Minimum velocity dispersion in stable stellar disks. Numerical simulations

Abstract

We used N -body dynamical simulations to analyze the conditions for the gravitational stability of a three-dimensional stellar disk in the gravitational field of two rigid spherical components -a bulge and a halo, whose central concentrations and relative masses vary over wide ranges. The number of point masses N in the simulations varied from 40 to 500 thousands and the evolution of the simulated models is followed over 10-20 rotation periods of the outer edge of the disk. The initially unstable disks are heated and, as a rule, reach a quasi-stationary equilibrium with a steady-state radial-velocity dispersion c r over five to eight periods of rotation. The radial behavior of the Toomre stability parameter Q T (r) for the final state of the disk is estimated. Numerical models are used to analyze the dependence of the gravitational stability of the disk on the relative masses of the spherical components, disk thickness, degree of differential rotation, and initial state of the disk. Formal application of existing analytical local criteria for marginal stability of the disk can lead to errors in c r of more than a factor of 1.5. It is suggested that the approximate constancy of Q T ≃ 1.2 ÷ 1.5 for r ≃ (1 ÷ 2) × L (where L is the radial scale of a disk surface density), valid for a wide range of models, can be used to estimate upper limits for the disc mass and density based on the observed distributions of the rotational velocity of the gaseous component and of the stellar velocity dispersion.

On the surface density of dark matter haloes

“…where cT = 3.36Gσ d /κ and parameter QT depends on the radius and lies in the range 1 < QT < 3 (see Khoperskov et al 2003). Thus, if the radial stellar velocity dispersion cr is known, one can assume that the disc is in a marginally stable state, estimate the surface density of the disc independently and then use it in mass modelling.…”

Gravitational stability and mass estimation of stellar disks

“…Extrapolating these estimates, we constrained the total mass of the disks M d = 2πh 2 σ(2h) e 2 and compare these estimates to those based on the photometry and color of stellar populations. We assumed Q(2h) ≈ 1.5 (Khoperskov et al (2003)) and the ratio m = 0.5. To compare the obtained disk masses with the photometric estimates we calculated disk mass-to-light ratios in B band (M/L B ) d .…”

“…As numerical simulations of 2D and 3D disks show, the parameter Q c for a wide range of r lies in the interval 1.2 -2.5 (see e.g. Bottema (1993), Khoperskov et al (2003)). Radial velocity dispersion can be estimated from the observed line-of-sight velocity dispersion measured along the major axis: c obs (r) = (c z ·cos…”

“…Numerical simulations of models of initially weakly unstable 3D disks show the rapid transition of a disk into the marginally stable state, after which the growth of velocity dispersion practically ceases (see e.g. Khoperskov et al (2003)). …”

Long-slit spectral observations and stellar mass-to-light ratio of spiral galaxy UGC11919

“…Numerical simulations show that for the marginal stability of exponential discs with finite thickness the parameter QT ≈ 1.2 -3 is slowly growing to the disc periphery (see f.e. Khoperskov et al 2003). In general case, one have to take into account the presence of the additional dynamically cold component of the galaxy (gas) which makes the disc more unstable (see for example Romeo & Wiegert 2011).…”