Formation of low-mass X-ray binaries .1. Constraints on hydrogen-rich donors at the onset of the X-ray phase

We identify and quantify the set of constraints that neutron star-normal star binaries must satisfy in order to become observable low-mass X-ray binaries (LMXBs). These constraints are related to (i) the thermal and hydrostatic equilibrium of the donors, (ii) the degree to which the mass transfer process is conservative, and (iii) the age of the systems. They divide the parameter space of potential LMXBs in several distinct parts, of which those that actually become LMXBs at the onset of mass transfer occupy only a small part. Of the remainder, many become unstable to dynamical timescale mass transfer, either at the onset or later in the course of mass transfer, and enter common envelope evolution. Others experience super-Eddington mass transfer but may eventually survive to become LMXBs. These survivors arguably include binary millisecond pulsars with orbital periods in excess of 100 days, ultra-short-period LMXBs with hydrogen-deficient donors, and long-period LMXBs with giant donors.