The violent past of Cygnus X-2

Cygnus X-2 appears to be the descendant of an intermediate-mass X-ray binar y (IMXB). Using Mazzitelli's stellar code we compute detailed evolutionary sequences for the system and find that its prehistory is sensitive to stell ar input parameters, in particular the amount of core overshooting during t he main-sequence phase. With standard assumptions for convective overshooti ng a case B mass transfer starting with a 3.5-M. donor star is the most lik ely evolutionary solution for Cygnus X-2. This makes the currently observed state rather short-lived, of order 3 Myr, and requires a formation rate > 10(-7)-10(-6) yr(-1) of such systems in the Galaxy. Our calculations show t hat neutron star IMXBs with initially more massive donors (greater than or similar to 4 M.) encounter a delayed dynamical instability; they are unlike ly to survive this rapid mass transfer phase. We determine limits for the a ge and initial parameters of Cygnus X-2 and calculate possible dynamical or bits of the system in a realistic Galactic potential, given its observed ra dial velocity. We find trajectories which are consistent with a progenitor binary on a circular orbit in the Galactic plane inside the solar circle th at received a kick velocity less than or equal to 200 km s(-1) at the birth of the neutron star. The simulations suggest that about 7 per cent of IMXB s receiving an arbitrary kick velocity from a standard kick velocity spectr um would end up in an orbit similar to Cygnus X-2, while about 10 per cent of them reach yet larger Galactocentric distances.