Unified model for cosmic rays above ${10}^{17}\mathrm{eV}$ and the diffuse gamma-ray and neutrino backgrounds

We investigate how the extragalactic proton component derived within the “escape model” can be explained by astrophysical sources. We consider as possible cosmic ray (CR) sources normal or starburst galaxies and radio-loud active galactic nuclei (AGN). We find that the contribution to the total extragalactic proton flux from normal and starburst galaxies is only subdominant and does not fit the spectral shape deduced in the escape model. In the case of radio-loud AGN, we show that the complete extragalactic proton spectrum can be explained by a single source population, BL Lac/FR I, for any of the potential acceleration sites in these sources. We calculate the diffuse neutrino and $\gamma$-ray fluxes produced by these CR protons interacting with gas inside their sources. For a spectral slope of CRs close to $\alpha =2.1–2.2$ as suggested by shock acceleration, we find that these UHECR sources contribute the dominant fraction of both the isotropic $\gamma$-ray background and of the extragalactic part of the astrophysical neutrino signal observed by IceCube.

Figure 1

Extragalactic proton flux deduced in Ref. [14] within the escape model from KASCADE-Grande and Auger data (brown error bars) together with the original KASCADE and KASCADE-Grande proton data and the total CR flux from Auger. Also shown is the predicted proton flux from BL Lacs (red line).

Figure 2

Interaction depth $\tau$ in a starburst galaxy, as a function of CR energy $E$, for Fe (top, green line), Al (magenta line), C (black line), He (blue line) and protons (bottom, red line).

Figure 3

Rate $\dot{\rho }$ of type II SNe (green curve) and effective comoving source density $N_c(z)$ of BL Lacs (red line) as a function of redshift, normalized to their present values at $z=0$.

Figure 4

Left panel: Diffuse CR flux from normal spiral (dashed lines) and starburst galaxies (solid lines) within scenario (i), as a function of energy. Total flux is shown in black. We show the individual contributions of protons (orange line), He (blue line), N (green line), Al (red line) and Fe (magenta line). Right panel: Diffuse CR flux from normal spirals (dashed lines), star-forming AGNs (thick solid line)—both starburst and nonstarburst ones—and starburst galaxies (thin solid lines) as a function of energy, within scenario (iii). For both panels, we show IGMF with strength $B=10^{-17}\mathrm{G}$ and coherence length $l_c=1\mathrm{Mpc}$.

Figure 5

Diffuse CR proton (blue lines), gamma-ray (red lines) and neutrino (magenta lines) fluxes from starburst galaxies together with CR proton data from KASCADE, KASCADE-Grande [5] and Auger (black error bars) [4, 45], the IGRB and the EGB from Fermi-LAT (red error bars) [16], and high-energy neutrino flux from IceCube (magenta error bars) [17]. Solid red and magenta lines are for gamma-ray and neutrino fluxes with $n=1{\mathrm{cm}}^{-3}$, and dashed lines are for $n=10{\mathrm{cm}}^{-3}$.

Figure 6

Diffuse flux of CR protons from BL Lacs (thick blue line) and Galactic proton flux in the escape model (thin blue line), together with the resulting photon (red line) and neutrino (magenta line) fluxes. Upper panel: ${\alpha }_p=2.17$ and $E_{\text{esc}}=3\times {10}^{11}\mathrm{eV}$; middle panel: ${\alpha }_p=2.10$ and $E_{\text{esc}}=3\times {10}^{11}\mathrm{eV}$; lower panel: ${\alpha }_p=2.10$ and $E_{\text{esc}}={10}^{14}\mathrm{eV}$. $E_{\max }={10}^{19}\mathrm{eV}$ for all three panels. We show CR proton data from KASCADE, KASCADE-Grande [5] and Auger (black error bars) [4, 45]. IGRB and EGB from Fermi-LAT (red error bars) [16] and high-energy neutrino flux from IceCube (magenta error bars) [17] are also shown in the figure.