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 jet seen off-axis , and a cocoon ( both using numerical studies ) .
In this study we present an analytical model of the synchrotron and SSC emission for an off-axis jet and a cocoon .
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 jet , and a cocoon , when both are decelerated in either a homogeneous or a wind-like circumburst medium .
We find that the synchrotron emission generated by the cocoon and off-axis jet increase as F _ { \nu } \propto t ^ { \alpha } with \alpha \lesssim 0.8 and \alpha > 3 , respectively .
We show that the synchrotron emission of the cocoon is stronger than that of the off-axis jet during the first \sim 10 - 30 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 the observations .
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 .