TY - JOUR

T1 - The biphase explained

T2 - Understanding the asymmetries in coupled fourier components of astronomical time series

AU - Maccarone, Thomas J.

PY - 2013/11

Y1 - 2013/11

N2 - 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 bispectrummeasures two key non-linear properties of a time series-its reversibility 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 ratio 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.

AB - 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 bispectrummeasures two key non-linear properties of a time series-its reversibility 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 ratio 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.

KW - Methods

KW - Stars:Variables:general

KW - Statistical

KW - X-rays:Binaries

UR - http://www.scopus.com/inward/record.url?scp=84885764641&partnerID=8YFLogxK

U2 - 10.1093/mnras/stt1546

DO - 10.1093/mnras/stt1546

M3 - Article

AN - SCOPUS:84885764641

SN - 0035-8711

VL - 435

SP - 3547

EP - 3558

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

IS - 4

ER -