Non-parametric characterization of gravitational-wave polarizations

Gravitational waves are polarized. Their polarization is essential to characterize the physical and dynamical properties of the source i.e., a coalescing binary of two compact objects such as black holes or neutron stars. Observations with two or more non coaligned detectors like Virgo and LIGO allow to reconstruct the two polarization components usually denoted by h+(t) and h×(t). The amplitude and phase relationship between the two components is related to the source orientation with respect to the observer. Therefore the evolution of the polarization pattern provides evidence for changes in the orientation due to precession or nutation of the binary. Usually, some specific direct dynamical model is exploited to identify the physical parameters of such binaries. Recently, a new framework for the time-frequency analysis of bivariate signals based on a quaternion Fourier transform has been introduced in [1]. It permits to analyze the bivariate signal combining h+(t) and h×(t) by defining its quaternion embedding as well as a set of non-parametric observables, namely Stokes parameters. These parameters are remarkably capable of measuring fine properties of the source, in particular by deciphering precession, without close bounds to a specific dynamical model.