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Multiplicative Model Components N-Z

notch

A notch line absorption. This is model is equivalent to a very saturated absorption line.

$\begin{displaymath}\begin{array}{lcll} M(E) & = & (1-{\tt par3}) & {\rm for\ } {... ...t par2}/2\\ & = & 1 & {\rm for\ all\ other\ } \\ \end{array}\end{displaymath}$

where :

par1 = line energy (keV)

par2 = line width (keV)

par3 = covering fraction

pcfabs

A partial covering fraction absorption. The relative abundances are set by the abund command.

$\begin{displaymath}M(E) = {\tt par2} \exp(-{\tt par1} \sigma(E)) + (1-{\tt par2}) \end{displaymath}$

where $\sigma$ (E) is the photo-electric cross-section (NOT including Thomson scattering) (see phabs) and:

par1 = equivalent hydrogen column (in units of 10²² atoms/cm²)

par2 = covering fraction (0 < par2 <= 1.) (dimensionless)

phabs

A photoelectric absorption using cross-sections set by the xsect command. The relative abundances are set by the abund command.

$\begin{displaymath}M(E) = \exp (-{\tt par1} \sigma (E))\end{displaymath}$

where $\sigma (E)$ is the photo-electric cross-section (NOT including Thomson scattering). Note that the default He cross-section changed in v11. The old version can be recovered using the command xsect obcm.

par1 = equivalent hydrogen column (in units of 10²² atoms/cm²)

plabs

Absorption as a power-law in energy. Useful for things like dust.

$\begin{displaymath}M(E) ={\tt par2} (E/1 {\rm keV})^{-{\tt par1}}\end{displaymath}$

par1 = index

par2 = coefficient

pwab

An extension of partial covering fraction absorption into a power-law distribution of covering fraction as a function of column density, built from the wabs code. See Done & Magdziarz 1998 (MNRAS 298, 737) for details.

par1 = minimum equivalent hydrogen column (in units of 10²² atoms/cm²)

par2 = maximum equivalent hydrogen column (in units of 10²² atoms/cm²)

par3 = power law index for covering fraction.

redden

IR/optical/UV extinction from Cardelli et al. (1989, ApJ, 345, 245). The transmission is set to unity shortward of the Lyman limit. This is incorrect physically but does allow the model to be used in combination with an X-ray photoelectric absorption model such as phabs.

par1 = E(B-V)

smedge

A smeared edge (Ebisawa PhD thesis, implemented by Frank Marshall).

$\begin{displaymath}\begin{array}{lcll} M(E) & = & 1. & {\rm for\ } E \leq {\tt p... ...))/{\tt par4})) & {\rm for\ } E \geq {\tt par1}\\ \end{array}\end{displaymath}$

par1 = the threshold energy (keV)

par2 = the maximum absorption factor at threshold

par3 = index for photo-electric cross-section (normally -2.67)

par4 = smearing width (keV)

spline

A cubic spline modification.

par1 = start x-value

par2 = start y-value

par3 = end y-value

par4 = start dy/dx

par5 = end dy/dx

par6 = end x-value

SSS ice

The Einstein Observatory SSS ice absorption.

par1 = ice thickness parameter

tbabs

The Tuebingen-Boulder ISM absorption model. This model calculates the cross section for X-ray absorption by the ISM as the sum of the cross sections for X-ray absorption due to the gas-phase ISM, the grain-phase ISM, and the molecules in the ISM. In the grain-phase ISM, the effect of shielding by the grains is accounted for, but is extremely small. In the molecular contribution to the ISM cross section, only molecular hydrogen is considered. In the gas-phase ISM, the cross section is the sum of the photoionization cross sections of the different elements, weighted by abundance and taking into account depletion onto grains. In addition to the updates to the photoionization cross sections, the gas-phase cross section differs from previous values as a result of updates to the ISM abundances. These updated abundances are available through the abund wilm command. Details of updates to the photoionization cross sections as well as to abundances can be found in Wilms, Allen and McCray (2000, ApJ 542, 914).

par1 = equivalent hydrogen column (in units of 10²² atoms/cm²)

tbgrain

par1 = equivalent hydrogen column (in units of 10²² atoms/cm²)

par2 = molecular hydrogen column (in units of 10²² atoms/cm²)

par3 = grain density (in gm/cm³)

par4 = grain minimum size (in micron)

par5 = grain maximum size (in micron)

par6 = power-law index of grain sizes

tbvarabs

par1 = equivalent hydrogen column (in units of 10²²atoms/cm²)

par2 - par18 = abundance (relative to Solar) of He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl, Ar, Ca, Cr, Fe, Co, Ni

par19 = molecular hydrogen column (in units of 10²² atoms/cm²)

par20 = grain density (in gm/cm³)

par21 = grain minimum size (in micron)

par22 = grain maximum size (in micron)

par23 = power-law index of grain sizes

par24 - par41 = grain depletion fractions of He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl, Ar, Ca, Cr, Fe, Co, Ni

par42 = redshift

uvred

A UV reddening using Seaton's law (M.N.R.A.S., 187, 75p). Valid from 1000-3704Å. The transmission is set to unity shortward of the Lyman limit. This is incorrect physically but does allow the model to be used in combination with an X-ray photoelectric absorption model such as phabs.

