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 ≤ M₁₄₅₀ ≤ -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 M₁₄₅₀ = -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^-_,corr²⁵ (R_p^-_,corr²⁵ µ (1 + z)^-3.79±^1.72) over 5.8 ≤ z ≤ 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^-_,corr²⁵ (≤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.