Global stability and the mass-to-light ratio of galactic disks

Abstract

We examine the global stability of an exponential stellar disk embedded in a dark matter halo and constrain the mass-to-light ratio of observed disks in the I-band, Y_I. Assuming only that the radial surface density distribution of disks is exponential, we derive an analytic upper limit: Y_I <~ 2.4h, for a Hubble constant of 100h~\kms\mpc^{-1}. Using N-body simulations we derive a stability criterion significantly different from that of previous authors. Using this criterion we argue that, almost independent of the concentration of the halo, Y_I <~ 1.9h. We discuss this result in relation to other independent determinations of Y_I, its limitations and its implications for theories of disk formation and barred galaxies.