Upper Limit on the Cosmic Gamma-Ray Burst Rate from High Energy Diffuse Neutrino Background

TL;DR

This paper establishes upper limits on the ratio of gamma-ray burst rates to core-collapse supernovae rates using neutrino background data, constraining the GRB contribution to cosmic high-energy phenomena.

Contribution

It provides the first upper limits on the GRB to supernova rate ratio derived from diffuse neutrino background measurements, independent of electromagnetic observations.

Findings

Upper limits on $f_{GRB/CCSN}(0)$ are $5.0 imes 10^{-3}$ for $eta=0$ and $1.1 imes 10^{-3}$ for $eta=2$.

Current neutrino background limits are comparable or more restrictive than other astronomical constraints.

Future IceCube observations could tighten these limits or confirm the GRB proton acceleration hypothesis.

Abstract

We derive upper limits on the ratio $f_{GRB/CCSN}(z) \equiv R_{GRB}(z)/R_{CCSN}(z) \equiv f_{GRB/CCSN}(0)(1+z)^\alpha$, the ratio of the rate, $R_{GRB}$, of long-duration Gamma Ray Bursts (GRBs) to the rate, $R_{CCSN}$, of core-collapse supernovae (CCSNe) in the Universe ($z$ being the cosmological redshift and $\alpha\geq 0$), by using the upper limit on the diffuse TeV--PeV neutrino background given by the AMANDA-II experiment in the South Pole, under the assumption that GRBs are sources of TeV--PeV neutrinos produced from decay of charged pions produced in $p\gamma$ interaction of protons accelerated to ultrahigh energies at internal shocks within GRB jets. For the assumed ``concordance model'' of cosmic star formation rate, $R_{SF}$, with $R_{CCSN}(z) \propto R_{SF}(z)$, our conservative upper limits are $f_{GRB/CCSN}(0)\leq 5.0\times10^{-3}$ for $\alpha=0$, and $f_{GRB/CCSN}(0)\leq 1.1\times10^{-3}$ for $\alpha=2$, for example. These limits are already comparable to (and, for $\alpha\geq 1$ already more restrictive than) the current upper limit on this ratio inferred from other astronomical considerations, thus providing a useful independent probe of and constraint on the CCSN-GRB connection. Non-detection of a diffuse TeV--PeV neutrino background by the up-coming IceCube detector in the South pole after three years of operation, for example, will bring down the upper limit on $f_{GRB/CCSN}(0)$ to below few $\times10^{-5}$ level, while a detection will confirm the hypothesis of proton acceleration to ultrahigh energies in GRBs and will potentially also yield the true rate of occurrence of these events in the Universe.