par1 = E(B-V)

varabs

A photoelectric absorption with variable abundances using Balucinska-Church and McCammon (ApJ 400, 699) cross-sections. The column for each element is in units of the column in a solar abundance column of an equivalent hydrogen column density of 10²² cm^-2. The Solar abundance table used is set by the abund command.

par1- par18 = equivalent columns for H, He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl, Ar, Ca, Cr, Fe, Co, Ni

vphabs

A photoelectric absorption with variable abundances using Balucinska-Church and McCammon (ApJ 400, 699) cross-sections. The relative abundances are set by the abund command. This model is identical to varabs except for the way that the parameters are defined.

$\begin{displaymath}M(E) = \exp (-{\tt par1} \sigma (E))\end{displaymath}$

where $\sigma (E)$ is the photo-electric cross-section (NOT including Thomson scattering) and

par1 = equivalent hydrogen column (in units of 10²² atoms/cm²)

par2- par18 = abundances for He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl, Ar, Ca, Cr, Fe, Co, Ni wrt to Solar (defined by the abund command)

wabs

A photo-electric absorption using Wisconsin (Morrison and McCammon; ApJ 270, 119) cross-sections.

$\begin{displaymath}M(E) = \exp (-{\tt par1} \sigma (E))\end{displaymath}$

where $\sigma$ (E) is the photo-electric cross-section (NOT including Thomson scattering). Note that this model uses the Anders & Ebihara relative abundances (1982, Geochimica et Cosmochimica Acta 46, 2363) regardless of the abund command.

par1 = equivalent hydrogen column (in units of 10²² atoms/cm²)

wndabs

Photo-electric absorption from approximation to a warm absorber using Balucinska-Church and McCammon (ApJ 400, 699) cross-sections. Relative abundances are set by the abund command.

$\begin{displaymath}\begin{array}{lcll} M(E) & = & \exp (-{\tt par1} \sigma(E)) ... ...r2}\\ & = & 1. & {\rm for\ } E \leq {\tt par2}\\ \end{array}\end{displaymath}$

where $\sigma$ (E) is the photo-electric cross-section (NOT including Thomson scattering) and

par1 = equivalent hydrogen column (in units of 10²² atoms/cm²)

par2 = window energy (keV)

xion

This model describes the reflected spectra of a photo-ionized accretion disk or a ring if one so chooses. The approach is similar to the one used for tables with stellar spectra. Namely, a large number of models are computed for a range of values of the spectral index, the incident X-ray flux, disk gravity, the thermal disk flux and iron abundance. Each model's output is an un-smeared reflected spectrum for 5 different inclination angles ranging from nearly pole-on to nearly face on, stored in a look-up table. The default geometry is that of a lamppost, with free parameters of the model being the height of the X-ray source above the disk, h_X, the dimensionless accretion rate through the disk, $\dot m,$ the luminosity of the X-ray source, L_X, the inner and outer disk radii, and the spectral index. This defines the gravity parameter, the ratio of X-ray to thermal fluxes, etc., for each radius, which allows the use of a look-up table to approximate the reflected spectrum. This procedure is repeated for about 30 different radii. The total disk spectrum is then obtained by integrating over the disk surface, including relativistic smearing of the spectrum for a non-rotating black hole (e.g., Fabian 1989).

In addition, the geometry of a central sphere (with power-law optically thin emissivity inside it) plus an outer cold disk, and the geometry of magnetic flares are available (param(13)=2 and 3, respectively). One can also turn off relativistic smearing to see what the local disk spectrum looks like (param(12) = 2 in this case; otherwise leave it at 4). In addition, param(11)=1 produces reflected plus direct spectrum/direct; param(11)=2 produces (incident + reflected)/incident [note that normalization of incident and direct are different because of solid angles covered by the disk; 2 should be used for magnetic flare model]; and param(11)=3 produces reflected/incident. Abundance is controlled by param(9) and varies between 1 and 4 at the present. A much more complete description of the model will be presented in Nayakshin et al. 2001 (currently a draft is available at http://lheawww.gsfc.nasa.gov/users/serg/ms.ps)

par1 = height of the source above the disk (in Schwarzschild radii)

par2 = ratio of the X-ray source luminosity to that of the disk

par3 = accretion rate (in Eddington units)

par4 = $\cos i,$ the inclination angle (1 = face-on)

