Evaluating galaxy dynamical masses from kinematics and jeans equilibrium in simulations

We provide prescriptions to evaluate the dynamical mass (M_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_⋆ ∼ 10^9.5 M_⊙ out to 5 effective radii (R_e). When both measurements of the rotation velocity v_ϕ and of the radial velocity dispersion σ_r 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 σ_r. For spheroids, α is inversely proportional to the Sérsic index n and α ≃ 2.5 within R_{e, stars} for the simulated galaxies. The prediction for a self-gravitating exponential disc, α = 3.36(r/R_e), is invalid in the simulations, where the dominant spheroid causes a weaker gradient from α ≃ 1 at R_{e, gas} to 4 at 5R_{e, gas}. The correction in α for the stars due to the gradient in σ_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 σ_l 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 v_ϕ/σ_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.