Coalescing binary systems of compact objects to(post)52-Newtonian order. IV. The gravitational wave tail

The contribution to gravitational radiation from the gravitational wave "tail" is studied using an expression previously obtained by Blanchet and Damour. The expression for the tail of the radiation contains integrals over the past history of the system, thus exhibiting the backscattering nature of radiation in curved spacetime; however the dependence on the remote past of the system is shown to be weak for relevant astrophysical systems. In the cases of circular orbits and high-speed, low-deflection (bremsstrahlung) encounters, the integrals can be evaluated analytically. For circular orbits the frequency of the tail radiation is twice the orbital frequency, just as for the quadrupole radiation, but is phase shifted from it. Using explicit two-body multipoles of the radiation we have published elsewhere, along with the tail terms developed here, we present gravitational waveforms which are accurate to ${\left(\mathrm{post}\right)}^{\frac{3}{2}}$-Newtonian order [i.e., $O\left({\left(\frac{\mathrm{Gm}}{r{c}^2}\right)}^{\frac{3}{2}}\right)=O\left({\left(\frac{v}{c}\right)}^3\right)$ beyond the usual quadrupole radiation] for a coalescing binary system of compact objects in a nearly circular orbit. For the case of two orbiting neutron stars very near coalescence we estimate the tail contribution to the waveform to be roughly half the amplitude of the usual quadrupole radiation. We also compute the correction to the radiation energy flux produced by the tail radiation. We show that this results in an increased rate of decay for a binary in a circular orbit. We show that the same orbital decay rate can also be obtained directly from the tail-transported part of the near-zone radiation reaction force. In the Appendix we give a heuristic, "physical" explanation of the behavior of the tail radiation.