and Cosmology

7.5 Non-Linear Structure Evolution
(which is difficult to resolve numerically) is more complicated
than a power law. For large radii, the different
research groups agree on the shape of the profile ∝ r −3 .
Comparison with Observations. The comparison of
these theoretical profiles with an observed density distribution
is by no means simple because the density
profile of dark matter is of course not directly observable.
For instance, in normal spiral galaxies, ρ(r) is
dominated by baryonic matter at small radii. For example,
in the Milky Way, roughly half of the matter within
R 0 consists of stars and gas, so that only little information
is provided on ρ DM in the central region. In general,
it is assumed that galaxies with very low surface brightness
(LSBs) are dominated by dark matter well into the
center. The rotation curves of LSB galaxies are apparently
not in agreement with the expectations from the
NFW model (Fig. 7.15); in particular, they provide no
evidence of a cusp in the central density distribution
(ρ →∞for r → 0).
Part of this discrepancy may perhaps be explained
by the finite angular resolution of the 21-cm line
measurements of the rotation curves; however, the discrepancy
remains if higher-resolution rotation curves
are measured using optical long-slit and integral-field
spectroscopy. As an additional point, the kinematics of
these galaxies may be more complicated, and in some
cases their dynamical center is difficult to determine.
The orbits of stars and gas in these galaxies may show
a more complex behavior than expected from a smooth
density profile. The mass distribution in the (inner parts
of a) dark matter halo is neither smooth nor axially
symmetric, and stars and gas do not move on circular
orbits in a thin plane of symmetry. Instead, simulations
show that the pressure support of the gas, together with
non-circular motions and projection effects systematically
underestimate the rotational velocity in the center
of dark matter halos, thereby creating the impression
of a constant density core. Nevertheless, the observed
rotation curves of LSB galaxies may prove to be a major
problem for the CDM model – hence, this potential
discrepancy must be resolved.
An additional complication is the fact that not only is
baryonic matter present in the inner regions of galaxies
301
Fig. 7.15. The rotation curves in the NFW
density profiles from Fig. 7.13, in units of
the rotational velocity at r 200 . All curves initially
increase, reach a maximum, and then
decrease again; over a fairly wide range
in radius, the rotation curves are approximately
flat. The solid curves are taken
directly from the simulation, while dashed
curves indicate the rotation curves expected
from the NFW profile. The dotted curve in
each panel presents a fit to the low-mass
halo data with the so-called Hernquist profile,
a mass distribution frequently used in
modeling – it fits the rotation curve very
well in the inner part of the halo, but fails
beyond ∼ 0.1R 200 . In these scaled units,
halos of low mass have a relatively higher
maximum rotational velocity