Subaru High-z Exploration of Low-luminosity Quasars (SHELLQs). XI. Proximity Zone Analysis for Faint Quasar Spectra at z ∼ 6

We present measurements of the size of the quasar proximity zone (R_p) for 11 low-luminosity ( $-26.16\leqslant {M}_{1450}\leqslant -22.83$ ) quasars at z ∼ 6, discovered by the Subaru High-z Exploration of Low-Luminosity Quasars project. Our faint quasar sample expands the R_p measurement down to ${M}_{1450}=-22.83$ mag, where more common quasar populations dominate at the epoch. We restrict the sample to quasars whose systemic redshifts have been precisely measured by [C II] 158 μm or Mg II λ2798 emission lines. We also update the R_p measurements for 26 luminous quasars presented in Eilers et al. by using the latest systemic redshift results. The luminosity dependence on R_p is found to be consistent with the theoretical prediction assuming a highly ionized intergalactic medium. We find a shallow redshift evolution of the luminosity-corrected R_p, ${R}_{p,\mathrm{corr}}^{-25}$ ( ${R}_{p,\mathrm{corr}}^{-25}\propto {(1+z)}^{-3.79\pm 1.72}$ ) over $5.8\lesssim z\lesssim 6.6$ . This trend is steeper than that of Eilers et al., but significantly shallower than those of the earlier studies. Our results suggest that R_p,corr is insensitive to the neutral fraction of the universe at z ∼ 6. Four quasars show exceptionally small ${R}_{p,\mathrm{corr}}^{-25}$ ( $\lesssim 0.90$ proper Mpc), which could be the result of their young age (<10⁴ yr) in the reionization epoch, though statistics on this are still scarce.