Gravity Modes in ZZ Ceti Stars. II. Eigenvalues and Eigenfunctions

Abstract

We report on numerical calculations of nonadiabatic eigenvalues and eigenfunctions for g-modes in ZZ Ceti variables. The spectrum of overstable l = 1 modes delineates the instability strip. Its blue edge occurs where ωτ_c ≈ 1 for the n = 1 mode. Here ω is radian frequency and τ_c is about 4 times the thermal time at the bottom of the surface convection zone. As a ZZ Ceti cools, its convection zone deepens, longer period modes become overstable, but the critical value of ωτ_c separating overstable and damped modes rises. The latter is a consequence of enhanced radiative damping for modes that propagate immediately below the convection zone. The critical value of ωτ_c is of observational significance, because modes with the smallest value of ωτ_c are most observable photometrically. Maximum periods for overstable modes predicted for our cooler model envelopes are about a factor of 2 longer than the observational upper limit of 1200 s. We assess a number of plausible resolutions for this discrepancy among which convective overshoot and nonlinear saturation look promising. The nonadiabatic eigenfunctions enable us to predict relative amplitudes and phases of photospheric variations of flux and velocity, quantities made accessible by recent observations. We also present asymptotic formula for damping rates of high-order modes, a result of consequence for future investigations of nonlinear saturation of the amplitudes of overstable modes.