学术文献库

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 $v_ϕ$ and of the radial velocity dispersion $σ_r$ are available, the dynamical mass $M_{\rm dyn} \!\simeq\! G^{-1} V_c^2 r$ can be evaluated from the Jeans equation $V_c^2= v_ϕ^2 + ασ_r^2$ assuming cylindrical symmetry and a constant, isotropic $σ_r$. For spheroids, $α$ is inversely proportional to the Sérsic index $n$ and $α\simeq 2.5$ within $R_e$ 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 $α\!\simeq\! 1$ at $R_e$ to 4 at $5R_e$. 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 $M_{\rm dyn} = K G^{-1} R_e σ_l^2$, 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.