Coherent algorithm for reconstructing the location of a coalescing binary system using a network of three gravitational interferometers

The Virgo project is one of the ground based interferometers on the earth surface that aim to detect gravitational waves. This thesis work concerns the data analysis for the coalescing binaries stars, that are among the most promising gravitational waves sources, since the shape of their signal is well known. The gravitational waves emission from a binary system of compact stars acts like a sort of feedback: the system radiates loosing its orbital energy, so the orbit shrinks and the emission becomes stronger. The signal is therefore called a chirp, due to this characteristic amplitude and frequency increasing with time. The expectation rate for the double neutron stars merging is 3.4 · 10−5 per year. Translated in detection expectation rate this corresponds to a detected event every 125 years for the LIGO detectors, and one every 148 years for the Virgo one. For the advanced new generation of detectors, that will be working within the next years, the expectation rate with the 2004 proposed configuration of advanced detectors is definitely better: 6 events per year for the so called Enhanced LIGO, and 3 every two years for the Advanced Virgo (updated scenarios for detection rates, with a more recent Advanced Virgo configuration are under development). The technique that suites at best the analysis of this kind of signal is the matched filter, that consists in computing the correlation between the data stream (output of the gravitational waves interferometer) and a set of theoretical tem- plates. From this analysis, using a single detector, it is possible to determine the masses of the two stars, and the so called optimal orientation distance, that is the source distance provided that the orbit has the best inclination with respect to the interferometer line of sight. Reconstructing the source position, so as to draw a gravitational waves sources sky map, requires at least three non-coincident detectors, in order to make a triangula- tion. Another very good reason to use a network of gravitational waves interferometers is that the detection rate can be improved considering a network of three detectors (Virgo, Hanford and Livingston) and operating a coherent analysis, since in this case the expected rate corresponds to one event each 26 years. There are two different methods used for the network analysis: the coincident method, and the coherent one. The first is the most intuitive one, and simply consists in a separate single detec- tor analysis performed by each interferometer, and a successive comparison between the single detector candidates, searching for compatible events. After that process, only the coincidences remain as candidate events, and they can be used for the source position reconstruction, using the time delays between detectors. The basic idea of the coherent method is to construct an ideal detector equivalent to the network, to which each real interferometer coherently contributes with its sensitivity, location, orientation. For this purpose a so called network statistic to maximize in order to extrapolate the source pa- rameters is constructed, first, and maximized then. For this thesis we have worked on coalescing binaries network analysis, trying to determine the best strategy for source position reconstruction. We have developed a pipeline that implements a fully coherent method, in a few different variations, and we have compared them with the classical time- of-light coincidence analysis. The coincident method has been optimized in order to make a fair comparison; in particular we have adopted the reference time, for implementing the coincidence, and we have further improved the arrival time accuracy by fitting the shape of the matched filter response. Among the coherent techniques tested, the sim- plest has been a direct maximization of the network likelihood. A fit of the likelihood to improve the determination of the likelihood maximum has also been attempted but the fitting procedure resulted unstable; instead, we have found most effective to define the most likely declination and right ascension by means of an average procedure weighted by the corresponding network likelihood. This procedure allows to remove the discretization effect due to the finite sampling rate of the analysis, and provides results compatible with the ones obtained with the time-of-light technique, and in a relatively automatic way. The study of the accuracy problem, comparing the two methods of analysis gives in a certain way two important consequences: first of all the determination of the best coherent strategy for reconstructing the source position among all the alternatives, both in terms of efficiency, and in term of computational costs; and as a secondary effect it gives us the incipit for push the coincident method to its best, provided that one uses all the correlators information. If we give a glance to the future, since new interferometric gravitational waves detectors are under construction and under project, another important feature of the coherent method is its exibility to be adapted to a larger number of detectors. The coherent method can tell us how to combine them in order to obtain with the best accuracy the source position, instead of analyzing all the possible independent triangulations, and loosing in that way part of the event astrophysical information.