#acl All:read

The XSPEC [http://xspec.gsfc.nasa.gov/docs/xanadu/xspec/manual/XSmodelProjct.html projct] model is used to estimate parameters in 3-D space from the 2-D projected spectra. It is used as follows.

Suppose you have a Chandra observation of a cluster of galaxies and you extract three spectra file1.sp, file2.sp, and file3.sp from concentric annuli of width 20 arcsec ie the file1.sp is from the center to a radius of 20", file2.sp is from 20" to 40", and file3.sp is from 40" to 60". For simplicity we will assume that these are all circular annuli. The first step required is to add some keywords to each of the files. 

  ||Filename||XFLT0001||XFLT0002||XFLT0003||
  ||file1.sp||20.0    ||20.0    ||0.0     ||
  ||file2.sp||40.0    ||40.0    ||0.0     ||
  ||file3.sp||60.0    ||60.0    ||0.0     ||

Now read these files into XSPEC as three separate datagroups

XSPEC12> data 1:1 file1.sp 2:2 file2.sp 3:3 file3.sp

We will assume that these files have background and response keywords set so these associated files are read in automatically. Now we define the model

XSPEC12> model projct(mekal)

You will be prompted three times for projct and mekal parameter values. You should keep the defaults for the projct parameters and set the mekal parameters appropriately. The mekal parameters are now for the emission in a sphere of radius 20", a spherical shell from 20-40", and a spherical shell from 40-60", respectively. You can go ahead and fit for the mekal parameters just as you would without the projct model. 

The projct parameters are used to specify an inner radius for the first shell/annulus. In most cases this will be zero (the default). One case where you would want non-zero values of the parameters is if there is a radio source at the center of the cluster (eg Cygnus-A) displacing the X-ray emitting plasma. In all cases the parameters should be kept frozen. If any of them are allowed to be free parameters the model will be significantly slowed down.