The core helium flash revisited

II. Two and three-dimensional hydrodynamic simulations

¹ Max-Planck-Institut für Astrophysik, Postfach 1312, 85741 Garching, Germany e-mail: mmocak@mpa-garching.mpg.de
² Institut d'Astronomie et d'Astrophysique, Université Libre de Bruxelles, CP 226, 1050 Brussels, Belgium e-mail: mmocak@ulb.ac.be

Received: 25 November 2008
Accepted: 3 April 2009

Abstract

Context. We study turbulent convection during the core helium flash close to its peak by comparing the results of two and three-dimensional hydrodynamic simulations.

Aims. In a previous study we found that the temporal evolution and the properties of the convection inferred from two-dimensional hydrodynamic studies are similar to those predicted by quasi-hydrostatic stellar evolutionary calculations. However, as vorticity is conserved in axisymmetric flows, two-dimensional simulations of convection are characterized by incorrect dominant spatial scales and exaggerated velocities. Here, we present three-dimensional simulations that eliminate the restrictions and flaws of two-dimensional models and that provide a geometrically unbiased insight into the hydrodynamics of the core helium flash. In particular, we study whether the assumptions and predictions of stellar evolutionary calculations based on the mixing-length theory can be confirmed by hydrodynamic simulations.

Methods. We used a multidimensional Eulerian hydrodynamics code based on state-of-the-art numerical techniques to simulate the evolution of the helium core of a 1.25  Pop I star.

Results. Our three-dimensional hydrodynamic simulations of the evolution of a star during the peak of the core helium flash do not show any explosive behavior. The convective flow patterns developing in the three-dimensional models are structurally different from those of the corresponding two-dimensional models, and the typical convective velocities are lower than those found in their two-dimensional counterparts. Three-dimensional models also tend to agree more closely with the predictions of mixing length theory. Our hydrodynamic simulations show the turbulent entrainment that leads to a growth of the convection zone on a dynamic time scale. In contrast to mixing length theory, the outer part of the convection zone is characterized by a subadiabatic temperature gradient.