Probing for correlated neutrino emission from gamma-ray bursts with Antarctic Cherenkov telescopes: A theoretical modeling and analytical search paradigm in the context of the fireball phenomenolgy
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Intrinsic neutrino properties qualify them as unique cosmic messengers, which may open a new window on the most energetic and enigmatic processes in the universe. Canonical fireball phenomenology, in the context of hadronic acceleration, predicts correlated MeV to EeV neutrinos from gamma-ray bursts (GRBs). Ideal for detection are ~ TeV-PeV muon neutrinos, which are expected to be in spatial and temporal coincidence with prompt γ-ray emission, which is tantamount to nearly background-free searches in operational and planned neutrino observatories such as the Antarctic Muon and Neutrino Detector Array (AMANDA) and IceCube, respectively. A positive detection of such high energy neutrinos would confirm hadronic acceleration in the relativistic GRB-wind, providing critical insight to the associated micro-physics of the fireball, while possibly revealing an astrophysical acceleration mechanism for the highest energy cosmic rays. Depending on the signal model assumption(s), a null detection may constrain some GRB progenitor scenarios, as well as restrict models featuring GRBs as cosmic ray accelerators. We describe the theoretical modeling and analysis techniques associated with a search for correlated leptonic emission from GRB030329, which triggered the High Energy Transient Explorer (HETE-II). Under the assumption of associated hadronic acceleration, the expected neutrino energy flux is directly derived, based upon confronting the fireball description with GRB030329's individual (discrete) set of observed electromagnetic parameters, for various models. In particular, spectral analysis, featuring a prompt photon energy fit to the Band function, and a spectroscopically observed redshift, due to doppler analysis of the optical transient afterglow, have been used to characterize various neutrino spectra and their response in AMANDA and IceCube. The effects of anisotropic emission, via an inferred beaming angle, and the consequences of non-trivial neutrino mass, such as flavor oscillations and possible time of flight delay, have been addressed. Although our results our consistent with a null detection, the effects of individual modeling are qualitatively demonstrated via order of magnitude differences in both detector observables, such the mean muon neutrino energy and event rate, and the relative constraint upon the astrophysical models tested from the flux upper limit. Implications for future searches in the era of Swift, are also discussed.