Long-Term Optical Follow Up of S231206cc: Multi-Model Constraints on BBH Merger Emission in AGN Disks

The majority of gravitational wave events detected by the LIGO, Virgo, and KAGRA Collaboration originate from binary black hole (BBH) mergers, for which no confirmed electromagnetic counterparts have been identified to date. However, if such mergers occur within the disk of an active galactic nucleus (AGN), they may generate observable optical flares induced by relativistic jet activity and shock-heated gas. We present results from a long-term optical follow-up of the gravitational wave event S231206cc, conducted with the T80-South telescope as part of the S-PLUS Transient Extension Program (STEP). Our search prioritized AGN-hosted environments by crossmatching the gravitational wave localization with known AGN catalogs. No candidate met the criteria for a viable optical counterpart. We explored three BBH merger scenarios predicting optical emission in AGN disks: (i) ram pressure stripping, (ii) long-term emission from an emerging jet cocoon, and (iii) jet breakout followed by shock cooling. Using our observational cadence and depth, we constrained the BBH parameter space, including the remnant's location within the AGN disk, kick velocity, and supermassive black hole (SMBH) mass. Detectable flares are most likely when mergers occur at 0.01-0.1 parsecs from SMBHs with masses between 10^7 and 10^8 solar masses, where short delay times and long durations best align with our follow-up strategy. These results provide a framework for identifying AGN-hosted BBH counterparts and guiding future multimessenger efforts.