Analytical approximation of the emission line Fe $K_\alpha$ in QSO's spectra

TL;DR

This paper develops an analytical approximation method for the Fe Kα emission line in QSO spectra, enabling rapid modeling of relativistic effects in accretion disks around black holes.

Contribution

It introduces a numerical approximation of the Fe Kα line profile that accounts for general relativity, significantly reducing computation time in spectral analysis.

Findings

Approximation reduces computation time by up to a million times.

The method accurately models the line profile across various disk parameters.

Available online for use in astrophysical research.

Abstract

In spectra of many Seyfert galaxies there is a wide emission line of Fe $K_\alpha$. The line profile with two maxima supposes that the line emerges in innermost regions of an accretion disk around a black hole, hence, it is necessary to take into account General Relativity (GR) effects. In order to determine GR processes which occur in active galactic nuclei (AGN) an inverse problem of reconstructing the accreting system parameters from the line profile has to be solved quickly. In this paper we present a numerical approximation of the emission line Fe $K_\alpha$ with analytical functions. The approximation is accomplished for a range of the disk radial coordinate $r$ and the angle $\theta$ between line of sight and perpendicular to the disk and allows one to decrease computing time by $10^6$ times in certain astrophysical problems taking into account all GR effects. The approximation results are available in the Internet at http://www.iki.rssi.ru/people/repin/approx