In this review, we shall consider only the SZ effect, since
this the only secondary anisotropy to have been observed to date.
The SZ effect is in fact made up of two separate effects: One is
due to the bulk velocity of the cluster, and the other due to the
thermal velocities of the electrons in the cluster gas. These are
called the kinematic and thermal SZ effects respectively. The
kinematic effect measures the cluster peculiar velocity, whereas
the thermal effect can be used, in conjunction with images and
spectra of its X-ray emission, to study the cluster gas. In
particular, for a dynamically relaxed cluster, we can use the
thermal SZ effect and X-ray data to estimate the physical size of
the cluster, and hence its distance. This, in turn, yields an
estimate of the Hubble constant
.
If the cluster has a peculiar velocity
along the observer's line of sight, then the temperature of a
CMB photon is Doppler-shifted by an amount
where
is the temperature of the CMB,
is the electron number density,
is the Thomson scattering cross-section and the integral is
taken along the line of sight. In terms of the Rayleigh-Jeans
brightness temperature this becomes
or as an intensity
where we have set
.
The effect due to thermal motions of the electrons is second-order in the electron velocity, and does not preserve the blackbody shape of the CMB spectrum. For the thermal SZ effect the change in the Rayleigh-Jeans brightness temperature is given by
where
is the electron temperature and
the electron mass. In terms of intensity this becomes
It is usual to describe the magnitude of the thermal effect in terms of the y parameter, which is given by
The frequency dependencies of the kinetic and thermal effects
(i.e. those functions in curly brackets in Equations
6
-
9
), are shown in Figure
8
.
Note that at
GHz, the maximum change in intensity due to the kinematic
effect coincides with the null of the thermal effect. This, in
principle, allows one to separate the two effects. The magnitude
of the thermal effect for a hot, dense cluster is
mK, and for reasonable cluster velocities the kinematic effect
is an order of magnitude smaller.
Observations of the SZ effect have been made in Cambridge
using the Ryle telescope, which is an 8-dish interferometer
operating at 15 GHz [87], in Caltech using the Owen's Valley 5.5m telescope [73], the Owen's Valley 40m telescope [60] and the Owen's Valley Millimeter Array (OVMMI) [39] [40], at NASA using the MSAM balloon experiment [91], at the Caltech Submillimeter Observatory using a purpose built
instrument called the Sunyaev-Zel'dovich Infrared Experiment
(SuZIE) [58] and by various other groups. The magnitude of the observed SZ
effect in these clusters can be combined with X-ray data from
ROSAT and ASCA to place limits on
. This has been reviewed in Lasenby & Jones [69].
Another important feature of the SZ effect is that the decrement does not change with redshift. Therefore, it should be possible to detect clusters out to very high redshift. To test this the Ryle telescope has been making observations towards quasar pairs. Figure 9
shows the Ryle telescope map of the sky towards the quasar
pair PC1643+4631 (Jones
et al.
1997) [63]. These two quasars are at a redshift of
and are
apart on the sky. They are a strong candidate for a
gravitational lensed object due to the similarity in their
spectra. As there is no X-ray detection with ROSAT the cluster
responsible for the lensing must be at a redshift greater than
2.5 and from modelling of the gravitational lensing, or from
fitting for a density profile in the SZ effect, it must have a
total mass of about
.
With observations of distant clusters it is possible to predict the mass density of the Universe. Using the Press-Schecter formalism the number of clusters in terms of SZ flux counts can be predicted. Figure 10
shows the results from Bartlett
et al.
[34]. From this figure it is seen that, if the decrements are really
due to the SZ effect and there was no bias in selecting the
fields (e.g. the field was chosen because of the magnification of
the quasar pair images), then the
model of the Universe is ruled out. An open model is required to
be consistent with the data. Confirmation of the detections are
needed. Until these follow up observations have been made, it is
impossible to say how accurate these findings are.
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The Cosmic Microwave Background
Aled W. Jones and Anthony N. Lasenby http://www.livingreviews.org/lrr-1998-11 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |