Limits on Mode Coherence in Pulsating DA White Dwarfs Due to a Non-static Convection Zone. (arXiv:2001.05048v1 [astro-ph.SR])

<a href="http://arxiv.org/find/astro-ph/1/au:+Montgomery_M/0/1/0/all/0/1">M. H. Montgomery</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Hermes_J/0/1/0/all/0/1">J. J. Hermes</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Winget_D/0/1/0/all/0/1">D. E. Winget</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Dunlap_B/0/1/0/all/0/1">B. H. Dunlap</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Bell_K/0/1/0/all/0/1">K. J. Bell</a>

The standard theory of pulsations deals with the frequencies and growth rates

of infinitesimal perturbations in a stellar model. Modes which are calculated

to be linearly driven should increase their amplitudes exponentially with time;

the fact that nearly constant amplitudes are usually observed is evidence that

nonlinear mechanisms inhibit the growth of finite amplitude pulsations. Models

predict that the mass of convection zones in pulsating hydrogen-atmosphere

(DAV) white dwarfs is very sensitive to temperature (i.e., $M_{rm CZ} propto

T_{rm eff}^{-90}$), leading to the possibility that even low-amplitude

pulsators may experience significant nonlinear effects. In particular, the

outer turning point of finite-amplitude g-mode pulsations can vary with the

local surface temperature, producing a reflected wave that is out of phase with

what is required for a standing wave. This can lead to a lack of coherence of

the mode and a reduction in its global amplitude. In this paper we show that:

(1) whether a mode is calculated to propagate to the base of the convection

zone is an accurate predictor of its width in the Fourier spectrum, (2) the

phase shifts produced by reflection from the outer turning point are large

enough to produce significant damping, and (3) amplitudes and periods are

predicted to increase from the blue edge to the middle of the instability

strip, and subsequently decrease as the red edge is approached. This amplitude

decrease is in agreement with the observational data while the period decrease

has not yet been systematically studied.

The standard theory of pulsations deals with the frequencies and growth rates

of infinitesimal perturbations in a stellar model. Modes which are calculated

to be linearly driven should increase their amplitudes exponentially with time;

the fact that nearly constant amplitudes are usually observed is evidence that

nonlinear mechanisms inhibit the growth of finite amplitude pulsations. Models

predict that the mass of convection zones in pulsating hydrogen-atmosphere

(DAV) white dwarfs is very sensitive to temperature (i.e., $M_{rm CZ} propto

T_{rm eff}^{-90}$), leading to the possibility that even low-amplitude

pulsators may experience significant nonlinear effects. In particular, the

outer turning point of finite-amplitude g-mode pulsations can vary with the

local surface temperature, producing a reflected wave that is out of phase with

what is required for a standing wave. This can lead to a lack of coherence of

the mode and a reduction in its global amplitude. In this paper we show that:

(1) whether a mode is calculated to propagate to the base of the convection

zone is an accurate predictor of its width in the Fourier spectrum, (2) the

phase shifts produced by reflection from the outer turning point are large

enough to produce significant damping, and (3) amplitudes and periods are

predicted to increase from the blue edge to the middle of the instability

strip, and subsequently decrease as the red edge is approached. This amplitude

decrease is in agreement with the observational data while the period decrease

has not yet been systematically studied.

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