Relation between the β value, the core radius (r_c), the significant radius (R_sig), and the total number of photons within the significant radius. In these panels, the grey dots, blue empty circles, and red empty squares represent the Silver+Bronze sample, Faint Gold sample, and Bright Gold sample, respectively. The Bright Gold and Faint Gold samples are divided from the Gold sample by F₅₀₀ = 3 × 10⁻¹² erg s⁻¹ cm⁻². Bottom-right panel: β histogram of the same samples, with colors matching with the other panels.