A MODEL OF THE GALACTIC-X-RAY BINARY POPULATION .2. LOW-MASS X-RAY BINARIES IN THE GALACTIC DISK

A numerical scenario program is used to find those systems which are p ermitted by the modern theory of binary star evolution and which consi st of a low-mass donor filling its Roche lobe and transferring mass to a neutron star or black hole accretor (with mass transfer being drive n by evolutionary expansion of the donor, a magnetic stellar wind, or gravitational wave radiation). The birthrate of low-mass X-ray binarie s(LMXBs) in the Galactic disk is found to be nu similar to (1-4) X 10( -5) yr(-1) when the parameter which measures the efficiency of orbital shrinkage in common envelope events is alpha(CE) = 0.5-1.0. The numbe r of LMXBs of various kinds in the Galactic disk is calculated in the approximation that mass is transferred conservatively. Algol-like LMXB s (subgiant or giant donor and black hole or neutron star accretor) ar e formed at orbital periods in the range 5-40 days, and their number i s similar to 1200 when alpha(CE) = 0.5 and is similar to 6400 when alp ha(CE) = 1.0 Cataclysmic variable-like( CV-like) LMXBs(main-sequence d onor) are formed at periods longer than 3.8 hr, evolve at first under the influence of a magnetic stellar wind, and then eventually evolve t o shorter periods under the influence of gravitational wave radiation. The number of long-period CV-like LMXBs is similar to 190 when alpha( CE) = 0.5 and is similar to 1900 when alpha(CE) = 1.0. The number of s hort-period (and dim) CV-like LMXBs is similar to 3600 when alpha(CE) = 0.5 and is similar to 30,000 when alpha(CE) = 1.0. Since only simila r to 100 bright disk LMXBs are observed, possibilities for reducing th e theoretical birthrate, the theoretical lifetime, or both are explore d. It has been suggested before that an irradiation-induced wind can c arry away from the system an order of magnitude more mass than is tran sferred to the accretor. We use a simple model, which fits to within a factor of 2 the results of detailed calculations in the literature, t o show that the lifetime of the LMXB phase is reduced by a factor of 6 -60 relative to that given in the mass-conservative approximation, and that the number of theoretically estimated LMXBs is reduced by a simi lar factor. In the irradiation-induced wind scenario, the mass transfe rred(0.01-0.1 Mo) is sufficient for the neutron star to achieve rotati on periods in the range of observed millisecond pulsars (MSPs). For Al gol-like systems in which the donor evolves into a helium white dwarf, the final relationship between rotation period and orbital period is consistent with the relationship defined by evolved binary MSPs in the Galactic disk. The predicted ratio of single to binary MSPs in the di sk is consistent with the observed ratio. We interpret these consisten cies to mean that LMXBs are probably the major precursors of MSPs. If the relativistic component in an LMXB typically accretes about 10% of the mass lost by the donor, the semiempirical birthrate of bright LMXB s is similar to (3-30) x 10(-6) yr(-1), which is consistent with the t heoretical estimates produced by the scenario program. Semiempirical e stimates of the birthrate of MSPs give nu similar to (4-20) X 10(-6) y r(-1), close enough to the estimates of the birthrate of LMXBs to sugg est a causal connection between LMXBs and MSPs. All birthrate estimate s are now within a factor of similar to 3 of 10(-5) yr(-1), but large uncertainties in all estimates remain. The scenario program produces a bimodal distribution of LMXBs with respect to their peculiar space ve locities. Systems in which a neutron star has been formed in consequen ce of an accretion-induced collapse have low peculiar space velocities (similar to 10-16 km s(-1)), and systems arising from initially massiv e binaries with a high initial component mass ratio achieve peculiar s pace velocities of similar to 40-100 km s(-1) as a result of recoil in response to mass loss during the supernova explosion which produces a neutron star or black hole. The supernova explosion is assumed to be spherically symmetric, with the remnant relativistic star having the s ame instantaneous orbital velocity as its precursor. The facts that ag reement between observed and model LMXBs with regard to space distribu tion in the z-coordinate is achieved and that agreement between observ ed MSPs and model LMXBs with regard to peculiar space velocities is al so achieved demonstrate that it is not necessary to invoke extra, ad h oc ''kicks'' associated with an asymmetric supernova explosion in orde r to achieve consistency with the observations. According to the model , the birthrate of neutron stars with envelopes at the base of which a nuclear fuel is burning (Thorne-Zytkow objects [TZOs]) is much larger (similar to 0.0015 yr(-1)) than the birthrate of MSPs, and one may In fer that Ties do not, as a rule, evolve into MSPs, but possibly evolve into typical radio pulsars. A consideration of angular momentum trans fer supports this inference. The predicted birthrate of systems which consist of a neutron star and a Roche lobe filling helium star is in t he range (1.1-2.3) X 10(-4) yr(-1), but an initial spike in the mass-t ransfer rate probably causes these systems to become Ties rather than LMXBs, Further study of these systems is necessary to clarify their pr operties.