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

Wu, Yanqin and Goldreich, Peter (1999) Gravity Modes in ZZ Ceti Stars. II. Eigenvalues and Eigenfunctions. Astrophysical Journal, 519 (2). pp. 783-792. ISSN 0004-637X. https://resolver.caltech.edu/CaltechAUTHORS:20130227-085742039

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1086/307412DOIUNSPECIFIED
http://iopscience.iop.org/0004-637X/519/2/783PublisherUNSPECIFIED
Additional Information:© 1999 American Astronomical Society. Received 1998 December 3; accepted 1999 February 18. We are indebted to P. Bradley for supplying us with models of DA white dwarfs. The final version of this paper benefited from constructive comments offered by W. Dziembowski. Financial support for this research was provided by NSF grant 94-14232.
Funders:
Funding AgencyGrant Number
NSF94-14232
Subject Keywords:stars : oscillations - stars : variables : other
Issue or Number:2
Record Number:CaltechAUTHORS:20130227-085742039
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130227-085742039
Official Citation:Gravity Modes in ZZ Ceti Stars. II. Eigenvalues and Eigenfunctions Yanqin Wu and Peter Goldreich 1999 ApJ 519 783
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37164
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:28 Feb 2013 15:40
Last Modified:03 Oct 2019 04:45

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