Modeling the Spectrum

You are now ready to build 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 add on components as necessary. (If you skipped the general discussions on models: What is a Model in Science? and How Good is the Model?, now might be a good time to look at those pages.)

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 start with a simple model that describes a blackbody. A black body is an idealized object that absorbs all electromagnetic radiation that falls on it, and it is characterized by a temperature. Previous studies have shown that this is a good model for accretion disks.

In the Xspec command window, type:

model wabs * bbody

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.
• bbody models the continuous emission due to blackbody radiation. 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 a value 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.

Xspec Command Window showing the initial model inputs.

(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 as discussed in 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.

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. (You may need to resize the Xpsec command window, or scroll up, to see the entire table.)

Screen shot of the Xspec command window showing the results of fitting the blackbody radiation model. Arrows indicate how to read the results.

(Click for a larger view.)