We present ellipsoidal light‐curve fits to the quiescent B, V, R and I light curves of GRO J1655–40 (Nova Scorpii 1994). The fits are based on a simple model consisting of a Roche‐lobe‐filling secondary and an accretion disc around the black hole primary. Unlike previous studies, no assumptions are made concerning the interstellar extinction or the distance to the source; instead these are determined self‐consistently from the observed light curves. In order to obtain tighter limits on the model parameters, we used the distance determination from the kinematics of the radio jet as an additional constraint. We obtain a value for the extinction that is lower than was assumed previously; this leads to lower masses for both the black hole and the secondary star of 5.4±0.3 and 1.45±0.35 M⊙, respectively. The errors in the determination of the model parameters are dominated by systematic errors, in particular arising from uncertainties in the modelling of the disc structure and uncertainties in the atmosphere model for the chemically anomalous secondary in the system. A lower mass of the secondary naturally explains the transient nature of the system if it is in either a late case A or early case B mass‐transfer phase.

We present a new analysis of the light curve for the secondary star in the eclipsing binary millisecond pulsar system PSR B1957+20. Combining previous data and new data points at minimum from the Hubble Space Telescope, we have 100 per cent coverage in the R-band. We also have a number of new K-s-band data points, which we use to constrain the infrared magnitude of the system. We model this with the eclipsing light-curve (ELC) code. From the modelling with the ELC code we obtain colour information about the secondary at minimum light in BVRI and K. For our best-fitting model we are able to constrain the system inclination to 65 degrees +/- 2 degrees for pulsar masses ranging from 1.3 to 1.9 M-circle dot. The pulsar mass is unconstrained. We also find that the secondary star is not filling its Roche lobe. The temperature of the unirradiated side of the companion is in agreement with previous estimates and we find that the observed temperature gradient across the secondary star is physically sustainable

The incidence of evaporating ‘black widow’ pulsars (BWPs) among all millisecond pulsars is far higher in globular clusters than in the field. This implies a special formation mechanism for them in clusters. Cluster millisecond pulsars in wide binaries with white dwarf companions exchange them for turnoff‐mass stars. These new companions eventually overflow their Roche lobes because of encounters and tides. The millisecond pulsars eject the overflowing gas from the binary, giving mass loss on the binary evolution time‐scale. The systems are only observable as BWPs at epochs where this evolution is slow, making the mass loss transparent and the lifetime long. This explains why observed BWPs have low‐mass companions. We suggest that at least some field BWPs were ejected from globular clusters or entered the field population when the cluster itself was disrupted.

To measure the onset of mass transfer in eccentric binaries, we have developed a two‐phase smoothed particle hydrodynamics (SPH) technique. Mass transfer is important in the evolution of close binaries, and a key issue is to determine the separation at which mass transfer begins. The circular case is well understood and can be treated through the use of the Roche formalism. To treat the eccentric case, we use a newly developed two‐phase system. The body of the donor star is made up from high‐mass water particles, whilst the atmosphere is modelled with low‐mass oil particles. Both sets of particles take part fully in SPH interactions. To test the technique, we model circular mass‐transfer binaries containing a 0.6 M⊙ donor star and a 1 M⊙ white dwarf; such binaries are thought to form cataclysmic variable (CV) systems. We find that we can reproduce a reasonable CV mass‐transfer rate, and that our extended atmosphere gives a separation that is too large by approximately 16 per cent, although its pressure scale height is considerably exaggerated. We use the technique to measure the semimajor axis required for the onset of mass transfer in binaries with a mass ratio of q= 0.6 and a range of eccentricities. Comparing to the value obtained by considering the instantaneous Roche lobe at pericentre, we find that the radius of the star required for mass transfer to begin decreases systematically with increasing eccentricity.

We present numerical simulations of the runaway fractions expected amongst O and Wolf–Rayet star populations resulting from stars ejected from binaries by the supernova of the companion. Observationally, the runaway fraction for both types of star is similar, prompting the explanation that close dynamical interactions are the main cause of these high‐velocity stars. We show that, provided that the initial binary fraction is high, a scenario in which two‐thirds of massive runaways are from supernovae is consistent with these observations. Our models also predict a low frequency of runaways with neutron star companions and a very low fraction of observable Wolf–Rayet–compact companion systems.