Interpretation and implications of the non-detection of GeV spectrum excess by the Fermi Gamma-ray Space Telescope in most gamma-ray bursts

Since the launch of the Fermi Gamma-ray Space Telescope on 2008 June 11, significant detections of high-energy emission have been reported only in six gamma-ray bursts (GRBs) until now. In this work we show that the lack of detection of a GeV spectrum excess in almost all GRBs, though somewhat surprising, can be well understood within the standard internal shock model and several alternatives like the photosphere internal shock (gradual magnetic dissipation) model and the magnetized internal shock model. The delay of the arrival of the > 100 MeV photons from some Fermi bursts can be interpreted too. We then show that with the polarimetry of prompt emission these models may be distinguishable. In the magnetized internal shock model, a high linear polarization level should be typical. In the standard internal shock model, a high linear polarization level is still possible but much less frequent. In the photosphere internal shock model, the linear polarization degree is expected to be roughly anticorrelated with the weight of the photosphere/thermal component, which may be a unique signature of this kind of model. We also briefly discuss the implications of the current Fermi GRB data on the detection prospects of the prompt PeV neutrinos. The influences of the intrinsic proton spectrum and the enhancement of the neutrino number at some specific energies, due to the cooling of pions (muons), are outlined.