2007ApJ...660..923M

We make use of hydrodynamical simulations of the intergalactic medium (IGM) to create model quasar absorption spectra. We compare these model spectra with the observed Keck spectra of three z>6.2 quasars with full Gunn-Peterson troughs: SDSS J1148+5251 (z=6.42), SDSS J1030+0524 (z=6.28), and SDSS J1623+3112 (z=6.22). We fit the probability density distributions (PDFs) of the observed Lyα optical depths (τ_α) with those generated from the simulation by exploring a range of values for the size of the quasar's surrounding H II region, R_S; the volume-weighted mean neutral hydrogen fraction in the ambient IGM, x{d1}_HI_; and the quasar's ionizing photon emissivity, N{dot}_Q. In order to avoid averaging over possibly large sight line-to-sight line fluctuations in IGM properties, we analyze each observed quasar independently. We find the following results for J1148+5251, J1030+0524, and J1623+3112: the best-fit sizes R_S are 40, 41, and 29 (comoving) Mpc, respectively. For the later two quasars, the value is significantly larger than the radius corresponding to the wavelength at which the quasar's flux vanishes. These constraints are tight, with only ∼10% uncertainties, comparable to those caused by redshift determination errors. The best-fit values of N{dot}_Q are 2.1, 1.3, and 0.9x10⁵⁷/s, respectively, with a factor of ∼2 uncertainty in each case. Finally, the best-fit values of x{d1}_HI_ are 0.16, 1.0, and 1.0, respectively. The uncertainty in the case of J1148+5251 is large, and x{d1}_HI_ is not well constrained. However, for both J1030+0524 and J1623+3112, we find a significant lower limit of x{d1}_HI_≳0.033. Our method is different from previous analyses of the GP absorption spectra of these quasars, and our results strengthen the evidence that the rapid end stage of reionization is occurring near z∼6.