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

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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, Yᵢ. Assuming only that the radial surface density distribution of disks is exponential, we derive an analytic upper limit: Yᵢ < 2.4h, for a Hubble constant of 100h ⁻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, Yᵢ < 1.9h. We discuss this result in relation to other independent determinations of Yᵢ, its limitations and its implications for theories of disk formation and barred galaxies.