Improved AGN light curve analysis with the z-transformed discrete correlation function

TL;DR

The paper introduces the z-transformed discrete correlation function (ZDCF), a robust method for analyzing sparse, unevenly sampled AGN light curves, improving accuracy over traditional methods and providing error estimates.

Contribution

It presents the ZDCF method, which corrects biases of previous correlation functions, enabling reliable analysis of sparse AGN light curves with error estimation.

Findings

ZDCF provides more robust correlation estimates for sparse data.

It uncovers correlations between AGN magnitude and variability time scale.

The method accurately estimates time-lags between light curves.

Abstract

The cross-correlation function (CCF) is commonly employed in the study of AGN, where it is used to probe the structure of the broad line region by line reverberation, to study the continuum emission mechanism by correlating multi-waveband light curves and to seek correlations between the variability and other AGN properties. The z -transformed discrete correlation function (ZDCF) is a new method for estimating the CCF of sparse, unevenly sampled light curves. Unlike the commonly used interpolation method, it does not assume that the light curves are smooth and it does provide errors on its estimates. The ZDCF corrects several biases of the discrete correlation function method of Edelson & Krolik (1988) by using equal population binning and Fisher's z -transform. These lead to a more robust and powerful method of estimating the CCF of sparse light curves of as few as 12 points. Two examples of light curve analysis with the ZDCF are presented. 1) The ZDCF estimate of the auto-correlation function is used to uncover a correlation between AGN magnitude and variability time scale in a small simulated sample of very sparse and irregularly sampled light curves. 2) A maximum likelihood function for the ZDCF peak location is used to estimate the time-lag between two light curves. Fortran 77 and 95 code implementations of the ZDCF and the maximum likelihood peak location (PLIKE) algorithms are freely available (see http://www.weizmann.ac.il/weizsites/tal/research/software/).