Relativistic iron lines in accretion disks: the contribution of higher order images in the strong deflection limit

TL;DR

This paper presents a semi-analytical method to accurately compute higher order gravitational lensing images contributing to relativistic iron lines in black hole accretion disks, highlighting their significance depending on disk inclination.

Contribution

It introduces the most accurate semi-analytical calculation of higher order images in iron line profiles using the strong deflection limit for Schwarzschild black holes.

Findings

Higher order images significantly affect iron line shapes at certain inclinations.

Analytical formulas for higher order contributions are derived.

The method improves modeling accuracy of relativistic iron lines.

Abstract

The shapes of relativistic iron lines observed in spectra of candidate black holes carry the signatures of the strong gravitational fields in which the accretion disks lie. These lines result from the sum of the contributions of all images of the disk created by gravitational lensing, with the direct and first-order images largely dominating the overall shapes. Higher order images created by photons tightly winding around the black holes are often neglected in the modeling of these lines, since they require a substantially higher computational effort. With the help of the strong deflection limit, we present the most accurate semi-analytical calculation of these higher order contributions to the iron lines for Schwarzschild black holes. We show that two regimes exist depending on the inclination of the disk with respect to the line of sight. Many useful analytical formulae can be also derived in this framework.