Method to search for long duration gravitational wave transients from isolated neutron stars using the generalized frequency-Hough transform

We describe a method to detect gravitational waves lasting $O(\text{hours}--\text{days})$ emitted by young, isolated neutron stars, such as those that could form after a supernova or a binary neutron star merger, using advanced LIGO/Virgo data. The method is based on a generalization of the frequency-Hough transform, a pipeline that performs hierarchical searches for continuous gravitational waves by mapping points in the time/frequency plane of the detector to lines in the frequency/spindown plane of the source. We show that signals of which the spindowns are related to their frequencies by a power law can be transformed to coordinates in which the behavior of these signals is always linear and can therefore be searched for by the frequency-Hough transform. We estimate the sensitivity of our search across different braking indices and describe the portion of the parameter space we could explore in a search using varying fast Fourier transform lengths.