On the True Energy Budget of GRB970508 and GRB971214

We emphasize the already known idea that since GRB970508 released an energy of Qγ ≈ 10 δΩ ergs in soft gamma rays alone, where δΩ is the solid angle of the beam, the actual energy of the eep fireball driving the blast wave could be considerably higher than this value, QFB > Qγ . We further argue that, for reasonably large values of δΩ, as is probably suggested by the radio observations, the value of QFB ∼ 5.10 t3m n1 erg, for GRB970508; where n1 is the number density of the ambient medium in units of 1 proton/cm 3 and tm is the epoch in months when the associated radio-blastwave degrades to become mildly relativistic. Thus the value of QFB for GRB970508 could be as large as 10erg or even much higher. This idea is corroborated by GRB971214 for which the value of Qγ ≈ 2.10 δΩ is much higher than the corresponding value for GRB970508. It is likely that GRB971214 has a correspondingly higher value of QFB. We discuss that it is unlikely that this energy, QFB ∼ 10erg was liberated by the central engine by a direct electromagnetic mode. On the other hand, as conceived by several previous authors and as is suggested by supernova theories, the eep fireball (FB) driving the blast wave is likely to be preceded by a much stronger neutrino burst: ν + ν̄ → e + e. Although, the efficiency for ee production by this latter route is usually found to be as low as η± ∼ 10, we point out that for very high values of neutrino energy release Qν > QFB, it is possible that, the value of η± increses substantially. By considering that, the value of QFB for such GRBs is indeed ∼ 10 erg, we envisage that the energy of the actual neutrino burst/wind could be as high as ∼ 10−10 erg (here we ignore likely loss of energy by gravitational energy mode). This energy might be had from general relativistic collapse of a massive stellar core having initial gravitational mass, say, Mi ∼ few M⊙ to a stage having a potential well much deeper than what is present on a canonican neutron star surface. Accordingly, we predict that the new generation large neutrino telescopes may detect neutrino burst of energy Qν ∼ 10 − 10 ergs, with neutrino energies touching ∼ 1 GeV, in coincidence with GRBs.