ALMA Lensing Cluster Survey:Bright [C ii] 158 mu m Lines from a Multiply Imaged Sub-L* Galaxy at z=6.0719

We present bright [C ii] 158 mu m line detections from a strongly magnified and multiply imaged (mu similar to 20-160) sub-L* (MUV=-19.75-0.44+0.55) Lyman-break galaxy (LBG) at z = 6.0719 +/- 0.0004, drawn from the ALMA Lensing Cluster Survey (ALCS). Emission lines are identified at 268.7 GHz at >= 8 sigma exactly at the positions of two multiple images of the LBG, behind the massive galaxy cluster RXCJ0600-2007. Our lens models, updated with the latest spectroscopy from VLT/MUSE, indicate that a sub region of the LBG crosses the caustic, and is lensed into a long (similar to 6 '') arc with a local magnification of mu similar to 160, for which the [C ii] line is also significantly detected. The source plane reconstruction resolves the interstellar medium (ISM) structure, showing that the [C ii] line is co-spatial with the rest-frame UV continuum at a scale of similar to 300 pc. The [C ii] line properties suggest that the LBG is a rotation-dominated system, whose velocity gradient explains a slight difference in redshifts between the whole LBG and its sub-region. The star formation rate (SFR)-L-[CII] relations, for whole and sub-regions of the LBG, are consistent with those of local galaxies. We evaluate the lower limit of the faint-end of the [C ii] luminosity function at z = 6, finding it to be consistent with predictions from semi-analytical models and from the local SFR-L-[CII] relation with a SFR function at z = 6. These results imply that the local SFR-L-[CII] relation is universal for a wide range of scales, including the spatially resolved ISM, the whole region of the galaxy, and the cosmic scale, even in the epoch of reionization.