Reverse Shock Emission in an Off-axis Top-hat Jet Model for Gamma-Ray Bursts

The afterglow of a gamma-ray burst (GRB) has been widely argued to arise from the interaction of a relativistic outflow with its ambient medium. During such an interaction, a pair of shocks are generated: a forward shock that propagates into the medium, and a reverse shock that propagates into the outflow. Extensive studies have been conducted on the emission from the forward shock viewed off-axis. Furthermore, the observation of a reverse shock in an on-axis short GRB suggests that the reverse shock can produce an electromagnetic counterpart to a gravitational wave-detected merger. In this paper, we investigate the contribution of the reverse shock to the afterglow from a top-hat jet viewed off-axis, and apply our model to some short GRBs previously modeled by an off-axis emission. We employ the Markov Chain Monte Carlo (MCMC) method to get the model parameters (i.e., the jet's half-opening angle $\theta_j$, the viewing angle $\theta_\text{obs}$, the initial Lorentz factor $\Gamma_0$, and the isotropic energy $E_\mathrm{iso}$). Our model successfully reproduces off-axis afterglow emission without a structured jet. In addition, our calculations suggest that the reverse shock may produce a prominent feature in an early afterglow, which can be potentially observed in an orphan optical afterglow.