Exploring higher order images with Fe K_{\alpha}-lines from relativistic disks: black hole spin determination and bias

TL;DR

This study examines how higher order images influence the relativistic Fe Kα line profile in black hole accretion disks, revealing their potential to bias spin measurements and be detected with future X-ray missions.

Contribution

It introduces the analysis of higher order image contributions to the Fe Kα line profile and assesses their impact on black hole spin measurements.

Findings

HOIs add 0.4-1.3% to the line flux.

HOIs can bias spin measurements by up to 0.3.

Future X-ray observations can detect HOI effects.

Abstract

We study the contributions to the relativistic Fe $K_{\alpha}$ line profile from higher order images (HOIs) produced by strongly deflected rays from the disk which cross the plunging region, located between the innermost stable circular orbit (ISCO) radius and the event horizon of a Kerr black hole. We investigate the characteristics features imprinted by the HOIs in the line profile for different black hole spins, disk emissivity laws and inclinations. We find that they extend from the red wing of the profile up to energies slightly lower than those of the blue peak, adding $\sim 0.4 - 1.3$\% to the total line flux. The contribution to the specific flux is often in the $\sim 1$\% to 7\% range, with the highest values attained for low and negative spin ($a\lesssim 0.3$) black holes surrounded by intermediate inclination angle ($i\sim40^{\circ}$) disks. We simulate future observations of a black hole X-ray binary system with the Large Area Detector of the planned X-ray astronomy \emph{enhanced X-ray Timing and Polarimetry Mission} (eXTP) and find that the \fekal\ of systems accreting at $\lesssim 1 $\% the Eddington rate are affected by the HOI features for a range of parameters. This would provide evidence of the extreme gravitational lensing of HOI rays. Our simulations show also that not accounting for HOI contributions to the Fe $K_{\alpha}$ line profile may systematically bias measurements of the black hole spin parameter towards values higher by up to $\sim 0.3$ than the inputted ones.