PROPAGATION AND NEUTRINO OSCILLATIONS IN THE BASE OF A HIGHLY MAGNETIZED GAMMA-RAY BURST FIREBALL FLOW

Abstract

Neutrons play an important role in the dynamics of gamma-ray bursts. The presence of neutrons in the baryon-loaded fireball is expected. If the neutrons abundance is comparable to that of protons, important features may be observed such as quasi-thermal multi-GeV neutrinos in coincidence with a subphotospheric $\gamma$-ray emission, nucleosynthesis at later times and rebrightening of the afterglow emission. Additionally, thermal MeV neutrinos are created by electron-positron annihilation, electron (positron) capture on protons (neutrons) and nucleonic bremsstrahlung. Although MeV neutrinos are difficult to detect, quasi-thermal GeV neutrinos are expected in km$^3$ detectors and/or DeepCore+IceCube. In this paper, we show that neutrino oscillations have outstanding implications for the dynamics of the fireball evolution and also that they can be detected through their flavor ratio on Earth. For that we derive the resonance and charged-neutrality conditions as well as the neutrino self-energy and effective potential up to order $m_W^{-4}$ at strong, moderate and weak magnetic field approximation to constrain the dynamics of the fireball. We found important implications: i) resonant oscillations are suppressed for high baryon densities as well as neutrons abundance larger than that of protons and ii) the effect of magnetic field is to decrease the proton-to-neutron ratio aside from the number of multi-GeV neutrinos expected in DeepCore detector. Also we estimate the GeV neutrino flavor ratios along the jet and on Earth.