Convective heating of the inner core of red giants prior to the peak of the core helium flash

The effects of convective overshooting across the temperature inversion in red giant cores have been investigated theoretically, using a two-dimensional and three-dimensional hydrodynamic model of the core helium flash. The model is based on a simple heating algorithm which can be easily incorporated into a variety of stellar evolution codes. On the basis of the numerical results it is found that: (1) convective overshooting led to substantial heating of the material underneath the temperature inversion, producing a smoother temperature profile; (2) up until one week before the time of maximum temperature, interior heating is unimportant, but alters the standard relation of maximum temperature and density at the point of maximum temperature; and (3) overshooting redistributed the mass from the location of maximum temperature. The contribution of internal heating to the subsequent evolution of the core of a red giant is also discussed. Model estimates of the selected properties of core helium flash sequences at the time of maximum temperature are given in a table.