The Optical Two and Three-Dimensional Fundamental Plane Correlations for Nearly 180 Gamma-Ray Burst Afterglows with Swift/UVOT, RATIR, and the SUBARU Telescope

Gamma-ray bursts (GRBs) are fascinating events due to their panchromatic nature. We study optical plateaus in GRB afterglows via an extended search into archival data. We comprehensively analyze all published GRBs with known redshifts and optical plateaus observed by many ground-based telescopes (e.g., Subaru Telescope, RATIR) around the world and several space-based observatories such as the Neil Gehrels Swift Observatory. We fit 500 optical light curves (LCs), showing the existence of the plateau in 179 cases. This sample is 75% larger than the previous one (arXiv:2105.10717), and it is the largest compilation so far of optical plateaus. We discover the 3D fundamental plane relation at optical wavelengths using this sample. This correlation is between the rest-frame time at the end of the plateau emission, $T^{*}_{\rm opt}$, its optical luminosity, $L_{\rm opt}$, and the peak in the optical prompt emission, $L_{\rm peak, opt}$, thus resembling the three-dimensional (3D) X-ray fundamental plane relation (arXiv:1604.06840). We correct our sample for redshift evolution and selection effects, discovering that this correlation is indeed intrinsic to GRB physics. We investigate the rest-frame end time distributions in X-rays and optical ($T^{*}_{\rm opt}$, $T^{*}_{\rm X}$), and conclude that the plateau is achromatic only when selection biases are not considered. We also investigate if the 3D optical correlation may be a new discriminant between optical GRB classes and find that there is no significant separation between the classes compared to the Gold sample plane after correcting for evolution.