A Numerical Study of the Stability of Flattened Galaxies: or, can Cold Galaxies Survive?

To study the stability of flattened galaxies, we have followed the evolution of simulated galaxies containing 150 to 500 mass points. Models which begin with characteristics similar to the disk of our Galaxy (except for increased velocity dispersion and thickness to assure local stability) were found to be rapidly and grossly unstable to barlike modes. These modes cause an increase in random kinetic energy, with approximate stability being reached when the ratio of kinetic energy of rotation to total gravitational energy, designated t, is reduced to the value of 0.14 + 0.02. Parameter studies indicate that the result probably is not due to inadequacies of the numerical N-body simulation method. A survey of the literature shows that a critical value for limiting stability t 0.14 has been found by a variety of methods. Models with added spherical (halo) component are more stable. it appears that halo-to-disk mass ratios of 1 to 2 , and an initial value of t 0.14 + 0.03, are required for stability. if our Galaxy (and other spirals) do not have a substantial unobserved mass in a hot disk component, then apparently the halo (spherical) mass interior to the disk must be comparable to the disk mass. Thus normalized, the halo masses of our Galaxy and of other spiral galaxies exterior to the observed disks may be extremely large. Subject headings: galactic structure - stellar dynamics