Relativistic Hydrodynamics in Close Binary Systems: Analysis of Neutron-Star Collapse

We discuss the underlying relativistic physics which causes neutron stars to compress and collapse in close binary systems as has recently been observed in numerical (3+1) dimensional general relativistic hydrodynamic simulations. We show that compression is driven by velocity-dependent relativistic hydrodynamic terms which describe the response of the stars to their orbital motion against the curved space-time of the system. We present numerical and analytic results which confirm that such terms are insignificant for uniform translation or when the hydrodynamics is constrained to rigid corotation. However, when the hydrodynamics is unconstrained, the neutron star fluid relaxes to a compressed nonsynchronized state of almost no net intrinsic spin. We also show that tidal decompression is much less than the velocity-dependent compression. This study explains why several recent attempts to analyze this effect with constrained hydrodynamics or an analysis of tidal forces do not observe compression. We show that the central density grows with spatial four velocity $\propto U^4$. Hence, this effect would not appear in a first post-Newtonian or weak-field expansion truncated at order $U^2\sim m/R$. The implication of this study is that the neutron-star compression effect has not yet been independently tested. An independent test of this effect ought to include unconstrained completely relativistic hydrodynamics.