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Using N-body experiments we investigate the global stability of a series of models designed to match the observed photometric and kinematic properties of disc galaxies. The models, therefore, have an exponential surface density profile and rotation curves which are flat at large radii. We find a simple delineator of stability to bar-like modes for a cold disc: | ₌/ (MDG) ^1/2=1. 1, \, where\, ₌| is the maximum rotational velocity, |^-1| is the scale length of the exponential disc and MD is the total disc mass. This is to be compared to a self-gravitating exponential disc for which | ₘ/ (MDG) ^1/2=0. 63|, thus a hot ‘halo’ component is required to increase this ratio in a cool disc and provide stability to bar formation. This criterion has been found to apply independent of the concentration of the halo (bulge) component. In addition, the results appear to be insensitive to a substantial increase in random motions in the central part of the disc and also to changes in the shape of the rotation curve or the adopted surface density profile. The results from the models are compared with available photometric and kinematic data of disc galaxies and are used to set limits on the mass-to-light ratio of the disc component. In particular we find that the cool disc component of unbarred Sc galaxies must have | (M/L) D\, \, 1. 5\, h| (where h is Hubble's constant in units of |100\, km\, s^-1\, Mpc^-1|) compared with a total mass-to-light ratio interior to the Holmberg radius of ≈ 8 h, derived from their rotation curves. Normalizing the stellar population models of Larson & Tinsley (1978) and Tinsley (1981) to the results for Sc galaxies and data in the solar neighbourhood, we find that the later- type galaxies (Sd–Sm) may have a total H I mass comparable to or exceeding the mass in disc stars. The population models also predict lower masses for the disc components of early-type disc galaxies than those deduced from their rotation curves suggesting that they possess enough dark matter to stabilize their discs.
Efstathiou et al. (Sun,) studied this question.