Cumulative Neutrino and Gamma-Ray Backgrounds from Halo and Galaxy Mergers

The merger of dark matter halos and the gaseous structures embedded in them results in strong shocks that are capable of accelerating cosmic rays (CRs) to $\sim10~\rm PeV$. In this work, we study the contributions of these halo mergers to the diffuse neutrino flux and to the non-blazar portion of the $\gamma$-ray background. We formulate the redshift dependence of the shock parameters over the dark matter halo distribution up to a redshift $z=10$. We find that high-redshift mergers contribute a significant amount of the cosmic-ray energy luminosity density, and the resulting neutrino spectra could explain a large part of the observed diffuse neutrino flux above 0.1 PeV up to several PeV. Our model can somewhat alleviate tensions with the extragalactic $\gamma$-ray background. First, since a larger fraction of the CR energy luminosity density comes from high redshifts, the accompanying $\gamma$-rays are more strongly suppressed through $\gamma\gamma$ annihilations with the cosmic microwave background and the extragalactic background light. Second, mildly radiative-cooled shocks may lead to a harder CR spectrum with spectral indices of $1.5\leq s\leq2.0$. Our study suggests that halo mergers can be promising neutrino emitters without violating the non-blazar $Fermi$ constraints.