par5 = inner radius of the disk (in Schwarzschild radii)

par6 = outer radius of the disk (in Schwarzschild radii)

par7 = photon index of the source

par8 = redshift z

par9 = Fe abundance relative to Solar (which is defined as $3.16 \times 10^{-5}$ by number relative to H)

par10 = Exponential high energy cut-off energy for the source

par11 = 1 $\Rightarrow$ (reflected+direct)/direct, 2 $\Rightarrow$ (reflected+incident)/incident, 3 $\Rightarrow$ reflected/incident

par12 = 2 $\Rightarrow$ no relativistic smearing, 4 $\Rightarrow$ relativistic smearing

par13 = 1 $\Rightarrow$ lamppost, 2 $\Rightarrow$ central hot sphere with outer cold disk, 3 $\Rightarrow$ magnetic flares above a cold disk. Note that setting par13 to 2.y gives a central hot sphere with luminosity law $dL/dR = 4 \pi R^2 R^{-10y}.$ The inner radius of the sphere is 3 Schwarzschild radii and the outer radius is equal to par1. Only the case with ${{\tt p}ar5}>={{\tt p}ar1}$ has been tested so far.

zhighect

A redshifted high energy cutoff.

$\begin{displaymath}\begin{array}{lcll} A(E) & = & \exp (({\tt par1}-E (1+{\tt pa... ...r1}\\ A(E) & = & 1 & {\rm for\ } E < {\tt par1}\\ \end{array}\end{displaymath}$

where :

par1 = cutoff energy in keV

par2 = e-folding energy in keV

par3 = redshift

zpcfabs

A redshifted partial covering fraction absorption. Relative abundances are set by the abund command.

$\begin{displaymath}M(E) = {\tt par2} \exp(-{\tt par1} \sigma(E (1+{\tt par3}))) + (1-{\tt par2}) \end{displaymath}$

where $\sigma$ (E) is the photo-electric cross-section (NOT including Thomson scattering) (see phabs) and

par1 = equivalent hydrogen column (in units of 10²² atoms/cm²)

par2 = covering fraction (0 < par2 $\leq 1$ .) (dimensionless)

par3 = redshift

zphabs

A redshifted photoelectric absorption using Balucinska-Church and McCammon (ApJ 400, 699) cross-sections. The relative abundances are set by the abund command.

$\begin{displaymath}M(E) = \exp (-{\tt par1} \sigma (E(1+{\tt par2}))\end{displaymath}$

where $\sigma (E)$ is the photo-electric cross-section (NOT including Thomson scattering) and

par1 = equivalent hydrogen column (in units of 10²² atoms/cm²)

par2 = redshift

ztbabs

The Tuebingen-Boulder ISM absorption model. This model calculates the cross section for X-ray absorption by the ISM as the sum of the cross sections for X-ray absorption due to the gas-phase ISM and the molecules in the ISM. In the molecular contribution to the ISM cross section, only molecular hydrogen is considered. In the gas-phase ISM, the cross section is the sum of the photoionization cross sections of the different elements, weighted by abundance and taking into account depletion onto grains. In addition to the updates to the photoionization cross sections, the gas-phase cross section differs from previous values as a result of updates to the ISM abundances. These updated abundances are available through the abund wilm command. Details of updates to the photoionization cross sections as well as to abundances can be found in Wilms, Allen and McCray (2000, ApJ 542, 914). Note that this model differs from tbabs in that grains are not included.

par1 = equivalent hydrogen column (in units of 10²²atoms/cm²)

par2 = redshift

zvarabs

A photoelectric absorption with variable abundances using Balucinska-Church and McCammon (ApJ 400, 699) cross-sections. The column for each element is in units of the column in a solar abundance column of an equivalent hydrogen column density of 10²² cm². The Solar abundance table used is set by the abund command.

par1- par18 = equivalent columns for H, He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl, Ar, Ca, Cr, Fe, Ni, Co

par19 = redshift

zvfeabs

Redshifted photoelectric absorption with all abundances tied to Solar except for iron. The Fe K edge energy is a free parameter.

par1 = equivalent hydrogen column (in units of 10²² cm^-2)

par2 = abundance relative to Solar

par3 = iron abundance relative to Solar

par4 = Fe K edge energy

par5 = Redshift

zvphabs

A redshifted photoelectric absorption with variable abundances using Balucinska-Church and McCammon (ApJ 400, 699) cross-sections. The abundances are specified relative to the Solar abundance table set using the abund command. This model is identical to zvarabs except for the way that the parameters are defined.

$\begin{displaymath}M(E) = \exp (-{\tt par1} \sigma (E(1+{\tt par2}))\end{displaymath}$

where $\sigma (E)$ is the photo-electric cross-section (NOT including Thomson scattering) and

zwabs

A photo-electric absorption using Wisconsin (Morrison and McCammon; ApJ 270, 119) cross-sections.

