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

TL;DR

This paper introduces the concept of biphase analysis for astronomical time series, providing a new way to interpret nonlinear properties like asymmetry and reversibility in signals such as X-ray binaries and stellar variability.

Contribution

It is the first to estimate and interpret biphase data in astronomy, offering intuitive examples and applying the method to analyze quasi-periodic oscillations in GRS 1915+105.

Findings

Biphase analysis reveals asymmetries in astrophysical signals.

Application to GRS 1915+105 shows coupling of oscillations and noise.

Provides a new tool for understanding nonlinear time series in astronomy.

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 to give a more intuitive understanding of the meaning of the bispectrum to readers, in order to help to understand where it may be applicable in astronomy. In particular, we give illustrative examples of what biphases may be shown by common astrophysical time series such as pulsars, eclipsers, stars in the instability strip, and solar flares. We then discuss applications to the biphase data for understanding the shapes of the quasi-periodic oscillations of GRS 1915+105 and the coupling of the quasi-periodic oscillations to the power-law noise in that system.