and Cosmology

7. Cosmology II: Inhomogeneities in the Universe
298
Fig. 7.12. Distribution of
matter in slices of thickness
15h −1 Mpc each, computed
in the Millennium
simulation. This simulation
took about a month,
running on 512 CPU processors.
The output of the
simulation, i.e., the position
and velocities of all
10 10 particles at 64 times
steps, has a data volume of
∼ 27 TB. The region shown
in the two lower slices is
larger than the simulated
box which has a sidelength
of 500h −1 Mpc; nevertheless,
the matter distribution
shows no periodicity in the
figure as the slice was cut at
a skewed angle to the box
axes
7.5.4 Profile of Dark Matter Halos
As already mentioned above, dark matter halos can be
identified in mass distributions generated by numerical
simulations. Besides the abundance of halos as a function
of their mass and redshift, their radial mass profile
can also be analyzed if individual halos are represented
by a sufficient number of dark matter particles. The
ability to obtain halo mass profiles depends on the mass
resolution of a simulation. A surprising result has been
obtained from these studies, namely that halos seem to
show a universal density profile. We will briefly discuss
this result in the following.
If we define a halo as described above, i.e., as a spherical
region within which the average density is ∼ 200
times the critical density at the respective redshift, the
mass M of the halo is related to its (virial) radius r 200 by
M = 4π 3 r3 200 200 ρ cr(z).
Since the critical density at redshift z is specified by
ρ cr (z) = 3H 2 (z)/(8πG), we can write this as
M = 100r3 200 H2 (z)
, (7.37)
G
so that at each redshift, a unique relation exists between
the halo mass and its radius. We can also define the
virial velocity V 200 of a halo as the circular velocity at
the virial radius,
V200 2 = GM . (7.38)
r 200