Fast and Accurate Computation Tools for Gravitational Waveforms from Binary Stars with any Orbital Eccentricity

Gravitational wave detection experiments in space, including satellite Doppler-Tracking (Bertotti and Iess, 1999) and LISA (http://lisa.jpl.nasa.gov), will hopefully open a window on the low-frequency part of the gravitational wave (henceforth GW) spectrum of cosmic origin. In these frequency bands, binary stars are among the most promising continuous detectable source. A substantial fraction of binaries are expected to have orbits with non negligible eccentricity (Barone et al., 1988; Hils et al., 1992; Pierro and Pinto, 1996c) resulting into the emission of several harmonics of the fundamental orbital frequency. The importance of this fact from the standpoint of signal detection and estimation has been already noted. For coalescing binaries, Pierro and Pinto (1996b) and Martel and Poisson (1999) pointed out that neglecting residual (albeit very small) orbital eccentricities may seriously deteriorate matched-filter detection performance. Their results, obtained in the frame of the simplest (newtonian) Peters Mathews (henceforth PM) model (Peters and Mathews, 1963; Peters 1964; Pierro and Pinto 1996c), support the qualitative conclusion that residual orbital eccentricities cannot be bona fide disregarded in building templates for matched-filter detection of gravitational wave chirps from inspiraling binaries⋆. For steady-state binaries with non-zero orbital eccentricity, on the other hand, using circular-orbit waveform templates, i.e. neglecting higher order harmonics, implies a potentially large loss of signal-to-noise ratio (henceforth SNR), leading to significantly worse detector’s performance, as will be shown in the sequel. The main goals of the present paper are: