The Brightest Cluster X-ray Sources
  There have been several recent claims of black hole binaries in globular
clusters. I show that these candidate systems could instead be ultracompact
X-ray binaries (UCXBs) in which a neutron star accretes from a white dwarf.
They would represent a slightly earlier evolutionary stage of known globular
cluster UCXBs such as 4U 1820--30, with white dwarf masses $\sim 0.2\msun$, and
orbital periods below 5 minutes. Accretion is slightly super--Eddington, and
makes these systems ultraluminous sources (ULXs) with rather mild beaming
factors $b \sim 0.3$. Their theoretical luminosity function flattens slightly
just above $\le$ and then steepens at $\sim 3\le$. It predicts of order 2
detections in elliptical galaxies such as NGC 4472, as observed.
  The very bright X-ray source HLX--1 lies off the plane of its host S0a
galaxy. If this is an indication of globular cluster membership, it could
conceivably be a more extreme example of a UCXB with white dwarf mass $M_2
\simeq 0.34\msun$. The beaming here is tighter ($b \sim 2.5 - 9 \times
10^{-3}$), but the system's distance of 95 Mpc easily eliminates any need to
invoke improbable alignment of the beam for detection. If its position instead
indicates membership of a satellite dwarf galaxy, HLX-1 could have a much
higher accretor mass $\sim 1000\msun$
