Compact Ionized Gas Region Surrounded by Porous Neutral Gas in a Dusty Lyman Break Galaxy at Redshift $z=8.312$

Porous interstellar medium (ISM) structure in galaxies at the epoch of reionization (EoR) gives us a hint to understand what types of galaxies contribute to reionization. Although recent studies have pointed out the positive correlation between high ionizing photon escape fractions and high [O III] $88~μ\mathrm{m}$-to-[C II] $158~μ\mathrm{m}$ ratios found in UV-luminous star-forming galaxies at $z > 6$ with ALMA, previous studies have paid little attention to the neutral gas porosity that allows ionizing photons to escape. Here, we present a detailed analysis of a $z=8.312$ Lyman break galaxy, MACS0416_Y1 with a high $L_\mathrm{[OIII]88}/L_\mathrm{[CII]158}$ ratio ($\approx9$) and dust continuum detection. We construct a multi-phase ISM model incorporating the neutral gas covering fraction ($cov_\mathrm{PDR}$). The best-fit model reveals a $cov_\mathrm{PDR}\approx25 \%$, indicating that $\approx75 \%$ of the ionized gas region is exposed to intercloud space. We confirm that our conclusions hold even when varying star-formation history, stellar age, gas/stellar metallicity, and carbon-to-oxygen abundance ratio. This finding meets one of the necessary conditions for galaxies to have a non-zero escape fraction of ionizing photons and supports recent studies that galaxies with a high [O III] $88~μ\mathrm{m}/$[C II] $158~μ\mathrm{m}$ ratio, such as MACS0416_Y1, could contribute to cosmic reionization. Furthermore, the modeled H II region with the best-fitting parameters has a typical size ($D=0.90~\mathrm{pc}$) and gas density ($\log n_\mathrm{H,c}/\mathrm{cm^{-3}}=2.7$) that are comparable to local compact H II regions. This suggests that the H II regions in MACS0416_Y1 are in an early evolutionary stage.