The presence of a hot teneous and fully ionised gas (Te = 108 K, ne = 103 m-3) in the intracluster medium was revealed with the first X-ray measurements toward clusters of galaxies. This gas which fell in the deep gravitational well of clusters of galaxies and thus heated up to very high temperature can only cool down via the free-free emission process. Only in the very center of clusters is the density of the electrons and nuclei enough for the cooling timescale to be less than the age of the Universe. Another cooling process exists via inverse Compton scattering on the (cold) cosmic microwave background.
This secondary cooling is called the Sunyaev-Zel'dovich (hereafter SZ) effect [1]. This effect preserves the number of CMB photons. If it were a pure scattering effect without energy change the CMB would not be globally affected. But there is a net energy gain by the CMB photons in the direction of clusters. The CMB is thus spectrally distorted. The adimensional Comptonisation parameter y measures the SZ distortion:
where Te, me, Ne =
nedl, and ne
are resp. the electronic temperature, mass, column density and density. The
integral is taken along the line of sight through the cluster.
T
is the Thomson cross-section. The second (and usually much weaker) SZ effect
called kinetic effect is due to the peculiar cluster velocity
vc and is measured by:
Figure 1 shows the universal distortion spectrum produced by the thermal (dots) and kinetic (dashes) SZ effects.
|
Figure 1. Differential CMB brightness change as a function of wavelength, towards a cluster with y = 10-4 (dotted curve) and b = -10-4 (dashed curve). The lower panel gives the atmospheric transmission (between 0 and 1) for 3 mm of precipitable water and the two Diabolo instrument bandpasses. The upper solid curve gives the colour of the atmospheric noise. |
The SZ effect is thus a radio, millimetre and submillimetre phenomenon. The
thermal SZ effect has a very specific spectral signature (always negative for
1.4 mm) whereas the kinetic SZ
effect is undistinguishable
from the spectrum of the CMB primordial anisotropies. Both SZ effects
are brightness
effects which are spectrally independent of redshift in the observer's frame,
contrary to X-ray emission which shows the usual (1 +
z)-4 brightness
dimming. A well-resolved cluster will show the same SZ effect whether it is
at low or high redshift.
The energy density (which is the focus of this conference) of the CMB is enhanced towards clusters by the following amount:
The opacity 
=
T
Ne and comptonisation parameter y
are of the order of a few 10-2 and 10-4 resp. in
the richest
clusters which therefore make the SZ effect a relatively small and
linear distortion.
It has recently been acknowledged that one cannot neglect relativistic corrections to the (non-relativistic) universal spectral template, shown in Fig. 1, and independent on redshift. A complete review of the SZ effect is enhanced clearly beyond this presentation. An exhaustive recent review was made by Birkinshaw [2].