Coalescence of neutron star binaries

The two-body problem may seem an easy problem. Indeed it is exactly solved in Newtonian physics, in the case of point masses. But if one looks at General Relativity, one finds at once that the highly non-linear character of the theory makes it impossible to solve analytically even this putatively simple problem. So when general relativistic effects are to be taken into account, one is forced to turn to numerical methods. And this is clearly the case for binary Neutron Stars.

Actually, the inspiralling, i.e. the first and longest (hundreds of millions of years) part of the life of a binary Neutron Star system, can be fruitfully studied using Newtonian and post-Newtonian approximations. In this stage, in fact, the Neutron Stars are still far enough apart that finite size effect (such as tidal interaction) and General Relativistic effects (such as Gravitational Wave emission) are negligible on the timescale of single orbits, even if Gravitational Wave emission is of course crucial to the long term evolution of the system. Indeed, it is because of the small but steady amount of energy and angular momentum carried away from the system by gravitational radiation that the two stars keep approaching and eventually merge. The merger phase takes place in about an orbital period (few milliseconds) and is characterized by the strongest emission of Gravitational Waves. So the knowledge of the waveform at this stage is very important in view of the first attempts at detection of gravitational radiation. The accurate simulation of a binary neutron star coalescence is however one of the most challenging tasks in numerical relativity. In addition to involving strong gravitational fields, matter motion with (ultra-) relativistic speeds and/or strong shock waves, and in addition to the inherent complexities of Einstein's theory of gravity, such as coordinate degrees of freedom and the possible formation of curvature singularities (e.g. collapse of matter to black holes), the difficulties of a successful numerical integration are exacerbated by the intrinsic multidimensional character of the problem: no symmetries can in fact be assumed and a full 3D simulation must be sought for even as the first step in the calculation. The computation of the dynamics and so of the waveform of the emitted gravitational radiation depends also crucially on hydrodynamical finite-size effects. One further reason forcing to go to numerical solutions.
 


Images taken from J.A. Font, Numerical Hydrodynamics in General Relativity, in Living Reviews:http://livingreviews.org




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Page created by: Luca Baiotti
Last change made: May 20, 2002