The core helium flash revisited I. One and two-dimensional hydrodynamic simulations

Context. We investigate the hydrodynamics of the core helium flash close to its peak. Past research concerned with the dynamics of this event is inconclusive. However, the most recent multidimensional hydrodynamic studies suggest a quiescent behavior and seem to rule out an explosive scenario. Aims. Depending on initial conditions, turbulence models, grid resolution, and dimensionality of the simulation, previous work indicated that the core helium flash could lead either to the disruption of a low-mass star or to a quiescent quasi-hydrostatic evolution. We attempt to clarify this issue by simulating the evolution with advanced numerical methods and detailed microphysics. Methods. Assuming spherical or axial symmetry, we simulate the evolution of the helium core of a 1.25 M-circle dot star with a metallicity Z = 0.02 during the core helium flash at its peak with a grid-based hydrodynamical code. Results. We find that the core helium flash neither rips the star apart, nor significantly alters its structure, since convection plays a crucial role in keeping the star in hydrostatic equilibrium. In addition, our simulations indicate the presence of overshooting, which implies new predictions concerning mixing of chemical species in red giants.