Minimum Orbital Period of Precataclysmic Variables

More than 20 precataclysmic variable (pre-CV) systems have now been discovered with very short orbital periods ranging from 250 minutes down to 68 minutes. A pre-CV consists of a white dwarf (WD) or hot subdwarf primary and a low-mass companion star, where the companion star has successfully ejected the common envelope (CE) of the primary progenitor, but mass transfer from the companion star to the primary has not yet commenced. In this short-period range, a substantial fraction of the companion stars are likely to be either brown dwarfs with masses less than or similar to 0.07 M-circle dot or stars at the bottom of the main sequence (MS;. less than or similar to 0.1 M-circle dot). The discovery of these short-period pre-CVs raises the question, what is the shortest possible orbital period of such systems? We ran 500 brown dwarf/low-mass MS models with Modules for Experiments in Stellar Astrophysics that cover the mass range from 0.002 to 0.1 M-circle dot. We find that the shortest possible orbital period is 40 minutes, with a corresponding brown dwarf mass of 0.07 M-circle dot for an age equal to a Hubble time. We discuss the past evolution of these systems through the CE and suggest that many of the systems with present-day WD primaries may have exited the CE with the primary as a helium-burning hot subdwarf. We also characterize the future evolution of the observed systems, which includes a phase as CVs below the conventional period minimum.