On the size of HII regions around high-redshift quasars

We investigate the possibility of constraining the ionization state of the intergalactic medium (IGM) close to the end of reionization (z≈ 6) by measuring the size of H ii regions in high-z quasar spectra. We perform a combination of multiphase smoothed particle hydrodynamics and three-dimensional radiative transfer simulations to predict reliably the properties of typical high-z quasar H ii regions, embedded in a partly neutral IGM (xH i= 0.1). In this work we assume a fixed configuration for the quasar lifetime and luminosity, i.e. tQ= 107 yr and graphic. From the analysis of mock spectra along lines of sight through the simulated QSO environment, we find that the H ii region size derived from quasar spectra is on average 30 per cent smaller than the physical one. Additional maximum likelihood analysis shows that this offset induces an overestimate of the neutral hydrogen fraction, xH i, by a factor of ≈3. By applying the same statistical method to a sample of observed QSOs, our study favours a mostly ionized (xH i < 0.06) universe at z= 6.1.