If the first ( PopIII ) stars were very massive , their final fate is to collapse into very massive black holes .
Once a proto-black hole has formed into the stellar core , accretion continues through a disk .
It is widely accepted , although not confirmed , that magnetic fields drive an energetic jet which produces a burst of TeV neutrinos by photon-meson interaction , and eventually breaks out of the stellar envelope appearing as a Gamma Ray Burst ( GRB ) .
Based on recent numerical simulations and neutrino emission models , we predict the expected neutrino diffuse flux from these PopIII GRBs and compare it with the capabilities of present and planned detectors as AMANDA and IceCube .
If beamed into 1 % of the sky , we find that the rate of PopIII GRBs is \leq 4 \times 10 ^ { 6 } yr ^ { -1 } .
High energy neutrinos from PopIII GRBs could dominate the overall flux in two energy bands [ 10 ^ { 4 } -10 ^ { 5 } ] GeV and [ 10 ^ { 5 } -10 ^ { 6 } ] GeV of neutrino telescopes .
The enhanced sensitivities of forthcoming detectors in the high-energy band ( AMANDA-II , IceCube ) will provide a fundamental insight on the characteristic explosion energies of PopIII GRBs and will constitute a unique probe of the the Initial Mass Function ( IMF ) of the first stars and of the redshift z _ { f } marking the metallicity-driven transition from a top-heavy to a normal IMF .
The current upper limit set by AMANDA-B10 implies that such transition must have occurred not later than z _ { f } = 9.2 for the most plausible jet energies .
Based on such results , we speculate that PopIII GRBs , if not chocked , could be associated with a new class of events detected by BeppoSax , the Fast X-ray Transient ( FXTs ) , which are bright X-ray sources , with peak energies in the 2 - 10 keV band and durations between 10 - 200 s .