Energetics of high-energy cosmic radiations

The luminosity densities of high-energy cosmic radiations are studied to find connections among the various components, including high-energy neutrinos measured with IceCube and gamma rays with the Fermi satellite. Matching the cosmic-ray energy generation rate density in a GeV–TeV range estimated for Milky Way with the ultra-high-energy component requires a power-law index of the spectrum $s_{\mathrm{cr}}\approx 2.1–2.2$, somewhat harder than $s_{\mathrm{cr}}\approx 2.3–2.4$ for the local index derived from the AMS-02 experiment. The soft GeV–TeV cosmic-ray spectrum extrapolated to higher energies can be compatible with PeV cosmic rays inferred from neutrino measurements, but overshoots the CR luminosity density to explain GeV–TeV gamma rays. The extrapolation from ultrahigh energies with a hard spectrum, on the other hand, can be consistent with both neutrinos and gamma rays. These point towards either reacceleration of galactic cosmic rays or the presence of extragalactic sources with a hard spectrum. We discuss possible cosmic-ray sources that can be added.

Figure 1

Local ($z=0$) CR energy generation rate density estimated from the AMS-02, Voyager and other relevant CR data. UHE CR luminosity density is based on the Auger experiment. High-energy neutrino and gamma-ray luminosity densities use IceCube and Fermi Large Area Telescope, respectively. With the IceCube data both results from the global analysis and the upgoing muon neutrino analysis are included. For gamma rays, both total “extragalactic gamma-ray background” (EGB: including resolved gamma-ray sources) and “isotropic diffuse gamma-ray background (IGRB)” are displayed. The star-formation history is assumed for the neutrino and gamma-ray luminosity densities as discussed in the text.

Figure 2

Local ($z=0$) energy densities of cosmic particles (in unit of ${\varrho }_{\mathrm{crit}}{c}^2$ for the left axis). We ignore possible energy losses of CRs injected in the past. Unavoidable energy losses of UHE CRs are taken into account, and we show both proton ankle and mixed composition models. The energy density of CRs confined in normal galaxies is indicated assuming $t_{\mathrm{esc}}=15–100\mathrm{Myr}$ at $R=1\mathrm{GV}$. The softening of the EGB and IGRB spectra is caused by the attenuation by the extragalactic background light.

Figure 3

Similar to Fig. 1, but neutrino and gamma-ray luminosity densities are converted into CR energy generation rate densities assuming that they are produced by inelastic $pp$ interactions. The high-energy neutrino background gives constraints on the CR energy generation rate density, while the IGRB is taken as an upper limit for a given value of the effective optical depth to meson production ($f_{\text{meson}}$): the cases for $f_{\text{meson}}\ge 1$ and $f_{\text{meson}}=0.1$ are displayed.