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Abstract: We calculate the diffuse high energy (TeV–PeV) neutrino emission from hyperflares of soft-gamma repeaters (SGRs), like the hyperflare risen from SGR 1806-20 on December 27 of 2004, within the framework of the fireball model. The fireball model for gamma-ray bursts (GRBs) can explain well the main features of this hyperflare and the subsequent multi-frequency afterglow emission. The expected rate, , of such hyperflares is well in excess of the GRBs rate. Our result shows that the contribution to the diffuse TeV–PeV neutrino background from such hyperflares is less than 10% of the contribution from GRBs. We also discuss the high energy cosmic rays (CRs) from these sources. [Copyright &y& Elsevier]

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Abstract: Gamma-ray bursts are most luminous explosions in the universe. Their ejecta are believed to move towards Earth with a relativistic speed. The interaction between this “relativistic jet” and a circumburst medium drives a pair of (forward and reverse) shocks. The electrons accelerated in these shocks radiate synchrotron emission to power the broad-band afterglow of GRBs. The external shock theory is an elegant theory, since it invokes a limit number of model parameters, and has well predicted spectral and temporal properties. On the other hand, depending on many factors (e.g. the energy content, ambient density profile, collimation of the ejecta, forward vs. reverse shock dynamics, and synchrotron spectral regimes), there is a wide variety of the models. These models have distinct predictions on the afterglow decaying indices, the spectral indices, and the relations between them (the so-called “closure relations”), which have been widely used to interpret the rich multi-wavelength afterglow observations. This review article provides a complete reference of all the analytical synchrotron external shock afterglow models by deriving the temporal and spectral indices of all the models in all spectral regimes, including some regimes that have not been published before. The review article is designated to serve as a useful tool for afterglow observers to quickly identify relevant models to interpret their data. The limitations of the analytical models are reviewed, with a list of situations summarized when numerical treatments are needed. [Copyright &y& Elsevier]