The Evolutionary Status of 4U 1820-30

The authors calculate the evolution of an ultracompact binary wherein mass transfer is driven by the emission of gravitational radiation, with emphasis on a systematic study of how the rate of change in orbital period depends on the various system parameters. The authors derive analytic scaling laws describing how the mass of the secondary, the mass transfer rate, and Pdepend on the binary system parameters, and they apply these simple relations to the 4U 1820-30 system, located in the globular cluster NGC 6624. The authors then carry out detailed numerical evolutionary calculations utilizing Zapolsky-Salpeter (1969) models for cold stars, but allowing for the possibility that the secondary has not yet reached a completely degenerate configuration. Finally, the results are used to set significant constraints on the deviation from a completely degenerate configuration of the secondary, the systemic mass-loss parameters, and the mass of the neutron star in the 4U 1820-30 system.