Balmer Decrement Anomalies in Galaxies at z ~ 6 Found by JWST Observations: Density-Bounded Nebulae or Excited H I Clouds?

We investigate the physical origins of the Balmer decrement anomalies in GS-NDG-9422 (Cameron et al. 2023) and RXCJ2248-ID (Topping et al. 2024) galaxies at z~ 6 whose Hα/Hβ values are significantly smaller than $2.7$, the latter of which also shows anomalous Hγ/Hβ and Hδ/Hβ values beyond the errors. Because the anomalous Balmer decrements are not reproduced under the Case B recombination, we explore the nebulae with the optical depths smaller and larger than the Case B recombination by physical modeling. We find two cases quantitatively explaining the anomalies; 1) density-bounded nebulae that are opaque only up to around Lyγ-Ly8 transitions and 2) ionization-bounded nebulae partly/fully surrounded by optically-thick excited H{ i} clouds. The case of 1) produces more Hβ photons via Lyγ absorption in the nebulae, requiring fine tuning in optical depth values, while this case helps ionizing photon escape for cosmic reionization. The case of 2) needs the optically-thick excited H{ i} clouds with N₂ 10¹²-10¹³ cm⁻², where N₂ is the column density of the hydrogen atom with the principal quantum number of $n=2$. Interestingly, the high N₂ values qualitatively agree with the recent claims for GS-NDG-9422 with the strong nebular continuum requiring a number of $2s$-state electrons and for RXCJ2248-ID with the dense ionized regions likely coexisting with the optically-thick clouds. While the physical origin of the optically-thick excited H{ i} clouds is unclear, these results may suggest gas clouds with excessive collisional excitation caused by an amount of accretion and supernovae in the high-z galaxies.