The BeppoSAX Wide Field Cameras have revealed a population of faint neutron
star X-ray transients in the Galactic bulge. King conjectured that these n
eutron stars are accreting from brown dwarfs with a time-averaged mass tran
sfer 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 parame
ters of the 401 Hz accreting millisecond pulsar SAX J1808.4-3658 support th
is hypothesis. A main-sequence mass donor requires a nearly face-on inclina
tion and a higher [(M) over dot] than observed, and can thus be excluded. H
owever, 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 rad
ius required (0.13 R.) to fill the Roche lobe. Recent observational and the
oretical work has shown that all transiently accreting neutron stars have a
minimum luminosity in quiescence set by the time-averaged mass transfer ra
te onto the neutron star. We show here that the constant heating of the bro
wn dwarf by this quiescent neutron star emission appears adequate to mainta
in the higher entropy implied by a 0.13 R. radius. All of our consideration
s very strongly bolster the case that SAX J1808.4-3658 is a progenitor to c
ompact millisecond radio pulsar binaries (e.g., like those found by Camilo
and collaborators in 47 Tuc). The very low [(M) over dot] of SAX J1808.4-36
58 implies that the progenitors to these radio pulsars are long-lived (simi
lar to Gyr) transient systems, rather than short-lived (similar to Myr) Edd
ington-limited accretors. Hence, the accreting progenitor population to mil
lisecond radio pulsars in 47 Tuc could still be present and found in quiesc
ence with Chandra.