Boosting the sensitivity of continuous gravitational waves all-sky searches using advanced filtering techniques

The work presented in this PhD thesis has been done in the context of gravitational-waves searches. Since the first detection on the 14th September 2015 by the LIGO-Virgo collaboration, a growing number of gravitational-wave events has been detected, all emitted by the coalescence of binary systems involving black holes and/or neutron stars. My work is focused on the search for continuous gravitational waves, which still miss the first detection. These signals are expected to be emitted, for instance, by spinning neutron stars with an asymmetric shape with respect to the rotation axis, and are at least five orders of magnitude weaker than the typical amplitude of detected binary coalescences. In this PhD thesis I report on the work done in four different projects, with the common purpose of increasing the sensitivity of continuous-wave searches, involving both data analysis and instrumental aspects. The first project is a contribution to the commissioning of the Virgo interferometer in view of the next observing run, O4, which will start in May 2023. My contribution has been mainly devoted to the noise hunting activity, focused on the identification and mitigation of instrumental-noise sources that can degrade the sensitivity of continuous-wave searches. The other three projects are related to data analysis. I have focused, in particular, on all-sky searches for sources without electromagnetic counterpart and long-lasting signals from rapidly evolving newly-born neutron stars. I have studied in great detail the robustness of an all-sky data analysis method in the case of overlapping signals. This is relevant for some exotic classes of continuous wave sources and, more generally, in view of third generation detectors, like Einstein Telescope. I have developed a two-dimensional filter, called triangular filter, to be applied to the search for long-lasting gravitational waves from unstable neutron stars, showing that thanks to this method an increase of the search sensitivity of about $20\%$ is achievable. Finally, I describe the first steps of a wide work to develop a new procedure for all-sky continuous-wave searches, exploiting a statistics based on the sidereal modulation, that affects astrophysical signals, due to the Earth rotation.