Evaluating Galaxy Dynamical Masses From Kinematics and Jeans Equilibrium
  in Simulations
  We provide prescriptions to evaluate the dynamical mass ($M_{\rm dyn}$) of
galaxies from kinematic measurements of stars or gas using analytic
considerations and the VELA suite of cosmological zoom-in simulations at
$z=1-5$. We find that Jeans or hydrostatic equilibrium is approximately valid
for galaxies of stellar masses above $M_\star \!\sim\! 10^{9.5}M_\odot$ out to
$5$ effective radii ($R_e$). When both measurements of the rotation velocity
$v_\phi$ and of the radial velocity dispersion $\sigma_r$ are available, the
dynamical mass $M_{\rm dyn} \!\simeq\! G^{-1} V_c^2 r$ can be evaluated from
the Jeans equation $V_c^2= v_\phi^2 + \alpha \sigma_r^2$ assuming cylindrical
symmetry and a constant, isotropic $\sigma_r$. For spheroids, $\alpha$ is
inversely proportional to the S\'ersic index $n$ and $\alpha \simeq 2.5$ within
$R_e$ for the simulated galaxies. The prediction for a self-gravitating
exponential disc, $\alpha = 3.36(r/R_e)$, is invalid in the simulations, where
the dominant spheroid causes a weaker gradient from $\alpha \!\simeq\! 1$ at
$R_e$ to 4 at $5R_e$. The correction in $\alpha$ for the stars due to the
gradient in $\sigma_r(r)$ is roughly balanced by the effect of the aspherical
potential, while the effect of anisotropy is negligible. When only the
effective projected velocity dispersion $\sigma_l$ is available, the dynamical
mass can be evaluated as $M_{\rm dyn} = K G^{-1} R_e \sigma_l^2$, where the
virial factor $K$ is derived from $\alpha$ given the inclination and
$v_\phi/\sigma_r$. We find that the standard value $K=5$ is approximately valid
only when averaged over inclinations and for compact and thick discs, as it
ranges from 4.5 to above 10 between edge-on and face-on projections.
