The MOSDEF Survey: Dynamical and Baryonic Masses and Kinematic Structures of Star-Forming Galaxies at $1.4 \leq z \leq 2.6$

We present H$\alpha$ gas kinematics for 178 star-forming galaxies at z~2 from the MOSFIRE Deep Evolution Field survey. We have developed models to interpret the kinematic measurements from fixed-angle multi-object spectroscopy, using structural parameters derived from CANDELS HST/F160W imaging. For 35 galaxies we measure resolved rotation with a median $(V/\sigma_{V,0})_{R_E}=2.1$. We derive dynamical masses from the kinematics and sizes and compare them to baryonic masses, with gas masses estimated from dust-corrected H$\alpha$ star formation rates (SFRs) and the Kennicutt-Schmidt relation. When assuming that galaxies with and without observed rotation have the same median $(V/\sigma_{V,0})_{R_E}$, we find good agreement between the dynamical and baryonic masses, with a scatter of $\sigma_{RMS}=0.34$dex and a median offset of $\Delta\log_{10}M=0.04$dex. This comparison implies a low dark matter fraction (8% within an effective radius) for a Chabrier initial mass function (IMF), and disfavors a Salpeter IMF. Moreover, the requirement that $M_{dyn}/M_{baryon}$ should be independent of inclination yields a median value of $(V/\sigma_{V,0})_{R_E}=2.1$ for galaxies without observed rotation. If instead we treat the galaxies without detected rotation as early-type galaxies, the masses are also in reasonable agreement ($\Delta\log_{10}M=-0.07$dex, $\sigma_{RMS}=0.37$dex). The inclusion of gas masses is critical in this comparison; if gas masses are excluded there is an increasing trend of $M_{dyn}/M_{*}$ with higher specific SFR (SSFR). Furthermore, we find indications that $V/\sigma$ decreases with increasing H$\alpha$ SSFR for our full sample, which may reflect disk settling. We also study the Tully-Fisher relation and find that at fixed stellar mass $S_{0.5}=(0.5V_{2.2}^2+\sigma_{V,0}^2)^{1/2}$ was higher at earlier times. At fixed baryonic mass, we observe the opposite trend. [abridged]