Cosmic radiation backgrounds from primordial black holes

Recent measurements of the cosmic X-ray and radio backgrounds (CXB/CRB, respectively) obtained with Chandra and ARCADE2 report signals in excess of those expected from known sources, suggesting the presence of a yet undiscovered population of emitters. We investigate the hypothesis that such excesses are due to primordial black holes (PBHs) which may constitute a substantial fraction of dark matter (DM). We present a novel semi-analytical model which predicts X-ray and radio emission due to gas accretion onto PBHs, assuming that they are distributed both inside DM halos and in the intergalactic medium (IGM). Our model includes a self-consistent treatment of heating/ionization feedback on the surrounding environment. We find that (i) the emission from PBHs accreting in the IGM is subdominant at all times ($1\mathrm{\%}\le I_{\mathrm{I}\mathrm{G}\mathrm{M}}\mathrm{/}{I}_{\mathrm{t}\mathrm{o}\mathrm{t}}\le 40\mathrm{\%}$); (ii) most of the CXB/CRB emission comes from PBHs in DM mini-halos ($M_h\le {10}^6{M}_{\odot }$) at early epochs ($z>6$). While a small fraction ($f_{\mathrm{P}\mathrm{B}\mathrm{H}}\simeq 0.3\mathrm{\%}$) of DM in the form of PBHs can account for the total observed CXB excess, the CRB one cannot be explained by PBHs. Our results set the strongest existing constraint on $f_{\mathrm{P}\mathrm{B}\mathrm{H}}\le 3\times {10}^{-4}(30\mathrm{/}{M}_{\mathrm{P}\mathrm{B}\mathrm{H}})$ in the mass range $1-1000M_{\odot }$. Finally, we comment on the implications of our results on the global ${\mathrm{H}}_{\mathrm{I}}$ 21cm signal.