Annu. Rev. Astron. Astrophys. 1998. 36:
599-654
Copyright © 1998 by . All rights reserved |

**5.4. Radial Profiles of Dark Matter Halos**

Numerical simulations of hierarchical models
(Section 4) show that most
of the mass is drawn into dense clumps by gravity. The dark matter
components of these clumps are identified with extended dark matter
halos around galaxies
(Frenk et al 1985).
*N*-body simulations have
allowed cosmologists to address a straightforward question: What is
the shape of dark matter halos formed by hierarchical clustering?
This question is relevant observationally to the cusps of elliptical
galaxies (e.g.
Faber et al 1997)
and the profiles of clusters of galaxies.

Gunn & Gott (1972),
Fillmore & Goldreich
(1984) presented analytical
models for spherical "secondary" infall of collisionless matter
onto a density peak in an expanding universe. Building on this work,
Hoffman & Shaham
(1985)
proposed that virialized dark matter halos
should have a power-law radial profile
(*r*)
*r*^{-},
where is related to the
logarithmic slope *n* of the power
spectrum on the scales of interest. For *n* < -1, the slope relevant
on galaxy scales in plausible models, the prediction of the secondary
infall model is = 2,
corresponding to flat rotation curves such as
those observed for the baryonic component of galaxies. For
*n* > -1, the
profiles steepen to = (9 +
3*n*) / (4 + *n*), corresponding to falling rotation curves.

The predictions of
Hoffman & Shaham
(1985) have been supported by many *N*-body simulations (e.g.
Quinn et al 1986,
Zurek et al 1988,
Warren et al 1992,
Crone et al 1994,
Zaroubi et al 1996).
However, high-resolution simulations (e.g.
Frenk et al 1988)
showed a steepening of the density profile with radius.
Dubinski & Carlberg
(1991) found that the halos
formed in the CDM model have a logarithmic slope
varying between
1 and 4, in good agreement with the
Hernquist (1990)
model. However,
Navarro et al (1995,
1996)
found instead a better fit to

(14) |

where *r*_{s} is a scale radius. Their most surprising
result was that
this profile is universal for all hierarchical clustering models, regardless
of the halo mass, the initial power spectrum, or cosmological parameters.

Navarro et al's results have been confirmed by
Cole & Lacey
(1996),
Kravtsov et al (1997)
and in higher-resolution simulations by
Tormen et al (1997),
Navarro et al (1997).
The latter paper also shows that
earlier work is, in fact, consistent with Equation 14.
The characteristic density at *r = r _{s}* correlates with
mass in a way that reproduces the trends of the
Hoffman & Shaham
(1985) model. However, in a still higher-resolution simulation,
Fukushige & Makino
(1997)
found that the profile remains steeper than

Why are the central profiles shallower than isothermal ( = 2)? Teyssier et al (1997) showed that when the Fillmore & Goldreich (1984) model is modified for gas, or dark matter with isotropic orbits, the limiting profile is = 1 instead of = 2. Alternatively, Evans & Collett (1997) examined the effect of diffusion driven by gravitational scattering and showed that the collisional Boltzmann equation of stellar dynamics has an attractor solution with = 4/3.

Halo shapes and angular momenta have also been studied with
*N*-body simulations (e.g.
Barnes & Efstathiou
1987,
Dubinski & Carlberg
1991,
Warren et al 1992).
Numerically simulated dark matter halos are found to
be generally triaxial and slowly rotating.