Evaluating Galaxy Dynamical Masses From Kinematics and Jeans Equilibrium in Simulations

TL;DR

This paper develops prescriptions to accurately estimate galaxy dynamical masses from kinematic data using simulations, considering equilibrium assumptions, galaxy morphology, and projection effects.

Contribution

It introduces new analytic methods and correction factors for dynamical mass estimation from kinematic measurements, validated with cosmological simulations across a range of galaxy types and orientations.

Findings

Jeans equilibrium is valid for galaxies with stellar mass > 10^{9.5} M_sun out to 5 R_e.

The dynamical mass can be estimated using v_phi and sigma_r with a correction factor alpha.

The virial factor K varies significantly with inclination and galaxy morphology.

Abstract

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 $v_\phi$ and of the radial velocity dispersion $\sigma_r$ are available, the dynamical mass $M_{\rm dyn} \!\simeq\! G^{-1} V_c^2 r$ can be evaluated from the Jeans equation $V_c^2= v_\phi^2 + \alpha \sigma_r^2$ assuming cylindrical symmetry and a constant, isotropic $\sigma_r$. For spheroids, $\alpha$ is inversely proportional to the S\'ersic index $n$ and $\alpha \simeq 2.5$ within $R_e$ for the simulated galaxies. The prediction for a self-gravitating exponential disc, $\alpha = 3.36(r/R_e)$, is invalid in the simulations, where the dominant spheroid causes a weaker gradient from $\alpha \!\simeq\! 1$ at $R_e$ to 4 at $5R_e$. The correction in $\alpha$ for the stars due to the gradient in $\sigma_r(r)$ is roughly balanced by the effect of the aspherical potential, while the effect of anisotropy is negligible. When only the effective projected velocity dispersion $\sigma_l$ is available, the dynamical mass can be evaluated as $M_{\rm dyn} = K G^{-1} R_e \sigma_l^2$, where the virial factor $K$ is derived from $\alpha$ given the inclination and $v_\phi/\sigma_r$. 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.