2023ApJ...958...74T

The plateau phase in radio afterglows has been observed in very few gamma-ray bursts (GRBs), and in this paper, 27 radio light curves with plateau phases were acquired from the published literature. We obtain the related parameters of the radio plateau, such as temporal indexes during the plateau phase (α₁ and α₂), break time (T_b,z), and the corresponding radio flux (F_b). The two-parameter Dainotti relation between the break time of the plateau and the corresponding break luminosity (L_b,z) in the radio band is ${L}_{{\rm{b}},{\rm{z}}}\propto {T}_{{\rm{b}},{\rm{z}}}^{-1.20\pm 0.24}$. Including the isotropic energy E_γ,iso and peak energy E_p,i, the three-parameter correlations for the radio plateaus are written as ${L}_{{\rm{b}},{\rm{z}}}\propto {T}_{{\rm{b}},{\rm{z}}}^{-1.01\pm 0.24}{E}_{\gamma ,\mathrm{iso}}^{0.18\pm 0.09}$ and ${L}_{{\rm{b}},{\rm{z}}}\propto {T}_{{\rm{b}},{\rm{z}}}^{-1.18\pm 0.27}{E}_{{\rm{p}},{\rm{i}}}^{0.05\pm 0.28}$, respectively. The correlations are less consistent with those of the X-ray and optical plateaus, implying that radio plateaus may have a different physical mechanism. The typical frequencies crossing the observational band may be a reasonable hypothesis that causes the breaks of the radio afterglows. We calibrate the GRB empirical luminosity correlations as a standard candle for constraining cosmological parameters and find that our samples can constrain the flat ΛCDM model well but are not sensitive to the nonflat ΛCDM model. By combining GRBs with other probes, such as supernovae and the CMB, the constraints on the cosmological parameters are Ω_m = 0.297 ± 0.006 for the flat ΛCDM model and Ω_m = 0.283 ± 0.008, Ω_Λ = 0.711 ± 0.006 for the nonflat ΛCDM model.