Recently, a new measurement of the auto- and cross-correlation angular power spectrum (APS) of the isotropic gamma-ray background was performed, based on 81 months of data of the Fermi Large-Area Telescope (LAT). Here, we fit, for the first time, the new APS data with a model describing the emission of unresolved blazars. These sources are expected to dominate the anisotropy signal. The model we employ in our analysis reproduces well the blazars resolved by Fermi LAT. When considering the APS obtained by masking the sources in the 3FGL catalogue, we find that unresolved blazars under-produce the measured APS below $sim$1 GeV. Contrary to past results, this suggests the presence of a new contribution to the low-energy APS, with a significance of, at least, 5$sigma$. The excess can be ascribed to a new class of faint gamma-ray emitters. If we consider the APS obtained by masking the sources in the 2FGL catalogue, there is no under-production of the APS below 1 GeV, but the new source class is still preferred over the blazars-only scenario (with a significance larger than 10$sigma$). The properties of the new source class and the level of anisotropies induced in the isotropic gamma-ray background are the same, independent of the APS data used. In particular, the new gamma-ray emitters must have a soft energy spectrum, with a spectral index ranging, approximately, from 2.7 to 3.2. This complicates their interpretation in terms of known sources, since, normally, star-forming and radio galaxies are observed with a harder spectrum. The new source class identified here is also expected to contribute significantly to the intensity of the isotropic gamma-ray background.
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