GRAVITATIONAL-WAVE TAILS AND BINARY STAR SYSTEMS

Gravitational wave tails are produced by back-scattering of the outgoi ng gravitational radiation (emitted by an isolated system) off the cur ved spacetime associated with the total mass of the system. This paper investigates the spectral (or Fourier) decomposition of gravitational wave tails at large distances from the system, at the 1.5 post-Newton ian order in the wave field. It is shown that the effects of wave tail s are (i) to increase the amplitude of the Fourier components of the ( linear) waves by a factor linearly depending on the frequency, and (ii ) to add to the phase of the waves a supplementary phase depending on the frequency as omega ln omega. The latter frequency-dependent phase introduces a new effect which should be observable in any radiation co ntaining more than one frequency, for instance in the radiation emitte d by a binary star system orbiting a Keplerian ellipse with non-zero e ccentricity, or in the radiation emitted by an inspiralling (compact) binary star system. We propose in this paper to include the tail-induc ed effects (i) and (ii) in the matched filters of the future data anal ysis of inspiralling compact binary signals in laser interferometer gr avity-wave detectors (at least in future, very sensitive, such detecto rs). In this way, the filters will be highly correlated with the actua l signal, and in particular will remain, as the frequency of the signa l increases, in accurate phase with it. The contribution of the wave t ail in the total gravitational energy emitted by a binary system is al so calculated, and a numerical application to the binary pulsar PSR 19 13+16 is presented. We find that the tail-induced relative correction in the orbital P(Th) of the pulsar is equal to -1.65 x 10(-7) (too sma ll to be observed).