Prevalence and properties of dark matter in elliptical galaxies

Given the recently deduced relationship between X-ray temperatures and stellar velocity dispersions (the T-sigma relation) in an optically complete sample of elliptical galaxies (see recent work of Davis & White), we demonstrate that L > L-* elliptical galaxies contain substantial amounts of dark matter in general. We present constraints on the dark matter scale length and on the dark-to-luminous mass ratio within the optical half-light radius and within the entire galaxy. For example, we find that minimum values of dark matter core radii scale as r(dm) > 4(L-V/3L(*))(3/4) h(80)(-1) kpc and that the minimum dark matter mass fraction is greater than or similar to 20% within one optical effective radius r(e) and is greater than or similar to 39%-85% within 6r(e), depending on the stellar density profile and observed value of beta(spec). We also confirm the prediction of Davis & White that the dark matter is characterized by velocity dispersions that are greater than those of the luminous stars: sigma(dm)(2) approximate to 1.4-2 sigma(*)(2). The T-sigma relation implies a nearly constant mass-to-light ratio within six half-light radii: M/L-V approximate to 25 h(80) M./L-V.. This conflicts with the simplest extension of cold dark matter theories of large-scale structure formation to galactic scales; we consider several modifications that can better account for the observed T-sigma relation.