses updated calculations of ionization fractions using dielectronic recombination rates from Mazzotta et al (1988), and xset neivers 2.0 uses the same ionization fractions as 1.1 but uses APED to calculate the resulting spectrum. Note that versions 1.x have no emission from Ar. The default is version 1.1.

par1     =  plasma temperature (keV)
par2     =  Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni. Abundances are given by the Anders & Grevesse mixture.
par3     =  Ionization timescale in units of s/cm3.
par4     =  Ionization timescale averaged plasma temperature (keV).
par5     =  redshift z
K     =  $(10^{-14} / (4 \pi (D_A (1+z))^2)) \int n_e n_H dV$, where DA is the angular size distance to the source (cm), ne and nH are the electron and H densities (cm-3)

  
grad

General Relativistic Accretion Disk model around a Schwarzschild black hole. Inner radius is fixed to be 3 Schwarzschild radii, thus the energy conversion efficiency is 0.057. See Hanawa, T., 1989, ApJ, 341, 948 and Ebisawa, K. Mitsuda, K. and Hanawa, T. 1991, ApJ, 367, 213. Several bugs were found in the old GRAD model which was included in xspec 11.0.1ae and before. Due to these bugs, it turned out that the mass obtained by fitting the old GRAD model to the observation was 1.4 times over-estimated. These bugs were fixed, and a new parameter (par6) was added to make the distinction between the old and new codes clear.

par1     =  distance (kpc)
par2     =  disk inclination angle (deg; 0 for face-on)
par3     =  mass of the central object (solar units)
par4     =  mass accretion rate (1018 g/s)
par5     =  spectral hardening factor, Tcol/Teff. Should be greater than 1.0, and considered to be 1.5-1.9 for accretion disks around a stellar-mass black hole. See, e.g., Shimura and Takahara, 1995, ApJ, 445, 780
par6     =  A flag to switch on/off the relativistic effects (never allowed to be free). If positive, relativistic calculation; if negative or zero, Newtonian calculation (inner radius is still fixed at 3 Schwarzschild radii, and the efficiency is 1/12).
K     =  Should be fixed to 1.

  
grbm

A model for gamma-ray burst continuum spectra developed by D. Band, et. al., 1993 (ApJ 413, 281).


\begin{displaymath}\begin{array}{lcll}
A(E) & = & {\tt K}\ (E/100.)^{{\tt par1}}...
...m for\ }
E > ({\tt par1}-{\tt par2})*{\tt par3} \\
\end{array}\end{displaymath}

where:

par1     =  first power law index
par2     =  second power law index
par3     =  characteristic energy in keV
K     =  normalization constant

  
laor

An emission line from an accretion disk around a black hole. Ari Laor's calculation including GR effects (ApJ 376, 90).

par1     =  Line energy in keV
par2     =  power law depend. of emissivity (scales as $R^{-{\tt par2}}$)
par3     =  inner radius (units of GM/c2)
par4     =  outer radius (units of GM/c2)
par5     =  inclination (degrees)
K     =  photons/cm2/s in the line

  
lorentz

A Lorentzian line profile.


\begin{displaymath}A(E) = {\tt K}\ ({\tt par2}/(2\pi)) / ( (E-{\tt par1})^2 + ({\tt par2}/2)^2 ) \end{displaymath}

where :

par1     =  line energy in keV
par2     =  line width ($\sigma$) in keV
K     =  total photons/cm2/s in the line

  
meka

An emission spectrum from hot diffuse gas based on the model calculations of Mewe and Gronenschild (as amended by Kaastra). The model includes line emissions from several elements.

par1     =  plasma temperature in keV
par2     =  hydrogen density in cm-3
par3     =  Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni. Abundances are set by the abund command.
par4     =  redshift, z
K     =  $(10^{-14} / (4 \pi (D_A (1+z))^2)) \int n_e n_H dV$, where DA is the angular size distance to the source (cm), ne and nH are the electron and H densities (cm-3)

The references for the MEKA model are as follows :

Similar credit may also be given for the adopted ionization balance

  
mekal

An emission spectrum from hot diffuse gas based on the model calculations of Mewe and Kaastra with Fe L calculations by Liedahl. The model includes line emissions from several elements. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate.

par1     =  plasma temperature in keV
par2     =  hydrogen density in cm-3
par3     =  Metal abundances (He fixed at cosmic). The elements included are C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, Ni. Abundances are set by the abund command.
par4     =  redshift, z
par5     =  0 $\Rightarrow$ calculate, 1 $\Rightarrow$ interpolate
K     =  $(10^{-14} / (4 \pi (D_A (1+z))^2)) \int n_e n_H dV$, where DA is the angular size distance to the source (cm), ne and nH are the electron and H densities (cm-3)

The references for the MEKAL model are as follows :

Similar credit may also be given for the adopted ionization balance

  
mkcflow

A cooling flow model after Mushotzky & Szymkowiak (``Cooling Flows in Clusters and Galaxies" ed. Fabian, 1988). This one uses the mekal model for the individual temperature components and differs from cflow in setting the emissivity function to be the inverse of the bolometric luminosity. The model assumes H0 = 50 and q0 = 0. Abundance ratios are set by the abund command. The switch parameter determines whether the mekal code will be run to calculate the model spectrum for each temperature or whether the model spectrum will be interpolated from a pre-calculated table. The former is slower but more accurate. There are two versions of this model available. xset cflow_version 1 gives the original (11.2.0 and earlier) version which has an error in the calculation of the emission measure distribution at the ends of the temperature range. The default is xset cflow_version 2 which uses a number of emission measure steps that can be set by xset cflow_ntemps <number>

par1     =  low temperature (keV)
par2     =  high temperature (keV)
par3     =  abundance relative to Solar
par4     =  redshift
par5     =  0 $\Rightarrow$ calculate, 1 $\Rightarrow$ interpolate
K     =  Mass accretion rate (solar mass/yr)


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Next: Additive Model Components N-Z Up: XSPEC V11.3 Models Previous: Summary of Models
Ben Dorman
2003-11-28