Indication of a local fog of subankle ultrahigh energy cosmic rays

During their propagation through intergalactic space, ultrahigh energy cosmic rays (UHECRs) interact with the background radiation fields. These interactions give rise to energetic electron/positron pairs and photons which in turn feed electromagnetic cascades, contributing to the isotropic gamma-ray background (IGRB). The gamma-ray flux level generated in this way highly depends upon the UHECR propagation distance, as well as the evolution of their sources with redshift. Recently, the Fermi-LAT Collaboration reported that the majority of the total extragalactic gamma-ray flux originates from extragalactic point sources. This posits a stringent upper limit on the IGRB generated via UHECR propagation, and subsequently constrains their abundance in the distant Universe. Focusing on the contribution of UHECR at energies below the ankle within a narrow energy band ($(1–4)\times {10}^{18}\mathrm{eV}$), we calculate the diffuse gamma-ray flux generated through UHECR propagation, normalizing the total cosmic ray energy budget in this band to that measured. We find that in order to not over-produce the new IGRB limit, a local “fog” of UHECR produced by nearby sources may exist, with a possible non-negligible contribution from our Galaxy. Following the assumption that a given fraction of the observed IGRB at 820 GeV originates from UHECR, we obtain a constraint on the maximum distance for the majority of their sources. With other unresolved source populations still contaminating the new IGRB limit, and UHECR above the ankle invariably contributing also to this background, the results presented here are rather conservative.

Figure 1

Fitting to the UHECR spectrum below the ankle and the corresponding diffuse gamma-ray flux initiated by CR propagation with different source distributions [(a): SFR evolution; (b): no evolution; (c): sources located at 120 Mpc]. In the upper panels, the green solid lines represent the best-fit UHECR fluxes for each source distribution considered, while the dashed lines represent the unattenuated flux. The thin blue lines show the results for a soft injection spectrum of $p=2.6$, normalized to the data at 1 EeV. Hollow circles show the PAO [5] data. The adopted values of the power-law index $p$ and the local energy production rate are provided within the figure. The lower panels show the corresponding diffuse gamma-ray emission resulting from the cascade initiated by UHE protons, where thick lines and thin lines are respectively for the best-fit case and $p=2.6$ case. The black filled circles show the IGRB measured by Fermi/LAT [3]. The IGRB upper limit for the non-point-source component (or the truly diffuse component) is shown as a red bar with an arrow. The orange hatched region represents the uncertainty of the limit due to the uncertainties in the obtained source count distribution (i.e., $dN/dS$). The cascade flux in the right panel is multiplied by 10.

Figure 2

The inferred fraction of the measured IGRB upper limit at 820 GeV caused by $\sim 10^{18}\mathrm{eV}$ cosmic ray propagation as a function of source distance. The energy budget of the cosmic rays is normalized with the measured UHECR spectrum from $10^{18}$ to $4\times 10^{18}\mathrm{eV}$. The results are based on the assumption of rectilinear propagation of particles.