Sound Speed Dependence of Alignment in Accretion Disks Subjected to Lense–Thirring Torques

Abstract

We present a series of simulations in both pure hydrodynamics (HD) and magnetohydrodynamics (MHD) exploring the degree to which alignment of disks subjected to external precessional torques (e.g., as in the `Bardeen-Petterson' effect) is dependent upon the disk sound speed c_s. Across the range of sound speeds examined, we find that the influence of the sound speed can be encapsulated in a simple "lumped-parameter" model proposed by Sorathia et al. (2013a). In this model, alignment fronts propagate outward at a speed ~0.2 rOmega_precess(r), where Omega_precess is the local test-particle precession frequency. Meanwhile, transonic radial motions transport angular momentum both inward and outward at a rate that may be described roughly in terms of an orientation diffusion model with diffusion coefficient ~2c_s^2/Omega, for local orbital frequency Omega. The competition between the two leads, in isothermal disks, to a stationary position for the alignment front at a radius proportional to c_s^(-4/5). For alignment to happen at all, the disk must either be turbulent due to the magnetorotational instability in MHD, or, in HD, it must be cool enough for the bending waves driven by disk warp to be nonlinear at their launch point. Contrary to long-standing predictions, warp propagation in MHD disks is diffusive independent of the parameter c_s/(alpha v_orb$, for orbital speed v_orb and ratio of stress to pressure of alpha. In purely HD disks, i.e., those with no internal stresses other than bulk viscosity, warmer disks align weakly or not at all; cooler disks align qualitatively similarly to MHD disks.