Elliptical galaxies are quite compact objects which mostly do not rotate so their mass cannot be derived from rotation curves. The total dynamical mass is then the virial mass as derived from the velocity dispersions of stars and the anisotropies of their orbits. However, to disentangle the total mass profile into its dark and its stellar components is not straightforward, because the dynamical mass decomposition of dispersions is not unique. The luminous matter in the form of visible stars is a crucial quantity, indispensable to infer the dark component. When available one also makes use of strong and weak lensing data, and of the X-ray properties of the emitting hot gas. The gravity is then balanced by pressure gradients as given by Jeans' Equation.
Inside the half light radius Re the contribution of the dark matter halo to the central velocity dispersion is often very small, < 100 km s-1, so that the dark matter profile is intrinsically unresolvable. The outer mass profile is compatible with NFW, Eq.(7), and with Burkert, Eq.(9), as well. Important information on the mass distribution can be obtained from the Fundamental Plane, Eq. (6). which yields the coefficients a = 1.8, b = 0.8. Note that this is in some tension with the Virial Theorem, perhaps due to variations in the central dispersions, σ0, of the stellar populations.
O. Tiret & al.  concluded from a study of 23 giant elliptical galaxies with central velocity dispersions ≥ 330 km s-1, that the mass within 5 - 10 kpc is dominated by the stars, not by DM. On the average the dark matter component contributes less than 5% to the total velocity dispersions.
The ELIXR survey is a volume-limited (≤ 110 Mpc) study by P. J. Humphrey & al. , of optically selected, isolated, L* elliptical galaxies in particular the NGC 1521, for which X-ray data from Chandra and XMM exist. The isolation condition selects the appropriate galaxy halo and reduces the influence of a possible group-scale or cluster-scale halo.
Most of the baryons are in a morphologically relaxed hot gas halo detectable out to ≈ 200 kpc, that is well described by hydrostatic models. The baryons and the dark matter conspire to produce a total mass density profile that can be well-approximated by a power law, ρtot ∝ r-α over a wide range (as has been noted before, see references in [35, 36]).
The fitting method involves solving the equation of hydrostatic equilibrium to compute temperature and density profile models, given parametrized mass and entropy profiles. The models are then projected onto the sky and fitted to the projected temperature and density profiles. A fit ignoring DM was poor, but inclusion of DM improved the fit highly significantly: DM was required at 8.2 σ. We show this fit in Fig. 9. In several studies [35, 37], for most of the radii the dark matter contribution is very small although statistically significant.
Figure 9. Radial mass profile of the elliptical galaxy NGC 1521 from a model calculation (not fitted to the measured points shown). The solid black line indicates the total enclosed mass (1 σ errors in grey), the dashed red line is the stellar mass, the dotted blue line is the dark matter, and the dash-dot magenta line is the gas mass contribution. From P. J. Humphrey & al. .