ALMA observations have revealed that [CII] 158$mu$m line emission in high-z galaxies is ~2-3$times$ more extended than the UV continuum emission. Here we explore whether surface brightness dimming (SBD) of the [CII] line is responsible for the reported [CII] deficit, and the large $L_{rm [OIII]}/L_{rm [CII]}$ luminosity ratio measured in early galaxies. We first analyse archival ALMA images of nine z>6 galaxies observed in both [CII] and [OIII]. After performing several uv-tapering experiments to optimize the identification of extended line emission, we detect [CII] emission in the whole sample, with an extent systematically larger than the [CII] emission. Next, we use interferometric simulations to study the effect of SBD on the line luminosity estimate. About 40% of the extended [CII] component might be missed at an angular resolution of 0.8$^{primeprime}$, implying that $L_{rm [CII]}$ is underestimated by a factor $approx2$ in data at low (<7) signal-to-noise ratio . By combining these results, we conclude that $L_{rm [CII]}$ of z>6 galaxies lies, on average, slightly below the local $L_{rm [CII]}-SFR$ relation ($Delta^{z=6-9}=-0.07pm0.3$), but within the intrinsic dispersion of the relation. SBD correction also yields $L_{rm [OIII]}/L_{rm [CII]}<10$, i.e. more in line with current hydrodynamical simulations.
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