Population synthesis of classical low-mass X-ray binaries in the
  Galactic Bulge
  Aims. We model the present-day population of 'classical' low-mass X-ray
binaries (LMXBs) with neutron star accretors, which have hydrogen-rich donor
stars. Their population is compared with that of hydrogen-deficient LMXBs,
known as ultracompact X-ray binaries (UCXBs). We model the observable LMXB
population and compare it to observations. Methods. We combine the binary
population synthesis code SeBa with detailed LMXB evolutionary tracks to model
the size and properties of the present-day LMXB population in the Galactic
Bulge. Whether sources are persistent or transient, and what their
instantaneous X-ray luminosities are, is predicted using the thermal-viscous
disk instability model. Results. We find a population of ~2.1 x 10^3 LMXBs with
neutron star accretors. Of these about 15 - 40 are expected to be persistent
(depending on model assumptions), with luminosities higher than 10^35 erg s^-1.
About 7 - 20 transient sources are expected to be in outburst at any given
time. Within a factor of two these numbers are consistent with the observed
population of bright LMXBs in the Bulge. This gives credence to our prediction
of the existence of a population of ~1.6 x 10^3 LMXBs with low donor masses
that have gone through the period minimum, and have present-day mass transfer
rates below 10^-11 Msun yr^-1. Conclusions. Even though the observed population
of hydrogen-rich LMXBs in the Bulge is larger than the observed population of
(hydrogen-deficient) UCXBs, the latter have a higher formation rate. While
UCXBs may dominate the total LMXB population at the present, the majority would
be very faint, or may have become detached and produced millisecond radio
pulsars. In that case UCXBs would contribute significantly more to the
formation of millisecond radio pulsars than hydrogen-rich LMXBs. [abridged]
