Optimal Coaddition of Imaging Data for Rapidly Fading Gamma-Ray Burst Afterglows

We present a technique for optimal coaddition of image data for rapidly varying sources, with specific application to gamma-ray burst (GRB) afterglows. Unweighted coaddition of rapidly fading afterglow lightcurve data becomes counterproductive relatively quickly. It is better to stop coaddition of the data once noise dominates late exposures. A better alternative is to optimally weight each exposure to maximize the signal-to-noise ratio (S/N) of the final coadded image data. By using information about GRB lightcurves and image noise characteristics, optimal image coaddition increases the probability of afterglow detection and places the most stringent upper limits on non-detections. For a temporal power law flux decay typical of GRB afterglows, optimal coaddition has the greatest potential to improve the S/N of afterglow imaging data (relative to unweighted coaddition), when the decay rate is high, the source count rate is low, and the background rate is high. The optimal coaddition technique is demonstrated with applications to Swift Ultraviolet/Optical Telescope (UVOT) data of several GRBs, with and without detected afterglows.