Exploring higher order images with Fe K_α-lines from relativistic disks: black hole spin determination and bias

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.