Spatially resolved [CII]-gas conversion factor in early galaxies

Determining how efficiently gas collapses into stars at high-redshift is key to understanding galaxy evolution in the Epoch of Reionization (EoR). Globally, this process is quantified by the gas depletion time ($t_{dep}$); on resolved scales, by the slope and normalization of the Kennicutt-Schmidt (KS) relation. This work explores the global ($\alpha_{[CII]}$) and spatially resolved ($W_{[CII]}$) [CII]-to-gas conversion factors at high-$z$ and their role in inferring reliable gas masses, surface densities, and $t_{dep}$ in the EoR. We select galaxies at 4<z<9 from the SERRA cosmological zoom-in simulation, that features on-the-fly radiative transfer and resolves interstellar medium properties down to $\approx$30 pc. The [CII] emission modelling from photodissociation regions allow us to derive global $\alpha_{ [CII]}$, and maps of $W_{[CII]}$. We study their dependence on gas metallicity (Z), density (n), Mach number (M), and burstiness parameter ($k_s$), and provide best fit relations. The $\alpha_{[CII]}$ decreases with increasing $Z$ and galaxy compactness, while the resolved $W_{[CII]}$ shows two regimes: at $Z< 0.2 Z_\odot$, it anticorrelates with n and Z, but not with $k_s$; above this threshold, it also depends on $k_s$, with more bursty regions showing lower conversion factors. This implies $W_{[CII]}\propto \Sigma_{[CII]}^{-0.5}$, as dense, metal-rich, and bursty regions exhibit higher [CII] surface brightness. Applying a constant $\alpha_{[CII]}$ overestimates $\Sigma_{gas}$ in bright $\Sigma_{[CII]}$ patches, thus flattening the KS slope and overestimating $t_{dep}$ by a factor of $\approx$4.