The origin of the power–law form of the extragalactic gamma–ray flux

Abstract The Fermi–LAT telescope has measured the extragalactic gamma–ray background (EGB) generated by the ensemble of all extragalactic sources. The energy distribution of the EGB is well described as a power–law with a spectral index approximately equal to 2.3, and an exponential cutoff, that is consistent with being the effect of absorption of high energy photons assuming an emission that is an unbroken power–law spectrum. The observations of the Fermi telescope have also resolved the EGB, determining that most of it is formed by the sum of the contributions of Active Galactic Nuclei (AGN) of the blazar class. The spectra of the individual AGN sources have a broad range of spectral shapes, and the brightest and most precisely measured sources have curved spectra that can be fitted with the “log–parabola” (or log–normal) form. This suggests that the power law form of the extragalactic gamma–ray flux emerges as a property of the ensemble of all sources, and not as a universal shape generated by each individual source. This result is consistent with the idea that particle acceleration in blazars can be considered as a “critical phenomenon”. A curved log–parabola (log–normal) form is also required to fit the spectra of many Galactic gamma–ray sources, including the emission from the brightest supernova remnants (SNR), and an intriguing possibility is that also the Galactic cosmic rays are injected in interstellar space by their sources not with a single universal power–law spectrum, as predicted by the commonly accepted models, but instead with a broad range of spectral shapes.