Abstract
The two leading hypotheses for the Galactic Center Excess (GCE) in the $\textit{Fermi}$ data are an unresolved population of faint millisecond pulsars (MSPs) and dark-matter (DM) annihilation. The dichotomy between these explanations is typically reflected by modeling them as two separate emission components. However, point-sources (PSs) such as MSPs become statistically degenerate with smooth Poisson emission in the ultra-faint limit (formally where each source is expected to contribute much less than one photon on average), leading to an ambiguity that can render questions such as whether the emission is PS-like or Poissonian in nature ill-defined. We present a conceptually new approach that describes the PS and Poisson emission in a unified manner and only afterwards derives constraints on the Poissonian component from the so obtained results. For the implementation of this approach, we leverage deep learning techniques, centered around a neural network-based method for histogram regression that expresses uncertainties in terms of quantiles. We demonstrate that our method is robust against a number of systematics that have plagued previous approaches, in particular DM / PS misattribution. In the $\textit{Fermi}$ data, we find a faint GCE described by a median source-count distribution (SCD) peaked at a flux of $\sim4 \times 10^{-11} \ \text{counts} \ \text{cm}^{-2} \ \text{s}^{-1}$ (corresponding to $\sim3 - 4$ expected counts per PS), which would require $N \sim \mathcal{O}(10^4)$ sources to explain the entire excess (median value $N = \text{29,300}$ across the sky). Although faint, this SCD allows us to derive the constraint $\eta_P \leq 66\%$ for the Poissonian fraction of the GCE flux $\eta_P$ at 95% confidence, suggesting that a substantial amount of the GCE flux is due to PSs.
Highlights
There is strong evidence for the existence of dark matter (DM) in the Universe, perhaps most notably thanks to the precise CMB measurements of the Planck satellite [2]
While we showed in Paper I that our neural network (NN) was generally able to accurately determine the flux fractions of different templates, we found that the probability of Galactic Center excess (GCE) point sources (PSs) flux being confused with Poissonian GCE flux increased as the PSs became fainter, and faint GCE PS flux injected into the Fermi map was frequently misattributed to the Poissonian template
As to the source-count distribution (SCD), we find a faint GCE that would require Oð104Þ PSs to explain the entire GCE flux, given that our NN gπ assigns almost all of the flux to PSs that emit < 10 counts each
Summary
There is strong evidence for the existence of dark matter (DM) in the Universe (see e.g., Ref. [1] for a review), perhaps most notably thanks to the precise CMB measurements of the Planck satellite [2]. Unlike existing template fitting methods, where the image likelihood is computed treating each pixel as statistically independent, CNNs base their judgment on properties of small patches in the photoncount maps This leads to important differences in the case of mismodeling—for example, CNNs seem to be fairly robust against a modest north-south asymmetry of the GCE flux (see Paper I; Fig. S8). In the hypothetical limit of infinitely many PSs N → ∞ emitting an infinitely small flux f → 0, where the limit is formed in such a way that the total flux Ftot remains constant, the PS emission becomes exactly degenerate with smooth Poisson emission In this limit, a template fitting method such as a neural network (NN) should recognize that, assuming no preference for Poissonian/PS emission imposed by prior knowledge, any split of the flux into a Poissonian and a PS fraction is likely. Whilst our less sophisticated framework presented in Paper I attributed the entire GCE flux to the smooth GCE template, the SCD of the GCE PSs that we identify in the present work is faint enough for the abovementioned confusion between PSs and Poissonian flux to explain this discrepancy
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