Abstract. We initiated a comprehensive state of the art binary population synthesis study of white dwarf main-sequence star (WDMS) binaries to serve as a foundation for subsequent studies on pre-cataclysmic variables, double white dwarfs, and white dwarf + B-star binaries. We considered seven distinct formation channels subdivided into three main groups according to the evolutionary process that gives rise to the formation of the white dwarf or its helium-star progenitor: dynamically stable Rochelobe overflow (Algol-type evolution), dynamically unstable Roche-lobe overflow (common-envelope evolution), or stellar winds (single star evolution). For each formation channel, we examine the sensitivity of the population to changes in the amount of mass lost from the system during dynamically stable Roche-lobe overflow, the common-envelope ejection efficiency, and the initial mass ratio or initial secondary mass distribution. In the case of a flat initial mass ratio distribution, the local space density of WDMS binaries is of the order of ∼10 −3 pc −3 . This number decreases to ∼10 −4 pc −3 when the initial mass ratio distribution is approximately proportional to the inverse of the initial mass ratio. More than 75% of the WDMS binary population originates from wide systems in which both components essentially evolve as if they were single stars. The remaining part of the population is dominated by systems in which the white dwarf is formed in a common-envelope phase when the primary ascends the first giant branch or the asymptotic giant branch. When dynamically stable mass transfer proceeds highly conservative and the common-envelope ejection process is very efficient, the birthrate of WDMS binaries forming through a common-envelope phase is about 10 times larger than the birthrate of WDMS binaries forming through a stable Roche-lobe overflow phase. The ratio of the number of helium white dwarf systems to the number of carbon/oxygen or oxygen/neon/magnesium white dwarf systems derived from large samples of observed WDMS binaries by, e.g., future planet-search missions such as SuperWASP, COROT, and Kepler may furthermore constrain the common-envelope ejection efficiency.

Current observations of double neutron stars provide us with a wealth of information that we can use to investigate their evolutionary history and the physical conditions of neutron star formation. Understanding this history and formation conditions further allow us to make theoretical predictions for the formation of other double compact objects with one or two black hole components and assess the detectability of such systems by ground-based gravitational-wave interferometers. In this paper we summarize our group's body of work in the past few years and we place our conclusions and current understanding in the framework of other work in this area of astrophysical research.

Abstract. We report new radial velocity observations of GP Vel / HD 77581, the optical companion to the eclipsing X-ray pulsar Vela X-1. Using data spanning more than two complete orbits of the system, we detect evidence for tidally induced nonradial oscillations on the surface of GP Vel, apparent as peaks in the power spectrum of the residuals to the radial velocity curve fit. By removing the effect of these oscillations (to first order) and binning the radial velocities, we have determined the semiamplitude of the radial velocity curve of GP Vel to be K o = 22.6 ± 1.5 km s −1 . Given the accurately measured semi-amplitude of the pulsar's orbit, the mass ratio of the system is 0.081 ± 0.005. We are able to set upper and lower limits on the masses of the component stars as follows. Assuming GP Vel fills its Roche lobe then the inclination angle of the system, i, is 70.1• ± 2.6• . In this case we obtain the masses of the two stars as M x = 2.27 ± 0.17 M for the neutron star and M o = 27.9 ± 1.3 M for GP Vel. Conversely, assuming the inclination angle is i = 90• , the ratio of the radius of GP Vel to the radius of its Roche lobe is β = 0.89 ± 0.03 and the masses of the two stars are M x = 1.88 ± 0.13 M and M o = 23.1 ± 0.2 M . A range of solutions between these two sets of limits is also possible, corresponding to other combinations of i and β. In addition, we note that if the zero phase of the radial velocity curve is allowed as a free parameter, rather than constrained by the X-ray ephemeris, a significantly improved fit is obtained with an amplitude of 21.2 ± 0.7 km s −1 and a phase shift of 0.033 ± 0.007 in true anomaly. The apparent shift in the zero phase of the radial velocity curve may indicate the presence of an additional radial velocity component at the orbital period. This may be another manifestation of the tidally induced non-radial oscillations and provides an additional source of uncertainty in the determination of the orbital radial velocity amplitude.

In recent years proper motion measurements have been added to the set of observational constraints on the current properties of Galactic X-ray binaries. We develop an analysis that allows us to consider all this available information and reconstruct the full evolutionary history of X-ray binaries back to the time of core collapse and compact object formation. This analysis accounts for five evolutionary phases: mass transfer through the ongoing X-ray phase, tidal circularization before the onset of Roche-lobe overflow, motion through the Galactic potential after the formation of the compact object, binary orbital dynamics at the time of core collapse, and hydrodynamic modeling of the core collapse that connects the compact object to its progenitor and any nucleosynthetic constraints available. In this first paper, we present this analysis in a comprehensive manner and we apply it to the soft X-ray transient GRO J1655-40. This is the first analysis that incorporates all observational constraints on the current system properties and uses the full 3D peculiar velocity constraints right after core collapse instead of lower limits on the current space velocity given by the present-day radial velocity. We find that the system has remained within 200 pc from the Galactic plane throughout its entire life time and that the mass loss and a kick possibly associated with the black hole formation imparted a kick velocity of ≃ 45-115 km s −1 to the binary's center of mass. Right after black hole formation, the system consists of a ≃ 3.5 − 6.3 M ⊙ black hole and a ≃ 2.3 − 4 M ⊙ main-sequence star. At -2the onset of the X-ray phase the donor is still on the main sequence. We find that a symmetric black hole formation event cannot be formally excluded, but that the associated system parameters are only marginally consistent with the currently observed binary properties. Black hole formation mechanisms involving an asymmetric supernova explosion with associated black hole kick velocities of a few tens of km s −1 , on the other hand, satisfy the constraints much more comfortably. We also derive an upper limit on the black hole kick magnitude of ≃ 210 km s −1 .

In recent years, an increasing number of proper motions have been measured for Galactic X-ray binaries. When supplemented with accurate determinations of the component masses, orbital period, and donor effective temperature, these kinematical constraints harbor a wealth of information on the system's past evolution. Here, we consider all this available information to reconstruct the full evolutionary history of the black hole X-ray binary XTE J1118+480, assuming that the system originated in the Galactic disk and the donor has solar metallicity. This analysis accounts for four evolutionary phases: mass transfer through the ongoing X-ray phase, tidal evolution before the onset of Roche-lobe overflow, motion through the Galactic potential after the formation of the black hole, and binary orbital dynamics due to explosive mass loss and possibly a black hole natal kick at the time of core collapse. We find that right after black hole formation, the system consists of a ≃ 6.0 − 10.0 M ⊙ black hole and a ≃ 1.0 − 1.6 M ⊙ main-sequence star. We also find that that an asymmetric natal kick is not only plausible but required for the formation of this system, and derive a lower and upper limit on the black hole natal kick velocity magnitude of 80 km s −1 and 310 km s −1 , respectively.