Supermassive Black Hole Spin Constraints from Polarimetry in an Equatorial Disk Model

TL;DR

This study demonstrates how polarization measurements of supermassive black holes, especially M87*, can constrain black hole spin using a semi-analytic equatorial disk model, highlighting the importance of polarization spiral angles and plasma properties.

Contribution

It introduces a semi-analytic model linking polarization spiral angles to black hole spin, emphasizing the role of plasma conditions and polarization measurements in constraining spin.

Findings

Polarization spiral angles are sensitive to black hole spin direction.

Accurate measurements of spiral pitch angles can estimate spin with ~0.15-0.25 uncertainty.

Radial velocity components in the accretion disk improve spin measurement prospects.

Abstract

The Event Horizon Telescope has released polarized images of the supermassive black holes Messier 87* (M87*) and Sagittarius A* (Sgr A*) accretion disks. As more images are produced, our understanding of the average polarized emission from near the event horizon improves. In this letter, we use a semi-analytic model for optically thin, equatorial emission near a Kerr black hole to study how spin constraints follow from measurements of the average polarization spiral pitch angle. We focus on the case of M87* and explore how the direct, weakly lensed image spiral is coupled to the strongly lensed indirect image spiral, and how a precise measurement of both provides a powerful spin tracer. We find a generic result that spin twists the direct and indirect image polarization in opposite directions. Using a grid search over model parameters, we find a strong dependence of the resulting spin constraint on plasma properties near the horizon. Grid constraints suggest that, under reasonable assumptions for the accretion disk, a measurement of the direct and indirect image spiral pitch angles to $\pm 5^\circ$ yields a dimensionless spin amplitude measurement with uncertainty $\sigma_{|a_*|}\sim0.25$ for radially infalling models, but otherwise provides only weak constraints; an error of $1^\circ$ can reach $\sigma_{|a_*|}\sim0.15$. We also find that a well-constrained rotation measure greatly improves spin measurements. Assuming that equatorial velocity and magnetic field are oppositely oriented, we find that the observed M87* polarization pattern favors models with strong radial velocity components, which are close to optimal for future spin measurements.