Deep MUSE observations in the HDFS. Morpho-kinematics of distant
  star-forming galaxies down to $10^8$M$_\odot$
  (Abridged) We make use of the deepest VLT/MUSE observations performed so far
on the Hubble Deep Field South (HDFS) to characterize the low-mass (<
$10^{10}$M$_\odot$) galaxy population at intermediate redshift. We identify a
sample of 28 spatially-resolved emission-line galaxies in the deep (27h
integration time) MUSE data cube, spread over a redshift interval of 0.2 < z <
1.4. The public HST images and multi-band photometry over the HDFS are used to
constrain the stellar mass and star formation rate (SFR) of the galaxies and to
perform a morphological analysis. We derive the resolved ionized gas properties
of these galaxies from the MUSE data and model the disk (both in 2D and with
GalPaK$^{\rm 3D}$) to retrieve their intrinsic gas kinematics. We build a
sample of resolved emission-line galaxies of much lower stellar mass and SFR
(by $\sim$1-2 orders of magnitude) than previous 3D spectroscopic surveys. Most
of the spatially-resolved MUSE-HDFS galaxies have gas kinematics consistent
with disk-like rotation, but about 20% have velocity dispersions larger than
the rotation velocities, and 30% are part of a close pair and/or show clear
signs of recent gravitational interactions. In the high-mass regime, the
MUSE-HDFS galaxies follow the Tully-Fisher relation defined from previous
surveys in a similar redshift range. This scaling relation extends also to
lower masses/velocities but with a higher dispersion. The MUSE-HDFS galaxies
follow the scaling relations defined in the local universe between the specific
angular momentum and the stellar mass. However, we find that
intermediate-redshift star-forming galaxies fill a continuum transition from
the spiral to elliptical local scaling relations, according to the dynamical
state of the gas. This indicates that some galaxies may lose their angular
momentum and become dispersion-dominated prior to becoming passive.
