Thin Disk Theory with a Non-Zero Torque Boundary Condition and Comparisons with Simulations

TL;DR

This paper develops an analytical model for thin accretion disks around Kerr black holes that includes non-zero inner boundary stresses, extends into the plunging region, and compares favorably with simulations, potentially improving spin measurements.

Contribution

It introduces a novel analytical solution for thin disks with non-zero boundary stresses and extends the model into the plunging region, aligning better with numerical simulations.

Findings

The model matches well with GRMHD simulations.

Including non-zero boundary stresses improves the accuracy of disk models.

The solution is consistent for thin disks with h < alpha.

Abstract

We present an analytical solution for thin disk accretion onto a Kerr black hole that extends the standard Novikov-Thorne alpha-disk in three ways: (i) it incorporates nonzero stresses at the inner edge of the disk, (ii) it extends into the plunging region, and (iii) it uses a corrected vertical gravity formula. The free parameters of the model are unchanged. Nonzero boundary stresses are included by replacing the Novikov-Thorne no torque boundary condition with the less strict requirement that the fluid velocity at the innermost stable circular orbit is the sound speed, which numerical models show to be the correct behavior for luminosities below ~30% Eddington. We assume the disk is thin so we can ignore advection. Boundary stresses scale as alpha*h and advection terms scale as h^2 (where h is the disk opening angle (h=H/r)), so the model is self-consistent when h < alpha. We compare our solution with slim disk models and general relativistic magnetohydrodynamic disk simulations. The model may improve the accuracy of black hole spin measurements.