  HII regions surrounding supermassive black holes (BHs) in an otherwise still
neutral intergalactic medium (IGM) are likely to be the most easily detectable
sources by future 21cm experiments like LOFAR. We have made predictions for the
size distribution of such HII 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 HII regions
does not only depend on the ionisation state of the intergalactic medium and
the decoupling of the spin temperature of the neutral hydrogen from the cosmic
microwave background (CMB) temperature, but is also strongly sensitive to the
rate of growth of BHs at high redshift. If the supermassive BHs 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 HII 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 HII regions surrounding supermassive BHs 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 supermassive BHs at z>6 have grown slowly. HII
regions around supermassive BHs may then be detected to significantly larger
redshifts.
