# Constraining Quasar Relativistic Reflection Regions and Spins with Microlensing

## TL;DR

This study uses microlensing of gravitationally lensed quasars to constrain the size and spin of relativistic reflection regions near supermassive black holes, revealing ultra-compact emission zones close to the black hole's event horizon.

## Contribution

It introduces a microlensing likelihood analysis to measure black hole spins and reflection region sizes in lensed quasars, providing new constraints on the innermost accretion structures.

## Key findings

- Black hole spins are constrained to be near maximal, with a > 0.92 for one target and around 0.8 for others.
- The relativistic reflection regions are ultra-compact, within a few gravitational radii of the black hole.
- Emission region sizes are constrained to less than 2.4 gravitational radii for one quasar and 5.9-7.4 for the combined sample.

## Abstract

We present an analysis of Chandra spectra of five gravitationally lensed active galactic nuclei. We confirm the previous detections of FeK$\alpha$ emission lines in most images of these objects with high significance. The line energies range from 5.8 to 6.8 keV with widths from unresolved to 0.6 keV, consistent with emission close to spinning black holes viewed at different inclination angles. We also confirm the positive offset from the Iwasawa-Taniguchi effect, the inverse correlation between the FeK$\alpha$ equivalent width and the X-ray luminosity in AGN, where our measured equivalent widths are larger in lensed quasars. We attribute this effect to microlensing, and perform a microlensing likelihood analysis to constrain the emission size of the relativistic reflection region and the spin of supermassive black holes, assuming that the X-ray corona and the reflection region, responsible for the iron emission line, both follow power-law emissivity profiles. The microlensing analysis yields strong constraints on the spin and emissivity index of the reflection component for Q2237+0305, with $a > 0.92$ and $n > 5.4$. For the remaining four targets, we jointly constrain the two parameters, yielding $a=0.8\pm0.16$ and an emissivity index of $n=4.0\pm 0.8$, suggesting that the relativistic X-ray reflection region is ultra-compact and very close to the innermost stable circular orbits of black holes, which are spinning at close to the maximal value. We successfully constrain the half light radius of the emission region to $< 2.4$ $r_g$ ($r_g = GM/c^2$) for Q2237+0305 and in the range 5.9--7.4 $r_g$ for the joint sample.