Gravity Modes in ZZ Ceti Stars. I. Quasi‐adiabatic Analysis of Overstability

We analyze the stability of g-modes in variable white dwarfs with hydrogenenvelopes. In these stars, the radiative layer contributes to mode dampingbecause its opacity decreases upon compression and the amplitude of theLagrangian pressure perturbation increases outward. The overlying convectiveenvelope is the seat of mode excitation because it acts as an insulatingblanket with respect to the perturbed flux that enters it from below. A crucialpoint is that the convective motions respond to the instantaneous pulsationalstate. Driving exceeds damping by as much as a factor of two provided$\omega\tau_c\geq 1$, where $\omega$ is the radian frequency of the mode and$\tau_c\approx 4\tau_{th}$ with $\tau_{th}$ being the thermal time constantevaluated at the base of the convective envelope. As a white dwarf cools, itsconvection zone deepens, and modes of lower frequency become overstable.However, the deeper convection zone impedes the passage of flux perturbationsfrom the base of the convection zone to the photosphere. Thus the photometricvariation of a mode with constant velocity amplitude decreases. These factorsaccount for the observed trend that longer period modes are found in coolerDAVs. The linear growth time, ranging from hours for the longest periodobserved modes ($P\approx 20$ minutes) to thousands of years for those ofshortest period ($P\approx 2 $ minutes), probably sets the time-scale forvariations of mode amplitude and phase. This is consistent with observationsshowing that longer period modes are more variable than shorter period ones.Our investigation confirms many results obtained by Brickhill in his pioneeringstudies of ZZ Cetis.Comment: 26 pages, including 5 figures, uses aaspp4.sty, submitted to Ap