Observations of GRB 970228 and GRB 970508, and the Neutron-Star Merger Model

We present the discovery observations for the optical counterpart of the $\gamma$-ray burster GRB 970508 and discuss its light curve in the context of the fireball model. We analyze the HST data for this object, and conclude that any underlying galaxy must be fainter than $R$ = 25.5. We also present a detailed analysis of the HST images of GRB 970228 claimed to show a proper motion of the optical counterpart and conclude that, within the uncertainties, there is no proper motion. We examine several aspects of the neutron-star merger model for $\gamma$-ray bursts. In particular, we use this model to predict the redshift distribution of $\gamma$-ray bursters, and adopting a recent determination of the cosmic star-formation history, we show that the predicted distribution of $\log N - \log P$ relation is consistent with that observed for GRBs.