Tully-Fisher Relation of Late-type Galaxies at $0.6 \leq z \leq 2.5$

We present a study of the stellar and baryonic Tully-Fisher relation within the redshift range of $0.6 \leq z \leq 2.5$ utilizing observations of \sfgs. This dataset, as explored in \citet{GS23}, comprises of disk-like galaxies spanning a stellar mass range of $8.89 \leq \log(M_{star} \ [\mathrm{M_\odot}]) \leq 11.5$, baryonic mass range of $9.0 \leq \log(M_{bar} [\mathrm{M_\odot}]) \leq 11.5$, and circular velocity range of $1.65 \leq \log(V_c \ [{\rm km/s}]) \leq 2.85$. Stellar masses of these objects are estimated using spectral energy distribution fitting techniques, while gas masses are determined via scaling relations. Circular velocities are directly derived from the Rotation Curves (RCs), after meticulously correcting for beam smearing and pressure support. Our analysis confirms that our sample adheres to the fundamental mass-size relations of galaxies and reflects the evolution of velocity dispersion in galaxies, in line with previous findings. This reaffirms the reliability of our photometric and kinematic parameters (i.e., $M_{star}$ and $V_c$), thereby enabling a comprehensive examination of the Tully-Fisher relation. To attain robust results, we employed a novel orthogonal likelihood fitting technique designed to minimize intrinsic scatter around the best-fit line, as required at \hz. For the STFR, we obtained a slope of $\alpha=3.03\pm 0.25$, an offset of $\beta = 3.34\pm 0.53$, and an intrinsic scatter of $\zeta_{int}=0.08$ dex. Correspondingly, the BTFR yielded $\alpha=3.21\pm 0.28$, $\beta=3.16\pm 0.61$, and $\zeta_{int}=0.09$ dex. Our findings suggest a subtle deviation in the stellar and baryonic Tully-Fisher relation with respect to local studies, which is most-likely due to the evolutionary processes governing disk formation.