Flat Rotation Curves of $z\sim 1$ Star-Forming Galaxies and Evidence of Disk-Scale Length Evolution

We investigate the shape of the Rotation Curves (RCs) of $z\sim 1$ star-forming galaxies and compare them with the local star-forming galaxies. For this purpose, we have used $409$ galaxies from the K-band Multi-Object Spectrograph (KMOS) for Redshift One Spectroscopic Survey (KROSS). This sample covers the redshift range $0.57\le z\le 1.04$, effective radii $0.69 \leq R_e \left[kpc \right] \leq 7.73$,absoluteH-bandmagnitude$-24.46 \leq M_H \leq -18.85$withmedianstellarmass$log\left(M_* \ \left[M_\odot \right]\right)=9.95$andmediantotalstar-formationrate$log\left(SFR_{tot}
\left[M_\odot \ yr^{-1} \right]\right)=1.49$\mathrm{.}Using$^{3D}$BAROLO (Barolo), we extract $H\alpha$ kinematic maps and corresponding Rotation Curves (RCs). The main advantage of Barolo is that it incorporates the beam smearing in the 3D observational space, which provide us with the intrinsic rotation velocity even in the low spatial resolution data. Using Asymmetric Drift Correction (ADC), we have corrected the RCs for the pressure gradient effect, which seems to be a more dominant effect than beam smearing in high-z galaxies. Nearly all objects ($0.1<v\mathrm{/}\sigma <15$) are affected by the pressure gradient, and we noticed that ADC improves the rotation velocity of these systems by $\sim 10-87\mathrm{\%}$. Only a combination of the three techniques (3D-kinematic modelling + 3D-Beamsmearing correction + ADC ) yields the intrinsic RC of an individual galaxy. Further, we present the co-added RCs constructed out of 237 high-quality objects to obtain intrinsic RC shapes out to 6.4 $\times$ disk scale length. We do not see any change in the shape of RCs with respect to the local star-forming disk-type galaxies. In contrast, we do find a significant evolution in the stellar-disk length ($R_D$) of the galaxies. Therefore, we conclude stellar disk evolves over cosmic time while total mass distribution stays constant.