Description
Tidal interactions and gravitational wave emission both drive the orbital evolution of compact binaries, yet their precise interplay in double white dwarf systems has not been fully explored. In this work, we focus on DA white dwarfs near and within the ZZ Ceti instability strip. We combine asteroseismic theory with the non-adiabatic oscillation codes MAD and MAD_tides, along with Peters’ gravitational wave formulas, to compute tidal and gravitational wave torques near spin-orbit synchronisation. We demonstrate that when the orbital forcing frequency matches a white dwarf’s eigenmode, tides and gravitational waves can balance, creating resonance locking points. We show that these locking points are favoured when white dwarf masses are lower and spin rates higher. By performing backward integrations of the gravitational wave equations from locking points, we show that these binaries must have had orbital periods below a few hours at earlier epochs. Comparison with Sloan Digital Sky Survey (SDSS)-selected extremely low-mass white dwarf binaries supports the existence of systems within this locking region.
