Searching for continuous gravitational wave sources in binary systems - art. no. 122001

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 b rightest x-ray source in the sky, might be marginally detectable with appro ximate to2 y coherent observation time by the Earth-based laser interferome ters expected to come on Line by 2002 and clearly observable by the second generation of detectors. Moreover, several radio pulsars, which could be de emed to be cw sources, are found to orbit a companion star or planet, and t he 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 less than or similar to 0.8) using match filtering techniques. These techniques provide the optimal signal-to-noise ratio and also a very clear and transparent th eoretical framework. Since matched filtering will be implemented in the fin al and the most computationally expensive stage of the hierarchical strateg ies, the theoretical framework provided here can be used to determine the c omputational costs. In order to disentangle the computational burden involv ed 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 analys is, we assume that the source is monochromatic (there is no intrinsic chang e in its frequency) and its location in the sky is exactly known. The orbit al elements, on the other hand, are either assumed to be completely unknown or only partly known. We provide ready-to-use analytical expressions for t he number of templates required to carry out the searches in the astrophysi cally relevant regions of the parameter space and how the computational cos t scales with the ranges of the parameters. We also determine the critical accuracy to which a particular parameter most be known, so that no search i s needed for it; we provide rigorous statements, based on the geometrical f ormulation of data analysis, concerning the size of the parameter space so that a particular neutron star is a one-filter target. This result is formu lated in a completely general form, independent of the particular kind of s ource, and can be applied to any class of signals whose waveform can be acc urately 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 v ersion of the radio pulsar catalog. For up to approximate to3 h of coherent integration time, Sco X-1 will need at most a few templates; for I week in tegration time the number of templates rapidly rises to similar or equal to 5 x 10(6). This is due to the rather poor measurements available today of t he 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, the n more refined measurements of the orbital parameters are called for-an imp rovement of about three orders of magnitude in the accuracy is required. Fu rther, we show that the five NS's (radio pulsars) for which the upper limit s on the signal strength are highest require no more than a few templates e ach and can be targeted very cheaply in terms of CPU time. Blind searches o f the parameter space of orbital elements are, in general, completely un-af fordable for present or near future dedicated computational resources, when the coherent integration time is of the order of the orbital period or lon ger. 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.