A semi-coherent generalization of the 5-vector method to search for continuous gravitational waves

The emission of continuous gravitational waves (CWs), with duration much longer than the typical data taking runs, is expected from several sources, notably spinning neutron stars, asymmetric with respect to their rotation axis and more exotic sources, like ultra-light scalar boson clouds formed around Kerr black holes and sub-solar mass primordial binary black holes. Unless the signal time evolution is well predicted and its relevant parameters accurately known, the search for CWs is typically based on semi-coherent methods, where the full data set is divided in shorter chunks of given duration, which are properly processed, and then incoherently combined. In this paper we present a semi-coherent method, in which the so-called \textit{5-vector} statistics is computed for the various data segments and then summed after the removal of the Earth Doppler modulation and signal intrinsic spin-down. The method can work with segment duration of several days, thanks to a double stage procedure in which an initial rough correction of the Doppler and spin-down is followed by a refined step in which the residual variations are removed. This method can be efficiently applied for directed searches, where the source position is known to a good level of accuracy, and in the candidate follow-up stage of wide-parameter space searches.