Measuring the Innermost Stable Circular Orbits of Supermassive Black Holes

TL;DR

This paper introduces the g-distribution method, a new technique using microlensing-induced energy shifts in iron lines to measure the spin, inclination, and ISCO of supermassive black holes in lensed quasars.

Contribution

The paper presents the g-distribution method, a novel approach for estimating black hole parameters from relativistic iron line shifts caused by microlensing.

Findings

Initial constraints on RX J1131-1231 indicate r_ISCO<8.5 r_g and i > 76 degrees.

Detection of two shifted Fe lines consistent with simulations.

Further monitoring expected to improve parameter estimates.

Abstract

We present a promising new technique, the g-distribution method, for measuring the inclination angle (i), the innermost stable circular orbit (ISCO), and the spin of a supermassive black hole. The g-distribution method uses measurements of the energy shifts in the relativistic iron line emitted by the accretion disk of a supermassive black hole due to microlensing by stars in a foreground galaxy relative to the g-distribution shifts predicted from microlensing caustic calculations. We apply the method to the gravitationally lensed quasars RX J1131-1231 (z_s=0.658, z_l=0.295), QJ 0158-4325 (z_s=1.294, z_l=0.317), and SDSS 1004+4112 (z_s=1.734, z_l=0.68). For RX J1131-1231 our initial results indicate that r_ISCO<8.5 gravitational radii (r_g) and i > 76 degrees. We detect two shifted Fe lines, in several observations, as predicted in our numerical simulations of caustic crossings. The current DeltaE-distribution of RX J1131-1231 is sparsely sampled but further X-ray monitoring of RX J1131-1231 and other lensed quasars will provide improved constraints on the inclination angles, ISCO radii and spins of the black holes of distant quasars.