Max Planck Institute for Astronomy - Annual Report 2005

74 III. Scientific Work
redshift surveys constructed to date, we have been able
to put strong constraints on the conditional luminosity
function and thus on the average relation between light
and mass. Fig. III.3.1 shows confidence levels on various
quantities computed from the CLF obtained for a typical
�CDM concordance cosmology. The open circles with
errorbars in the upper two panels indicate the 2dF GRS
data used to constrain the models: the galaxy luminosity
function (upper left panel) and the correlation length,
which is a measure of the clustering strength, as function
of luminosity (upper right panel). The shaded areas indicate
the 68 and 95 percent confidence levels obtained
from our model. Note the good agreement with the data,
indicating that the CLF can accurately match the observed
abundances and clustering properties of galaxies in
the 2dFGRS. In other words, we have quantified how
galaxies of different luminosities are distributed within
haloes of different masses.
The lower left-hand panel of Fig. III.3.1 plots the relation
between halo mass M and the total luminosity L, the
expectation value of which follows from the CLF. Note
that the confidence levels are extremely tight, especially
for the more massive haloes: apparently there is not
much freedom in how one can distribute light over haloes
of different masses while remaining consistent with the
data. Note that the average relation between light and
mass reveals a dramatic break at around M � 7 � 10 10
h –1 M � . This characteristic scale is not an artefact of
the model, but is actually required by the data. It tells us
that this scale is somehow picked out by the physics of
galaxy formation.
The lower right-hand panel of Fig. III.3.1 plots the
corresponding mass-to-light ratios as function of halo
mass. The characteristic break in the average relation
between light and mass now translates into a pronounced
minimum in mass-to-light ratios. The characteristic scale
therefore marks the mass scale at which galaxy formation
is most efficient, i.e., at which there is the largest amount
of light per unit mass. For less massive haloes, the massto-light
ratio increases drastically with decreasing halo
mass. It indicates that galaxy formation needs to become
extremely inefficient in haloes with M � 5 � 10 10 h –1
M � . One physical explanation that has been proposed for
this decreased efficiency in small mass halos is feedback
from supernovae. These stellar explosions produce enormous
amounts of energy, which can expel large fractions
of the baryonic mass from low mass haloes, which have
relatively low escape velocities. The results shown here
indicate how the efficiency of this process needs to scale
with halo mass, if the model is to successfully reproduce
the observed abundances and clustering properties of
galaxies. At the massive end, the average mass-to-light
ratio also increases. Numerical simulations of galaxy
formation have long been unable to reproduce such a
trend, which has become known as the overcooling problem.
Currently, many research groups are investigating
the role of feedback from Active Galactic Nuclei (AGN)
in preventing gas from cooling in massive haloes. Once
again, the statistical results obtained from our CLF analysis
put tight constraints on how the efficiency of this
so-called AGN feedback has to scale with halo mass.
Cosmological Parameters
Two of the most important cosmological parameters
are the average matter density, and the normalization of
the strength of the initial density perturbations. These
are typically parameterized via the matter density parameter
and the so-called power-spectrum normalization
parameter � 8 . Typically, increasing either of these parameters
will result in a larger abundance of massive
haloes and a stronger overall clustering strength of dark
matter haloes. A different cosmology therefore requires
a different galaxy-dark matter relationship (i.e., a different
CLF) to be consistent with the observed abundance
and clustering properties of the galaxies. For example,
if one increases the normalization of the matter power
spectrum, the dark matter haloes becomes more strongly
clustered. In order to match the observed clustering
strength, galaxies therefore have to be less strongly
biased. This can be accomplished by distributing galaxies
over lower mass haloes, which are less strongly
clustered than massive haloes. However, if one removes
more and more galaxies from cluster sized haloes to
Fig. III.3.2: Constraining cosmological parameters: The 68 and
95 percent confidence levels on the matter density � m and the
power spectrum normalization parameter � 8 obtained from
the cosmic microwave background by the WMAP satellite (red
contours) and from the combination of WMAP data and our
CLF analysis of the large scale structure of the Universe (blue
contours).
� 8
1.2
1
0.8
0.6
� m = 0.25 � 0.05
� 8 = 0.78 � 0.06
WMAP
WMAP + CLF
0.1 0.2 0.3 0.4 0.5 0.6
� m