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

TL;DR

This study investigates how disc galaxies' baryonic and angular-momentum scaling relations evolve by deriving the Tully-Fisher relation ($M_*/V_{circ,f}$) and Fall relation ($j_*/M_*$) at $z\approx0.9$ using 43 H$\alpha$-based IFU galaxies with JWST/HST NIR imaging. It employs rigorous 3D kinematic modelling, asymmetric-drift corrections, and SED-based stellar masses to obtain $V_{circ,f}$ and $j_*$ in a consistent framework with $z=0$ studies, enabling direct comparison. The authors find $z=0.9$ TFR: $\log(M_*/M_\odot)=3.82\log(V_{circ,f}/150\,\mathrm{km\,s^{-1}})+10.27$ and FR: $\log(j_*/{\rm kpc\,km\,s^{-1}})=0.44\log(M_*/10^{10.5}M_\odot)+2.86$, with moderate TFR evolution and stronger FR evolution relative to $z=0$, driven by changes in the galaxy–halo assembly parameters $f_{\rm M}$ and $f_{\rm j}$. By recasting the relations in terms of $f_{\rm M}=M_*/M_{vir}$ and $f_{\rm j}=j_*/j_{vir}$, the study demonstrates that cosmology-only evolution cannot explain the observations; both $f_{\rm V}f_{\rm M}^{-1/3}$ and $f_{\rm j}f_{\rm M}^{-2/3}$ must evolve with redshift. The inferred trends imply that the $z\approx0.9$ disc population is not simply the progenitor of the local disc population under a naive growth model, suggesting more complex mass assembly, merging, and gas accretion histories. These results provide essential empirical benchmarks for galaxy formation models within the CDM paradigm and underscore the importance of incorporating gas kinematics in high-$z$ dynamical studies.

Abstract

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$α$ 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$α$ 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$α$ kinematics may not be a reliable dynamical tracer. Such problems would also affect previous studies on the same subject.

Figures (10)

• Figure 1: Top left: SFMS defined by our high-$z$ galaxies, colour-coded by their redshift. The reference SFMS from leja2022 is shown. SFRs come from our SED fitting. Top right: Rotation to dispersion ratio for our galaxy sample. Bottom left: Sérsic index as a function of $M_\ast$. The inset shows the cumulative distribution of the Sérsic indices. Bottom right: Stellar mass-size relation. Our galaxies (green markers) are contrasted against 1) the individual measurements from martorano2024 at $0.8 \leq z \leq 1$ (blue markers) and their $1$ and $2\,\sigma$ ranges (blue bands), and 2) the relation from vanderwel2014 at $z=0.75$ after applying approximate corrections to account for the sizes differences in optical vs. NIR bands.
• Figure 2: Our $z=0.9$ scaling laws. The TFR is shown on the left, and the FR on the right. Our measurements are shown with the green markers, while the best-fit relations and their $1\,\sigma$ confidence bands are shown as pink solid curves and bands, respectively. For comparison, we show the $z=0$ TFR and FR from marasco_mstar.
• Figure 3: Posterior distributions of the best-fitting TFR and FR. The distributions of low- and high-$z$ disc galaxies are shown in blue (from marasco_mstar) and pink (this work), respectively. The contours encompass the 0.393, 0.865, and 0.989 percentiles, corresponding to 1, 2, and $3\,\sigma$ in 2D distributions.
• Figure 4: Drivers of the evolution in our scaling relations. The top panels compare how the local TFR and FR (blue curves) would evolve (orange curves) if the only changes are the $z$ evolution of the Hubble parameter and the density contrast, against our high-$z$ data (green markers) and best fits (pink curves). The results imply an evolution of $f_{\rm V}f_{\rm M}^{-1/3}$ and $f_{\rm j}f_{\rm M}^{-2/3}$. The bottom panels show $f_{\rm M}$ and $f_{\rm j}$ at $z=0$ (blue) and $z=0.9$ (pink) as a function of $M_\ast$, as implied by our best-fitting relations after assuming $f_{\rm V}=1.3\pm0.1$. The grey dashed line and bands in the bottom right panel show $f_{\rm j}$ at $z=0.9$ under the assumption that $f_{\rm M}$ does not evolve with redshift. In all the panels, bands correspond to $1\,\sigma$ confidence bands around the mean relations. Note that the vertical axis span in the bottom panels is the same, highlighting the stronger mass dependency of $f_{\rm M}$ over $f_{\rm j}$.
• Figure 5: Comparison between our inferred $f_{\rm M}-M_\ast$ (top) and $M_{\rm vir}-M_\ast$ (bottom) relations and an idealised toy model of mass assembly. The model considers a population of galaxies (blue circles) lying in the $z=0$ relations (blue curves), which are then traced back to $z=0.9$ (squares), assuming theoretical stellar and halo mass growths. Galaxy downsizing and halo growth histories yield $z=0.9$ relations (squares) with slopes different from those observed at $z=0$ (pink solid curves). The only way to reconcile the stellar mass growth of galaxies with our inferred relations at $z=0.9$ is if low-mass haloes grew more than high-mass haloes since $z=0.9$, contrary to CDM expectations. This suggests that the galaxies populating our $z=0.9$ relations do not follow this toy model and are unlikely to be the progenitors of the $z=0$ population.