9.3. Statistics, binning and more

The files nustar.spo and nustar.res contains the observed (not simulated!) spectrum of the pulsar PSR J1813-1246 as observed by the NuSTAR satellite. You can adopt a distance of 2.5 kpc to this source. You can assume that the spectrum is a simple power law with Galactic foreground absorption.

  1. Load the spectrum into SPEX, and rebin the spectrum properly. No need to ignore any data here.

  2. Define the proper model and make a fit.

  3. We will make a few alternative fits. Make a table and note down the following numbers for each fit starting with your current one: the best-fit parameters and their error bars of the three free parameters of your model; the correlation between these parameters; and the fit statistic with its expected values; your current fit is model A.

    Parameter

    Model A

    Model B

    Model C

    Model D

    Norm

    \Gamma

    Luminosity

    corr norm-\Gamma

    corr norm-n_{\mathrm H}

    corr n_{\mathrm H} - \Gamma

    C-stat or \chi^2

    Exp. C-stat or dof

  4. Same as before, but now use the 3-80 keV luminosity as free parameter instead of the norm (change “type” for the power law model and the status of some parameters). This is model B.

  5. As above, but now instead the 3-20 keV luminosity (model C).

  6. As above, but now change the fit statistic from C-stat to \chi^2 (model D). Be shocked by the bias in fit parameters that you will see!

Learning goals:

After having done this spectrum, you should know:

  • How to change from normalisation ot luminosity.

  • See the importance of “pivot” point for the luminosity / normalisation.

  • Understand the danger of using \chi^2-fitting.