A brown dwarf companion for the accreting millisecond pulsar Sax J1808.4-3658

The BeppoSAX Wide Field Cameras have revealed a population of faint neutron star X-ray transients in the Galactic bulge. King conjectured that these neutron stars are accreting from brown dwarfs with a time-averaged mass transfer rate [(M) over dot] approximate to 10(11) M. yr(-1) that is low enough for accretion disk instabilities. We show that the measured orbital parameters of the 401 Hz accreting millisecond pulsar SAX J1808.4-3658 support this hypothesis. A main-sequence mass donor requires a nearly face-on inclination and a higher [(M) over dot] than observed, and can thus be excluded. However, the range of allowed inclinations is substantially relaxed, and the predicted [(M) over dot] is consistent with that observed if a hot 0.05 M. dwarf is the donor. The remaining puzzle is explaining the brown dwarf radius required (0.13 R.) to fill the Roche lobe. Recent observational and theoretical work has shown that all transiently accreting neutron stars have a minimum luminosity in quiescence set by the time-averaged mass transfer rate onto the neutron star. We show here that the constant heating of the brown dwarf by this quiescent neutron star emission appears adequate to maintain the higher entropy implied by a 0.13 R. radius. All of our considerations very strongly bolster the case that SAX J1808.4-3658 is a progenitor to compact millisecond radio pulsar binaries (e.g., like those found by Camilo and collaborators in 47 Tuc). The very low [(M) over dot] of SAX J1808.4-3658 implies that the progenitors to these radio pulsars are long-lived (similar to Gyr) transient systems, rather than short-lived (similar to Myr) Eddington-limited accretors. Hence, the accreting progenitor population to millisecond radio pulsars in 47 Tuc could still be present and found in quiescence with Chandra.