The afterglow of a relativistic shock breakout and low-luminosity GRBs

The prompt emission of low-luminosity gamma-ray bursts (llGRBs) indicates that these events originate from a relativistic shock breakout. In this case, we can estimate, based on the properties of the prompt emission, the energy distribution of the ejecta. We develop a general formalism to estimate the afterglow produced by synchrotron emission from the forward shock resulting from the interaction of this ejecta with the circumburst matter. We assess whether this emission can produce the observed radio and X-ray afterglows of the available sample of four llGRBs. All four radio afterglows can be explained within this model, providing further support for shock breakouts being the origin of llGRBs. We find that in one of the llGRBs (GRB 031203), the predicted X-ray emission, using the same parameters that fit the radio, can explain the observed one. In another one (GRB 980425), the observed X-rays can be explained if we allow for a slight modification of the simplest model. For the last two cases (GRBs 060218 and 100316D), we find that, as is the case for previous attempts to model these afterglows, the simplest model that fits the radio emission underpredicts the observed X-ray afterglows. Using general arguments, we show that the most natural location of the X-ray source is, like the radio source, within the ejecta-external medium interaction layer but that emission is due to a different population of electrons or to a different emission process.