A limit on the space density of short-period binary white dwarfs

Abstract

We infer that detached binary white dwarfs with orbital periods of a few hours exist because we observe both their progenitors and their descendents. The binary LB 3459 has an orbital period of 6.3 hr and contains a pair of hot subdwaffs that will eventually cool to become white dwarfs (Kilkenny, Hill, and Penfold 1981). L870-2 is a pair of white dwarfs and, given enough time, its 1.55 d orbital period will decay to shorter periods (Saffer, Liebert, and Olszewski 1988). GP Corn, AM CVn, V803 Cen, and PG1346+082 are interacting binary white dwarfs with orbital periods between 1051 s for AM CVn and 46.5 mix for GP Corn (Nather, Robinson, and Stover 1981; Solheim et aL 1984; Wood et al. 1987; O'Donoghue and Kilkenny 1988). These ultrashort period systems must be descendents of detached pairs of white dwarfs. We also expect short-period binary white dwarfs to exist for theoretical reasons. All calculations of the evolution of binary stars show that main-sequence binaries can evolve to binary white dwarfs (e.g., Ibex and Tutukov 1984). Among Population I stars, 1/2 to 2/3 of all main-sequence stars are binaries and about 20% of these binaries should become double white dwarfs with short orbital periods (Abt 1983, Ibex and Tutukov 1986). Thus, about 1/10 of all white dwarfs could be close binaries (Paczynski 1985). Nevertheless, no detached binary white dwarfs with extremely short periods have yet been found. The space density of short-period binary white dwarfs is worth measuring for several reasons. Most generally, the space density, is a test of modern theories for the evolution of binary stars. In addition, short-period binary white dwarfs should be the dominant source of gravitational radiation at periods between about 0.5 mix and 1 hour (e.g., Clark and Epstein 1979, Evans, Iben and Smarr 1987). Plans to build detectors of gravitational radiation at these periods using space-based interferometers are now being seriously considered and this new generation of detectors should be sensitive enough to detect binary white dwarfs (Faller and Bender 1984). Finally, in the most commonly discussed model for Type la supernovae, the progenitor of the supernova is a short-period binary consisting of two white dwarfs with a total mass greater than the Chandrasekhar limit (Webbink 1979; Tutukov and Yungelson 1979; Ibex and Tutukov 1984; Paczynski 1985; Tornamb~ and Matteucci 1986). Gravitational radiation drives the binary to shorter orbital periods and ultimately disrupts the lower mass white dwarf. If enough mass accretes onto the higher-mass white dwarf, its mass will exceed the Chandrasekhar limit and it will collapse