Common envelope formation and the merging of degenerate dwarf binaries

When, as a consequence of gravitational wave radiation, the lighter of two massive orbiting white dwarfs fills its Roche lobe for the first time, a mass transfer rate typically in excess of 0.0001 solar mass/yr is expected. It is shown here explicitly that the response of the accreting white dwarf is to swell beyond its own Roche lobe. A common envelope must therefore form. It is estimated that true contact between the degenerate cores will be established after less than 0.05 solar mass of material is lost from the system. Evolution to contact is estimated to occur in a time which is long compared with the orbital period when Roche lobe contact is first established but short compared with both the initial mass transfer time scale and the time for a possible carbon burning front ignited near the surface to reach the center. After surface contact is established, a true dynamical coalescence occurs and, if the mass of the merged object exceeds the Chandrasekhar mass for a cold nonrotating white dwarf, carbon may ignite sufficiently deep in the interior for a star-disrupting explosion of supernova proportions to result.