Radio recombination lines from obscured quasars with the SKA

We explore the possibility of detecting hydrogen radio recombination lines from 0 < z < 10 quasars. We compute the expected Hnα flux densities as a function of absolute magnitude and redshift by considering (i) the range of observed active galactic nucleus spectral indices from UV to X-ray bands, (ii) secondary ionizations from X-ray photons, and (iii) stimulated emission due to non-thermal radiation. All these effects are important to determine the line fluxes. We find that the combination of slopes: αX,hard = -1.11, αX,soft = -0.7, αEUV = -1.3, αUV = -1.7, maximizes the expected flux, fHnα ~ 10 μJy for z ~ 7 quasars with MAB = -27 in the n ~ 50 lines; allowed spectral energy distribution variations produce variations by a factor of 3 around this value. Secondaries boost the line intensity by a factor of 2-4 , while stimulated emission in high-z quasars with MAB ≈ -26 provides an extra boost to radio recombination line flux observed at v ~ 1 GHz if recombinations arise in H II regions with Te ≈ 103 - 5 K, ne ≈ 103 - 5 cm-3. We compute the sensitivity required for a 5s detection of Hna lines using the Square Kilometre Array (SKA), finding that the SKA-MID could detect sources with MAB ≲ -27 (MAB ≲ -26) at z ≲ 8 (z ≲ 3) in less than 100 h of observing time. These observations could open new paths to searches for obscured SMBH progenitors, complementing X-ray, optical/IR and sub-mm surveys.