Two-Dimensional Simulations of the Thermonuclear Runaway in an Accreted Atmosphere of a C+O White Dwarf

We present the results of two-dimensional calculations of turbulent nuclear burning of hydrogen-rich material accreted onto a white dwarf of 1 solar mass. The main aim of the present paper is to investigate the question as to whether and how the general properties of the burning are affected by numerical resolution effects. In particular, we want to see whether or not convective overshooting into the surface layers of the C+O white dwarf can lead to self-enrichment of the initially solar composition of the hydrogen-rich envelope with carbon and oxygen from the underlying white dwarf core. Our explicit hydrodynamic code is based on the PPM-method and computes the onset of the thermonuclear runaway on a Cartesian grid. In contrast to previous works we do not observe fast mixing of carbon and oxygen from the white dwarf's surface into the envelope by violent overshooting of large eddies. The main features of the flow fields in our simulations are the appearance of small persistent coherent structures of very high vorticity (and velocity) compared to the background flow. Their typical linear scales are about 10 to 20 grid zones and thus their physical size depends on the numerical resolution, i.e, their size decreases with increasing resolution. The two simulations (low and high resolution) which are presented here show only moderate differences in spatially integrated quantities such as laterally averaged temperature, energy generation rate, and chemical composition. We have not expanded both simulations equally long, but for the physical time under consideration the major difference seems to be that the highly resolved simulation is a bit less violent. In conclusion, we do find some self-enrichment, but on time-scales much longer than in previous calculations.