Primordial black holes as dark matter candidates: Multi-frequency constraints from cosmic radiation backgrounds

Aims. This study investigates the role of primordial black holes (PBHs) in shaping cosmic radiation backgrounds--the cosmic X-ray background (CXB), the Lyman-Werner background (LWB), and the cosmic radio background (CRB)--and evaluates their viability as dark matter (DM) candidates based on observational constraints and theoretical limits. Methods. PBH accretion is modelled using analytical frameworks that include electron advection-dominated accretion flows (eADAF), standard advection-dominated accretion flows (ADAF), luminous hot accretion flows (LHAF), and thin disks. Emission from PBHs in both dark matter halos and the intergalactic medium (IGM) is computed. We assess the impact of variations in model assumptions, such as halo gas density profiles, gas velocities, and emission models. The results are compared with observational limits and theoretical thresholds to constrain the PBH fraction as DM for masses between 1 and 100 solar masses Results. PBHs may contribute up to 99, 93, 80, and 91 per cent of the unresolved soft X-ray background for masses of 1, 10, 33, and 100 solar masses, respectively, and about 33-39 per cent of the hard X-ray background. These contributions limit the PBH DM fraction to 7e-3, 6e-4, 6e-4, and 7e-4, respectively, in our baseline model. These constraints are consistent with those from the LWB, ensuring molecular cooling and early star formation are preserved. However, explaining the radio background excess and the EDGES signal would require PBH fractions well above these limits. For 1 solar mass, excluding ADAF subregimes relaxes the constraint to 3e-2, highlighting the sensitivity to accretion physics. Variations in model assumptions introduce only minor differences in the predicted backgrounds.