Modeling the Radio Background from the First Black Holes at Cosmic Dawn: Implications for the 21 cm Absorption Amplitude

We estimate the 21 cm Radio Background from accretion onto the first intermediate-mass Black Holes between $z\approx 30$ and $z\approx 16$. Combining potentially optimistic, but plausible, scenarios for black hole formation and growth with empirical correlations between luminosity and radio-emission observed in low-redshift active galactic nuclei, we find that a model of black holes forming in molecular cooling halos is able to produce a 21 cm background that exceeds the Cosmic Microwave Background (CMB) at $z \approx 17$ though models involving larger halo masses are not entirely excluded. Such a background could explain the surprisingly large amplitude of the 21 cm absorption feature recently reported by the EDGES collaboration. Such black holes would also produce significant X-ray emission and contribute to the $0.5-2$ keV soft X-ray background at the level of $\approx 10^{-13}-10^{-12}$ erg sec$^{-1}$ cm$^{-2}$ deg$^{-2}$, consistent with existing constraints. In order to avoid heating the IGM over the EDGES trough, these black holes would need to be obscured by Hydrogen column depths of $ N_\text{H} \sim 5 \times 10^{23} \text{cm}^{-2}$. Such black holes would avoid violating contraints on the CMB optical depth from Planck if their UV photon escape fractions were below $f_{\text{esc}} \lesssim 0.1$, which would be a natural result of $N_\text{H} \sim 5 \times 10^{23} \text{cm}^{-2}$ imposed by an unheated IGM.