Population synthesis of ultracompact X-ray binaries in the Galactic
  Bulge
  [abridged] Aims. We model the number and properties of ultracompact X-ray
binaries (UCXBs) in the Galactic Bulge. The objective is to learn about the
formation of UCXBs and their evolution, such as the onset of mass transfer and
late-time behavior. Methods. The binary population synthesis code SeBa and
stellar evolutionary tracks are used to model the UCXB population. The
luminosity behavior of UCXBs is predicted using long-term X-ray observations of
the known UCXBs and the thermal-viscous disk instability model. Results. In our
model, the majority of UCXBs initially have a helium burning star donor. In the
absence of a mechanism that destroys old UCXBs, we predict (0.2 - 1.9) x 10^5
UCXBs in the Galactic Bulge, mostly at orbital periods longer than 60 min (a
large number of long-period systems also follows from the observed short-period
UCXB population). About 5 - 50 UCXBs should be brighter than 10^35 erg/s,
mostly persistent sources with orbital periods shorter than 30 min and with
degenerate helium and carbon-oxygen donors. This is one order of magnitude more
than the observed number of (probably) three. Conclusions. This overprediction
of short-period UCXBs implies that fewer systems are formed, or that a
super-Eddington mass transfer rate is more difficult to survive than assumed.
The very small number of observed long-period UCXBs with respect to
short-period UCXBs, the surprisingly high luminosity of the observed UCXBs with
orbital periods around 50 min, and the properties of the PSR J1719-1438 system
all point to much faster UCXB evolution than expected from angular momentum
loss via gravitational wave radiation alone. Old UCXBs, if they still exist,
probably have orbital periods longer than 2 h and have become very faint due to
either reduced accretion or quiescence, or have become detached. UCXBs are
promising candidate progenitors of isolated millisecond radio pulsars.
