Tidally excited oscillations in hot white dwarfs

Abstract

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 $T=10\, {\rm kK}$ to $T=26\, {\rm kK}$. At linear order, we find the dynamical tide can significantly perturb the observed flux in hot WDs. If the temperature $T\gtrsim 14\, {\rm kK}$, then the dynamical tide may induce a fractional change in the flux by $\gt 1{{\ \rm per\ cent}}$ 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 $\mathcal {O}(10)$ if the WD has a radius R ≲ 0.03 R⊙. 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 $T\simeq 10\, {\rm kK}$, on the other hand, is unlikely to show observable pulsations due to the dynamical tide. At shorter orbital periods, the dynamical tide may break and become highly non-linear. We approximate this regime by treating the waves as one-way travelling waves and find the flux variation is typically reduced to 0.1–1 per cent and the excess phase is ∼90° (though with large uncertainty). Even in the travelling-wave limit, the flux perturbation due to dynamical tide could still exceed the ellipsoidal variability for compact WDs with R ≲ 0.02 R⊙. We further estimate the non-linear flux perturbations oscillating at four times the orbital frequency dominated by a self-coupled parent g-mode driving low-order daughter p modes. The non-linear flux variation could be nearly $50{{\ \rm per\ cent}}$ of the linear variation for very hot WD models with $T\gtrsim 26\, {\rm kK}$ and $1{{\ \rm per\ cent}}$ linear flux variation. We thus predict that both the linear and non-linear flux variations due to dynamical tides are likely to have significant observational signatures.