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Session 75 - Invited Talk: Goldreich.
Oral session, Thursday, June 11

[75.01] Oscillating White Dwarfs

P. Goldreich (Caltech)

As a hydrogen (DA) white dwarf cools, it passes through an instability strip centered at T_eff\approx 12,000 K having width \Delta T_eff\approx 1,000 K. Within this temperature range it exhibits photometric variations associated with excited g-modes of low angular degree. The pulsations undergo a pronounced evolution as the star travels across the instability strip. The periods of the dominant modes increase, and the modes display larger photometric amplitudes and greater temporal variability. These trends are consequences of the mechanism of linear overstability which excites the modes together with the nonlinear interactions that saturate their amplitudes.

Linear overstability is due to convective driving, a novel mechanism proposed by Brickhill. Convective driving relies on the ability of the convective motions to respond to the instantaneous pulsational state. It destabilizes modes whose periods are comparable to or shorter than the thermal timescale at the base of the star's surface convection zone. As a white dwarf cools, its convection zone deepens and modes of longer period become overstable. Longer period modes have smaller effective mass and thus faster growth and decay rates than modes of shorter period. This accounts for their increased variability.

Amplitude saturation is due to parametric instability which involves the destabilization of pairs of linearly damped daughter modes by an overstable parent mode. The frequencies and angular degrees of parent and daughter modes satisfy resonance relations. Parametric instability requires the amplitude of the parent mode to exceed a critical threshold. It thereby sets the envelope for the amplitudes of overstable modes. However, it cannot account for the uneven distribution of energy among modes which have similar linear growth rates. This feature is due to nonlinear interactions such as parametric up and down conversion which couple two excited modes to one damped mode.

Program listing for Thursday