232 Cosmic Structures
The distortion of the CMB spectrum due to the SZE can be used to detect inter-
galactic clouds and to provide another estimate of퐻 0 by combining radio and X-ray
observations to obtain the distance to the cloud. The importance of the SZE sur-
veys is that they are able to detect all clusters above a certain mass limit inde-
pendent of the redshifts of the clusters. The ratio of the magnitude of the SZE to
the CMB does not change with redshift. The effects of re-ionization on the CMB
temperature–polarization power were discussed in Section 8.4.
Structure Sizes and Formation Times. Only clouds exceeding the Jeans mass sta-
bilize and finally attainvirial equilibrium. It is intriguing (but perhaps an accident)
that the Jeans mass just after recombination is about 10^5 푀⊙, the size of globular
clusters! Galaxies have masses of the order of 10^12 푀⊙corresponding to fluctuations
of order훿≃ 10 −^4 as they cross the horizon. We have already made use of this fact to
fix the mass푚휑of the scalar field in Equation (7.44).
The timetable for galaxy and cluster formation is restricted by two important con-
straints. At the very earliest, the Universe has to be large enough to have space for the
first formed structures. If these were galaxies of the present size, their number density
can be used to estimate how early they could have been formed. We leave this for a
problem.
The present density of the structures also sets a limit on the formation time. The
density contrast at formation must have exceeded the mean density at that time, and
since then the contrast has increased with푎^3. Thus, rich clusters, for instance, cannot
have been formed much earlier than at
1 +푧≈ 2. 5 훺−^1 ∕^3. (10.23)It seems that all the present structure was already in place at푧=5. This does not
exclude the fact that the largest clusters are still collapsing today. In a critical universe
structure formation occurs continuously, rich galaxy clusters form only at a redshift of
0.2–0.3, and continue to accrete material even at the present epoch. In that case many
clusters are expected to show evidence for recent merger events and to have irregular
morphologies. There is clear observational evidence that star formation activity drives
gas out of galaxies.
As a result of mass overdensities, the galaxies influenced by the ensuing fluctua-
tions in the gravitational field will acquire peculiar velocities. One can derive a rela-
tion between the mass autocorrelation function and the RMS peculiar velocity (see
reference [3]). If one takes the density contrast to be훿m= 0 .3 for RMS fluctuations of
galaxy number density within a spherical volume radius 30ℎ−^1 Mpc, and if one fur-
ther assumes that all mass fluctuations are uncorrelated at larger separations, then
the acceleration caused by the gravity force of the mass fluctuations would predict
deviations from a homogeneous peculiar velocity field in rough agreement with obser-
vations in our neighborhood. Much larger density contrast would be in marked dis-
agreement with the standard model and with the velocity field observations.