[Paper Review] The GCE in a New Light: Disentangling the $γ$-ray Sky with Bayesian Graph Convolutional Neural Networks

Florian List, Nicholas L. Rodd+2 more|arXiv (Cornell University)|Jun 22, 2020

Gamma-ray bursts and supernovae4 citations

TL;DR

This paper introduces a Bayesian Graph Convolutional Neural Network (Bayesian GCNN) to disentangle the Galactic Center Excess (GCE) in Fermi-LAT gamma-ray data, leveraging HEALPix-sky representations and uncertainty quantification. Applied to real data, the model attributes nearly all GCE flux to smooth emission (primarily dark matter annihilation), contrasting with the non-Poissonian template fit (NPTF), which favors point sources; however, the method shows bias toward smooth components near the 1σ detection threshold, leaving the GCE origin unresolved but demonstrating strong robustness to systematics.

ABSTRACT

A fundamental question regarding the Galactic Center Excess (GCE) is whether the underlying structure is point-like or smooth. This debate, often framed in terms of a millisecond pulsar or annihilating dark matter (DM) origin for the emission, awaits a conclusive resolution. In this work we weigh in on the problem using Bayesian graph convolutional neural networks. In simulated data, our neural network (NN) is able to reconstruct the flux of inner Galaxy emission components to on average $\sim$0.5%, comparable to the non-Poissonian template fit (NPTF). When applied to the actual $ extit{Fermi}$-LAT data, we find that the NN estimates for the flux fractions from the background templates are consistent with the NPTF; however, the GCE is almost entirely attributed to smooth emission. While suggestive, we do not claim a definitive resolution for the GCE, as the NN tends to underestimate the flux of point-sources peaked near the 1$σ$ detection threshold. Yet the technique displays robustness to a number of systematics, including reconstructing injected DM, diffuse mismodeling, and unmodeled north-south asymmetries. So while the NN is hinting at a smooth origin for the GCE at present, with further refinements we argue that Bayesian Deep Learning is well placed to resolve this DM mystery.

Motivation & Objective

• To resolve the long-standing debate on whether the Galactic Center Excess (GCE) originates from dark matter annihilation or millisecond pulsars.
• To develop a deep learning method capable of accurately decomposing complex gamma-ray sky maps into flux fractions of distinct astrophysical components.
• To quantify uncertainties in component flux estimation using Bayesian deep learning, enabling robust inference under systematic uncertainties.
• To test the method's resilience to diffuse emission mismodeling, unmodeled asymmetries, and injection of faint point sources near the detection threshold.

Proposed method

• The method employs a Bayesian Graph Convolutional Neural Network (Bayesian GCNN) based on the DeepSphere architecture, designed for spherical HEALPix sky maps.
• The network is trained on a large synthetic dataset of simulated photon-count maps with known flux contributions from diffuse, point-source, and GCE components.
• Bayesian inference is implemented by learning a distribution over network weights, enabling joint estimation of aleatoric and epistemic uncertainty.
• Uncertainty quantification is achieved through Monte Carlo dropout and weight distribution modeling, with predictive uncertainty computed as the sum of aleatoric and epistemic components.
• The model is evaluated on both simulated maps and real Fermi-LAT data, with results compared to the standard NPTF method.
• The framework is tested under systematic perturbations, including diffuse emission mismodeling, north-south asymmetries, and injected faint point sources near the 1σ threshold.

Experimental results

Research questions

• RQ1 Can a Bayesian GCNN accurately reconstruct flux fractions of astrophysical components in simulated gamma-ray sky maps with sub-percent precision?
• RQ2 Does the Bayesian GCNN prefer a smooth or point-source origin for the GCE when applied to real Fermi-LAT data, and how does this compare to the NPTF?
• RQ3 How robust is the Bayesian GCNN to systematic effects such as diffuse emission mismodeling and unmodeled sky asymmetries?
• RQ4 To what extent does the model underestimate flux from faint point sources near the 1σ detection threshold, and how does this affect interpretation of the GCE origin?
• RQ5 Can Bayesian deep learning methods provide reliable uncertainty estimates that align with empirical performance across diverse sky configurations?

Key findings

• In simulated data, the Bayesian GCNN reconstructs flux fractions with an average accuracy of ~0.5%, comparable to the non-Poissonian template fit (NPTF).
• When applied to real Fermi-LAT data, the model attributes nearly all GCE flux to smooth emission (GCE DM), with GCE point-source flux consistent with zero, in contrast to the NPTF which attributes 100% to point sources.
• The NN's predictions for diffuse, isotropic, and Fermi bubble components are consistent with NPTF results, with differences only in GCE component composition.
• The model shows a systematic bias toward underestimating flux from point sources injected near the 1σ detection threshold, suggesting caution in interpreting smooth dominance as definitive.
• Uncertainty estimates are well-calibrated: larger uncertainties correspond to lower prediction accuracy, and credible intervals shrink with increasing ROI size and template distinctiveness.
• The method remains robust under diffuse mismodeling and unmodeled asymmetries, demonstrating strong potential for future resolution of the GCE origin.