Determining X-Ray Source Intensity and Confidence Bounds in Crowded Fields

TL;DR

This paper develops a Bayesian method for aperture photometry in high-energy astrophysics, accurately estimating source intensity and confidence bounds in crowded fields with Poisson noise, including overlapping sources.

Contribution

It introduces a comprehensive Bayesian framework for source intensity estimation in crowded, low-count X-ray fields, accounting for overlaps and prior information.

Findings

Provides full posterior probability distributions for source intensity.

Handles overlapping source and background apertures.

Valid in low-count regimes with Poisson noise.

Abstract

We present a rigorous description of the general problem of aperture photometry in high energy astrophysics photon-count images, in which the statistical noise model is Poisson, not Gaussian. We compute the full posterior probability density function for the expected source intensity for various cases of interest, including the important cases in which both source and background apertures contain contributions from the source, and when multiple source apertures partially overlap. A Bayesian approach offers the advantages that it allows one to (a) include explicit prior information on source intensities, (b) propagate posterior distributions as priors for future observations, and (c) use Poisson likelihoods, making the treatment valid in the low counts regime. Elements of this approach have been implemented in the Chandra Source Catalog.