Evaluating Galaxy Dynamical Masses From Kinematics and Jeans Equilibrium in Simulations

Michael Kretschmer; Avishai Dekel; Jonathan Freundlich; Sharon Lapiner; Daniel Ceverino; Joel Primack

doi:10.1093/mnras/stab833

paper

Evaluating Galaxy Dynamical Masses From Kinematics and Jeans Equilibrium in Simulations

arXiv:2010.04629 · doi:10.1093/mnras/stab833

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 $M_{⋆} \sim 1 0^{9.5} M_{⊙}$ 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 $R_{e}$ 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 $R_{e}$ to 4 at $5 R_{e}$ . 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 $M_{dyn} = K G^{- 1} R_{e} σ_{l}^{2}$ , 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.

arXiv comment16 pages, 11 figures, published in MNRAS

Evaluating Galaxy Dynamical Masses From Kinematics and Jeans Equilibrium in Simulations

Abstract

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