On the Nature of Angular Momentum Transport in Nonradiative Accretion Flows

The principles underlying a proposed class of black hole accretion models are examined. The flows are generally referred to as “convection-dominated,” and are characterized by inward transport of angular momentum by thermal convection and outward viscous transport, vanishing mass accretion, and vanishing local energy dissipation. In this paper we examine the viability of these ideas by explicitly calculating the leading order angular momentum transport of axisymmetric modes in magnetized, differentially rotating, stratified flows. The modes are destabilized by the generalized magnetorotational instability, including the effects of angular velocity and entropy gradients. It is explicitly shown that modes that would be stable in the absence of a destabilizing entropy gradient transport angular momentum outwards. There are no inward transporting modes at all unless the magnitude of the (imaginary) Brunt-Väisälä frequency is comparable to the epicyclic frequency, a condition requiring substantial levels of dissipation. When inward transporting modes do exist, they appear at long wavelengths, unencumbered by magnetic tension. Moreover, very general thermodynamic principles prohibit the complete recovery of irreversible dissipative energy losses, a central feature of convection-dominated models. Dissipationless flow is incompatible with the increasing inward entropy gradient needed for the existence of inward transporting modes. Indeed, under steady conditions, dissipation of the free energy of differential rotation inevitably requires outward angular momentum transport. Our results are in good agreement with global MHD simulations, which find significant levels of outward transport and energy dissipation, whether or not destabilizing entropy gradients are present. Subject headings: accretion — accretion disks — black hole physics — convection — instabilities — (magnetohydrodynamics:) MHD — turbulence