Elements of kinematical and dynamical modeling of elliptical galaxies are
presented.
In projection, NFW models resemble Sérsic models, but with a very narrow
range of shapes (m = 3±1).
The total density profile of ellipticals cannot be NFW-like because
the predicted local M/L and aperture velocity dispersion within an
effective radius (Re) are much lower than
observed. Stars must then dominate ellipticals
out to a few Re.
Fitting an NFW model to the total density profile of Sérsic+NFW (stars+dark
matter [DM]) ellipticals results in very high concentration parameters, as
found
by X-ray observers.
Kinematical modeling of ellipticals assuming an isotropic NFW DM model
underestimates M/L at the virial radius by a factor of 1.6 to 2.4, because
dissipationless ΛCDM halos have slightly different density profiles
and slightly radial velocity anisotropy.
In N-body+gas simulations of ellipticals as merger remnants of
spirals embedded in DM halos,
the slope of the DM density profile is steeper
when the initial spiral galaxies are gas-rich.
The Hansen & Moore (2006)
relation between anisotropy and the slope of the density profile breaks
down for gas and DM, but the stars follow an analogous relation with
slightly less radial anisotropies for a given density slope.
Using kurtosis (h4) to infer anisotropy in ellipticals is dangerous, as
h4 is also sensitive to small levels of rotation.
The stationary Jeans equation provides accurate masses out to 8Re.
The discrepancy between the modeling of Romanowsky et al. (2003),
indicating a dearth of DM in ellipticals,
and the simulations analyzed by Dekel et al. (2005), which
match the
spectroscopic observations of ellipticals,
is partly due to
radial anisotropy and to observing oblate ellipticals face-on.
However,
one of the 15 solutions
to the orbit modeling of Romanowsky et al. is found to have an amount and
concentration of
DM
consistent with
ΛCDM predictions.