INTRODUCTION

XSPEC has three models that allow a user to specify a filename from which the model spectra will be read. These models are atable for additive models, mtable for multiplicative models, and etable for exponential multiplicative models. An example use in XSPEC is:

XSPEC12> model phabs*atable{mymodel.fits}

The basic concept of a table model is that the file contains an N-dimensional grid of model spectra with each point on the grid having been calculated for particular values of the N parameters in the model. It is up to the creator of the table model file to decide what an appropriate spacing is for each parameter. XSPEC will interpolate on the grid to get the spectrum for the parameter values required at that point in the fit. There is the option for each parameter of linear or logarithmic interpolation. The tabulated parameter values must be in increasing order.

N-dimensional grids of model spectra can get rather large so a simplifying trick is available. If a parameter is decoupled from the other parameters and adds to the model spectrum in a linear fashion then it can be set up as an “additional parameter”. If there are N “interpolation” (ie standard) and M additional parameters then the grid of model spectra will be N-dimensional with each point on the grid containing M+1 model spectra. The first of these spectra is for the model with all the additional parameters being zero. The Ith spectrum (I=2,...,M+1) is the difference between the first spectrum and the spectrum from the model with the I-1th additional parameter set to one and all the other additional parameters set to zero.

An example of the use of additional parameters is a low density, collisional, plasma model where the contribution from each heavy element can be stored as a separate spectrum. In this case, there is one interpolation parameter (the temperature) and as many additional parameters as there are heavy elements in the model.

The atable model requires the table model to contain spectra in units of photons/cm/s (the standard for additive models models). XSPEC will include a normalization parameter. The mtable model requires a table model to contain multiplicative factors by which an additive model is to be modified. The etable model takes the numbers in the table model, multiplies them by -1 and exponentiates them. This is primarily intended for absorption models and is set up this way so that elemental abundances can be treated as additional parameters. For all these models XSPEC will add a redshift parameter if the REDSHIFT keyword in the table model file is set to true. If the redshift parameter is non-zero XSPEC will shift the model in energy space and divide by a (1+z) factor for time dilation.

Sometimes it is useful to be able to scale by energy without time dilation and this can be done by adding the ESCALE logical keyword to the table model file. If this keyword is set to true then an escale parameter is added to the model in XSPEC. This was added in HDUVERS=1.2.0.

The customary use of table model files is to interpolate on a single spectrum per grid point but there are circumstances where it is useful to have multiple spectra per grid point. An example is spectropolarimetry which involves simultaneous fitting of three spectra, one for each Stokes parameter, with a model which generates different spectra for each Stokes parameter. Thus, in this case, there needs to be three spectra for each grid point in the table. This is indicated by setting the NXFLTEXP keyword to 3 and the XFXP0001, XFXP0002, and XFXP0003 keywords to “Stokes:0”, “Stokes:1”, “Stokes:2”, respectively. These match to the XFLTnnnn keywords in the spectra to determine which model is used for each spectrum. In the SPECTRA extension there should be NXFLTEXP rows for each set of parameter values with the model spectra for that set of values ordered with that corresponding to XFXP0001 first, XFXP0002 second, and so on.

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Last modified: Monday, 18-Oct-2021 15:22:13 EDT