and Cosmology

7.5 Non-Linear Structure Evolution
clusters whose evolutionary history can be followed.
The spatial resolution of the simulation is ∼ 5h −1 kpc,
yielding a linear dynamic range of ∼ 10 5 . The resulting
mass distribution at z=0 is displayed in Fig. 7.12
in slices of 15h −1 Mpc thickness each, where the linear
scale changes by a factor of four from one slice to the
next. The images zoom in to a region around a massive
cluster that becomes visible with its rich substructure
in the uppermost slice, as well as filaments of the matter
distribution, at the intersections of which massive
halos form. The mass distribution in the Millennium
simulation is of great interest for numerous different investigations.
We will discuss some of its results further
in Chap. 9.
297
Fig. 7.11. The Hubble Volume Simulations: simulated is a box
of volume (3000h −1 Mpc) 3 , containing 10 9 particles, where
a ΛCDM model with Ω m = 0.3 andΩ Λ = 0.7 was chosen.
Displayed is the projection of the density distribution
of a 30h −1 Mpc thick slice of the cube. Simulations like this
can be used to analyze the statistical properties of the mass
distribution in the Universe on large scales. The sector in
the lower left corner represents roughly the size of the CfA
redshift survey (see Fig. 7.2)
Analysis of Numerical Results. The analysis of the
numerical results is nearly as intricate as the simulation
itself because the positions and velocities of ∼ 10 9
particles alone do not provide any new insights. The
output of the simulation needs to be analyzed with respect
to specific questions. Obviously, the (non-linear)
power spectrum P(k, z) of the matter distribution can be
computed from the spatial distribution of particles; the
corresponding results have led to the construction of the
analytic fit formulae presented in Fig. 7.6. Furthermore,
one can search for voids in the resulting particle distribution,
which can then be compared to the observed
abundance and typical size of voids.
One of the main applications is the search for collapsed
mass concentrations (i.e., dark matter halos), and
their number density can be compared to predictions
from the Press–Schechter model and to observations.
From this, it has been found that the Press–Schechter
mass function represents the basic aspects of the mass
spectrum astonishingly well, but even more accurate
formulae for the mass spectrum of halos have been constructed
from the simulations (see Fig. 7.9). However,
the identification of a halo and the determination of its
mass from the positions and velocities of the particles
is by no means trivial, and various methods for this
are applied. For instance, we can concentrate on spatial
overdensities of particles and define a halo as a spherical
region, within which the average density is just
200 times the critical density – this definition of a halo
is suggested by the spherical collapse model. Alternatively,
those particles which are gravitationally bound,
as can be obtained from the particle velocities, can be
assigned to a halo.
The direct link between the results from dark matter
simulations and the observed properties of the Universe
requires an understanding of the relation between
dark matter and luminous matter. Dark matter halos in
simulations cannot be compared to the observed galaxy
distribution without further assumptions, e.g., on
the mass-to-light ratio. We will return to these aspects
later.