On the Luminosity of White Dwarfs in Close Binaries Merging under the Influence of Gravitational Wave Radiation

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Abstract
Close binary white dwarfs that are being drawn together by the loss of orbital angular momentum due to gravitational wave radiation are heated internally to high temperatures by viscous dissipation if tidal interactions maintain synchronism between spin periods and the orbital period. A balance between heating and cooling leads to a luminosity that, just prior to merger, varies from ~0.15 L☉ for a white dwarf of mass 0.3 M☉ to ~1000 L☉ for a white dwarf of mass 1.3 M☉. The high luminosity due to tidal heating increases the probability of finding very close, old binary white dwarfs in the process of merging. For example, for those types that merge most frequently (0.3 M☉ helium white dwarf pairs), the typical distance between merging pairs is ~500 pc. Adopting this distance from the Earth gives an apparent brightness of about 17 mag; this is ~5 mag brighter than if tidal heating were absent. Partial and complete mutual occultations of 0.2-2 minutes duration are expected to occur in a significant fraction of premerger systems, and this enhances the probability of eventual detections at optical wavelengths. Similar considerations suggest that, if γ-ray bursts are the consequence of neutron star mergers, every burst (of ~1-10 s duration) may be preceded by X-ray emission at the Eddington luminosity or higher for approximately 1 yr.

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