Phase decomposition of the template metric for continuous gravitational-wave searches

A type of gravitational-wave signal in the LIGO-Virgo data is expected to be emitted by spinning asymmetric neutron stars, with rotational frequencies that could plausibly emit continuous gravitational radiation in the most sensitive band of the LIGO-Virgo detectors. The most important feature of such signals is in their phase evolution, which is stable over a long observation run. When using analysis based on matched filtering, the phase evolution of long-coherent signals is needed to define how to build a proper template grid in order to gain the best signal-to-noise ratio possible. This information is encoded in a matrix called a phase metric, which characterizes the geometry for the likelihood given by matched filtering. Most of the time, the metric for long-coherent signals cannot be computed analytically, and even its numerical computation is not possible due to the numerical precision needed. In this paper, we show a general phase decomposition technique that is able to make the template metric semianalytically computable. We also show how these variables can be employed to distinguish robustly between astrophysical signals and nonstationary noise artifacts that may affect analysis pipelines.