The impact of a percolating IGM on redshifted 21-cm observations of quasar H II regions

We assess the impact of inhomogeneous reionization on detection of H ii regions surrounding luminous high-redshift quasars using planned low-frequency radio telescopes. Our approach is to implement a seminumerical scheme to calculate the three-dimensional structure of ionized regions surrounding a massive halo at high redshift, including the ionizing influence of a luminous quasar. As part of our analysis we briefly contrast our scheme with published seminumerical models. We calculate mock 21-cm spectra along the line of sight towards high-redshift quasars, and estimate the ability of the planned Murchison Widefield Array to detect the presence of H ii regions. The signal-to-noise ratio for detection will drop as the characteristic bubble size grows during reionization because the quasar's influence becomes less prominent. However, quasars will imprint a detectable signature on observed 21-cm spectra that is distinct from a region of typical intergalactic medium (IGM). At epochs where the mean hydrogen neutral fraction is ≈30 per cent or greater we find that neutral gas in the IGM surrounding a single quasar will be detectable (at a significance of 5σ) within 100-h integrations in more than 50 per cent of cases. 1000-h integrations will be required to detect a smaller neutral fraction of 15 per cent in more than 50 per cent of cases. A highly significant detection will be possible in only 100 h for a stack of 10 smaller 3 proper Mpc H ii regions. The accurate measurement of the global average neutral fraction (〈x_{H i}〉) will be limited by systematic fluctuations between lines of sight for single H ii regions. We estimate the accuracy with which the global neutral fraction could be measured from a single H ii region to be 50, 30 and 20 per cent for 〈x_{H i}〉 ≈ 0.15, 0.3 and 0.5, respectively.