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 subdwarfs 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 Com, AM CVn, V803 Cen, and PG1346+082 are interacting binary white dwarfs with orbital periods between 1051 s for AM CVn and 46.5 min for GP Com (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., Iben 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, Iben 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.
Selection Functions in Astronomical Data Modeling, with the Space Density of White Dwarfs as a Worked Example
