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

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. In this model, alignment fronts propagate outward at a speed 0.2rΩprecess(r), where Ωprecess is the local test-particle precession frequency. Meanwhile, transonic radial motions transport angular momentum both inward and outward at a rate that can, in steady-state, be described roughly in terms of an orientation diffusion model with diffusion coefficient , for local orbital frequency Ω. The competition between the two leads, in isothermal disks, to a stationary position for the alignment front at a radius . 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 dynamics in MHD disks appears to be independent of the ratio c s /(αv orb), for orbital speed v orb and ratio of stress to pressure α. 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.