IceCube Non-detection of GRBs: Constraints on the Fireball Properties

TL;DR

This paper refines neutrino flux predictions from gamma-ray bursts and uses IceCube non-detections to constrain fireball properties like baryon loading, dissipation radius, and Lorentz factors, impacting models of GRB physics.

Contribution

It provides a revised analytic calculation of neutrino flux, compares predictions with IceCube limits, and derives new constraints on GRB fireball parameters based on non-detection.

Findings

Predicted neutrino flux is an order of magnitude lower than previous estimates.

Non-detection constrains baryon loading ratio <10 for certain models.

Constraints on dissipation radius R>4^{12} cm derived from non-detection.

Abstract

The increasingly deep limit on the neutrino emission from gamma-ray bursts (GRBs) with IceCube observations has reached the level that could put useful constraints on the fireball properties. We first present a revised analytic calculation of the neutrino flux, which predicts a flux an order of magnitude lower than that obtained by the IceCube collaboration. For benchmark model parameters (e.g. the bulk Lorentz factor is \Gamma=10^{2.5}, the observed variability time for long GRBs is t_v=0.01 s and the ratio between the energy in accelerated protons and in radiation is \eta_p=10 for every burst) in the standard internal shock scenario, the predicted neutrino flux from 215 bursts during the period of the 40-string and 59-string configurations is found to be a factor of ~3 below the IceCube sensitivity. However, if we accept the recently found inherent relation between the bulk Lorentz factor and burst energy, the expected neutrino flux increases significantly and the spectral peak shifts to lower energy. In this case, the non-detection then implies that the baryon loading ratio should be \eta_p<10 if the variability time of long GRBs is fixed to t_v=0.01 s. Instead, if we relax the standard internal shock scenario but keep to assume \eta_p=10, the non-detection constrains the dissipation radius to be R>4x10^{12} cm assuming the same dissipation radius for every burst and benchmark parameters for fireballs. We also calculate the diffuse neutrino flux from GRBs for different luminosity functions existing in the literature. The expected flux exceeds the current IceCube limit for some luminosity functions, and thus the non-detection constrains \eta_p<10 in such cases when the variability time of long GRBs is fixed to t_v=0.01 s.