The effects of sudden mass loss and a random kick velocity produced in a supernova explosion on the dynamics of a binary star of arbitrary orbital eccentricity - Applications to X-ray binaries and to the binary pulsars

Long-period binaries may survive a supernova explosion in which more than half of the mass is lost if the presupernova orbit is moderately eccentric and the supernova goes off near apastron if the kick velocity is small or near periastron if it is large. If the pre-explosion orbit is highly eccentric, the post-supernova orbit is usually less eccentric. Any random kick velocity given to the neutron star in the explosion decreases the probability of binary survival if the mass loss is moderate. However, an impulse opposite in direction to the orbital motion of the neutron star may allow the binary to survive even if the fractional mass loss is high enough to otherwise dissociate it. Because of the rotation of the orbital plane by the impulse velocity, newly formed neutron stars in binaries usually do not have their rotational axes aligned with their orbital axes. If the impulse velocity is comparable to or greater than the orbital velocity, the sense of rotation of a neutron star in a surviving binary is commonly opposite that of the orbital revolution. The spin-down of these retrograde spinning neutron stars may explain the anomalously long rotation periods found in about half the X-ray binaries. If the orbit is initially circular, the kick velocity reduces the pericenter distance. If orbital dissipation occurs after the supernova explosion, the orbit will be smaller than before the explosion. In some cases the binary components may even coalesce. The kick velocity greatly increases the pericenter distances of highly eccentric orbits such as those of the long-period comets. Only an old neutron star can have comet-fueled y-ray bursts because it may take several billion years for passing stars to re-thermalize the orbits of its comets sufficiently that some of them pass close enough to hit the neutron star. The nearly circular orbits found in the widely spaced binary pulsars PSR 0655+64 and PSR 0820+02 require some dissipative mechanism to have occurred after the supernova explosion. This may require the survival of a gaseous envelope around the neutron star after the explosion. Such envelopes may also explain the lack of pulsars in recently formed supernova remnants.