chapter  17
23 Pages

Post-Newtonian computation of binary inspiral waveforms

Astrophysical systems known as inspiralling compact binaries are among the most interesting sources to hunt for gravitational radiation in the future network of laser-interferometric detectors, composed of the large-scale interferometers VIRGO and LIGO, and the medium-scale ones GEO and TAMA (see the books [1-3] for reviews, and the contribution of B Schutz in this volume). These systems are composed of two compact objects, i.e. gravitationally-condensed neutron stars or black holes, whose orbit follows an inward spiral, with decreasing orbital radius r and increasing orbital frequency ω. The inspiral is driven by the loss of energy associated with the gravitational-wave emission. Because the dynamics of a binary is essentially aspherical, inspiralling compact binaries are strong emitters of gravitational radiation. Tidal interactions between the compact objects are expected to play a little role during most of the inspiral phase; the mass transfer (in the case of neutron stars) does not occur until very late, near the final coalescence. Inspiralling compact binaries are very clean systems, essentially dominated by gravitational forces. Therefore, the relevant model for describing the inspiral phase consists of two point-masses moving under their mutual gravitational attraction. As a simplification for the theoretical analysis, the orbit of inspiralling binaries can be considered to be circular, apart from the gradual inspiral, with a good approximation. At some point in the evolution, there will be a transition from the adiabatic inspiral to the plunge of the two objects followed by the collision and final merger. Evidently the model of point-masses

breaks down at this point, and is to be replaced by a fully relativistic numerical computation of the plunge and merger (see the contribution of E Seidel in this volume).