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Model Spectra for Spectral-Fitting Program

For on-line information type: cl> help using_spectral

The models provided are:

• abs - absorption of x-rays by neutral gas with solar abundances.

  parameter 1 =	logarithmic value of Galactic NH in units of cm-2
  parameter 2 =	logarithmic value of Intrinsic NH in units of cm-2
  parameter 3 =	redshift of source

  If only one parameter is given, it is assumed to be the Galactic N_H.

  If only two parameters are given, they are assumed to be the Intrinsic N_H and the redshift.

• pow - power law

  parameter 1 =	normalization - logarithmic value of the flux density at 1 keV in units of keV cm-2 s-1 keV-1
  parameter 2 =	energy index defined as $S_{\nu}\propto E^{-\alpha}$, where $S_{\nu}$ is the flux density

• bre - thermal bremsstrahlung (exponential plus gaunt factor)

  parameter 1 =	normalization - logarithmic value of the flux density at 1 keV in units of keV cm-2 s-1 keV-1
  parameter 2 =	temperature in the source frame in KeV

• exp - pure exponential

  parameter 1 =	normalization - logarithmic value of the flux density at 1 keV in units of keV cm-2 s-1 keV-1
  parameter 2 =	temperature in the source frame in KeV

• bla - black body

  parameter 1 =	normalization - logarithmic value of the flux density at 1 keV in units of keV cm-2 s-1 keV-1
  parameter 2 =	temperature in the source frame in keV

• ray - optically thin thermal spectrum with metallic lines (Raymond code)

  parameter 1 =	normalization - logarithmic value of the ratio of the volume emission measure to $4\pi D^{2}$, where D is the distance to the target. Units of the normalization are cm-5.
  parameter 2 =	temperature in the source frame in keV
  parameter 3 =	abundance table
  	c - cosmic
  	m - Meyer
  parameter 4 =	percentage of heavy elements (100 is the solar value)

• line - single gaussian line model

  parameter 1 =	normalization - logarithmic value of the normalization of the gaussian in units of keV cm-2 s-1.
  parameter 2 =	line centroid in keV
  parameter 3 =	FWHM of the line in keV

For detailed information on model parameters, please refer to the science specifications in xspectraldoc$spectral.(tex,dvi).

The spectral model and its parameters are passed to the fitting tasks as:

absorption(params)*model(params)

More than one absorption and more than one spectral model can be combined in the following ways:

absorption1(params)*model1(params)+absorption2(params)*model2(params)...

or

absorption(params)*(model1(params)+model2(params)...+modelN(params))

Some basic rules for writing a model description:

• Commas or spaces separate parameters
• Lo:hi should be given when a parameter should vary within these boundaries. A single number indicates a fixed parameter value.
• There are no implicit parameters (i.e., all parameters must be specified). The exception is the normalization. For a single model the normalization does not need to be specified and will be calculated. For a combination of models, however, either a range or a specific value for the normalization must be given for all but the first model. The normalization in the first model will be calculated as before. A single value for the normalization (i.e., fixed normalization) will force the program to use that value.
• Normalization for models 2 ... N are relative to that of model 1. To specify a fixed normalization for model 2, 50% that of model 1, the syntax is:

  abs(18:20) * ( power(0:2) + brems ( log(0.5), 0:20) )

NOTE: When different spectral models with different units for the normalization are combined, the relative normalization of the second model can be quite large.

For example: ray(1:2,c,100)+pow(11:13,1:2)

specifies a power-law model with a flux of approximately 1% of the flux in the Raymond model.

See cl> help models_spectral for more information on syntax.

Note: The program fit starts at the midpoint of the parameter range specified, then changes the parameters to determine the direction in which $\chi ^{2}$ is decreasing and heads in that direction to find the parameter values that give the minimum $\chi ^{2}$. If the initial parameter range is large, only part of the parameter space may be tested, and the program can settle into a secondary minimum. The real minimum can be missed. Choose parameter limits carefully.

Examples:

1.

abs(20:21)*pow(1:2)

to describe a power law model spectrum, with energy index varying between 1 and 2, and a galactic absorption varying between 10²⁰ and 10²¹ cm^-2.

2.

abs(20:21,23,1.0)*(pow(1:2)+pow(log(0.5):log(0.6),1.5)

for two power law models, and one absorption applied to both of them. The galactic absorption can vary between 10²⁰ and 10²¹ cm^-2, the intrinsic absorption is fixed at 10²³, for an object at z=1. The energy index of the first power law model can vary between 1 and 2, with the best fit normalization calculated by the program. The second power law has a fixed index of 1.5, and its normalization is allowed to vary between 50 and 60 % of the first one.

3.

abs(20:21)*pow(1:2)+abs(21:22)*pow(0.1,2:3)

to describe two power law models, each with galactic absorption in two different ranges.