The core helium flash revisited III. From Population I to Population III stars

Context. Degenerate ignition of helium in low-mass stars at the end of the red giant branch phase leads to dynamic convection in their helium cores. One-dimensional (1D) stellar modeling of this intrinsically multi-dimensional dynamic event is likely to be inadequate. Previous hydrodynamic simulations imply that the single convection zone in the helium core of metal-rich Pop I stars grows during the flash on a dynamic timescale. This may lead to hydrogen injection into the core and to a double convection zone structure as known from one-dimensional core helium flash simulations of low-mass Pop III stars. Aims. We perform hydrodynamic simulations of the core helium flash in two and three dimensions to better constrain the nature of these events. To this end we study the hydrodynamics of convection within the helium cores of a 1.25 M-circle dot metal-rich Pop I star (Z = 0.02), and, for the first time, a 0.85 M-circle dot metal-free Pop III star (Z = 0) near the peak of the flash. These models possess single and double convection zones, respectively. Methods. We use 1D stellar models of the core helium flash computed with state-of-the-art stellar evolution codes as initial models for our multidimensional hydrodynamic study, and simulate the evolution of these models with the Riemann solver based hydrodynamics code Herakles, which integrates the Euler equations coupled with source terms corresponding to gravity and nuclear burning. Results. The hydrodynamic simulation of the Pop I model involving a single convection zone covers 27 h of stellar evolution, while the hydrodynamic simulations of a double convection zone, in the Pop III model, span 1.8 h of stellar life. We find differences between the predictions of mixing length theory and our hydrodynamic simulations. The simulation of the single convection zone in the Pop I model shows a strong growth of the size of the convection zone due to turbulent entrainment. We therefore predict that for the Pop I model a hydrogen injection phase (i.e., hydrogen injection into the helium core) will commence after about 23 days, which should eventually lead to a double convection zone structure known from 1D stellar modeling of low-mass Pop III stars. Our two and three-dimensional hydrodynamic simulations of the double (Pop III) convection zone model show that the velocity field in the convection zones is different from that given by stellar evolutionary calculations. The simulations suggest that the double convection zone decays quickly, the flow eventually being dominated by internal gravity waves. The decay could be an artefact caused by the mapping of the initial stellar model to the numerical grid of our hydrodynamics code.