The pulsations of ZZ Ceti stars

Abstract

The linear non-adiabatic calculations of Dolez & Vauclair show that for the g-modes associated with a given value of l there is a critical frequency for each model. Only modes which vary on a shorter time-scale are vibrationally unstable. In this paper it is shown that in these modes the perturbation to the pressure varies little through the hydrogen driving zone and, on this basis, flux variations of finite amplitude have been computed. The results of these calculations explain many of the characteristic features of the ZZ Cetis. In particular it is shown that for a given star there is a restricted interval in frequency where pulsations of large amplitude can be observed. As the effective temperature decreases this interval moves into the range where the frequency is smaller than the critical value for all the g-modes. This point coincides with the upper limit in the observed period range of the ZZ Cetis and explains the observational red edge.