Multiplicative Model Components A-M

Multiplicative, convolution, and mixing models represent media intervening between sources and the observer that modify the source flux in an energy-dependent way.

  
absori

An ionized absorber based on that of Done et al. (1992, ApJ 395, 275) and developed by Magdziarz & Zdziarski. See also Zdziarski et al. (1995, ApJ 438, L63). Photoionization rates are from Reilman & Manson (1979, ApJS 40, 815), who employ the Hartree-Slater approximation (accurate to about 5%), and recombination rates are from Shull & Steenburg (1982, ApJS 48, 95). The cross sections are extrapolated with E^-3 above 5 keV. The abundances are set up by the command abund. Send questions or comments to aaz@camk.edu.pl.

par1			=		power-law photon index.
par2			=		Hydrogen column in units of 1022 cm-2.
par3			=		Absorber temperature in K.
par4			=		Absorber ionization state (L/nR2), see Done et al. (1992).
par5			=		Redshift.
par6			=		Iron abundance relative to that defined by the command abund.

  
acisabs

This model accounts for the decay in the ACIS quantum efficiency most likely caused by molecular contamination of the ACIS filters. The user needs to supply the number of days between Chandra launch and observation. The acisabs parameters related to the composition of the hydrocarbon and the rate of decay should be frozen and not modified. The present version of acisabs is to be used for the analysis of bare ACIS I and ACIS S data. For the present version of acisabs one must use the standard qe file vN0003 instead of the optional vN0004 file.

Because of the present large uncertainity in the ACIS gain at energies below 350eV we recommend that events in the 0-350eV range be ignored in the spectral analysis until the gain issue is resolved.

acisabs calculates the mass absorption coefficients of the contaminant from atomic scattering factor files provided at http://www-cxro.lbl.gov/optical_constants/asf.html

par1			=		Days between Chandra launch and ACIS observation
par2			=		Slope of linear quantum efficiency decay
par3			=		Offset of linear quantum efficiency decay
par4			=		Number of carbon atoms in hydrocarbon
par5			=		Number of hydrogen atoms in hydrocarbon
par6			=		Number of oxygen atoms in hydrocarbon
par7			=		Number of nitrogen atoms in hydrocarbon

  
cabs

Non-relativistic, optically-thin Compton scattering.

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

where $\sigma (E)$ is the Thomson cross-section.

par1

=

hydrogen column (in units of 1022 atoms/cm2)

  
constant

An energy-independent multiplicative factor.

par1

=

factor

  
cyclabs

A cyclotron absorption line as used in pulsar spectra. See Mihara et al., Nature, 1990 or Makishima et al. PASJ, 1990.

$$\begin{array}{lcl} M(E) & = & \exp(-{\tt par1} ({\tt par3} E/... ...(2{\tt par2}))^2/((E-2{\tt par2})^2+{\tt par5}^2))) \end{array}$$

par1			=		depth of the fundamental
par2			=		cyclotron energy
par3			=		width of the fundamental
par4			=		depth 2nd harmonic
par5			=		width of the 2nd harmonic

  
dust

A modification of a spectrum due to scattering off dust on the line-of-sight. The model assumes that the scattered flux goes into a uniform disk whose size has a 1/E dependence and whose total flux has a 1/E² dependence.

par1			=		scattering fraction at 1 keV
par2			=		size of halo at 1 keV in units of the detector beamsize

  
edge

An absorption edge.

$$\begin{array}{lcll} M(E) & = & 1 & {\rm for\ } E \leq {\tt p... ...tt par1})^{-3})) & {\rm for\ } E \geq {\tt par1}\\ \end{array}$$

where :

par1			=		threshold energy
par2			=		absorption depth at the threshold

  
etable

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

XSPEC>model etable{mymod.mod}

uses mymod.mod as the input for the model. XSPEC will multiply the contents of the model by -1 then take the exponential ie this model is for calculating absorption functions. 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).

  
expabs

A low-energy exponential rolloff.

$$M(E) = \exp(-{\tt par1}/E)$$

where :

par1

=

e-folding energy for the absorption

  
expfac

An exponential modification of a spectrum.

$$\begin{array}{lcll} M(E) & = & 1.+{\tt par1} \exp(-{\tt par2}... ... \\ M(E) & = & 1. & {\rm for\ } E < {\tt par3} \\ \end{array}$$

par1			=		amplitude of effect
par2			=		exponential factor
par3			=		start energy of modification

  
highecut

A high energy cutoff.

$$\begin{array}{lcll} A(E) & = & \exp (({\tt par1}-E)/{\tt par... ...\ A(E) & = & 1 & {\rm for\ } E \leq {\tt par1}\\ \end{array}$$

where :

par1			=		cutoff energy in keV
par2			=		e-folding energy in keV

  
hrefl

A simple multiplicative reflection model due to Tahir Yaqoob. Parameters are as follows:

par1			=		minimum angle (degrees) between source photons incident on the slab and the slab normal (=arctan(Ri/H).
par2			=		maximum angle (degrees) between source photons incident on the slab and the slab normal (=arctan(Ro/H).
par3			=		Angle (degrees) between the observer's line of sight and the slab normal.
par4			=		Iron abundance relative to Solar.
par5			=		Iron K-edge energy.
par6			=		Fraction of the direct flux seen by the observer.
par7			=		Normalization of the reflected continuum.
par8			=		redshift.

This model gives the reflected X-ray spectrum from a cold, optically thick, circular slab with inner and outer radii (Ri & Ro, respectively) illuminated by a point source a height H above the centre of the slab. The main difference between this model and other reflection models is that analytic approximations are used for the Chandrasekar H functions (and their integrals) and ELASTIC SCATTERING is assumed (see Basko 1978, ApJ, 223, 268). The elastic-scattering approximation means that the model is ONLY VALID UP TO $\approx$15 keV in the source frame. Future enhancements will include fudge factors that will allow extension up to 100 keV. The fact that no integration is involved at any point makes the routine very fast and particularly suitable for generating error contours, especially when fitting a large number of data channels. The model is multiplicative, and so can be used with ANY incident continuum. Suppose the incident photon spectrum is N(E) photons/cm/cm/s/keV and that the incident continuum is steady in time, and suppose further that the reflected continuum from the slab is R(E). When you multiply the incident spectrum with HREFL, what you actually get is the following:

$$model(E) = {\tt par6} N(E) + {\tt par7} R(E)$$

Thus, the actual physical situation described above corresponds to par6=1.0 and par7=1.0. You may decide to float par6 and/or par7. In that case, you must decide what the best-fitting values of these parameters mean physically for your case. It may imply time-lags between the direct and reflected components, different source and/or disk geometries to those assumed, or something else.

  
mtable

A multiplicative table model. The filename to be used should be given immediately after mtable in the model command. For example

XSPEC>model mtable{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). An example multiplicative table model file is testpcfabs.mod in $XANADU/src/spectral/session.