DAVs: Red Edge and Outbursts

Abstract

As established by photometric surveys, white dwarfs with hydrogen atmospheres and surface gravity, log(g)≈8.0 pulsate as they cool across the temperature range of 12,500 KT eff 10,800 K. Known as DAVs or ZZ Ceti stars, their oscillations are attributed to gravity modes excited by convective driving. Overstability requires convective driving to exceed radiative damping. Previous works have demonstrated that ωmax(τ c −1 , L ℓ,b ) is a necessary and sufficient condition for overstability. Here τ c and L ℓ,b are the effective thermal timescale and Lamb frequency at the base of the surface convection zone. Below the observational red edge, L ℓ,b ?τ c −1 , so overstable modes all have ωτ c ?1. Consequently, their photometric amplitudes are reduced by that large factor rendering them difficult to detect. Although proposed previously, the condition ωL ℓ,b has not been clearly interpreted. We show that modes with ω<L ℓ,b suffer enhanced radiative damping that exceeds convective driving rendering them damped. A quasi-adiabatic analysis is adequate to account for this enhancement. Although this approximation is only marginally valid at the red edge, it becomes increasingly accurate toward both higher and lower T eff . Recently, Kepler discovered a number of cool DAVs that exhibit sporadic flux outbursts. Typical outbursts last several hours, are separated by days, and release ∼10 33 -10 34 erg. We attribute outbursts to limit cycles arising from sufficiently resonant 3-mode couplings between overstable parent modes and pairs of radiatively damped daughter modes. Limit cycles account for the durations and energies of outbursts and their prevalence near the red edge of the DAV instability strip.

Limits on Mode Coherence in Pulsating DA White Dwarfs Due to a Nonstatic Convection Zone

“…Finally, many DAVs observed with the Kepler and K2 missions undergo outbursts, increases in average brightness of 10%-40% that can typically last from 5 to 15 hr (Bell et al 2015(Bell et al , 2017Hermes et al 2015). While the best-known theory for this process involves a resonant transfer of energy from a driven parent mode to damped daughter modes as an amplitude threshold is reached (Wu & Goldreich 2001;Luan & Goldreich 2018), we speculate that the mechanism we have proposed involving phase shifts of reflected modes could be relevant as well. It is possible that some pulsators reach an amplitude threshold in which there is a slight increase in the damping, and this increased damping leads to a slight heating of the surface layers.…”

“…This in turn causes a net thinning of the convection zone, leading to larger phase shift mismatches, which leads to further damping, and the cycle reinforces itself. In addition, as the surface convection zone becomes thinner, radiative damping may play an important role in removing energy from the high overtone modes (Luan & Goldreich 2018).…”

White-Dwarf Asteroseismology With the Kepler Space Telescope

“…This strongly suggests that outbursts could be related to the origin of the cool edge of the DAV instability domain, that is, the cessation of the g-mode pulsations (Bell et al, 2017a). A possible explanation for both the occurrence of outbursts and the origin of the cool edge of the ZZ Ceti instability strip, has been proposed by Luan and Goldreich (2018). It is connected with parametric instability through mode coupling of white-dwarf pulsations (Dziembowski, 1982;Wu and Goldreich, 2001;Luan and Goldreich, 2018).…”

“…This is discouraging, since even detailed calculations that take into account the interaction between convection and pulsations (Van Grootel et al, 2012) fail to reproduce the location of the red edges in the cases of DAVs and DBVs. Recently, Luan and Goldreich (2018) proposed a theoretical framework that accounts for the existence of the red edge of the DAV instability strip.…”

White-dwarf asteroseismology: An update

“…At present, a total of 8 outbursting isolated ZZ Ceti stars have been discovered (Bell et al 2016(Bell et al , 2017, close to the red edge of the ZZ Ceti instability strip. A possible explanation is connected with parametric instability via mode coupling of white dwarf pulsations (Dziembowski 1982;Wu & Goldreich 2001;Luan & Goldreich 2018).…”