Non-dissipative tidal synchronization in accreting binary white dwarf systems

We study a non-dissipative hydrodynamical mechanism that can stabilize the spin of the accretor in an ultra-compact double white dwarf binary. This novel synchronization mechanism relies on a nonlinear wave interaction spinning down the background star. The essential physics of the synchronization mechanism is summarized as follows. As the compact binary coalesces due to gravitational wave emission, the largest star eventually fills its Roche lobe and accretion starts. The accretor then spins up due to infalling material and eventually reaches a spin frequency where a normal mode of the star is resonantly driven by the gravitational tidal field of the companion. If the resonating mode satisfies a set of specific criteria, which we elucidate in this paper, it exchanges angular momentum with the background star at a rate such that the spin of the accretor locks at this resonant frequency, even though accretion is ongoing. Some of the accreted angular momentum that would otherwise spin up the accretor is fed back into the orbit through this resonant tidal interaction. Two modes capable of stabilizing the accretor's spin are the l=4,m=2 and l=5,m=3 CFS unstable hybrid r-modes, which stabilize the spin of the accretor at frequency 2.6 and 1.5 times the binary's orbital frequency respectively. Since the stabilization mechanism relies on continuously driving a mode at resonance, its lifetime is limited since eventually the mode amplitude saturates due to non-linear mode-mode coupling. Rough estimates of the lifetime of the effect lie from a few orbits to millions of years.