Parameter Estimation and Confidence Regions in the Method of Light Curve Simulations for the Analysis of Power Density Spectra

TL;DR

This paper introduces a Neyman construction-based method for estimating confidence regions of Power Density Spectrum model parameters derived from light curve simulations, improving the accuracy of black hole mass diagnostics in AGN.

Contribution

It presents a novel application of Neyman construction for confidence regions in PDS model fitting using light curve simulations, enhancing parameter estimation accuracy.

Findings

Provides a more accurate confidence region estimation method.

Demonstrates advantages over previous methods in parameter constraint precision.

Plans application to real X-ray observations of AGN.

Abstract

The Method of Light Curve Simulations is a tool that has been applied to X-ray monitoring observations of Active Galactic Nuclei (AGN) for the characterization of the Power Density Spectrum (PDS) of temporal variability and measurement of associated break frequencies (which appear to be an important diagnostic for the mass of the black hole in these systems as well as their accretion state). It relies on a model for the PDS that is fit to the observed data. The determination of confidence regions on the fitted model parameters is of particular importance, and we show how the Neyman construction based on distributions of estimates may be implemented in the context of light curve simulations. We believe that this procedure offers advantages over the method used in earlier reports on PDS model fits, not least with respect to the correspondence between the size of the confidence region and the precision with which the data constrain the values of the model parameters. We plan to apply the new procedure to existing RXTE and XMM observations of Seyfert I galaxies as well as RXTE observations of the Seyfert II galaxy NGC 4945.