Modeling X-ray photon pile-up with a normalizing flow

TL;DR

This paper introduces a machine learning approach using normalizing flows to accurately infer physical parameters from piled-up X-ray data, overcoming traditional limitations and enabling better analysis of bright X-ray sources.

Contribution

The paper presents a novel simulation-based inference method employing normalizing flows to improve parameter estimation from piled-up X-ray observations.

Findings

Normalizing flows yield more constrained posterior distributions than traditional methods.

The approach accounts for model and calibration uncertainties.

Potential applicability to real eROSITA data is discussed.

Abstract

The dynamic range of imaging detectors flown on-board X-ray observatories often only covers a limited flux range of extrasolar X-ray sources. The analysis of bright X-ray sources is complicated by so-called pile-up, which results from high incident photon flux. This nonlinear effect distorts the measured spectrum, resulting in biases in the inferred physical parameters, and can even lead to a complete signal loss in extreme cases. Piled-up data are commonly discarded due to resulting intractability of the likelihood. As a result, a large number of archival observations remain underexplored. We present a machine learning solution to this problem, using a simulation-based inference framework that allows us to estimate posterior distributions of physical source parameters from piled-up eROSITA data. We show that a normalizing flow produces better-constrained posterior densities than traditional mitigation techniques, as more data can be leveraged. We consider model- and calibration-dependent uncertainties and the applicability of such an algorithm to real data in the eROSITA archive.