Star formation governs galaxy evolution, shaping stellar mass assembly and gas consumption across cosmic time. The Kennicutt-Schmidt (KS) relation, linking star formation rate (SFR) and gas surface densities, is fundamental to understand star formation regulation, yet remains poorly constrained at z > 2 due to observational limitations and uncertainties in locally calibrated gas tracers. The CII 158 μm line has recently emerged as a key probe of the cold ISM and star formation in the early Universe. We investigate whether the resolved CII-SFR and KS relations established at low redshift remain valid at 4 < z < 6 by analysing 13 main-sequence galaxies from the ALPINE and CRISTAL surveys, using multi-wavelength data (HST, JWST, ALMA) at 2 kpc resolution. We perform pixel-by-pixel spectral energy distribution (SED) modelling with CIGALE on resolution-homogenised images. We develop a statistical framework to fit the CII-SFR relation that accounts for pixel covariance and compare our results to classical fitting methods. We test two CII-to-gas conversion prescriptions to assess their impact on inferred gas surface densities and depletion times. We find a resolved CII-SFR relation with a slope of 0. 87 0. 15 and intrinsic scatter of 0. 19 0. 03 dex, which is shallower and tighter than previous studies at z5. The resolved KS relation is highly sensitive to the CII-to-gas conversion factor: using a fixed global α ₂₈₈ yields depletion times of 0. 5-1 Gyr, while a surface brightness-dependent W ₂₈₈, places some galaxies with high gas density in the starburst regime (<0. 1 Gyr). Future inputs from both simulations and observations are required to better understand how the CII-to-gas conversion factor depends on local ISM properties. We need to break this fundamental limit to properly study the KS relation at z4.
Accard et al. (Mon,) studied this question.
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