EVOLUTION OF ECCENTRIC ORBITS OF NEUTRON-STAR BINARIES EMITTING GRAVITATIONAL-WAVES

The evolution of elliptical orbits of binary systems due to gravitational radiation is considered for arbitrary initial parameters and initial eccentricity e0. On the basis of existing solutions of the evolution problem [1, 2], which is reduced to the monotonic dependence a = a(e) of the semimajor axis a on eccentricity e, expressions for the neutron star binary system parameters are obtained. The solutions obtained are applicable up to the onset of mass exchange, that is, until the low-mass companion fills its Roche lobe. The final orbital eccentricity e(f) is shown to be very small (roughly e(f) less-than-or-similar-to 0.1) for arbitrary input parameters. Therefore, within the framework of the collapsing supernova explosion scenario [3], the orbits of neutron star binaries become nearly circular before the onset of mass exchange, so that the necessary conditions for the Roche approximation are fulfilled. The same solutions allowed the characteristic time scales of the neutron binary shrinking to be evaluated for arbitrary initial parameters. The time scales evaluated are compared with restrictions obtained from observations of SN 1987A. We show a posteriori that the analytical solution obtained is applicable provided that (1) the orbital motion of companions is nonrelativistic and (2) the evolution of the binary system is quasistationary. In the conclusion, the effects of neutron star finite dimensions and axial rotation that were not taken into account are discussed.