We consider implications of the IceCube signal for hadronuclear ($pp$) scenarios of neutrino sources such as galaxy clusters/groups and star-forming galaxies. Since the observed neutrino flux is comparable to the diffuse $\gamma$-ray background flux obtained by Fermi, we place new, strong upper limits on the source spectral index, $\Gamma \lesssim 2.1–2.2$. In addition, the new IceCube data imply that these sources contribute at least 30%–40% of the diffuse $\gamma$-ray background in the 100 GeV range and even $\sim 100\%$ for softer spectra. Our results, which are insensitive to details of the $pp$ source models, are one of the first strong examples of the multimessenger approach combining the measured neutrino and $\gamma$-ray fluxes. The $pp$ origin of the IceCube signal can further be tested by constraining $\Gamma$ with sub-PeV neutrino observations, by unveiling the sub-TeV diffuse $\gamma$-ray background and by observing such $pp$ sources with TeV $\gamma$-ray detectors. We also discuss specific $pp$ source models with a multi-PeV neutrino break/cutoff, which are consistent with the current IceCube data.

• Received 15 June 2013

DOI:https://doi.org/10.1103/PhysRevD.88.121301