  Almost all Galactic black hole binaries with low mass donor stars are
transient X-ray sources; we expect most of the X-ray transients observed in
external galaxies to be black hole binaries also. Obtaining period estimates
for extra-galactic transients is challenging, but the resulting period
distribution is an important tool for modeling the evolution history of the
host galaxy. We have obtained periods, or upper limits, for 12 transients in
M31, using an updated relation between the optical and X-ray luminosities. We
have monitored the central region of M31 with Chandra for the last ~12 years,
and followed up promising transients with HST; 4\sigma B magnitude limits for
optical counterparts are ~26--29, depending on crowding. We obtain period
estimates for each transient for both neutron star and black hole accretors.
Periods range from <0.4 to 490+/-90 hours (<0.97 to <175 hrs if all are BH
systems). These M31 transients appear to be somewhat skewed towards shorter
periods than the Milky Way (MW) transients; indeed, comparing the M31 and MW
transients with survival analysis techniques used to account for some data with
only upper limits yield probabilities of ~0.02--0.08 that the two populations
are drawn from the same distribution. We also checked for a correlation between
orbital period and distance from the nucleus, finding a 12% probability of no
correlation. Further observations of M31 transients will strengthen these
results.