$\begin{displaymath}M(E) = \exp (-{\tt par1} \sigma (E (1+={\tt par2}) ) ) \end{displaymath}$

where $\sigma$ (E) is the photo-electric cross-section (NOT including Thomson scattering) and

par1 = equivalent hydrogen column (in units of 10²² atoms/cm²)

par2 = redshift

zwndabs

Photo-electric absorption from approximation to a warm absorber using Balucinska-Church and McCammon (ApJ 400, 699) cross-sections. Relative abundances are set by the abund command.

$\begin{displaymath}\begin{array}{lcll} M(E) & = & \exp (-{\tt par1} \sigma (E (... ... par2}\\ & = & 1. & {\rm for\ } E \leq {\tt par2} \end{array}\end{displaymath}$

where $\sigma$ (E) is the photo-electric cross-section (NOT including Thomson scattering) and

par1 = equivalent hydrogen column (in units of 10²² atoms/cm²)

par2 = Window energy (keV)

par3 = redshift

Next: Convolution Model Components Up: XSPEC V11.3 Models Previous: Multiplicative Model Components A-M

Ben Dorman
2003-11-28

`par1`	=	line energy (keV)
`par2`	=	line width (keV)
`par3`	=	covering fraction

`par1`			=		equivalent hydrogen column (in units of 10²² atoms/cm²)
`par2`			=		covering fraction (0 < par2 <= 1.) (dimensionless)

`par1`	=	minimum equivalent hydrogen column (in units of 10²² atoms/cm²)
`par2`	=	maximum equivalent hydrogen column (in units of 10²² atoms/cm²)
`par3`	=	power law index for covering fraction.

`par1`	=	the threshold energy (keV)
`par2`	=	the maximum absorption factor at threshold
`par3`	=	index for photo-electric cross-section (normally -2.67)
`par4`	=	smearing width (keV)

`par1`	=	start x-value
`par2`	=	start y-value
`par3`	=	end y-value
`par4`	=	start dy/dx
`par5`	=	end dy/dx
`par6`	=	end x-value

`par1`	=	equivalent hydrogen column (in units of 10²²atoms/cm²)
`par2` - `par18`	=	abundance (relative to Solar) of He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl, Ar, Ca, Cr, Fe, Co, Ni
`par19`	=	molecular hydrogen column (in units of 10²² atoms/cm²)
`par20`	=	grain density (in gm/cm³)
`par21`	=	grain minimum size (in micron)
`par22`	=	grain maximum size (in micron)
`par23`	=	power-law index of grain sizes
`par24` - `par41`	=	grain depletion fractions of He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl, Ar, Ca, Cr, Fe, Co, Ni
`par42`	=	redshift

`par1`			=		equivalent hydrogen column (in units of 10²² atoms/cm²)
`par2`- `par18`			=		abundances for He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl, Ar, Ca, Cr, Fe, Co, Ni wrt to Solar (defined by the abund command)

`par1`	=	height of the source above the disk (in Schwarzschild radii)
`par2`	=	ratio of the X-ray source luminosity to that of the disk
`par3`	=	accretion rate (in Eddington units)
`par4`	=	$\cos i,$ the inclination angle (1 = face-on)
`par5`	=	inner radius of the disk (in Schwarzschild radii)
`par6`	=	outer radius of the disk (in Schwarzschild radii)
`par7`	=	photon index of the source
`par8`	=	redshift z
`par9`	=	Fe abundance relative to Solar (which is defined as $3.16 \times 10^{-5}$ by number relative to H)
`par10`	=	Exponential high energy cut-off energy for the source
`par11`	=	1 $\Rightarrow$ (reflected+direct)/direct, 2 $\Rightarrow$ (reflected+incident)/incident, 3 $\Rightarrow$ reflected/incident
`par12`	=	2 $\Rightarrow$ no relativistic smearing, 4 $\Rightarrow$ relativistic smearing
`par13`	=	1 $\Rightarrow$ lamppost, 2 $\Rightarrow$ central hot sphere with outer cold disk, 3 $\Rightarrow$ magnetic flares above a cold disk. Note that setting par13 to 2.y gives a central hot sphere with luminosity law $dL/dR = 4 \pi R^2 R^{-10y}.$ The inner radius of the sphere is 3 Schwarzschild radii and the outer radius is equal to par1. Only the case with ${{\tt p}ar5}>={{\tt p}ar1}$ has been tested so far.

`par1`	=	cutoff energy in keV
`par2`	=	e-folding energy in keV
`par3`	=	redshift

`par1`- `par18`			=		equivalent columns for H, He, C, N, O, Ne, Na, Mg, Al, Si, S, Cl, Ar, Ca, Cr, Fe, Ni, Co
`par19`			=		redshift