Signatures from a quasi-spherical outflow and an off-axis top-hat jet launched in a merger of compact objects: An analytical approach

The production of both gravitational waves and short gamma-ray bursts (sGRBs) is widely associated with the merger of compact objects. Several studies have modelled the evolution of the electromagnetic emission using the synchrotron emission produced by the deceleration of both a relativistic top-hat jet seen off-axis, and a wide-angle quasi-spherical outflow (both using numerical studies). In this study we present an analytical model of the synchrotron and synchrotron self-Compton (SSC) emission for an off-axis top-hat jet and a quasi-spherical outflow. We calculate the light curves obtained from an analytic model in which the synchrotron and SSC emission (in the fast- or slow-cooling regime) of an off-axis top-hat jet and a quasi-spherical outflow are decelerated in either a homogeneous or a wind-like circumburst medium. We show that the synchrotron emission of the quasi-spherical outflow is stronger than that of the off-axis jet during the first $\sim$ 10 - 20 days, and weaker during the next $\gtrsim$ 80 days. Moreover, we show that if the off-axis jet is decelerated in a wind-like medium, then the SSC emission is very likely to be detected. Applying a MCMC code to our model (for synchrotron emission only), we find the best-fit values for the radio, optical and X-ray emission of GRB 170817A which are in accordance with observations. For GRB 170817A, we find using our model that the synchrotron emission generated by the quasi-spherical outflow and off-axis top-hat jet increase as $F_\nu\propto t^{\alpha}$ with $\alpha\lesssim 0.8$ and $\alpha>3$, respectively. Finally, we obtain the correspondent SSC light curves which are in accordance with the very-high-energy gamma-ray upper limits derived with the GeV - TeV observatories.