The observed clustering of galaxies is expected to evolve with time,
as structure continues to grow due to gravity. The exact evolution
depends on cosmological parameters such as
and
matter.
Larger values of
, for example, lead
to larger
voids and higher density contrasts between overdense and underdense
regions. By measuring the clustering of galaxies at higher redshift,
one can break degeneracies that exist between the galaxy bias and
cosmological parameters that are constrained by low redshift
clustering measurements. It is therefore useful to determine the
clustering of galaxies as a function of cosmic epoch, not only to
further constrain cosmological parameters but also galaxy evolution.
One might expect the galaxy clustering amplitude r0 to
increase
over time, as overdense regions become more overdense as galaxies move
towards groups and clusters due to gravity. However, the exact
evolution of the clustering of galaxies depends not only on gravity,
but also on the expansion history of the Universe and therefore
cosmological parameters such as
. Additionally,
over time
new galaxies form while existing galaxies grow in both mass and
luminosity. Therefore, the expected changes of galaxy clustering as a
function of redshift depend both on relatively well-known cosmological
parameters and more unknown galaxy formation and evolution physics
which likely depends on gas accretion, star formation, and feedback
processes, as well as mergers.
For a given cosmological model, one can predict how the clustering of
dark matter should evolve with time using cosmological N-body
simulations. For a
CDM Universe,
r0 for dark matter particles is
expected to increase from ~ 0.8 h-1 Mpc at z =
3 to ~ 5 h-1 Mpc at z = 0
(Weinberg et
al. 2004).
However, according to hierarchical
structure formation theories, at high redshifts the first galaxies to
form will be the first structures to collapse, which will be biased
tracers of the mass. The galaxy bias is expected to be a strong
function of redshift, initially >1 at high redshift and approaching
unity over time. Therefore, r0 for galaxies may be a
much weaker
function of time than it is for dark matter, as the same galaxies are
not observed as a function of redshift, and over time new galaxies
form in less biased locations in the Universe.
The projected angular and three dimensional correlation functions of galaxies have been observed to z ~ 5. Star-forming Lyman break galaxies at z ~ 3-5 are found to have r0 ~ 4-6 h-1 Mpc, with a bias relative to dark matter of ~ 3-4 (Ouchi et al. 2004, Adelberger et al. 2005). Brighter Lyman break galaxies are found to cluster more strongly than fainter Lyman break galaxies. The correlation length, r0, is found to be roughly constant between z = 5 and z = 3, implying that the bias is increasing at earlier cosmic epoch. Spectroscopic galaxy surveys at z > 2 are currently limited to samples of at most a few thousand galaxies, so most clustering measurements are angular at these epochs. In one such study by Wake et al. (2011), photometric redshifts of tens of thousands of galaxies at 1 < z < 2 are used to measure the angular clustering as a function of stellar mass. They find a strong dependence of clustering amplitude on stellar mass in each of three redshift intervals in this range.
At z ~ 1 larger spectroscopic galaxy samples exist, and three
dimensional two-point clustering analyses have been performed as a
function of luminosity, color, stellar mass, and spectral type. The
same general clustering trends with galaxy property that are observed
at z ~ 0 are also seen at z ~ 1, in that galaxies that are
brighter, redder, early spectral type, and/or more massive are more
clustered. The clustering scale length of red galaxies is found to be
~ 5-6 h-1 Mpc while for blue galaxies it is ~ 3.5-4.5
h-1 Mpc, depending on luminosity
(Meneux et al. 2006,
Coil et al. 2008).
At a given luminosity the observed correlation length is only ~ 15% smaller
at z = 1 than z = 0, indicating that unlike for dark
matter the galaxy r0 is roughly constant over
time. These results are consistent with predictions from
CDM simulations.
The measured values of r0 at z ~ 1 imply that are more biased at z = 1 than at z = 0. Within the DEEP2 sample, the bias measured on scales of ~ 1-10 h-1 Mpc varies from ~ 1.25-1.55, with brighter galaxy samples being more biased tracers of the dark matter (Coil et al. 2006). These results are consistent with the idea that galaxies formed early on in the most overdense regions of space, which are biased.
As in the nearby Universe, the clustering amplitude is a stronger
function of color than of luminosity at z ~ 1. Additionally, the
color-density relation is found to already be in place at z = 1, in
that the relative bias of red to blue galaxies is as high at z =
1 as at z = 0.1
(Coil et al. 2008).
This implies that the color-density
relation is not due to cluster-specific physics, as most galaxies at
z = 1 in field spectroscopic surveys are not in clusters. Therefore
it must be physical processes at play in galaxy groups that initially
set the color and morphology-density relations. Red galaxies show
larger "Fingers of God" in
(rp,
) measurements
than blue galaxies
do, again showing that red galaxies at z = 1 lie preferentially in
virialized, more massive overdensities compared to blue galaxies.
Both red and blue galaxies show coherent infall on large scales.