Energy losses by gravitational radiation in inspiraling compact binaries to52post-Newtonian order

This paper derives the total power or energy loss rate generated in the form of gravitational waves by an inspiraling compact binary system to the $\frac{5}{2}$ post-Newtonian (2.5PN) approximation of general relativity. Extending a recently developed gravitational-wave generation formalism valid for arbitrary (slowly moving) systems, we compute the mass multipole moments of the system and the relevant tails present in the wave zone to 2.5PN order. In the case of two point masses moving on a quasicircular orbit, we find that the 2.5PN contribution in the energy loss rate is entirely due to tails. Relying on an energy balance argument we derive the laws of variation of the instantaneous frequency and phase of the binary. The 2.5PN order in the accumulated phase is significantly large, being grossly of the same order of magnitude as the previous 2PN order, but opposite in sign. However, finite mass effects at 2.5PN order are small. The results of this paper should be useful when analyzing the data from inspiraling compact binaries in future gravitational-wave detectors such as VIRGO and LIGO.