Examining Two-dimensional Luminosity-Time Correlations for Gamma-Ray Burst Radio Afterglows with VLA and ALMA

Gamma-ray burst (GRB) afterglow emission can be observed from sub-TeV to radio wavelengths, though only 6.6% of observed GRBs present radio afterglows. We examine GRB radio light curves (LCs) to look for the presence of radio plateaus resembling the plateaus observed at X-ray and optical wavelengths. We analyze 404 GRBs from the literature with observed radio afterglow and fit 82 GRBs with at least five data points with a broken power-law model, requiring four parameters. From these, we find 18 GRBs that present a break feature resembling a plateau. We conduct the first multiwavelength study of the Dainotti correlation between the luminosity L _a and the rest-frame time of break T _a * for those 18 GRBs, concluding that the correlation exists and resembles the corresponding correlation at X-ray and optical wavelengths after correction for evolutionary effects. We compare T _a * for the radio sample with T _a * values in X-ray and optical data, finding significantly later break times in the radio. We propose that this late break time and the compatibility in slope suggest either a long-lasting plateau or the passage of a spectral break in the radio band. We also correct the distribution of the isotropic energy E _iso versus the rest-frame burst duration T ^* ₉₀ for evolutionary effects and conclude that there is no significant difference between the T*₉₀ distributions for the radio LCs with a break and for those without.