The plunging region of thin accretion discs across the black hole spin range

We compute and test analytic models for the plunging region dynamics, thermodynamics, and magnetic fields against dedicated 3D global general relativistic magnetohydrodynamics (MHD) simulations of thin accretion discs around black holes across the spin range, using the code ATHENAK. We find that the dynamics of the plunging fluid closely resembles that of a gravity-dominated geodesic plunge, with the best agreement at low spins. Additionally, we find good agreement between the thermodynamic framework and the simulated quantities across the spin range. Finally, we develop a new model for the magnetic fields in the plunging region that assumes a fixed geodesic inflow, into which the magnetic fields are frozen. Overall, our simulations are in good concordance with this model, albeit with some discrepancies that suggest a degree of non-ideal MHD dissipation. In addition, we investigate how the MHD stresses in the plunging region depend on the black hole spin, interpreting our results through the lens of our flux-freezing model. We find that the magnitude of the stress increases as the black hole spin is increased in the prograde direction. This question is of particular importance for observers who wish to determine the black hole spin from X-ray measurements of the inner accretion disc, since a low-stress, high-spin solution is degenerate with a high-stress, low-spin solution. The spin-stress relationship that we report is approximately orthogonal to the contour of degenerate spin-stress pairings, indicating that the degeneracy is not fundamental. We show this explicitly for the case of M33 X-7.