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]