The cross-correlation search has been previously applied to map the gravitational wave (GW) stochastic background in the sky and also to target GW from rotating neutron stars/pulsars. Here we investigate how the cross-correlation method can be used to target a small region in the sky spanning at most a few pixels, where a pixel in the sky is determined by the diffraction limit which depends on the (i) baseline joining a pair of detectors and (ii) detector bandwidth. Here as one of the promising targets, we consider the Virgo cluster - a hot spot spanning few pixels - which could contain, as estimates suggest $sim 10^{11}$ neutron stars, of which a small fraction would continuously emit GW in the bandwidth of the detectors. For the detector baselines, we consider advanced detector pairs among LCGT, LIGO, Virgo, ET etc. Our results show that sufficient signal to noise can be accumulated with integration times of the order of a year. The results improve for the multibaseline search. This analysis could as well be applied to other likely hot spots in the sky and other possible pairs of detectors.
In this paper we study the use of cross-correlations between multiple gravitational wave (GW) data streams for detecting long-lived periodic signals. Cross-correlation searches between data from multiple detectors have traditionally been used to search for stochastic GW signals, but recently they have also been used in directed searches for periodic GWs. Here we further adapt the cross-correlation statistic for periodic GW searches by taking into account both the non-stationarity and the long term-phase coherence of the signal. We study the statistical properties and sensitivity of this search, its relation to existing periodic wave searches, and describe the precise way in which the cross-correlation statistic interpolates between semi-coherent and fully-coherent methods. Depending on the maximum duration over we wish to preserve phase coherence, the cross-correlation statistic can be tuned to go from a standard cross-correlation statistic using data from distinct detectors, to the semi-coherent time-frequency methods with increasing coherent time baselines, and all the way to a full coherent search. This leads to a unified framework for studying periodic wave searches and can be used to make informed trade-offs between computational cost, sensitivity, and robustness against signal uncertainties.
