We investigate the characteristics of young (<20 Myr) and bright (L X > 1 × 10 36 erg s −1 ) high-mass X-ray binaries (HMXBs) and find the population to be strongly metallicity dependent. We separate the model populations among two distinct formation pathways: (1) systems undergoing active Roche lobe overflow (RLO) and (2) wind accretion systems with donors in the (super)giant stage, which we find to dominate the HMXB population. We find metallicity to primarily affect the number of systems which move through each formation pathway, rather than the observable parameters of systems which move through each individual pathway. We discuss the most important model parameters affecting the HMXB population at both low and high metallicities. Using these results, we show that (1) the population of ultra-luminous X-ray sources can be consistently described by very bright HMXBs which undergo stable RLO with mild super-Eddington accretion and (2) the HMXB population of the bright starburst galaxy NGC 1569 is likely dominated by one extremely metal-poor starburst cluster.

We investigate the existence and properties of equipotential surfaces and Lagrangian points in nonsynchronous, eccentric binary star and planetary systems under the assumption of quasi-static equilibrium. We adopt a binary potential that accounts for nonsynchronous rotation and eccentric orbits and calculate the positions of the Lagrangian points as functions of the mass ratio, the degree of asynchronism, the orbital eccentricity, and the position of the stars or planets in their relative orbit. We find that the geometry of the equipotential surfaces may facilitate nonconservative mass transfer in nonsynchronous, eccentric binary star and planetary systems, especially if the component stars or planets are rotating supersynchronously at the periastron of their relative orbit. We also calculate the volume-equivalent radius of the Roche lobe as a function of the four parameters mentioned above. Contrary to common practice, we find that replacing the radius of a circular orbit in the fitting formula of Eggleton with the instantaneous distance between the components of eccentric binary or planetary systems does not always lead to a good approximation to the volumeequivalent radius of the Roche lobe. We therefore provide generalized analytic fitting formulae for the volumeequivalent Roche lobe radius appropriate for nonsynchronous, eccentric binary star and planetary systems. These formulae are accurate to better than 1% throughout the relevant two-dimensional parameter space that covers a dynamic range of 16 and 6 orders of magnitude in the two dimensions.

The rapid circularization and synchronization of the stellar components in an eccentric binary system at the onset of Roche lobe overflow is a fundamental assumption common to all binary stellar evolution and population synthesis codes, even though the validity of this assumption is questionable both theoretically and observationally. Here we calculate the evolution of the orbital elements of an eccentric binary through the direct three-body integration of a massive particle ejected through the inner Lagrangian point of the donor star at periastron. The trajectory of this particle leads to three possible outcomes: direct accretion onto the companion star within a single orbit, self-accretion back onto the donor star within a single orbit, or a quasi-periodic orbit around the companion star, possibly leading to the formation of a disk. We calculate the secular evolution of the binary orbit in the first two cases and conclude that direct impact accretion can increase as well as decrease the orbital semi-major axis and eccentricity, while self-accretion always decreases the orbital semi-major axis and eccentricity. In cases where mass overflow contributes to circularizing the orbit, circularization can set in on timescales as short as a few per cent of the mass transfer timescale. In cases where mass overflow increases the eccentricity, the orbital evolution is governed by competition between mass overflow and tidal torques. In the absence of tidal torques, mass overflow results in direct impact can lead to substantially subsynchronously rotating donor stars. Contrary to assumptions common in the literature, direct impact accretion furthermore does not always provide a strong sink of orbital angular momentum in close mass-transferring binaries; in fact we instead find that a significant part can be returned to the orbit during the particle orbit. The formulation presented in this paper together with our previous work can be combined with stellar and binary evolution codes to generate a better picture of the evolution of eccentric, Roche lobe overflowing binary star systems.