Using observations made with MOSFIRE on Keck I as part of the ZFIRE survey , we present the stellar mass Tully-Fisher relation at 2.0 < z < 2.5 .
The sample was drawn from a stellar mass limited , K _ { s } - band selected catalog from ZFOURGE over the CANDELS area in the COSMOS field .
We model the shear of the H \alpha emission line to derive rotational velocities at 2.2 \times the scale radius of an exponential disk ( V _ { 2.2 } ) .
We correct for the blurring effect of a two-dimensional PSF and the fact that the MOSFIRE PSF is better approximated by a Moffat than a Gaussian , which is more typically assumed for natural seeing .
We find for the Tully-Fisher relation at 2.0 < z < 2.5 that \mathrm { log } V _ { 2.2 } = ( 2.18 \pm 0.051 ) + ( 0.193 \pm 0.108 ) ( \mathrm { log } M / M _ { \odot } -10 ) and infer an evolution of the zeropoint of \Delta \mathrm { M } / \mathrm { M _ { \odot } } = -0.25 \pm 0.16 dex or \Delta \mathrm { M } / \mathrm { M _ { \odot } } = -0.39 \pm 0.21 dex compared to z = 0 when adopting a fixed slope of 0.29 or 1/4.5 , respectively .
We also derive the alternative kinematic estimator S _ { 0.5 } , with a best-fit relation \mathrm { log } S _ { 0.5 } = ( 2.06 \pm 0.032 ) + ( 0.211 \pm 0.086 ) ( \mathrm { log } M / M _ { \odot } -10 ) , and infer an evolution of \Delta \mathrm { M } / \mathrm { M _ { \odot } } = -0.45 \pm 0.13 dex compared to z < 1.2 if we adopt a fixed slope .
We investigate and review various systematics , ranging from PSF effects , projection effects , systematics related to stellar mass derivation , selection biases and slope .
We find that discrepancies between the various literature values are reduced when taking these into account .
Our observations correspond well with the gradual evolution predicted by semi-analytic models .