Estimation of error on the cross-correlation, phase and time lag between evenly sampled light curves

TL;DR

This paper introduces analytical expressions to estimate errors in cross-correlation, phase, and time-lag measurements between light-curves, verified through simulations, enabling efficient analysis of astrophysical data with fewer data points.

Contribution

The paper presents new analytical methods for error estimation in cross-correlation analysis, reducing computational cost compared to previous simulation-based approaches.

Findings

Validated error estimates using simulations of white and 1/f noise.

Applicable to light-curves with around 1000 data points.

Demonstrated technique on AGN X-ray data from XMM-Newton.

Abstract

Temporal analysis of radiation from Astrophysical sources like Active Galactic Nuclei, X-ray Binaries and Gamma-ray bursts provide information on the geometry and sizes of the emitting regions. Establishing that two light-curves in different energy bands are correlated and measuring the phase and time-lag between them is an important and frequently used temporal diagnostic. In the present work, expressions to estimate the errors on the cross-correlation, phase and time-lag between two light-curves are presented and the same have been verified using simulations. Earlier estimates depended upon numerically expensive simulations or on dividing the light-curves in large number of segments to find the variance. The estimates presented here allow for analysis of light-curves with relatively small (~1000) number of points, as well as to obtain information on the longest time-scales available. The error estimation is verified using simulations of light-curves derived from both white and 1/f stochastic processes with measurement errors. As a demonstration, we apply this technique to the XMM-Newton light-curves of the Active Galactic Nucleus, Akn 564.