DarwinRiemann Problems in Newtonian Gravity
Abstract
In this paper, we have reviewed the present status of the theory of equilibrium configurations of compact binary star systems in Newtonian gravity. Evolutionary processes of compact binary star systems due to gravitational wave emission can be divided into three stages according to the time scales and configurations. The evolution is quasistationary until a merging process starts, since the time scale of the orbital change due to gravitational wave emission is longer than the orbital period. In this stage, equilibrium sequences can be applied to evolution of compact binary star systems. Along the equilibrium sequences, there appear several critical states where some instability sets in or configuration changes drastically. We have discussed relations among these critical points and have stressed the importance of the mass overflow as well as the dynamical instability of orbital motions. Concerning the equilibrium sequences of binary star systems, we have summarized classical results of incompressible ellipsoidal configurations. Recent results of compressible binary star systems obtained by the ellipsoidal approximation and by numerical computations have been shown and discussed. It is important to note that numerical computational solutions to exact equations show that compressibility may lead realistic neutron star binary systems to mass overflows instead of dynamical disruptions for a wide range of parameters.
 Publication:

Progress of Theoretical Physics Supplement
 Pub Date:
 1999
 DOI:
 10.1143/PTPS.136.199
 arXiv:
 arXiv:grqc/9909055
 Bibcode:
 1999PThPS.136..199E
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 17 pages, 10 figures, PTPTeX style files are included