The iron $K_α$-line diagnostics of a rotational black hole metric

The original idea to show the spacetime geometry using few geodesics was developed by Johnson and Ruffini (1974). We used this idea to interpret the observational data for rotating BH's. We developed the imitation approach to simulate a propagation of radiation near BH's. An important problem for this approach is the diagnostics of a black hole metric using X-ray observational data of the iron $K_α$-line. Observations of Seyfert galaxies in X-ray region reveal the broad emissiion lines in their spectra, which can arise in inner parts of accretion disks, where the effects of General Relativity (GR) must be counted. A spectrum of a solitary emission line (the $K_α$-line of iron, for example) of a hot spot in Kerr accretion disk is simulated, depending on the radial coordinate $r$ and the angular momentum $a=J/M$ of a black hole, under the assumption of an equatorial circular motion of a hot spot. Using results of numerical simulations it is shown that the characteristic two-peak line profile with the sharp edges arises at a large distance, (about $r \approx (3-10)r_g$). The inner regions emit the line, which is observed with one maximum and extremely broad red wing. High accuracy future spectral observations, being carried out, could detect the angular momentum $a$ of the black hole. We analyzed the different parameters of problems on the observable shape of this line and discussed some possible kinds of these shapes. The total number of geodesics is about $10^9$ (to simulate possible shapes of the $K_α$-line), so the number is great enough, especially in comparison with few geodesics in the original paper by Johnson and Ruffini (1974).

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