Probing the growth of supermassive black holes at z > 6 with LOFAR

H-II regions surrounding supermassive black holes (SMBHs) in an otherwise still neutral intergalactic medium (IGM) are likely to be the most easily detectable sources by future 21-cm experiments like LOFAR. We have made predictions for the size distribution of such H-II regions for several physically motivated models for BH growth at high redshift and compared this to the expected LOFAR sensitivity to these sources. The number of potentially detectable H-II regions does not only depend on the ionization state of the IGM and the decoupling of the spin temperature of the neutral hydrogen from the cosmic microwave background temperature, but is also strongly sensitive to the rate of growth of BHs at high redshift. If the SMBHs at redshift 6 were built up via continuous Eddington-limited accretion from low mass seed BHs at high redshift, then LOFAR is not expected to detect isolated QSO H-II regions at redshifts much larger than 6, and only if the IGM is still significantly neutral. If the high-redshift growth of BHs starts with massive seed BHs and is driven by short-lived accretion events following the merging of BH hosting galaxies then the detection of H-II regions surrounding SMBHs may extend to redshifts as large as 8-9 but is still very sensitive to the redshift to which the IGM remains significantly neutral. The most optimistic predictions are for a model where the SMBHs at z > 6 have grown slowly. H-II regions around SMBHs may then be detected to significantly larger redshifts.