Search methods for continuous gravitational-wave signals from unknown sources in the advanced-detector era

Continuous gravitational waves are long-lasting forms of gravitational radiation produced by persistent quadrupolar variations of matter. Standard expected sources for ground-based interferometric detectors are neutron stars presenting non-axisymmetries such as crustal deformations, r-modes or free precession. More exotic sources could include decaying ultralight boson clouds around spinning black holes. A rich suite of data-analysis methods spanning a wide bracket of thresholds between sensitivity and computational efficiency has been developed during the last decades to search for these signals. In this work, we review the current state of searches for continuous gravitational waves using ground-based interferometer data, focusing on searches for unknown sources. These searches typically consist of a main stage followed by several post-processing steps to rule out outliers produced by detector noise. So far, no continuous gravitational wave signal has been confidently detected, although tighter upper limits are placed as detectors and search methods are further developed.