A large population of neutron star low-mass X-ray binaries with long outburst recurrence time?

Low-mass X-ray binaries (LMXBs) with neutron stars show quite different features that depend on the rate of mass transfer from the donor star. With a high transfer rate, the Z sources are in a persistent soft spectral state, and with a moderate transfer rate the transient Atoll sources have outburst cycles like the black hole X-ray binaries. The observations document very long outburst recurrence times for quite a number of sources. We follow with our computations the evolution of the accretion disc until the onset of the ionization instability. For sources with a low mass transfer rate, the accumulation of matter in the disc is essentially reduced due to the continuous evaporation of matter from the disc to the coronal flow. Different mass transfer rates result in nearly the same amount of matter accumulated for the outburst, which means that the outburst properties are similar for sources with short outburst cycles and sources with long outburst cycles, contrary to some expectations. Then, for systems with long recurrence time, less sources will be detected and the total population of LMXBs could be larger than it appears. This would relieve the apparent problem that the observed number of LMXBs as progenitors of millisecond pulsars (MSPs) is too small compared to the number of MSPs. Concerning the few quasi-persistent sources with year-long soft states, we argue that these states are not outbursts, but quasi-stationary hot states as in Z sources.