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A deep learning framework for jointly extracting spectra and source-count distributions in astronomy

Florian Wolf, Florian List, Nicholas L. Rodd, Oliver Hahn

TL;DR

The paper tackles the challenge of characterizing sub-threshold point-source populations from energy-resolved photon-count maps by introducing a two-stage deep-learning framework that jointly infers emission spectra and source-count distributions. Built on the DeepSphere/Healpix geometry, the method uses energy-binned inputs to recover spectra for each component and discretized SCDs via a second network that employs quantile regression, enabling uncertainty quantification. Demonstrated on simulated gamma-ray maps with multiple overlapping components, the approach accurately recovers complex spectral shapes and captures SCD bimodality, illustrating the value of incorporating spectral information in population studies. This energy-aware framework has potential applications to Fermi data and other messengers, with prospects for incorporating priors and cross-component covariances in future work to tighten constraints and expand applicability.

Abstract

Astronomical observations typically provide three-dimensional maps, encoding the distribution of the observed flux in (1) the two angles of the celestial sphere and (2) energy/frequency. An important task regarding such maps is to statistically characterize populations of point sources too dim to be individually detected. As the properties of a single dim source will be poorly constrained, instead one commonly studies the population as a whole, inferring a source-count distribution (SCD) that describes the number density of sources as a function of their brightness. Statistical and machine learning methods for recovering SCDs exist; however, they typically entirely neglect spectral information associated with the energy distribution of the flux. We present a deep learning framework able to jointly reconstruct the spectra of different emission components and the SCD of point-source populations. In a proof-of-concept example, we show that our method accurately extracts even complex-shaped spectra and SCDs from simulated maps.

A deep learning framework for jointly extracting spectra and source-count distributions in astronomy

TL;DR

The paper tackles the challenge of characterizing sub-threshold point-source populations from energy-resolved photon-count maps by introducing a two-stage deep-learning framework that jointly infers emission spectra and source-count distributions. Built on the DeepSphere/Healpix geometry, the method uses energy-binned inputs to recover spectra for each component and discretized SCDs via a second network that employs quantile regression, enabling uncertainty quantification. Demonstrated on simulated gamma-ray maps with multiple overlapping components, the approach accurately recovers complex spectral shapes and captures SCD bimodality, illustrating the value of incorporating spectral information in population studies. This energy-aware framework has potential applications to Fermi data and other messengers, with prospects for incorporating priors and cross-component covariances in future work to tighten constraints and expand applicability.

Abstract

Astronomical observations typically provide three-dimensional maps, encoding the distribution of the observed flux in (1) the two angles of the celestial sphere and (2) energy/frequency. An important task regarding such maps is to statistically characterize populations of point sources too dim to be individually detected. As the properties of a single dim source will be poorly constrained, instead one commonly studies the population as a whole, inferring a source-count distribution (SCD) that describes the number density of sources as a function of their brightness. Statistical and machine learning methods for recovering SCDs exist; however, they typically entirely neglect spectral information associated with the energy distribution of the flux. We present a deep learning framework able to jointly reconstruct the spectra of different emission components and the SCD of point-source populations. In a proof-of-concept example, we show that our method accurately extracts even complex-shaped spectra and SCDs from simulated maps.
Paper Structure (9 sections, 3 equations, 1 figure, 2 tables)

This paper contains 9 sections, 3 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Modeling
  4. Extracting spectra
  5. Extracting source-count distributions
  6. Deep learning model
  7. Results
  8. Conclusions
  9. Details of the neural network architecture and training

Figures (1)

  • Figure 1: NN predictions for three selected test maps. Top: Count fractions for the isotropic PS and the diffuse background component as a function of photon energy. The solid lines represent the true values, whereas the shaded areas cover the 1$\sigma$ NN predictions. Bottom: True vs. reconstructed SCD of the isotropic PS component. Here, the black line is the median prediction (bin-wise in terms of the associated cumulative histogram, see Sec. \ref{['subsec:scds']}), while the faint colored regions indicate the quantiles from 5% to 95%. The blue line shows the true SCD. The orange vertical line corresponds to a single expected photon count per source. In the top right corner, we show the maps (summed over all energy bins) to which the spectra and SCDs belong. The color map is scaled logarithmically. The SCDs are modeled as a mixture of two skew-normal distributions, and their bimodality is clearly visible.