Cataclysmic Variables in MHD

Abstract

We present results of global magnetohydrodynamic (MHD) simulations of accretion disks in Cataclysmic Variables fed by Roche lobe overflow, including vertical stratification, in order to investigate the roles of spiral shocks, magnetorotational instability (MRI), and the accretion stream on disk structure and evolution. In preparation for these global models, we test the effects of numerical diffusion relevant to studies of accretion disks. We perform one- and two-dimensional simulations of a dense cold Keplerian ring surrounded by a hot hydrostatic atmosphere, varying the Riemann solver, resolution, and the reconstruction method used. Finding HLLC/Roe Riemann solver and PLM reconstruction to be the best fit for our needs, we build our global models of CV disks. We include a simple treatment of gas thermodynamics designed to approximate conditions typical of dwarf nova outbursts, with orbital Mach numbers at the inner edge of the disk M_in of 5 and 10.

We find mass accretion rates in our global models to vary considerably on all time scales, with only the Mach 5 model reaching a clear quasi-stationary state. For Mach 10, the model undergoes an outside-in magnetically-driven accretion event occurring on a time scale of ~10 orbital periods of the binary. Both models exhibit spiral shocks inclined with respect to the binary plane, with their position and inclination changing rapidly. However, the time-averaged location of these shocks in the equatorial plane is well-fit by simple linear models. MRI turbulence in the disk generates toroidal magnetic field patterns (butterfly diagrams) that are in some cases irregular, perhaps due to interaction with spiral structure.

While many of our results are in good agreement with local studies, we find some features (most notably those related to spiral shocks) can only be captured in global models such as studied here. Thus, while global studies remain computationally expensive, we find them essential (along with more sophisticated treatment of radiation transport and disk thermodynamics) for furthering our understanding of accretion in binary systems. Finally, we discuss future improvements to our framework including the use of orbital advection, where early tests indicate 50-100% improvement in code performance.