Tom Maccarone (University of Southampton, United Kingdom)

Higher order statistics as probes for understanding QPOs and noise

The power spectrum has traditionally been the workhorse method for analysing astrophysical time series. It
has several key positive features - e.g. ease of computation and interpretation, but it makes no use of the
phase information of the different Fourier components. For decades, scientists and engineers in other areas
of research have been using higher order statistics like the bispectrum and trispectrum to analyze time series
data. Because these techniques require very large numbers of cycles to be implemented, it is not surprising
that they have come into use in astronomical time series analysis only with investigations of rapid variability.
I will introduce the bispectrum, discuss its advantages and limitations, and show how it gives information
about non-linear coupling of different Fourier components. I will further show the results of some theoretical
calculations that may shed light on the nature of high frequency quasi-periodic oscillations given good
enough signal-to-noise and long enough observations.