Kinematic scaling relations of disc galaxies from ionised gas at $z\sim1$ and their connection with dark matter haloes

We derive the Tully-Fisher (TFR, $M_\ast-V_{\rm circ,f}$) and Fall (FR, $j_\ast-M_\ast$) relations at redshift $z = 0.9$ using a sample of 43 main-sequence disc galaxies with H$\alpha$ IFU data and JWST/HST imaging. The strength of our analysis lies in the use of state-of-the-art 3D kinematic models to infer galaxy rotation curves, the inclusion and morphological modelling of NIR bands, and the use of SED modelling applied to our photometry measurements to estimate stellar masses. After correcting the inferred H$\alpha$ velocities for asymmetric drift, we find a TFR of the form $\log(M_\ast / M_\odot) = a \log(V_{\rm circ,f} / 150~\mathrm{km\,s^{-1}}) + b$, with $a=3.82^{+0.55}_{-0.40}$ and $b=10.27^{+0.06}_{-0.07}$, as well as a FR of the form $\log(j_\ast / \mathrm{kpc\,km\,s^{-1}}) = a \log(M_\ast / 10^{10.5} M_\odot) + b$, with $a=0.44^{+0.06}_{-0.06}$ and $b=2.86^{+0.02}_{-0.02}$. Compared with their $z=0$ counterparts, we find moderate evolution in the TFR and strong evolution in the FR over the past 8 Gyr. We interpret our findings in the context of the galaxy-to-halo scaling parameters $f_{\rm M}=M_\ast/M_{\rm vir}$ and $f_{\rm j}=j_\ast/j_{\rm vir}$. We infer that $f_{\rm j}$ shows little redshift evolution and depends very weakly on $M_\ast$, with typical values around $f_{\rm j}\sim0.8$. As for $f_{\rm M}$, we find it to be higher and less dependent on $M_\ast$ at $z=0.9$ than at $z=0$. Interpreting our observed $f_{\rm M}-M_\ast$ relations within the Cold Dark Matter framework implies necessarily that the galaxy populations at $z=0.9$ and $z=0$ are not the progenitor/descendant of one another. The alternative scenario is that the $z=0.9$ relations are incorrect due to strong selection effects, unidentified systematics, or the possibility that H$\alpha$ kinematics may not be a reliable dynamical tracer. Such problems would also affect previous studies on the same subject.