On Hydromagnetic Stresses in Accretion Disk Boundary Layers

TL;DR

This paper investigates the physical mechanisms of angular momentum transport in accretion disk boundary layers, finding that hydromagnetic waves are inefficient, challenging standard models and suggesting different disk structures.

Contribution

It provides analytic solutions for non-MRI hydromagnetic waves in boundary layers, showing their inefficiency in transporting angular momentum, which aligns with numerical simulation results.

Findings

Hydromagnetic waves can be amplified but oscillate around zero stress.

Standard MRI-driven transport is ineffective in boundary layers with increasing angular frequency.

Results challenge the assumption of efficient angular momentum transport in inner accretion disk regions.

Abstract

Detailed calculations of the physical structure of accretion disk boundary layers, and thus their inferred observational properties, rely on the assumption that angular momentum transport is opposite to the radial angular frequency gradient of the disk. The standard model for turbulent shear viscosity satisfies this assumption by construction. However, this behavior is not supported by numerical simulations of turbulent magnetohydrodynamic (MHD) accretion disks, which show that angular momentum transport driven by the magnetorotational instability (MRI) is inefficient in disk regions where, as expected in boundary layers, the angular frequency increases with radius. In order to shed light into physically viable mechanisms for angular momentum transport in this inner disk region, we examine the generation of hydromagnetic stresses and energy density in differentially rotating backgrounds with angular frequencies that increase outward in the shearing-sheet framework. We isolate the modes that are unrelated to the standard MRI and provide analytic solutions for the long-term evolution of the resulting shearing MHD waves. We show that, although the energy density of these waves can be amplified significantly, their associated stresses oscillate around zero, rendering them an inefficient mechanism to transport significant angular momentum (inward). These findings are consistent with the results obtained in numerical simulations of MHD accretion disk boundary layers and challenge the standard assumption of efficient angular momentum transport in the inner disk regions. This suggests that the detailed structure of turbulent MHD accretion disk boundary layers could differ appreciably from those derived within the standard framework of turbulent shear viscosity.