Evaluating galaxy dynamical masses from kinematics and jeans equilibrium in simulations. Issue 4 (22nd March 2021) - Kretschmer, Michael; Dekel, Avishai; Freundlich, Jonathan; Lapiner, Sharon; Ceverino, Daniel; Primack, Joel
ABSTRACT: 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_dyn \!\! G^-1 V_c^2 r, can be evaluated from the Jeans equation V_c^2= v_φ ^2 + α σ _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 5 R 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_dyn = K G^-1 R_e σ _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.