On the resonant detonation of sub-Chandrasekhar mass white dwarfs during
  binary inspiral
  White dwarfs (WDs) are believed to detonate via explosive Carbon-fusion in a
Type Ia Supernova when their temperature and/or density reach the point where
Carbon is ignited in a runaway reaction. Observations of the Type Ia supernova
(SN) rate imply all WD binaries that merge through the emission of
gravitational radiation within a Hubble time should result in SNe, regardless
of total mass. Here we investigate the conditions under which a single WD in a
binary system might extract energy from its orbit, depositing enough energy
into a resonant mode such that it detonates before merger. We show that,
ignoring non-linear effects, in a WD binary in tidal lock at small binary
separations, the sustained tidal forcing of a low-order quadrupolar g-mode or a
harmonic of a low-order quadrupolar p-mode could in principle drive the average
temperature of Carbon nuclei in the mode over the runaway fusion threshold. If
growing mode energy is thermalized at a core/atmosphere boundary, rapid Helium
burning and inward-travelling p-waves may result in core detonation.
Thermalization at a boundary in the core can also result in detonation. If
energy can be efficiently transferred from the orbit to modes as the WD binary
passes through resonances, the WD merger timescale will be shortened by Myr-Gyr
compared to expected timescales from GW-emission alone and GW detectors will
observe deviations from predicted chirp profiles in resolved WD binaries.
Future work in this area should focus on whether tidal locking in WD binaries
is naturally driven towards low-order mode frequencies.
