# How to constrain mass and spin of supermassive black holes through their disk emission

## TL;DR

This paper develops an analytical model of accretion disk emission around Kerr black holes to estimate their mass and spin, applying it to high-redshift blazars with jet signatures to constrain black hole properties.

## Contribution

It introduces a new analytic approximation of disk emission features based on the Kerr blackbody model, linking radiation patterns to black hole parameters.

## Key findings

- High spin values are required for jet-powered black holes.
- The model constrains black hole masses as a function of spin.
- Application to blazars supports the spin-mass relationship.

## Abstract

We investigate the global properties of the radiation emitted by the accretion disk around Kerr black holes. Using the Kerr blackbody (KERRBB) numerical model, we build an analytic approximation of the disk emission features focusing on the pattern of the produced radiation as a function of the black hole spin, mass, accretion rate and viewing angle. The assumption of having a geometrically thin disk limits our analysis to systems emitting below ~0.3 of the Eddington luminosity. We apply this analytical model to four blazars (whose jets are pointing at us) at high redshift that show clear signatures of disk emission. For them, we derive the black hole masses as a function of spin. If these jetted sources are powered by the black hole rotation, they must have high spin values, further constraining their masses.