Evaluating galaxy dynamical masses from kinematics and jeans equilibrium in simulations

We provide prescriptions to evaluate the dynamical mass (Mdyn) 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⋆ ∼109.5 Mpdbl out to 5 effective radii (Re). When both measurements of the rotation velocity vφ and of the radial velocity dispersion σr are available, the dynamical mass $M-{\rm dyn} \!\simeq \! G{-1} V-{\rm c}2 r$, can be evaluated from the Jeans equation $V-{\rm c}2= v_\phi 2 + \alpha \sigma -{\rm r}2$ assuming cylindrical symmetry and a constant, isotropic σr. For spheroids, α is inversely proportional to the Sérsic index n and α 2.5 within Re, stars for the simulated galaxies. The prediction for a self-gravitating exponential disc, α = 3.36(r/Re), is invalid in the simulations, where the dominant spheroid causes a weaker gradient from α 1 at Re, gas to 4 at 5Re, gas. The correction in α for the stars due to the gradient in σr(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 σl is available, the dynamical mass can be evaluated as $M-{\rm dyn} = K G{-1} R-{\rm e} \sigma -{\rm l}2$, where the virial factor K is derived from α, given the inclination and vφ/σr. 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.