The biphase explained: understanding the asymmetries in coupled Fourier components of astronomical timeseries

Understand

We make the first attempt to estimate and interpret the biphase data for astronomical time series.

• The biphase is the phase of the bispectrum, which is the Fourier domain equivalent of the three-point correlation function.
• The bispectrum measures two key nonlinear properties of a time series -- its reversability in time, and the symmetry about the mean of its flux distribution -- for triplets of frequencies.
• Like other Fourier methods, it is especially valuable for working with time series which contain large numbers of cycles at the period of interest, but in which the signal-to-noise at a given frequency is small in any individual cycle, either because of measurement errors, or because of the contributions from signals at other frequencies.