# Statistical Measurement of the Gamma-ray Source-count Distribution as a Function of Energy

## TL;DR

This paper extends the 1pPDF method to analyze gamma-ray data across multiple energy bands, decomposing the sky into point sources, Galactic foreground, and diffuse background, revealing the source-count distribution and improving detection sensitivity.

## Contribution

It generalizes the 1pPDF technique to measure the gamma-ray source-count distribution across energies, surpassing previous catalog limits and characterizing unresolved sources.

## Key findings

- Source-count distribution follows a broken power law.
- Method improves sensitivity by about an order of magnitude.
- Provides upper limits on unresolved source contributions.

## Abstract

Photon counts statistics have recently been proven to provide a sensitive observable for characterizing gamma-ray source populations and for measuring the composition of the gamma-ray sky. In this work, we generalize the use of the standard 1-point probability distribution function (1pPDF) to decompose the high-latitude gamma-ray emission observed with Fermi-LAT into: (i) point-source contributions, (ii) the Galactic foreground contribution, and (iii) a diffuse isotropic background contribution. We analyze gamma-ray data in five adjacent energy bands between 1 and 171 GeV. We measure the source-count distribution dN/dS as a function of energy, and demonstrate that our results extend current measurements from source catalogs to the regime of so far undetected sources. Our method improves the sensitivity for resolving point-source populations by about one order of magnitude in flux. The dN/dS distribution as a function of flux is found to be compatible with a broken power law. We derive upper limits on further possible breaks as well as the angular power of unresolved sources. We discuss the composition of the gamma-ray sky and capabilities of the 1pPDF method.