High-energy gamma-ray afterglows from low-luminosity gamma-ray bursts

The observations of gamma-ray bursts (GRBs) such as 980425, 031203 and 060218, with luminosities much lower than those of other classic bursts, lead to the definition of a new class of GRBs -- low-luminosity GRBs. The nature of the outflow responsible for them is not clear yet. Two scenarios have been suggested: one is the conventional relativistic outflow with initial Lorentz factor of order of $\Gamma_0\ga 10$ and the other is a trans-relativistic outflow with $\Gamma_0\simeq 1-2$. Here we compare the high energy gamma-ray afterglow emission from these two different models, taking into account both synchrotron self inverse-Compton scattering (SSC) and the external inverse-Compton scattering due to photons from the cooling supernova or hypernova envelope (SNIC). We find that the conventional relativistic outflow model predicts a relatively high gamma-ray flux from SSC at early times ($<10^4 {\rm s}$ for typical parameters) with a rapidly decaying light curve, while in the trans-relativistic outflow model, one would expect a much flatter light curve of high-energy gamma-ray emission at early times, which could be dominated by both the SSC emission and SNIC emission, depending on the properties of the underlying supernova and the shock parameter $\epsilon_e$ and $\epsilon_B$. The Fermi Gamma-ray Space Telescope should be able to distinguish between the two models in the future.