Evaluating Galaxy Dynamical Masses From Kinematics and Jeans Equilibrium in Simulations

Abstract

We provide prescriptions to evaluate the dynamical mass ($M_{\mathrm{dyn}}$) 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 $v_{\ddot{I}}•$ and of the radial velocity dispersion $\ddot{I}{ƒ}_r$ are available, the dynamical mass $M_{\mathrm{dyn}}\simeq G^{-1}{V}_c^{2}r$ can be evaluated from the Jeans equation $V_c^2=v_{\ddot{I}}{•}^2+\hat{I}\pm \ddot{I}{ƒ}_r^2$ assuming cylindrical symmetry and a constant, isotropic $\ddot{I}{ƒ}_r$. For spheroids, $\hat{I}\pm$ is inversely proportional to the Sérsic index $n$ and $\hat{I}\pm \simeq 2.5$ within $R_e$ for the simulated galaxies. The prediction for a self-gravitating exponential disc, $\hat{I}\pm =3.36(r/R_e)$, is invalid in the simulations, where the dominant spheroid causes a weaker gradient from $\hat{I}\pm \simeq 1$ at $R_e$ to 4 at $5R_e$. The correction in $\hat{I}\pm$ for the stars due to the gradient in $\ddot{I}{ƒ}_r(r)$ is roughly balanced by the effect of the aspherical potential, while the effect of anisotropy is negligible. When only the effective projected velocity dispersion $\ddot{I}{ƒ}_l$ is available, the dynamical mass can be evaluated as $M_{\mathrm{dyn}}=K{G}^{-1}{R}_e\ddot{I}{ƒ}_l^2$, where the virial factor $K$ is derived from $\hat{I}\pm$ given the inclination and $v_{\ddot{I}}•/\ddot{I}{ƒ}_r$. 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.

16 pages, 11 figures, published in MNRAS