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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 $j\propto M_\star^α$ with an index $α$ varying from $α=0.3$ to $α=0.5$, 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 $\log j|_{M_*}\propto 0.65 \times \log(V_{\rm max}/σ)$ where $σ$ is the velocity dispersion at $2 R_{\rm e}$. In TNG50, SFGs also form a $j-M_{\star}-(V/σ)$ 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.