Tidally excited oscillations in hot white dwarfs

TL;DR

This paper investigates how dynamical tides in hot helium white dwarfs cause observable flux variations, highlighting their dependence on temperature, radius, and orbital period, and discusses nonlinear effects at short periods.

Contribution

It provides a detailed analysis of linear and nonlinear flux variations caused by dynamical tides in helium white dwarfs across a range of temperatures and orbital periods.

Findings

Dynamical tides can induce >1% flux variation in WDs with T > 14 kK at 20-60 min periods.

Flux modulation due to dynamical tide can exceed 10 times that of ellipsoidal variability in compact WDs.

Nonlinear effects can cause flux variations up to 50% of linear predictions in very hot WDs.

Abstract

We study the flux variation in helium white dwarfs (WDs) induced by dynamical tides for a variety of WD models with effective temperatures ranging from $T$=10 kK to $T$=26 kK. At linear order, we find the dynamical tide can significantly perturb the observed flux in hot WDs. If the temperature $T\gtrsim14$ kK, then the dynamical tide may induce a fractional change in the flux by >1% when the orbital period is $P_{\rm orb}\simeq 20-60\,{\rm min}$. The ratio between the flux modulation due to the dynamical tide and that due to the equilibrium tide (i.e., ellipsoidal variability) increases as the WD's radius decreases, and it could exceed O(10) if the WD has a radius $R\lesssim0.03 R_\odot$. Unlike the ellipsoidal variability which is in phase with the orbital motion, the pulsation caused by the dynamical tide may have a substantial phase shift. A cold WD with $T\lesssim 10$ kK, on the other hand, is unlikely to show observable pulsations due to the dynamical tide. At shorter orbital periods, the dynamical tide may become highly nonlinear. We approximate this regime by treating the waves as one-way traveling waves and find the flux variation is typically reduced to 0.1%-1% and the excess phase is likely to be 90 degrees (though with large uncertainty). Even in the traveling-wave limit, the flux perturbation due to dynamical tide could still exceed the ellipsoidal variability for compact WDs with $R\lesssim0.02 R_\odot$. We further estimate the nonlinear flux perturbations oscillating at four times the orbital frequency dominated by a self-coupled parent g-mode driving low-order daughter p-modes. The nonlinear flux variation could be nearly 50% of the linear variation for very hot WD models with $T\gtrsim26$ kK and 1% linear flux variation. We thus predict both the linear and nonlinear flux variations due to dynamical tides are likely to have significant observational signatures.