The plunging region of a thin accretion disc around a Schwarzschild black hole

TL;DR

This study validates analytic models of the plunging region in thin accretion discs around Schwarzschild black holes using 3D GRMHD simulations, highlighting the importance of non-zero stress and dissipation near the ISCO for accurate black hole spin measurements.

Contribution

The paper demonstrates that analytic solutions for the plunging region match GRMHD simulations when accounting for non-adiabatic heating, challenging the zero-stress boundary assumption in standard models.

Findings

Excellent agreement between analytic models and simulations with non-adiabatic heating.

Non-zero angular momentum drop (~5.3%) in the plunging region.

Stress is small but causes measurable dissipation near the ISCO.

Abstract

A set of analytic solutions for the plunging region thermodynamics have been developed recently under the assumption that the fluid undergoes a gravity-dominated geodesic plunge into the black hole. We test this model against a dedicated 3D global GRMHD simulation of a thin accretion disc around a Schwarzschild black hole using the code AthenaK. Provided that we account for non-adiabatic heating in the energetics, plausibly from grid-scale magnetic dissipation, we find an excellent agreement between the analytic model and the simulated quantities. These results are particularly important for existing and future electromagnetic black hole spin measurements, many of which do not to include the plunging fluid in their emission modelling. This exclusion typically stems from the assumption of a zero-stress boundary condition at the ISCO, forcing all thermodynamic quantities to vanish. Instead, we find a non-zero $\delta_\mathcal{J}\approx 5.3 \%$ drop in the angular momentum over the plunging region, which is consistent with both prior simulations and observations. We demonstrate that this stress is small enough for the dynamics of the fluid in the plunging region to be well-described by geodesic trajectories, yet large enough to cause measurable dissipation near to the ISCO - keeping thermodynamic quantities from vanishing. In the plunging region, constant $\alpha$-disc models are a physically inappropriate framework.