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The Kennicutt-Schmidt (KS) relation between the gas and the star formationrate (SFR) surface density ($\Sigma_{\rm gas}$-$\Sigma_{\rm SFR}$) is essentialto understand star formation processes in galaxies. So far, it has beenmeasured up to z~2.5 in main-sequence galaxies. In this letter, we aim to putconstraints at z~4.5 using a sample of four massive main-sequence galaxiesobserved by ALMA at high resolution. We obtained ~0.3"-resolution [CII] andcontinuum maps of our objects, which we then converted into gas and obscuredSFR surface density maps. In addition, we produced unobscured SFR surfacedensity maps by convolving Hubble ancillary data in the rest-frame UV. We thenderived the average $\Sigma_{\rm SFR}$ in various $\Sigma_{\rm gas}$ bins, andestimated the uncertainties using a Monte Carlo sampling. Our galaxy samplefollows the KS relation measured in main-sequence galaxies at lower redshiftand is slightly lower than predictions from simulations. Our data points probethe high end both in terms of $\Sigma_{\rm gas}$ and $\Sigma_{\rm gas}$, andgas depletion timescales (285-843 Myr) remain similar to z~2 objects. However,three of our objects are clearly morphologically disturbed, and we could haveexpected shorter gas depletion timescales (~100 Myr) similar to merger-drivenstarbursts at lower redshifts. This suggests that the mechanisms triggeringstarbursts at high redshift may be different than in the low- andintermediate-z Universe.

The ALMA-ALPINE [CII] survey: Kennicutt-Schmidt relation in four massive main-sequence galaxies at z~4.5