We combine newly measured rotation velocities, velocity dispersions, and stellar masses to construct stellar mass Tully-Fisher relations (M*TFRs) for 544 galaxies with strong emission lines at 0.1<z<1.2 from the All Wavelength Extended Groth Strip International Survey (AEGIS) and the Deep Extragalactic Evolutionary Probe 2 Survey (DEEP2). The conventional M*TFR using only rotation velocity (Vrot) shows large scatter (~1.5 dex in velocity). The scatter and residuals are correlated with morphology in the sense that disturbed, compact, and major merger galaxies have lower velocities for their masses. We construct an M*TFR using the kinematic estimator S_0.5 which is defined as sqrt(0.5Vrot^2 + sigma_g^2) and accounts for disordered or non-circular motions through the gas velocity dispersion (sigma_g). The new M*TFR, termed S_0.5/M*TFR, is remarkably tight over 0.1<z<1.2 with no detectable evolution of its intercept or slope with redshift. The average best fit relation has 0.47 dex scatter in stellar mass, corresponding to ~1.2 magnitudes, assuming a constant mass-to-light ratio. Interestingly, the S_0.5/M*TFR is consistent with the absorption-line based stellar mass Faber-Jackson relation for nearby elliptical galaxies in terms of slope and intercept, which might suggest a physical connection between the two relations.
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