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Abstract:
We consider the problem of searching for continuous gravitational wave (cw) sources orbiting a companion object. This issue is of particular interest because the Low mass x-ray binaries (LMXB’s), and among them Sco X-1, the brightest x-ray source in the sky, might be marginally detectable with ≈2 y coherent observation time by the Earth-based laser interferometers expected to come on line by 2002 and clearly observable by the second generation of detectors. Moreover, several radio pulsars, which could be deemed to be cw sources, are found to orbit a companion star or planet, and the LIGO-VIRGO-GEO600 network plans to continuously monitor such systems. We estimate the computational costs for a search launched over the additional five parameters describing generic elliptical orbits (up to e≲0.8) using match filtering techniques. These techniques provide the optimal signal-to-noise ratio and also a very clear and transparent theoretical framework. Since matched filtering will be implemented in the final and the most computationally expensive stage of the hierarchical strategies, the theoretical framework provided here can be used to determine the computational costs. In order to disentangle the computational burden involved in the orbital motion of the cw source from the other source parameters (position in the sky and spin down) and reduce the complexity of the analysis, we assume that the source is monochromatic (there is no intrinsic change in its frequency) and its location in the sky is exactly known. The orbital elements, on the other hand, are either assumed to be completely unknown or only partly known. We provide ready-to-use analytical expressions for the number of templates required to carry out the searches in the astrophysically relevant regions of the parameter space and how the computational cost scales with the ranges of the parameters. We also determine the critical accuracy to which a particular parameter must be known, so that no search is needed for it; we provide rigorous statements, based on the geometrical formulation of data analysis, concerning the size of the parameter space so that a particular neutron star is a one-filter target. This result is formulated in a completely general form, independent of the particular kind of source, and can be applied to any class of signals whose waveform can be accurately predicted. We apply our theoretical analysis to Sco X-1 and the 44 neutron stars with binary companions which are listed in the most updated version of the radio pulsar catalog. For up to ≈3 h of coherent integration time, Sco X-1 will need at most a few templates; for 1 week integration time the number of templates rapidly rises to ≃5×106. This is due to the rather poor measurements available today of the projected semi-major axis and the orbital phase of the neutron star. If, however, the same search is to be carried out with only a few filters, then more refined measurements of the orbital parameters are called for—an improvement of about three orders of magnitude in the accuracy is required. Further, we show that the five NS’s (radio pulsars) for which the upper limits on the signal strength are highest require no more than a few templates each and can be targeted very cheaply in terms of CPU time. Blind searches of the parameter space of orbital elements are, in general, completely un-affordable for present or near future dedicated computational resources, when the coherent integration time is of the order of the orbital period or longer. For wide binary systems, when the observation covers only a fraction of one orbit, the computational burden reduces enormously, and becomes affordable for a significant region of the parameter space.
