A New Approach for Measuring Power Spectra and Reconstructing Time Series in Active Galactic Nuclei

TL;DR

This paper introduces a Bayesian-based method leveraging Fourier transforms to accurately measure power spectra and reconstruct time series in active galactic nuclei, improving analysis efficiency and model comparison.

Contribution

It presents a novel approach that models AGN stochastic variations in the frequency domain using Gaussian random variables, enabling improved spectral analysis and reconstruction.

Findings

Effective power spectrum measurement in AGNs

Enhanced time series reconstruction accuracy

Facilitated model comparison using Bayesian framework

Abstract

We provide a new approach to measure power spectra and reconstruct time series in active galactic nuclei (AGNs) based on the fact that the Fourier transform of AGN stochastic variations is a series of complex Gaussian random variables. The approach parameterizes a stochastic series in frequency domain and transforms it back to time domain to fit the observed data. The parameters and their uncertainties are derived in a Bayesian framework, which also allows us to compare the relative merits of different power spectral density models. The well-developed fast Fourier transform algorithm together with parallel computation enable an acceptable time complexity for the approach.