Gravitational waves from coalescing binaries and Doppler experiments - art. no. 082001

Doppler tracking of interplanetary spacecraft provides the only method pres ently available for broadband searches of low frequency gravitational waves (similar to 10(-5)-1 Hz). The instruments have a peak sensitivity around t he reciprocal of thr round-trip light time T (similar to 10(3)-10(4) sec) o f the radio link connecting Earth to the space probe and therefore are part icularly suitable to search for coalescing binaries containing massive blac k holes in galactic nuclei. A number of Doppler experiments - the most rece nt involving the probes ULYSSES, GALILEO, and the Mars Observer - have been carried out so far: moreover, in 2001-2004 the CASSINI spacecraft will per form three 40-day data acquisition runs with an expected sensitivity about 20 times better than that achieved so far. The central aims of this paper a re (i) to explore, as a function of the relevant instrumental and astrophys ical parameters, the Doppler output produced by inspiral signals-sinusoids of increasing frequency and amplitude (the so-called chirp), (ii) to identi fy the most important parameter regions where to concentrate intense and de dicated data analysis, and (iii) to analyze the all-sky and all-frequency s ensitivity of the CASSINI experiments, with particular emphasis on possible astrophysical targets, such as our galactic center and the Virgo cluster. We consider first an ideal situation in which the spectrum of the noise is white and there are no cutoffs in the instrumental band, we can define an i deal signal-to-noise ratio (SNR) which depends in a simple way on the funda mental parameters of the source-chirp mass M and luminosity distance-and th e experiment-round-trip light time and noise spectral level. For any real e xperiment we define the sensitivity function Y as the degradation of the SN R with respect to its ideal value due to a colored spectrum, the experiment finite duration T-1, the accessible frequency band (f(b),f(e)) of the sign al, and the source's location in the sky. We show that the actual value of Y crucially depends on the overlap of the band (f(b),f(e)) with the instrum ent response: the sensitivity is best when f(b) less than or similar to 1/T and f(e) coincides with the frequency corresponding to the beginning of th e merging phase. Furthermore, for any fb and TI, there is an optimal value of the chirp mass-the critical chirp mass M-e proportional to f(b)(-8/5) T- 1(-3/5) - that produces the largest sensitivity function; lower values of M correspond to a smaller bandwidth and lower SNR. Also the optimal source's location in the sky strongly depends on (f(b), f(e)). We show that the lar gest distance at which a source is detectable with CASSINI experiments is s imilar to 600 Mpc and is attained for massive black holes of comparable mas ses similar to 10(7) M. and f(b)similar to 10(-5) Hz. Sources not far from coalescence in the Virgo cluster with 10(6) M. less than or similar to M le ss than or similar to 10(9) M. would be detectable with a SNR similar to 1- 30. The SNR and the range of accessible masses reduce drastically when a smalle r mass ratio is considered. We then turn our attention to galactic observat ions, in particular on the detectability of a coalescing binary in the gala ctic center, where a small black hole of mass M-2 could be orbiting around the central massive one M-1 similar or equal to 2 x 10(6) M.. CASSINI would be able to pick up such systems with M-2 greater than or similar to 50M.; for M-2 greater than or similar to 10(3)M. the SNR could be as high as simi lar to 100-1000. It may also be possible to detect such binaries in more th an one of the three CASSINI experiments, thus reenforcing the confidence of detection.