Radial pulsations of red giant branch stars

We performed hydrodynamic computations of nonlinear stellar pulsations of population I stars at the evolutionary stages of the ascending red giant branch and the following luminosity drop due to the core helium flash. Red giants populating this region of the Hertzsprung-Russel diagram were found to be the fundamental mode pulsators. The pulsation period is the largest at the tip of the red giant branch and for stars with initial masses from 1.1 M (aS (TM)) to 1.9 M (aS (TM)) ranges from a ae 254 day to a ae 33 day , respectively. The rate of period change during the core helium flash is comparable with rates of secular period change in Mira type variables during the thermal pulse in the helium shell source. The period change rate is largest (aIc/a ae -10(-2) yr(-1)) in stars with initial mass M (ZAMS) = 1.1 M (aS (TM)) and decreases to aIc/a similar to -10(-3) yr(-1) for stars of the evolutionary sequence M (ZAMS) = 1.9 M (aS (TM)). Theoretical light curves of red giants pulsating with periods a > 200 day show the presence of the secondary maximum similar to that observed in many Miras.