The MUSE Hubble Ultra Deep Field Survey XVI. The angular momentum of
  low-mass star-forming galaxies. A cautionary tale and insights from TNG50
  We investigate the specific angular momentum (sAM) $ j(<r)$ profiles of
intermediate redshift ($0.4<z<1.4$) star-forming galaxies (SFGs) in the
relatively unexplored regime of low masses (down to $M_\star\sim
10^8$M$_{\odot}$), and small sizes (down to $R_{\rm e}\sim 1.5$ kpc) and
characterize the sAM scaling relation and its redshift evolution. We have
developed a 3D methodology to constrain sAM profiles of the star-forming gas
using a forward modeling approach with \galpak{} that incorporates the effects
of beam smearing, yielding the intrinsic morpho-kinematic properties even with
limited spatial resolution data. Using mock observations from the TNG50
simulation, we find that our 3D methodology robustly recovers the star
formation rate (SFR)-weighted $j(<r)$ profiles down to low effective
signal-to-noise ratio (SNR) of $\gtrapprox3$. We applied our methodology
blindly to a sample of 494 \OII{}-selected SFGs in the MUSE Ultra Deep Field
(UDF) 9~arcmin$^2$ mosaic data, covering the unexplored $8<\log
M_*/$M$_{\odot}<9$ mass range. We find that the (SFR-weighted) sAM relation
follows $j\propto M_\star^{\alpha}$ with an index $\alpha$ varying from
$\alpha=0.3$ to $\alpha=0.5$, from $\log M_\star/$M$_{\odot}=8$ to $\log
M_*/$M$_{\odot}=10.5$. The UDF sample supports a redshift evolution consistent
with the $(1+z)^{-0.5}$ expectation from a Universe in expansion. The scatter
of the sAM sequence is a strong function of the dynamical state with $\log
j|_{M_*}\propto 0.65 \times \log(V_{\rm max}/\sigma)$ where $\sigma$ is the
velocity dispersion at $2 R_{\rm e}$. In TNG50, SFGs also form a
$j-M_{\star}-(V/\sigma)$ plane but it correlates more with galaxy size than
with morphological parameters. Our results suggest that SFGs might experience a
dynamical transformation before their morphological transformation to becoming
passive via either merging or secular evolution.
