Excitation and Saturation of White Dwarf Pulsations

Details Excitation and Saturation of White Dwarf Pulsations Excitation and Saturation of White Dwarf Pulsations

Jun 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998phdt........28w&link_type=abstract

Thesis (PHD). CALIFORNIA INSTITUTE OF TECHNOLOGY , Source DAI-B 59/07, p. 3499, Jan 1999, 215 pages.

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14

Turbulence, Oscillations, Convective Driving

Scientific paper

Variable hydrogen white dwarfs (DAV) pulsate in a number of low-order gravity-modes with periods from 100 s to 1200 s and amplitudes no larger than a few percent. We answer two questions in this thesis: the driving for these pulsations, and the saturation of their amplitudes. The surface convection zone in these stars, which adjusts its entropy level instantaneously during the pulsation, can drive the observed modes. This mechanism (called 'convective driving') was discovered by Brickhill but has been largely neglected so far. We find that modes with periods shorter than the thermal adjustment time of the convection zone can become overstable, but those with very short periods are hardly visible at the surface. As the star cools and the convection zone deepens, longer period modes can be excited. The driving rates increase sharply with period. We relate these to the time-scale of mode variability. We include complications arising from nonadiabaticity in the radiative interior and turbulent damping at the convective-radiative boundary. The former limits the driving and damping rates for strongly nonadiabatic modes, and relates the phase and amplitude of surface horizontal velocity in a gravity-mode to those of its flux variation. The turbulent damping results from the horizontal velocity shear below the convection zone, inside which there is little velocity shear and negligible damping. This suppresses the amplitudes of long period modes to below detection. The width of the theoretical DAV instability strip is about 1000 K. The growth of an overstable mode can be saturated by parametric instability, where energy transfers resonantly into two damped modes of roughly half its frequency. This occurs above a critical amplitude which depends on the 3-mode coupling coefficient and the nonadiabatic damping rates. The critical amplitudes all fall below a few percent, with longer period modes having larger surface amplitudes. Combined with the amplitude limits due to turbulent damping, our estimates compare well with observations. Other types of mode couplings are needed to explain the observed 'mode selection'. Finally, we show that the combination frequencies found in pulsation power spectra are produced by the time-varying convection zone which nonlinearly affects mode visibility.

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