Recent stacked ALMA observations have revealed that normal, star-forming galaxies at $zapprox 6$ are surrounded by extended ($approx 10,mathrm{kpc}$) [CII] emitting halos which are not predicted by the most advanced, zoom-in simulations. We present a model in which these halos are the result of supernova-driven cooling outflows. Our model contains two free parameters, the outflow mass loading factor, $eta$, and the parent galaxy dark matter halo circular velocity, $v_c$. The outflow model successfully matches the observed [CII] surface brightness profile if $eta = 3.20 pm 0.10$ and $v_c = 170 pm 10{,rm km,s^{-1}}$, corresponding to a dynamical mass of $approx 10^{11}, mathrm{M}_odot$. The predicted outflow rate and velocity range are $128 pm 5 ,mathrm{M}_odot {rm yr}^{-1}$ and $300-500 {,rm km,s^{-1}}$, respectively. We conclude that: (a) extended halos can be produced by cooling outflows; (b) the large $eta$ value is marginally consistent with starburst-driven outflows, but it might indicate additional energy input from AGN; (c) the presence of [CII] halos requires an ionizing photon escape fraction from galaxies $f_{rm esc} ll 1$. The model can be readily applied also to individual high-$z$ galaxies, as those observed, e.g., by the ALMA ALPINE survey now becoming available.
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