ALMA Lensing Cluster Survey: Bright [CII] 158 $\mu$m Lines from a
  Multiply Imaged Sub-$L^{\star}$ Galaxy at $z=6.0719$
  We present bright [CII] 158 $\mu$m line detections from a strongly magnified
and multiply-imaged ($\mu\sim20-160$) sub-$L^{*}$ ($M_{\rm UV}$ =
$-19.75^{+0.55}_{-0.44}$) Lyman-break galaxy (LBG) at $z=6.0719\pm0.0004$ from
the ALMA Lensing Cluster Survey (ALCS). Emission lines are identified at 268.7
GHz at $\geq$ 8$\sigma$ exactly at positions of two multiple images of the LBG
behind the massive galaxy cluster RXCJ0600$-$2007. Our lens models, updated
with the latest spectroscopy from VLT/MUSE, indicate that a sub region of the
LBG crosses the caustic and is lensed into a long ($\sim6''$) arc with a local
magnification of $\mu\sim 160$, for which the [CII] line is also significantly
detected. The source-plane reconstruction resolves the interstellar medium
(ISM) structure, showing that the [CII] line is co-spatial with the rest-frame
UV continuum at the scale of $\sim$300 pc. The [CII] line properties suggest
that the LBG is a rotation-dominated system whose velocity gradient explains a
slight difference of redshifts between the whole LBG and its sub region. The
star formation rate (SFR)-$L_{\rm [CII]}$ relations from the sub to the whole
regions of the LBG are consistent with those of local galaxies. We evaluate the
lower limit of the faint-end of the [CII] luminosity function at $z=6$, and
find that it is consistent with predictions from semi analytical models and
from the local SFR-$L_{\rm [CII]}$ relation with a SFR function at $z=6$. These
results imply that the local SFR-$L_{\rm [CII]}$ relation is universal for a
wide range of scales including the spatially resolved ISM, the whole region of
galaxy, and the cosmic scale, even in the epoch of reionization.
