论文标题
热白矮人的潮气激发振荡
Tidally excited oscillations in hot white dwarfs
论文作者
论文摘要
我们研究了动态潮汐引起的氦白矮人（WDS）的通量变化，用于各种WD模型，其有效温度从$ t $ = 10 kk到$ t $ = 26 kk。在线性阶时，我们发现动态潮汐可以显着扰动热WDS中观察到的通量。如果温度$ t \ gtrsim14 $ kk，则当轨道周期为$ p _ {\ rm orb} \ simeq 20-60 \，{\ rm min} $时，动态潮汐可能会导致速度的分数变化> 1％。由于动态潮汐而引起的通量调制和平衡潮汐（即椭圆形变异性）引起的比率随着WD的半径降低而增加，如果WD具有半径radius $ r \ r \ r \ lisssimsimsim0.03 r_ \ odot $，则可能会超过O（10）。与与轨道运动相相的椭圆形变异性不同，动态潮汐引起的脉动可能具有实质性的相移。另一方面，具有$ t \ Lessim 10 $ kk的冷wd不太可能显示出可观察到的脉动，这是由于动态潮汐而产生的。在较短的轨道时期，动态潮汐可能会变得高度非线性。我们通过将波视为单向行进波来近似这种状态，并发现通量变化通常降低到0.1％-1％，而多余相可能为90度（尽管不确定性很大）。即使在行进波限制中，由于动态潮汐而引起的磁通扰动仍然可能超过带有$ r \ lyssim0.02 r_ \ odot $的紧凑型WD的椭圆形变异性。我们进一步估计，非线性通量扰动在轨道频率的四倍以自耦合的父g模式为主导的轨道频率驱动。对于具有$ t \ gtrsim26 $ kk和1％线性通量变化的非常热的WD模型的非线性通量变化可能是线性变化的近50％。因此，我们预测由于动态潮汐而引起的线性和非线性通量变化很可能具有显着的观察性特征。
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.
