2.1. Astrophysical and Cosmological objectives
Witness the 3K remoteness
With several clusters firmly detected at a redshift up to about 0.5, the 3 K background cannot have an origin in the local Universe. There are not so many direct probes of the presence of the CMB at high redshift.
Measure the hot cluster gas distribution
The SZ effect directly measures the hot electron pressure along the line of sight. If one assumes a constant gas temperature, an electronic density following a King profile (with r the radius from the cluster center, and a the core radius) is often assumed:
and will produce a SZ angular distribution
The measurements are therefore linearly linked to the density of
baryonic matter.
Total mass of gas
The quantity that is directly measured in a given experiment
is really the brightness integrated over the instrument beam, something that
can be loosely defined as Y =
where the redshift function f depends on the cosmological parameters
(through the angular-diameter redshift dependence). The following table
(computed
for a critical standard model without cosmological constant) shows a subtle
dependence of the measured SZ effect with redshift.
Total gravitational mass
Through the hydrostatic equation and from the gas pressure profile, one can
deduce the total cluster mass MT. Although this has
been done with
X-ray measurements, the SZ effect could in principle be used for a
rather direct
measurement of the total mass. It would be valuable, when precise measurements
become available, to reassess the baryonic crisis: Mg
/ MT
Peculiar radial velocity
The kinetic SZ effect is a 10 times weaker effect that the thermal
effect. Accurate
measurements of it in many cluster could in principle probe the large scale
velocity field in the distant Universe. The CMB primary anistropies are in that
case a `pollution' to these measurements which could be attempted by the Planck
mission (Aghanim
[11]).
Ground-based attempts have so far provided upper
limits (Holzapfel et al.
[8])
H0 , q0 measurement
The measurements of
SZ Cluster number counts
Having SZ surveys over large area could provide a rather unbiased measurement
of the cluster number counts. Optical and X-ray surveys have been known to be
biased by chance alignments and resolution & surface brightness limits
respectively.
The weak dependence on redshift of the SZ effect (Eq. 6) makes
a (costly) survey quite attractive for two reasons:
Figure 2. A SZ map produced by a simulated
cube of Universe (Refregier
et al. [10]).
Only the darkest spots corresponding to cluster
cores can be measured now. Notice the SZ spider web like network that
crosses the sky.
Structured Matter Energy injection into the CMB
The average comptonisation parameter on any line of sight is about
y ~ 10-6 .
From Eq. 3, the energy injection into the Universe by large scale
non-linear structure formation is of the order of at most 10-5 of
the energy in the CMB itself.
Search for distant clusters : z > 1
The search of SZ effect without the a-priori of X-ray maps have so far led to
the as yet unconfirmed detection of two radio extended brightness decrements
(Richards et al.
[12],
Saunders et al.
[13]). The
secure detection
of just few clusters at redshift above 1 would severely endanger models of the
Universe with a critical matter density parameter (Bartlett et al.
[14]).
beam
yd
. The big virtue of
SZ measurements is to give an easy access which is weakly dependent on redshift
to the total gas mass of the cluster in the beam:
z f x 103
0.1 2
0.3 9
1.0 20
b /
0 .
Te
ne dl with the SZ effect and
ne2 dl
and Te with X-ray space observations yield an estimate
of the true
physical depth of the cluster. Assuming the cluster is spherical, this quantity
can be compared with the angular size of the cluster and its redshift to give
H0 . The weak dependence of that result on
q0 has been analysed,
but the prospect of a serious measurement of it is marred by cluster evolution
(see below). Measurements of the Hubble constant is clearly within reach, once
systematic effects are well understood over a statistically significant sample
of observed (local) clusters. The complementarity of the SZ effect with
XMM-Newton
and Chandra is obvious in that respect. This is one of the most
important cosmological targets for SZ measurements. The second one is:
