Evolution of highly compact binary stellar systems

We have calculated the evolution of close binary stellar systems composed of a collapsed star and a low-mass companion in an orbit with a period of approx.3 hours or less at the onset of mass transfer. The low-mass (secondary) star is assumed to transfer mass onto the collapsed (primary) star due to the decay of the orbit resulting from gravitational radiation. Under these circumstances, the secondary is well represented by an n = 3/2 polytrope. By utilizing this approximation, we are able to explore the effects of varying a number of physical parameters, including the stellar masses, the composition of the secondary, and mass and angular momentum losses from the system. Moreover, we are able to follow the evolution until the secondary has been almost completely consumed. For a wide range of parameters, even with extreme angular momentum losses (as long as those losses are proportional to the mass transfer rate), the transfer rate for a large portion of the evolution is tightly constrained to < or =2 x 10-10 M/sub sun/ yr-1, in good agreement with the rates inferred from many cataclysmic variables