Unresolved Gamma-Ray Sky through its Angular Power Spectrum

The gamma-ray sky has been observed with unprecedented accuracy in the last decade by the Fermi -large area telescope (LAT), allowing us to resolve and understand the high-energy Universe. The nature of the remaining unresolved emission [unresolved gamma-ray background (UGRB)] below the LAT source detection threshold can be uncovered by characterizing the amplitude and angular scale of the UGRB fluctuation field. This Letter presents a measurement of the UGRB autocorrelation angular power spectrum based on eight years of Fermi-LAT Pass 8 data products. The analysis is designed to be robust against contamination from resolved sources and noise systematics. The sensitivity to subthreshold sources is greatly enhanced with respect to previous measurements. We find evidence (with $\sim 3.7\sigma$ significance) that the scenario in which two classes of sources contribute to the UGRB signal is favored over a single class. A double power law with exponential cutoff can explain the anisotropy energy spectrum well, with photon indices of the two populations being $2.55\pm 0.23$ and $1.86\pm 0.15$.

Figure 1

Left: Mollweide projection of the all-sky intensity map for photon energies in the (1.7–2.8) GeV interval, after the application of the mask built for this specific energy bin; right: Mollweide projection of the UGRB map between (1.7–2.8) GeV. Masked pixels are set to 0; maps have been downgraded to order 7 for display purposes and smoothed with a Gaussian beam with $\sigma =0.5°$ and $\sigma =1°$, respectively.

Figure 2

Anisotropy energy spectrum ${\mathrm{C}}_P(\mathrm{E})$, whose values are reported in Table 1. We also show the best-fit models single power law with exponential cutoff (sPLE) and double power law with exponential cutoff (dPLE), and we stress that they have been obtained by considering the total set of ${\mathrm{C}}_P^{ij}$ from both auto- and cross-correlations between macro energy bins (see the last section for details about the fitting procedure).

Figure 3

Left: Cross-correlation coefficient $r_{ij}$ matrix. This matrix is symmetric and has 1 on the diagonal by construction; the column and the row involving the last energy bin have been removed because the autocorrelation value is negative there and the corresponding $r_{ij}$ values have negative roots. Right: mean values and standard deviation of the mean in each subrectangle of the $r_{ij}$ matrix. If only one population contributed to the anisotropy signal, the mean values in the off-diagonal subrectangles would be values compatible with one, which is not the case.