We present calculations of the wide angle emission of short-duration gamma-ray bursts from compact binary merger progenitors. Such events are expected to be localized by their gravitational wave emission, fairly irrespective of the orientation of the angular momentum vector of the system, along which the gamma-ray burst outflow is expected to propagate. We show that both the prompt and afterglow emission are dim and challenging to detect for observers lying outside of the cone within which the relativistic outflow is propagating. If the jet initially propagates through a baryon contaminated region surrounding the merger site, however, a hot cocoon forms around it. The cocoon subsequently expands quasi-isotropically producing its own prompt emission and external shock powered afterglow. We show that the cocoon prompt emission is detectable by Swift BAT and Fermi GBM, We also show that the cocoon afterglow peaks a few hours to a few days after the burst and is detectable for up to a few weeks at all wavelengths. The timing and brightness of the transient are however uncertain due to their dependence on unknown quantities such as the density of the ambient medium surrounding the merger site, the cocoon energy, and the cocoon Lorentz factor. For a significant fraction of the gravitationally-detected neutron-star-binary mergers, the cocoon afterglow could possibly be the only identifiable electromagnetic counterpart, at least at radio and X-ray frequencies.
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