Tomographic Constraints on High-Energy Neutrinos of Hadronuclear Origin

Mounting evidence suggests that the TeV–PeV neutrino flux detected by the IceCube telescope has mainly an extragalactic origin. If such neutrinos are primarily produced by a single class of astrophysical sources via hadronuclear ($pp$) interactions, a similar flux of gamma-ray photons is expected. For the first time, we employ tomographic constraints to pinpoint the origin of the IceCube neutrino events by analyzing recent measurements of the cross correlation between the distribution of GeV gamma rays, detected by the Fermi satellite, and several galaxy catalogs in different redshift ranges. We find that the corresponding bounds on the neutrino luminosity density are up to 1 order of magnitude tighter than those obtained by using only the spectrum of the gamma-ray background, especially for sources with mild redshift evolution. In particular, our method excludes any hadronuclear source with a spectrum softer than $E^{-2.1}$ as a main component of the neutrino background, if its evolution is slower than $(1+z{)}^3$. Starburst galaxies, if able to accelerate and confine cosmic rays efficiently, satisfy both spectral and tomographic constraints.

Figure 1

Top: Gamma-ray (blue) and neutrino (red) intensities for a model with $\alpha =2.2$, $\delta =2$, and $z_c=1.5$. The dotted curves correspond to the 95% C.L. upper limit due to the Fermi spectrum data (the green band represents the systematic uncertainty due to the subtraction of the Galactic emission [48]). The solid curves correspond to the same limit but due to the cross-correlation data. IceCube data for the neutrino intensity are shown above 10 TeV, whereas the orange band represents the 68% C.L. region of the corresponding best-fit single power-law model [5]. Bottom: Cross-correlation angular power spectrum between the Fermi data, above 1 GeV, and the 2MASS galaxies, compared with the measurements by Ref. [52]. Model parameters as well as line types are the same as the top panel.

Figure 2

The 95% C.L. upper limits on the local gamma-ray luminosity density ${\mathcal{E}}_{\gamma ,0}$, between 100 MeV and 100 GeV, as a function of $\alpha$ for $\delta =2$ and $z_c=1.5$. The limits due to the spectrum and cross-correlation data are shown as dotted and solid curves, respectively.

Figure 3

The 95% C.L. upper limits on the neutrino intensity integrated above 25 TeV as a function of $\delta$ for various values of $\alpha$ and fixed $z_c=1.5$. Thick and thin curves show the limits due to the tomographic and spectral analyses of the IGRB, respectively. The horizontal magenta band shows the 68% C.L. interval of the best-fit single power-law model for the IceCube neutrino data [5], corresponding to the neutrino band shown in Fig. 1.