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Astron. Astrophys. 337, 379-392 (1998)

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Two-dimensional simulations of the thermonuclear runaway in an accreted atmosphere of a C+O White Dwarf

A. Kercek 1, W. Hillebrandt 1 and J.W. Truran 2

1 Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Strasse 1, D-85740 Garching, Germany
2 Department of Astronomy and Astrophysics, Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA

Received 5 December 1997 / Accepted 29 April 1998


We present the results of two-dimensional calculations of turbulent nuclear burning of hydrogen-rich material accreted onto a white dwarf of 1.0 [FORMULA]. 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. Only part of the white dwarf 's surface is covered by the computational grid and curvature effects are ignored. 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. For the early phase of the thermonuclear runaway (TNR) they dominate the flow patterns and result in very little overshoot and mixing. Only at late times, after steady slow mixing and with increasing nuclear energy production, do these structures become weak, but show up again once hydrogen has mainly been burnt and the energy generation rate drops.

On the other hand, there are no big differences between high and low resolution simulations, as far as the overall properties of the TNR are concerned. The two simulations 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.

Key words: stars: novae, cataclysmic variables – stars: white dwarfs – convection – hydrodynamics – nuclear reactions, nucleosynthesis, abundances

© European Southern Observatory (ESO) 1998

Online publication: August 17, 1998