Prevalence and Properties of Dark Matter in Elliptical Galaxies

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Abstract
Given the recently deduced relationship between X-ray temperatures and stellar velocity dispersions (the T-σ 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 rdm>4(LV/3L*)3/4 h-180 kpc and that the minimum dark matter mass fraction is 20% within one optical effective radius re and is 39%-85% within 6re, depending on the stellar density profile and observed value of βspec. 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: σ2dm≈1.4-2σ2*. The T-σ relation implies a nearly constant mass-to-light ratio within six half-light radii: M/LV≈25 h80 M☉/LV☉. 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-σ relation.
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