Electromagnetic Radiation from Cosmic-Ray Scatterings on Relic Neutrinos

Abstract

Cosmic-ray scatterings on the cosmic neutrino background induce a flux of gamma-rays and X-rays from boosted meson decays and charged lepton processes. Here we present the first estimate of this flux and its cumulative cosmological contribution. Confronting expectations with Fermi-LAT diffuse gamma-ray data, we find a limit on the cosmic neutrino background overdensity at the level of $η\lesssim 2 \times 10^{4}$ for a lightest neutrino mass of $m_ν\gtrsim0.1$ eV, orders of magnitude stronger than current direct laboratory probes, and comparable to constraints on the cosmic neutrino background obtained with IceCube. We further show that X-ray synchrotron emission from cascade electron-positron pairs in intergalactic magnetic fields provides a complementary, albeit weaker, constraint. We discuss how anisotropic signatures and future gamma-ray data from CTA could further improve bounds on the relic neutrino overdensity, approaching in sensitivity the $Λ$CDM expected density.

Figures (5)

• Figure 1: Differential gamma-ray flux from cosmic-ray scatterings with the cosmic neutrino background on cosmological scales. Solid lines show the total flux summing all electromagnetic channels: neutral pion decay ($\pi^0\to\gamma\gamma$, dotted), charged pion decay ($\pi^{\pm}\to\mu\to e^{\pm}$, dashed), and charged-current lepton production. Both SFR and QSO models for the cosmic-ray emissivity evolution are shown assuming $\eta=1$ (standard C$\nu$B density), alongside a QSO prediction with local overdensity $\eta=10^5$. The shaded band is the Fermi-LAT isotropic gamma-ray background (IGRB) Fermi-LAT:2014ryh.
• Figure 2: Left: Synchrotron cooling fraction $f_{\rm syn} = u_B/(u_B + u_{\rm rad})$ as a function of magnetic field strength for several redshifts. At low $z$, synchrotron losses begin to dominate above $B \sim 1\,\mu$G; at higher redshifts the rising CMB energy density ($u_{\rm rad} \propto (1+z)^4$) shifts this transition to stronger fields. Right: Fractional energy budget of cascade $e^\pm$ at $z=0.5$, showing the partition between synchrotron (X-ray) and inverse-Compton ($\gamma$-ray) cooling channels. For intergalactic fields $B \lesssim 1$ nG virtually all energy goes into $\gamma$-rays, while in galaxy-cluster cores ($B \sim \mu$G) a significant fraction is redirected into X-ray synchrotron emission.
• Figure 3: Differential X-ray flux from synchrotron radiation of cascade $e^{\pm}$ pairs produced in cosmic-ray scatterings with the C$\nu$B. Solid lines show the QSO evolution model and dashed lines the SFR model, for intergalactic magnetic field strengths $B = 1\,\mu$G, $100\,$nG, and $10\,$nG, all assuming the $\Lambda$CDM-expected C$\nu$B density ($\eta = 1$). A QSO prediction with $B = 1\,\mu$G and local overdensity $\eta = 10^9$ is shown for comparison. The solid gold curve is the cosmic X-ray background (CXB) spectrum measured by HEAO-1 Gruber:1999yr. The large gap between predictions and the CXB reflects both the small synchrotron cooling fraction $f_{\rm syn} \ll 1$ in typical fields and the intrinsic brightness of the CXB.
• Figure 4: Expected dipole sky anisotropy of the gamma-ray flux induced by cosmic-ray scatterings with the C$\nu$B. The map shows the absolute intensity modulated by the assumed dipole at a reference energy of 10 GeV. The dashed lines indicate $|b|=20^\circ$, delimiting the region used in the Fermi-LAT isotropic background analysis.
• Figure 5: Upper limits on the C$\nu$B overdensity $\eta$ compared to the $\Lambda$CDM expectation, as a function of the lightest neutrino mass. The solid lines are obtained from $p\nu$ scatterings not inducing a gamma-ray flux that overshoots the diffuse IGRB gamma-ray measurements at Fermi-LAT Fermi-LAT:2014ryh, or projected sensitivities at CTA CTAConsortium:2010umy, while the dashed lines are obtained from not observing a large directional anisotropy in Fermi-LAT data, or future CTA data. The black lines correspond to a cosmic-ray evolution following the star forming rate from Hopkins:2006bw, and the purple lines correspond to the quasar evolution function from Hopkins:2006fq.