Observations of the [C i] (3P1–3P0) emission toward the massive star-forming region RCW 38: Further evidence for highly-clumped density distribution of the molecular gas

We present observations of the $^3P_1$-$^3P_0$ fine-structure line of atomic carbon using the ASTE 10 m sub-mm telescope towards RCW38, the youngest super star cluster in the Milky Way. The detected [CI] emission is compared with the CO $J$ = 1-0 image cube presented in Fukui et al. (2016) which has an angular resolution of 40$^{\prime \prime}$ ($\sim$ 0.33 pc). The overall distribution of the [CI] emission in this cluster is similar to that of the $^{13}$CO emission. The optical depth of the [CI] emission was found to be $\tau$ = 0.1-0.6, suggesting mostly optically thin emission. An empirical conversion factor from the [CI] integrated intensity to the H$_2$ column density was estimated as $X_{\rm [CI]}$ = 6.3 $\times$ 10$^{20}$ cm$^{-2}$ K$^{-1}$ km$^{-1}$ s (for visual extinction: $A_V$ $\le$ 10 mag) and 1.4 $\times$ 10$^{21}$ cm$^{-2}$ K$^{-1}$ km$^{-1}$ s (for $A_V$ of 10-100 mag). The column density ratio of the [CI] to CO ($N_{\rm [CI]}/N_{\rm CO}$) was derived as $\sim$ 0.1 for $A_V$ of 10-100 mag, which is consistent with that of the Orion cloud presented in Ikeda et al. (2002). However, our results cover an $A_V$ regime of up to 100 mag, which is wider than the coverage found in Orion, which reach up to $\sim$ 60 mag. Such a high [CI]/CO ratio in a high $A_V$ region is difficult to be explained by the plane-parallel photodissociation region (PDR) model, which predicts that this ratio is close to 0 due to the heavy shielding of the ultraviolet (UV) radiation. Our results suggest that the molecular gas in this cluster is highly clumpy, allowing deep penetration of UV radiation even at averaged $A_V$ values of 100 mag. Recent theoretical works have presented models consistent with such clumped gas distribution with a sub-pc clump size (e.g., Tachihara et al. 2018).