Stellar collisions and ultracompact X-ray binary formation

We report the results of new SPH calculations of parabolic collisions between a subgiant or slightly evolved red giant star and a neutron star (NS). Such collisions are likely to provide the dominant formation mechanism for ultracompact X-ray binaries (UCXBs) observed today in old globular clusters. In particular, we compute collisions of a 1.4 M_⊙ NS with realistically modeled parent stars of initial masses 0.8 and 0.9 M _⊙, each at three different evolutionary stages (corresponding to three different core masses m_c and radii R). The distance of closest approach for the initial orbit varies from r_p = 0.04R (nearly head-on) to 1.3R (grazing). These collisions lead to the formation of a tight binary, composed of the NS and the subgiant or red giant core, embedded in an extremely diffuse common envelope (CE) typically of mass ∼0.1-0.3 M _⊙. Our calculations follow the binary for many hundreds of orbits, ensuring that the orbital parameters we determine at the end of the calculations are close to final. Some of the fluid initially in the giant's envelope, from 0.003 to 0.023 M_⊙ in the cases we considered, is left bound to the NS. The eccentricities of the resulting binaries range from about 0.2 for our most grazing collision to about 0.9 for the nearly head-on cases. In almost all the cases we consider, gravitational radiation alone will cause sufficiently fast orbital decay to form a UCXB within a Hubble time, and often on a much shorter timescale. Our hydrodynamics code implements the recent SPH equations of motion derived with a variational approach by Springel & Hernquist and by Monaghan. Numerical noise is reduced by enforcing an analytic constraint equation that relates the smoothing lengths and densities of SPH particles. We present tests of these new methods to help demonstrate their improved accuracy.