Lev Arzamasskiy1 and Roman R. Rafikov2,3
Astrophysical Journal 854, 84 Link to Article [DOI: 10.3847/1538-4357/aaa8e8]
1Department of Astrophysical Sciences, Princeton University, Ivy Lane, Princeton, NJ 08540, USA
2Centre for Mathematical Sciences, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
3Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA
Spiral density waves are known to exist in many astrophysical disks, potentially affecting disk structure and evolution. We conduct a numerical study of the effects produced by a density wave, evolving into a shock, on the characteristics of the underlying disk. We measure the deposition of angular momentum in the disk by spiral shocks of different strengths and verify the analytical prediction of Rafikov for the behavior of this quantity, using shock amplitude (which is potentially observable) as the input variable. Good agreement between theory and numerics is found as we vary the shock amplitude (including highly nonlinear shocks), disk aspect ratio, equation of state, radial profiles of the background density and temperature, and pattern speed of the wave. We show that high numerical resolution is required to properly capture shock-driven transport, especially at small wave amplitudes. We also demonstrate that relating the local mass-accretion rate to shock dissipation in rapidly evolving disks requires accounting for the time-dependent contribution to the angular momentum budget caused by the time dependence of the radial pressure support. We provide a simple analytical prescription for the behavior of this contribution and demonstrate its excellent agreement with the simulation results. Using these findings, we formulate a theoretical framework for studying the one-dimensional (in radius) evolution of shock-mediated accretion disks, which can be applied to a variety of astrophysical systems.