Fourier Domain

TL;DR

This paper provides a practical overview of Fourier-based spectral timing methods used to analyze time variability in astronomical sources, aiding in understanding high-energy astrophysical processes.

Contribution

It offers a comprehensive, accessible summary of Fourier and spectral timing techniques applied to astrophysical data analysis.

Findings

Fourier methods effectively characterize periodicities and stochastic variability.

Spectral timing reveals complex relationships between time, energy, and flux.

These techniques improve models of accretion and high-energy physics.

Abstract

The changes in brightness of an astronomical source as a function of time are key probes into that source's physics. Periodic and quasi-periodic signals are indicators of fundamental time (and length) scales in the system, while stochastic processes help uncover the nature of turbulent accretion processes. A key method of studying time variability is through Fourier methods, the decomposition of the signal into sine waves, which yields a representation of the data in frequency space. With the extension into \textit{spectral timing} the methods built on the Fourier transform can not only help us characterize (quasi-)periodicities and stochastic processes, but also uncover the complex relationships between time, photon energy and flux in order to help build better models of accretion processes and other high-energy dynamical physics. In this Chapter, we provide a broad, but practical overview of the most important relevant methods.