Relativistic hydrodynamics in close binary systems: Analysis of neutron-star collapse

We discuss the underlying relativistic physics that causes neutron stars to compress and collapse in close binary systems as has been recently observed in numerical $\mathrm{}(3+1)\mathrm{}$-dimensional general relativistic hydrodynamic simulations. We show that compression is driven by velocity-dependent relativistic hydrodynamic terms which increase the self-gravity of the stars. They also produce fluid motion with respect to the corotating frame of the binary. We present numerical and analytic results that confirm that such terms are insignificant for uniform translation or when the hydrodynamics are constrained to rigid corotation. However, when the hydrodynamics are unconstrained, the neutron star fluid relaxes to a compressed nonsynchronized state of almost no net intrinsic spin with respect to a distant observer. We also show that tidal decompression effects are much smaller than the velocity-dependent compression terms for stars with a realistic compaction ratio. We discuss why several recent attempts to analyze this effect with constrained hydrodynamics or an analysis of tidal forces do not observe compression. We argue that an independent test of this effect must include unconstrained relativistic hydrodynamics to a sufficiently high order so that all relevant velocity-dependent terms and their possible cancellations are included.