Measuring the Innermost Stable Circular Orbits of Supermassive Black Holes

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 55° (99% confidence level). We detect two shifted Fe lines in several observations, as predicted in our numerical simulations of caustic crossings. The current ΔE 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.