Calculating Time Lags From Unevenly-Sampled Light Curves

TL;DR

This paper introduces a maximum likelihood method for calculating frequency-dependent time lags from unevenly-sampled light curves in astrophysics, enabling reverberation studies when continuous data is unavailable.

Contribution

It develops and validates a new statistical approach to estimate time lags from irregular light curves, extending reverberation analysis capabilities.

Findings

Method accurately recovers known lags in simulations.

Applied to Suzaku data, results agree with previous XMM-Newton findings.

Enables lag analysis with non-uniform sampling.

Abstract

Timing techniques offer powerful tools to study dynamical astrophysical phenomena. In the X-ray band, they offer the potential of probing accretion physics down to the event horizon. Recent work has used frequency and energy-dependent time lags as a tool for studying relativistic reverberation around the black holes in several Seyfert galaxies. This was achieved thanks to the evenly-sampled light curves obtained using XMM-Newton. Continuous-sampled data is however not always available and standard Fourier techniques are not applicable. Here, building on the work of Miller et al. (2010), we discuss and use a maximum likelihood method to obtain frequency-dependent lags that takes into account light curve gaps. Instead of calculating the lag directly, the method estimates the most likely lag values at a particular frequency given two observed light curves. We use Monte Carlo simulations to assess the method's applicability, and use it to obtain lag-energy spectra from Suzaku data for two objects, NGC 4151 and MCG-5-23-16, that had previously shown signatures of iron K reverberation. The lags obtained are consistent with those calculated using standard methods using XMM-Newton data.