We consider constraints on the formation of low–mass X–ray binaries containing neutron stars ( NLMXBs ) arising from the presence of soft X–ray transients among these systems .
For a neutron star mass M _ { 1 } \simeq 1.4 { M _ { \odot } } at formation , we show that in short–period ( \la 1 - 2 d ) systems driven by angular momentum loss these constraints require the secondary at the beginning of mass transfer to have a mass 1.3 { M _ { \odot } } \la M _ { 2 } \la 1.5 { M _ { \odot } } , and to be significantly nuclear–evolved , provided that supernova ( SN ) kick velocities are generally small compared with the pre–SN orbital velocity .
As a consequence a comparatively large fraction of such systems appear as soft X–ray transients even at short periods , as observed .
Moreover the large initial secondary masses account for the rarity of NLMXBs at periods P \la 3 hr .
In contrast , NLMXB populations forming with large kick velocities would not have these properties , suggesting that the kick velocity is generally small compared to the pre–SN orbital velocity in a large fraction of systems , consistent with a recent reevaluation of pulsar proper motions .
The results place also tight constraints on the strength of magnetic braking : if magnetic braking is significantly stronger than the standard form too many unevolved NLMXBs would form , if it is slower by only a factor \simeq 4 no short–period NLMXBs would form at all in the absence of a kick velocity .
The narrow range for M _ { 2 } found for negligible kick velocity implies restricted ranges near 4 { M _ { \odot } } for the helium star antecedent of the neutron star and near 18 { M _ { \odot } } for the original main–sequence progenitor .
The pre–common envelope period must lie near 4 yr , and we estimate the short–period NLMXB formation rate in the disc of the Galaxy as \sim 2 \times 10 ^ { -7 } yr ^ { -1 } .
Our results show that the neutron star mass at short–period NLMXB formation can not be significantly larger than 1.4 { M _ { \odot } } .
Systems with formation masses M _ { 1 } \la 1.2 { M _ { \odot } } would have disrupted , so observations implying M _ { 1 } \sim 1.4 { M _ { \odot } } in some NLMXBs suggest that much of the transferred mass is lost from these systems .