Mass transfer in eccentric binaries: the new oil-on-water smoothed particle hydrodynamics technique

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(circle dot) donor star and a 1 M(circle dot) 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.