The cold interstellar medium of a normal sub-$L^\star$ galaxy at the end of reionization

We present the results of a ~60-hr observational campaign with ALMA targeting a spectroscopically confirmed and lensed sub-$L^\star$ galaxy at z=6.07, identified during the ALMA Lensing Cluster Survey (ALCS). We sample the dust continuum emission from rest frame 90 to 370 $\mu$m at six different frequencies and set constraining upper limits on the molecular gas line emission and content via CO(7-6) and [CI](2-1) for two lensed images with $\mu\gtrsim20$. Complementing these sub-mm observations with deep optical and near-IR photometry and spectroscopy with JWST, we find this galaxy to form stars at a rate of SFR~7 Msun/yr, ~50-70% of which is obscured by dust. This is consistent with what is expected for a $M_\star$~7.5$\times10^{8}$ Msun object by extrapolating the $M_\star$-obscured SFR fraction relation at z<2.5 and with observations at 5<z<7. The dust temperature of ~50K is similar to that of more massive galaxies at similar redshifts, although with large uncertainties and with possible negative gradients. We measure a dust mass of $M_{\rm dust}$~1.5$\times10^6$ Msun and, by combining [CI], [CII], and a dynamical estimate, a gas mass of ~2$\times10^9$ Msun. Their ratio is in good agreement with the predictions from models in the literature. The $M_{\rm dust}$/$M_\star$ fraction of ~0.002 and the young stellar age are consistent with dust production via supernovae. Also, models predict a number density of galaxies with $M_{\rm dust}\sim10^{6}$ Msun at z=6 in agreement with our estimate from the parent ALCS survey. The combination of lensing and multiwavelength observations allow us to probe luminosity regimes up to two orders of magnitude lower than what has been explored so far for field galaxies at similar redshifts. Our results serve as a benchmark for future observations of faint sub-$L^\star$ galaxy population that might have driven the reionization of the Universe. [Abridged]