Using SPEX 2.00 to analyse stellar RGS spectra

SPEX is a spectral fitting package, designed specifically for high resolution 
X-ray spectra, written by Jelle Kaastra (SRON). The latest version (2.00) is 
installed at MSSL on the SUN msslhd. This document demonstrates the use of 
SPEX to analyse RGS spectra of stars. Further information and help on SPEX 
2.00 can be found on http://www.mssl.ucl.ac.uk/~ajb/spex/ including lists of 
commands and models.

RGS spectra are accompanied by a response matrix which parameterises the 
effective area of the spectrometer across its wavelength range. The SAS 
generates the spectrum and response in .pha and .rmf formats respectively, 
and these are converted to SPEX format (.spo and .res) using trafo, which is 
described in http://www.mssl.ucl.ac.uk/~ajb/spex/1_trafo.txt.

In the following discussion we assume that we have the files spectrum.spo 
and response.res in the working directory on msslhd.

Firstly, start SPEX by typing

        >spex

and read in the spectrum and response matrix:

        SPEX> data response spectrum

Note that you leave the .spo and .res off the filenames when you use this
command. Now plot the spectrum: set the plot device

        SPEX> plot device xw

set the plot type

        SPEX> plot type data

set the units on the x-axis to angstroms

        SPEX> p ux a

and set the y-axis to counts/second/angstrom

        SPEX> p uy a

and finally use the plot command:

        SPEX> p

Every time something is changed in the plot or model the plot command has to 
be repeated as the plot is not updated automatically.

Next, construct a spectral model. We will use a three-temperature thermal 
model. In SPEX, a spectral model is assembled by: firstly, defining the 
various model components; and secondly, defining the relationship of these 
components to each other. Before a model can be assembled though, since SPEX 
works using source luminosities rather than fluxes, one must set the distance 
to the source.

To set the source distance to 8.8 parsecs:

        SPEX> distance 8.8 pc

For a three-temperature thermal model, we need to define three cie (collisional 
ionisation equilibrium) components:

       SPEX> com cie
       SPEX> com cie
       SPEX> com cie

Some model components are additive and others are multiplicative. For each
additive component, you have to define which components it is multiplied by. 
In this case, cie is additive and no multiplicative components are required.

The model setup can be viewed by typing:

        SPEX> model show

and the values of the model parameters are displayed using:

        SPEX> par show

The cie model allows the user to specify emission measure (i.e. the 
normalisation), the electron temperature of the plasma, the electron density, 
ion temperature, microturbulance velocity, sigma (log T) and the relative (to  
Solar) abundances of all the individual elements from Helium to Zinc.

So, for the first cie component, let's set the electron temperature to 0.3 keV, 
the emission measure (normalisation in 1E64/m**3) to 0.000001 and the electron 
density to 0.0002 (in 1E20/m**3).

        SPEX> par 1 1 t value 0.3
        SPEX> par 1 1 norm value 0.000001
        SPEX> par 1 1 ed value 0.0002

The first number after 'par' refers to the dataset (multiple datasets can be 
read in by repeating the 'data response spectrum' command) and the second refers 
to the component number. We'll set the second component to 0.7 keV and the third 
to 1.126 keV:

        SPEX> par 1 2 t value 0.7
        SPEX> par 1 3 t value 1.126

then couple the electron densities of cie 2 and 3 to the electron density of 
cie 1:

        SPEX> par 1 2 ed couple 1 1 ed
        SPEX> par 1 3 ed couple 1 1 ed

and the normalisations and elemental abundances likewise:

        SPEX> par 1 2 norm couple 1 1 norm
        SPEX> par 1 3 norm couple 1 1 norm
        SPEX> par 1 2 02:30 couple 1 1 02:30
        SPEX> par 1 3 02:30 couple 1 1 02:30

and couple the electron and ion temperatures for each phase of the plasma:

        SPEX> par 1 1 it couple  1 1 t
        SPEX> par 1 2 it couple  1 2 t
        SPEX> par 1 3 it couple  1 3 t

After the model has been set up and some parameters defined, it can be 
calculated and plotted:

        SPEX> c
        SPEX> p
        
The model must be re-calculated every time a change is made, and re-plotted.

To zoom in on, say, the O VII triplet region, use:

        SPEX> p rx 20 24
        SPEX> p

Now we will fit the normalisation of cie 1 (which is now coupled to the 
normalisations of the other two components). The t and norm parameters are 
automatically set to 'thawed', i.e. allowed to vary in the fit, so we need to 
freeze the temperatures of the three components, as follows:

        SPEX> par 1 1 t status f
        SPEX> par 1 2 t status f
        SPEX> par 1 3 t status f
  
If we wanted to concentrate on the region of the O VII triplet when fitting, 
the rest of the spectrum could be ignored:

        SPEX> ignore 1:20.5 unit a
        SPEX> ignore 23:50 unit a
        SPEX> p

To ensure that the result of each fit iteration is plotted as the fitting 
algorithm progresses:

        SPEX> fit print 1

and then finally 

        SPEX> fit

to calculate the error on the normalisation, use:

        SPEX> error 1 1 norm

Then you can zoom out to view the whole spectrum again:

        SPEX> use 6:38 unit a
        SPEX> p rx 6 38
        SPEX> p

A postscript plot is produced using the following sequence of commands:

        SPEX> plot dev cps filename.ps
        SPEX> p rx 6 38
        SPEX> p
        SPEX> plot close 2

To exit from SPEX, type:

        SPEX> q