Shock cooling and breakout emission for optical flares associated with gravitational wave events

The astrophysical origin of stellar-mass black hole (BH) mergers discovered through gravitational waves (GWs) is widely debated. Mergers in the disks of active galactic nuclei (AGN) represent promising environments for at least a fraction of these events, with possible observational clues in the GW data. An additional clue to unveil AGN merger environments is provided by possible electromagnetic emission from post-merger accreting BHs. Associated with BH mergers in AGN disks, emission from shocks emerging around jets launched by accreting merger remnants is expected. In this paper we compute the properties of the emission produced during breakout and the subsequent adiabatic expansion phase of the shocks, and we then apply this model to optical flares suggested to be possibly associated with GW events. We find that the majority of the reported flares can be explained by the breakout and the shock cooling emission. If these events are real, then the merging locations of binaries are constrained depending on the emission processes. If the optical flares are produced by shock cooling emission, they would display moderate color evolution, possibly color variations among different events, a positive correlation between the delay time and the duration of flares, and accompanying breakout emission in X-ray bands before the optical flares. If the breakout emission dominates the observed lightcurve, it is expected that the color is distributed in a narrow range in the optical band, and the delay time from GW to electromagnetic emission is longer than $\sim 2$ days. Hence, further explorations of the distributions of delay times, color evolution of the flares, and associated X-ray emission will be useful to test the proposed emission model for the observed flares.