A Shallow Slope for the Stellar Mass--Angular Momentum Relation of Star-Forming Galaxies at $1.5 < z < 2.5$

We present measurements of the specific angular momentum $j_\star$ of 41 star-forming galaxies at $1.5<z<2.5$. These measurements are based on radial profiles inferred from near-IR \textit{HST} photometry, along with multi-resolution emission-line kinematic modelling using integral field spectroscopy (IFS) data from KMOS, SINFONI, and OSIRIS. We identified 24 disks (disk fraction of $58.6\pm 7.7\%$) and used them to parametrize the $j_\star$ \textit{vs} stellar mass $M_\star$ relation (Fall relation) as $j_\star\propto M_\star^{\beta}$. We measure a power-law slope $\beta=0.25\pm0.15$, which deviates by approximately $3\sigma$ from the commonly adopted local value $\beta = 0.67$, indicating a statistically significant difference. We find that two key systematic effects could drive the steep slopes in previous high-redshift studies: first, including irregular (non-disk) systems due to limitations in spatial resolution and second, using the commonly used approximation $\tilde{j}_\star\approx k_n v_s r_\mathrm{eff}$, which depends on global unresolved quantities. In our sample, both effects lead to steeper slopes of $\beta=0.48\pm0.21$ and $\beta=0.61\pm0.21$, respectively. To understand the shallow slope, we discuss observational effects and systematic uncertainties and analyze the retention of $j_\star$ relative to the angular momentum of the halo $j_h$ (angular momentum retention factor $f_j =j_\star/j_h$). For the $M_\star$ range covered by the sample $9.5 <\log_{10} (M_\star/M_\odot) < 11.5$ (halo mass $11.5 < \log_{10} (M_h/M_\odot) < 14$), we find large $f_j$ values ($>1$ in some cases) in low-mass haloes that decrease with increasing mass, suggesting a significant role of efficient angular momentum transport in these gas-rich systems, aided by the removal of low-$j_\star$ gas via feedback-driven outflows in low-mass galaxies.