  We analyze several aspects of the recently noted neutron star collapse
instability in close binary systems. We utilize (3+1) dimensional and spherical
numerical general relativistic hydrodynamics to study the origin, evolution,
and parametric sensitivity of this instability. We derive the modified
conditions of hydrostatic equilibrium for the stars in the curved space of
quasi-static orbits. We examine the sensitivity of the instability to the
neutron star mass and equation of state. We also estimate limits to the
possible interior heating and associated neutrino luminosity which could be
generated as the stars gradually compress prior to collapse. We show that the
radiative loss in neutrinos from this heating could exceed the power radiated
in gravity waves for several hours prior to collapse. The possibility that the
radiation neutrinos could produce gamma-ray (or other electromagnetic) burst
phenomena is also discussed.
