On X-ray emission lines from active galactic nuclei and disk models

Abstract

Abstract. An efficient numerical code to calculate line profiles from warped disks around nonrotating black holes is presented. Extensive numerical experiments suggest a method making it possible to distinguish between line profiles belonging to flat and warped accretion disks. The extension of our code to rotating black holes is briefly discussed.

Relativistic emission lines from accretion disks around black holes

“…The light propagation problem between any two points in the curved space-time of a non-rotating (Schwarzschild) black hole can be solved analytically by expressing the radial coordinate r as a function of the polar angle in terms of elliptic functions (Brajnik, 1999;Č adež and Gomboc, 1996;Gomboc, 2001;Č adež et al, 2003;Č adež and Kostić, 2004). In this way, one obtains an orbit equation for photons.…”

Relativistic emission lines from accretion discs around black holes

“…Dealing with a non‐rotating black hole (Schwarzschild metric) makes the problem of calculating line profiles quite simple, owing to the symmetry of the metric. In this case, the light propagation problem between any two points in the curved space–time can be solved analytically by expressing the radial coordinate r as a function of the polar angle in terms of elliptic functions (Čadež & Gomboc 1996; Brajnik 1999; Gomboc 2001; Čadež et al 2003; Čadež & Kostić 2004). In this way one obtains an orbit equation for photons that is quite similar to the solution of the Kepler problem.…”

“…The Schwarzschild code has been designed with the aim of studying the effects of different disc illuminations (Čadež et al 2003) and of disc warping, and to understand whether and how it is possible to deduce the emissivity law from the line profile (Čadež et al 2000). It works as follows: A mesh of constant‐ r curves is established on the disc surface (flat or warped).…”

“…Here we describe a new, fast and accurate method that uses analytic solutions for geodesic equations in the Kerr metric (Čadež, Fanton & Calvani 1998; Čadež et al 2003) to produce accretion disc images and line profiles. The speed of the method allows us to study and present the parameter space (black hole angular momentum parameter, disc inclination, optical thickness, disc emissivity) in some detail.…”

Optics in the Schwarzschild spacetime

“…The two constants of motion ω and a can now be determined in two steps. First we determine the type of the orbit following reasoning illustrated in Figure 3 and then we solve the two equations obtained from the orbit equation at the initial and the final point (Brajnik 1999, Gomboc 2001, Cadež et al 2003, Kostić 2003.…”