9.6. Relativistic lines

The file agnrel.spo contains a spectrum of an AGN at 1 Mpc distance. The response matrix to be used is corona.res. The two features that are visible in the spectrum are the O VIII L\alpha (\lambda=18.969 Å)and N VII L\alpha (\lambda=24.781 Å) lines. Because the emission from the disk is influenced by general relativistic effects, the lines appear to be broad and asymmetric. In SPEX we can model these lines by convolving a delta line with a so-called Laor profile (com laor) and learn a lot about the geometry of the system.

In this exercise we fix the \mathrm{N}_{\mathrm{H}} to 1 \times 10^{20} \ \mathrm{cm}^{-2}. The continuum emission can be well described with a powerlaw. The response file is corona.res.

  1. First start with the most simple model components: pow and Galactic foreground absorption. Plot the data. Hint: it may be useful to plot the flux as counts/\mathrm{m}^2/s/Å versus wavelength in Å. Try first to get a reasonable model spectrum for the continuum. You may do this by ignoring the part of the spectrum where you see lines.

  2. Set up next the full model by adding lines with delt and relativistic broadening by laor. Do not forget to use all data again, and it may be wise at this stage to freeze the parameters for the continuum (but do not forget to thaw them for your final fits).

  3. Fit the spectrum. Hint: do not thaw all parameters at the same time, but step by step.

    In the laor component you can free the parameters r1, r2, q and i. You can find the line energies of the oxygen and nitrogen lines also in the SPEX line list. Is the fit acceptable? Look at the residuals of the fit and check wether the lines are well fitted. If not, try to find out which parameter of the laor component should be altered.

  4. The inner radius of the disk r1 tells you immediately the spin of the black hole. A non-spinning black hole has r_1=6, a maximally spinning black hole has r_1\rightarrow 1. What can you tell about the spin of the black hole?

  5. Vary the parameters r1, r2, q and i to see how they influence the line profile (give them manually a different value and issue the “calc” command followed by the “plot” command).

Learning goals:

After having done this spectrum, you should know:

  • How to create a complex model with relativistic emission lines.

  • The usefullness of freezing parameters or omitting initially parts of the spectrum to get a first-step estimate of the spectrum.

  • How X-ray spectra tell you something about spinning black holes.