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

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Abstract

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. This has long been the case for studies of X-ray binaries, but is increasingly becoming true for stellar variability (both intrinsic and due to planetary transits) in the Kepler era. We attempt in this paper also to present some simple examples
Original languageEnglish
JournalMonthly Notices of the Royal Astronomical Society
StatePublished - Nov 2013

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