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

Abstract The Event Horizon Telescope has released polarized images of the supermassive black holes Messier 87* (M87*) and Sagittarius 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 semianalytic 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 the 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 ±5° yields a dimensionless spin amplitude measurement with uncertainty <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">∣</mml:mo> <mml:msub> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msub> <mml:mo stretchy="false">∣</mml:mo> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>0.25</mml:mn> </mml:math> for radially infalling models but otherwise provides only weak constraints; an error of 1 ∘ can reach <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">∣</mml:mo> <mml:msub> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msub> <mml:mo stretchy="false">∣</mml:mo> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>0.15</mml:mn> </mml:math> . 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.