KURVS: The outer rotation curve shapes and dark matter fractions of $z \sim 1.5 $ star-forming galaxies

We present first results from the KMOS Ultra-deep Rotation Velocity Survey (KURVS), aimed at studying the outer rotation curves shape and dark matter content of 22 star-forming galaxies at $z\sim1.5$. These galaxies represent `typical' star-forming discs at $z \sim 1.5$, being located within the star-forming main sequence and stellar mass-size relation with stellar masses $9.5\leqslant$log$(M_{\star}/\mathrm{M_{\odot}})\leqslant11.5$. We extract individual rotation curves out to 4 times the effective radius, on average, or $\sim 10-15$ kpc. Most rotation curves are flat or rising between three- and six-disc scale radii. Only three objects with dispersion-dominated dynamics ($v_{\rm rot}/\sigma_0\sim0.2$) have declining outer rotation curves at more than 5$\sigma$ significance. After accounting for seeing and pressure support, the nine rotation-dominated discs with $v_{\rm rot}/\sigma_0\geqslant1.5$ have average dark matter fractions of $50 \pm 20\%$ at the effective radius, similar to local discs. Together with previous observations of star-forming galaxies at cosmic noon, our measurements suggest a trend of declining dark matter fraction with increasing stellar mass and stellar mass surface density at the effective radius. Simulated EAGLE galaxies are in quantitative agreement with observations up to log$(M_{\star}R_{\rm eff}^{-2}/\mathrm{M_{\odot}kpc^{-2}}) \sim 9.2$, and over-predict the dark matter fraction of galaxies with higher mass surface densities by a factor of $\sim 3$. We conclude that the dynamics of typical rotationally-supported discs at $z \sim 1.5$ is dominated by dark matter from effective radius scales, in broad agreement with cosmological models. The tension with observations at high stellar mass surface density suggests that the prescriptions for baryonic processes occurring in the most massive galaxies (such as bulge growth and quenching) need to be reassessed.