1999ApJ...518...50L

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 r_dm>4(L_V/3L_*)^3/4 h^–1₈₀ kpc and that the minimum dark matter mass fraction is ≳20% within one optical effective radius r_e and is ≳39%-85% within 6r_e_, depending on the stellar density profile and observed value of β_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: σ²_dm~1.4-2σ²_*. The T-σ relation implies a nearly constant mass-to-light ratio within six half-light radii: M/L_V~25 h₈₀ 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-σ relation.