Brightness temperature of the radio background (T_b) as a function of frequency for PBHs accreting in halos, evaluated at z = 0 (top row) and z = 18 (bottom row). Columns correspond to different PBH masses (M_PBH = 1, 10, 33, 100 M_⊙), while the line styles (solid and dashed-dotted) represent the simple isothermal and Makino+1998 density profiles, respectively. The colour scheme indicates f_PBH: red for 1, green for 10⁻², purple for 10⁻⁴, and gold for f_max. The maximum fraction of DM allowed for each PBH mass, f_max, is determined from CXB observational and LWB theoretical constraints: 7 × 10⁻³ for M_PBH = 1 M_⊙, 6 × 10⁻⁴ for M_PBH = 10 M_⊙ and 33 M_⊙, and 7 × 10⁻⁴ for M_PBH = 100 M_⊙. In the top panels, the grey continuous line corresponds to the fit for the observed radio background excess at z = 0 from Condon et al. (2012).