Modeling the Spectrum
You are now ready to start to create a model for the spectrum you
just loaded into Xspec. Xspec has several standard models, and in
general, it is best to start with the simplest model and build on it as
necessary.
In the world of astrophysics, simple phenomena include those that
produce a continuous x-ray emission, much like a rainbow, where all
colors are represented. You will use a model of Bremsstrahlung
emission, which is one mechanism that produces continuous X-ray
emission. (Read more on continuous X-ray
emission and Bremsstrahlung.)
In the Xspec command window, type:
model wabs * brems
This model has two components:
- wabs models the effects of absorption. Space is not
empty. As light travels across the great distances to reach us,
some of it will be absorbed by matter that lies between us and the
source. This component of your model accounts for that absorption.
It is characterized by the free parameter, nH.
- brems models the continuous emission due to
Bremsstrahlung. This model component has two free parameters. The
first is kT, which characterizes the
temperature of the X-ray-emitting matter. The second is norm, which is a measure of the
intensity of the spectrum.
Xspec will prompt you to enter starting values for each of these
parameters, as shown below:
1:wabs:nH>
For these parameters, you can just use the default values in
Xspec. To do that, hit return when Xspec prompts for the values
for nH, kT, and
norm. Xspec will fill in the values for these
parameters.
Initial model input. (Click for a larger view.)
Recall that in our simple data
fitting example the first guess was not the best model for the data.
The same is true here – the first guess is probably not the best
fit of the spectrum. Xspec will fit the model to the data attempting to
minimize the Chi-squared value discussed alongside the data fitting
example.
Have Xspec minimize Chi-squared for the current model and determine the best-fit values for
the free parameters by typing:
fit
at the command line interface.
Xspec will go through a set number of trials trying to maximize the
fit between the model and the data. When that number of trials is
finished, Xspec will pause to let you know that it has not found the
best fit yet. Since you want Xspec to find the best fit, hit return
each time it gives you the following message:
Number of trials exceeded: continue fitting?
By hitting the return button, you are telling Xspec to continue
trying to find the best fit. You will have to hit return a couple of
times until Xspec finds the best fit and returns to the Xspec prompt
(XSPEC12> )
After one attempt at fitting the spectra. When asked whether to
continue fitting, hit Return. (Click for a larger view.)
When Xspec has finished fitting, you should see a summary of the fit
above the prompt. This summary has a table that lists the best-fit
values for each of the free parameters in the model. In addition, the
summary includes the Chi-squared value for the current fit. These are
shown in the screen-shot below.
Screen shot of the Xspec command window showing the results of fitting the
Bremsstrahlung model. Arrows indicate how to read the results.
(Click for a larger view.)
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