A Model of the Galactic X-Ray Binary Population. I. High-Mass X-Ray Binaries

Abstract

A numerical scenario program is used to find those systems which are permitted by the modem theory of binary star evolution and which consist of a low-mass donor filling its Roche lobe and transferring mass to a neutron star or black hole accretor (with mass transfer being driven by evolutionary expansion of the donor, a magnetic stellar wind, or gravitational wave radiation). The birthrate of low-mass X-ray binaries (LMXBs) in the Galactic disk is found to be ^ ~ (1-4) X 10-5 yr-1 when the parameter which measures the efficiency of orbital shrinkage in common envelope events is a C E = 0.5-1.0. The number of LMXBs of various kinds in the Galactic disk is calculated in the approximation that mass is transferred conservatively. Algol-like LMXBs (subgiant or giant donor and black hole or neutron star accretor) are formed at orbital periods in the range 5-40 days, and their number is ~ 1200 when a CE = 0.5 and is ~6400 when a C E = 1-0. Cataclysmic variable-like (CV-like) LMXBs (main-sequence donor) are formed at periods longer than 3.8 hr, evolve at first under the influence of a magnetic stellar wind, and then eventually evolve to shorter periods under the influence of gravitational wave radiation. The number of long-period CV-like LMXBs is ~ 190 when a C E = 0.5 and is ~ 1900 when a C E = L0. The number of short-period (and dim) CV-like LMXBs is-3600 when a CE = 0.5 and is-30,000 when a C E = L0. Since only-100 bright disk LMXBs are observed, possibilities for reducing the theoretical birthrate, the theoretical lifetime, or both are explored. It has been suggested before that an irradiation-induced wind can carry away from the system an order of magnitude more mass than is transferred to the accretor. We use a simple model, which fits to within a factor of 2 the results of detailed calculations in the literature, to 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 similar factor. In the irradiation-induced wind scenario, the mass transferred (0.01-0.1 M Q) is sufficient for the neutron star to achieve rotation periods in the range of observed millisecond pulsars (MSPs). For Algol-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 disk is consistent with the observed ratio. We interpret these consistencies 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 LMXBs is-(3-30) X 10-6 yr-1 , which is consistent with the theoretical estimates produced by the scenario program. Semiempirical estimates of the birthrate of MSPs give v-(4-20) X 10-6 yr-1 , close enough to the estimates of the birthrate of LMXBs to suggest a causal connection between LMXBs and MSPs. All birthrate estimates are now within a factor of-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 velocities. Systems in which a neutron star has been formed in consequence of an accretion-induced collapse have low peculiar space velocities (-10-16 km s _1), and systems arising from initially massive binaries with a high initial component mass ratio achieve peculiar space velocities of-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 same instantaneous orbital velocity as its precursor. The facts that agreement between observed and model LMXBs with regard to space distribution in the z-coordinate is achieved and that agreement between observed MSPs and model LMXBs with regard to peculiar space velocities is also achieved demonstrate that it is not necessary to invoke extra, ad hoc "kicks" associated with an asymmetric supernova explosion in order 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 (Thome-Zytkow objects [TZOs]) is much larger (~0.0015 yr-1) than the birthrate of MSPs, and one may infer that TZOs do not, as a rule, evolve into MSPs, but possibly evolve into typical radio pulsars. A consideration of angular momentum transfer supports this inference. The predicted birthrate of systems which consist of a neutron star and a Roche lobe filling helium star is in the range (1.1-2.3) X 10 4 yr 1 , but an initial spike in the mass-transfer rate probably causes these systems to become TZOs rather than LMXBs. Further study of these systems is necessary to clarify their properties.