We perform binary population synthesis calculations to investigate the incidence of low-mass X-ray binaries and their birth rate in the Galaxy. We use a binary evolution algorithm that models all the relevant processes including tidal circularization and synchronization. Parameters in the evolution algorithm that are uncertain and may affect X-ray binary formation are allowed to vary during the investigation. We agree with previous studies that under standard assumptions of binary evolution the formation rate and number of black-hole low-mass X-ray binaries predicted by the model are more than an order of magnitude less than what is indicated by observations. We find that the common-envelope process cannot be manipulated to produce significant numbers of black-hole low-mass X-ray binaries. However, by simply reducing the mass-loss rate from helium stars adopted in the standard model, to a rate that agrees with the latest data, we produce a good match to the observations. Including low-mass X-ray binaries that evolve from intermediate-mass systems also leads to favourable results. We stress that constraints on the X-ray binary population provided by observations are used here merely as a guide as surveys suffer from incompleteness and much uncertainty is involved in the interpretation of results.Comment: 17 pages and 9 figures; accepted by MNRA

The computation of theoretical pulsar populations has been a major component of pulsar studies since the 1970s. However, the majority of pulsar population synthesis has only regarded isolated pulsar evolution. Those that have examined pulsar evolution within binary systems tend to either treat binary evolution poorly or evolve the pulsar population in an ad hoc manner. Thus, no complete and direct comparison with observations of the pulsar population within the Galactic disc has been possible to date. Described here is the first component of what will be a complete synthetic pulsar population survey code. This component is used to evolve both isolated and binary pulsars. Synthetic observational surveys can then be performed on this population for a variety of radio telescopes. The final tool used for completing this work will be a code comprised of three components: stellar/binary evolution, Galactic kinematics and survey selection effects. Results provided here support the need for further (apparent) pulsar magnetic field decay during accretion, while they conversely suggest the need for a re-evaluation of the assumed typical millisecond pulsar formation process. Results also focus on reproducing the observed PṖ diagram for Galactic pulsars and how this precludes short time-scales for standard pulsar exponential magnetic field decay. Finally, comparisons of bulk pulsar population characteristics are made to observations displaying the predictive power of this code, while we also show that under standard binary evolutionary assumption binary pulsars may accrete much mass.

It has generally been assumed that neutron stars (NSs) that become millisecond pulsars (MSPs) originated in a core–collapse supernova. The possibility of formation by accretion‐induced collapse (AIC) of an oxygen/neon white dwarf (WD) has largely been ignored or considered negligible. Here, we demonstrate that population synthesis calculations with generic assumptions yield birthrates of binary MSPs via AIC that are comparable to and can exceed those for core collapse. Allowing both modes for NS formation, we estimate birthrates and orbital period distributions and compare these with observations of binary MSPs and low‐mass X‐ray binaries. Our calculations show that both the core–collapse and AIC routes lead to populations of binary systems that can be identified with X‐ray binaries while transferring matter and binary MSPs at the end of an accretion phase. The estimated birthrates indicate that the often‐neglected AIC route cannot be ignored. It also appears that this route can provide a better match to the period distributions of some types of binary MSPs. In particular, it appears to be the major route to the orbital period distribution of long‐period (a few days or greater) systems with helium WD companions under certain model assumptions. The birthrate problem confronting the low‐ and intermediate‐mass X‐ray binaries remains but can still be resolved by invocation of irradiation‐driven limit cycles.

Pulsar observations provide a suite of tests to which stellar and binary evolutionary theory may compare. Importantly, the number of pulsar systems found from recent surveys has increased the statistical significance of pulsar population synthesis results. To take advantage of this, we are in the process of developing a complete pulsar population synthesis code that accounts for isolated and binary pulsar evolution, Galactic spatial evolution and pulsar survey selection effects. In a recent paper, we described the first component of this code and explored how uncertainties in the parameters of binary and pulsar evolution affected the appearance of the pulsar population in terms of magnetic field and spin period. We now describe the second component which focuses on following the orbits of the pulsars within the Galactic potential. In combination with the first component, we produce synthetic populations of pulsars within our Galaxy and calculate the resulting scaleheights as well as the radial and space velocity distributions of the pulsars. Correlations between the binary and kinematic evolution of pulsars are also examined. Results are presented for isolated pulsars, binary pulsars and millisecond pulsars. We also test the robustness of the outcomes to variations in the assumed form of the Galactic potential, the birth distribution of binary positions and the strength of the velocity kick given to neutron stars at birth. We find that isolated pulsars have a greater scaleheight than binary pulsars. This is also true when restricted to millisecond pulsars unless we allow for low-mass stars to be ablated by radiation from their pulsar companion in which case the isolated and binary scaleheights are comparable. Double neutron stars are found to have a large variety of space velocities; in particular, some systems have speeds similar to the Sun. We look in detail at the predicted Galactic population of millisecond pulsars with black hole companions, including their formation pathways, and show where the short-period systems reside in the Galaxy. Some of our population predictions are compared in a limited way to observations but the full potential of this aspect will be realized in the near future when we complete our population synthesis code with the selection effects component.