A Fast-cadenced Search for Gamma-Ray Burst Orphan Afterglows with the Deeper, Wider, Faster Programme

The relativistic outflows that produce Long GRBs (LGRBs) can be described by a structured jet model where prompt $\gamma$-ray emission is restricted to a narrow region in the jet's core. Viewing the jet off-axis from the core, a population of afterglows without an associated GRB detection can be predicted. In this work, we conduct an archival search for these `orphan' afterglows (OAs) with minute-cadence, deep ($g\sim23$) data from the Dark Energy Camera (DECam) taken as part of the Deeper, Wider, Faster programme (DWF). We introduce a method to select fast-evolving OA candidates within DWF data that comprises a machine learning model, based on a realistic synthetic population of OAs. Using this classifier, we recover 51 OA candidates. Of these candidates, 42 are likely flare events from M-class stars. The remaining nine possess quiescent, coincident sources in archival data with angular profiles consistent with a star and are inconsistent with the expected population of LGRB host galaxies. We therefore conclude that these are likely Galactic events. We calculate an upper limit on the rate of OAs down to $g<22$ AB mag of 7.46\,deg$^{-2}$yr$^{-1}$ using our criteria and constrain possible jet structures. We also place an upper limit of the characteristic angle between the $\gamma$-ray emitting region and the jet's half opening angle. For a smooth power-law and a power-law with core jet model respectively, these values are $58.3^{\circ}$ and $56.6^{\circ}$, for a power-law index of 0.8 and $75.3^{\circ}$ and $76.8^{\circ}$ for a power-law index of 1.2.