3.5. Cosmic microwave diminution (Sunyaev-Zel'dovich effect)
X-ray observations indicate that clusters of galaxies contain significant amounts of diffuse, hot gas. In this section and the next, the effect of this gas on sources of radio emission lying behind the cluster will be discussed. The free electrons in this intracluster plasma will have an optical depth for scattering low frequency photons given by
![]() | (3.4) |
where T =
(8
/ 3)[e2
/ (me c2)]2 is the
Thompson electron scattering cross
section, ne is the electron density, and l is
the path length along any line of sight
through the gas. For a typical X-ray cluster, ne
10-3
cm-3 and l
1 Mpc, and
thus
T
10-(2-3). A fraction
T of the photons
from any radio source
behind a cluster will be scattered as the radiation passes through the
cluster.
One 'source' of radio emission which lies 'behind' everything is the cosmic
radiation which is a relic of the 'big bang' formation of the universe
(Sunyaev and Zel'dovich,
1980a).
This radiation has a spectrum that is nearly a blackbody,
with a temperature of Tr
2.7 K. Because this
radiation is nearly isotropic,
simply scattering the radiation would not have an observable
effect. However,
because the electrons in the intracluster gas are hotter than the cosmic
radiation
photons, they heat the cosmic radiation photons and change the spectrum
of the
cosmic radiation observed in the direction of a cluster of
galaxies. This effect was first suggested by
Zel'dovich and Sunyaev
(1969)
(Sunyaev and Zel'dovich,
1972).
Reviews of the theory and current observational status of this
Sunyaev-Zel'dovich effect have been given recently by Sunyaev and Zel'dovich
(1980a,
1981).
During an average scattering, a photon with frequency
has its frequency
changed by an amount
/
= 4kTg
/ me c2, where Tg
is the electron temperature
of the intracluster gas. In calculating the effect this has on the radiation
spectrum, it is conventional to measure the intensity in terms of a
'brightness
temperature' Tr; this is defined as the temperature of
a blackbody having the
same intensity. Then, the change in the brightness temperature of the
cosmic radiation due to passage through the intracluster gas is given by
![]() | (3.5) |
where I is
the radiation intensity and x
h
/
kTr. This expression is
actually derived in the diffusion limit and is valid only for
sufficiently small
x
10
(Sunyaev, 1981).
The change in brightness temperature or intensity is
negative for low frequencies x < 3.83 and positive for higher
frequencies. This change occurs at a wavelength
0 = 0.14
cm(2.7 K / Tr). It is somewhat
paradoxical that heating the background radiation lowers its brightness
temperature at low frequencies. This is because Compton scattering conserves
the number of photons, and shifting lower frequency photons to higher
energies lowers the intensity at low frequencies.
Nearly all of the measurements that have been made of this effect have been
at relatively low frequencies; taking the limit x
0 in equation
(3.5) gives
![]() | (3.6) |
This reduction in the cosmic radiation in the direction of clusters of
galaxies
in the microwave region is often referred to as the 'microwave diminution'.
Calculations of
Tr
and its variation with projected position for a large set of
models for the intracluster gas have been given by
Sarazin and Bahcall
(1977),
and specific predictions of the size of the effect for the
Coma,
Perseus, and Virgo/M87 clusters are given in
Bahcall and Sarazin
(1977).
Models for the Coma cluster have been given by
Gould and Rephaeli
(1978)
(but note that their
basic model for the intracluster gas is not physically consistent) and
Stimpel and Binney
(1979)
(these models included the effect of cluster ellipticity).
Unfortunately, it has proved to be very difficult to make reliable
measurements of this very small microwave diminution effect.
Pariiskii (1973)
claimed to
have detected a microwave diminution from the Coma cluster.
Gull and Northover
(1976)
claimed to have detected both Coma and A2218, and
found very small diminutions towards four other clusters. The claimed
detections of Coma were at a level much too high to be consistent with
models for the X-ray emission from this well-studied cluster
(Bahcall and Sarazin,
1977;
Gould and Rephaeli,
1978),
and subsequent observations have
not confirmed the microwave diminution in Coma.
Rudnick (1978)
gave upper limits for five clusters, including Coma; his limits were
consistent
with models for the X-ray emission, but inconsistent with the previously
claimed detections of Coma.
Lake and Partridge
(1977)
claimed three
detections of very rich clusters, but later withdrew the claim, saying that
the measurements were undermined by systematic problems with the
telescope. In a later survey of 16 clusters
(Lake and Partridge,
1980),
they detected only A576 at a level of
Tr
= -1.3 ± 0.3 mK. (Note that
1 mK
10-3 K).
Birkinshaw et al.
(1978,
1981b)
surveyed 10 clusters, detecting microwave diminutions in A576
(
Tr
= -1.12 ± 0.17 mK), A2218
(
Tr
= -1.05 ± 0.21 mK), and possibly A665 and A2319. A2218 was
not detected by
Lake and Partridge
(1980);
in fact, their measurements have the opposite sign.
Perrenod and Lada (1979)
made measurement at higher frequencies
(
= 9 mm >>
o) in order
to reduce the effects
of contamination by radio galaxies and beam smearing. They detected
A2218 at the same level as Birkinshaw et al.,
and also had a marginal detection of A665 at
Tr
= -1.3 ± 0.6 mK (A665 is the richest cluster in the Abell catalog).
Lasenby and Davies
(1983)
did not detect either A576 or
A2218.
The apparent microwave diminutions from A576 and A2218 require very large
masses of gas (comparable to the virial masses) at very high temperatures
Tg
3 ×
108 K. X-ray observations of A576 are completely inconsistent
with this much gas at these temperatures
(Pravdo et al.,
1979;
White and Silk, 1980),
and thus the measured microwave reductions must be
due to some other effect. While earlier low spatial resolution studies of
A2218 suggested that it was too weak an X-ray source to produce the
claimed microwave diminution
(Ulmer et al.,
1981),
a detailed high spatial
resolution study of the X-ray emission from A2218 with the Einstein
observatory
(Boynton et al.,
1982)
indicates that the required amounts of gas
are present in this cluster at the required temperatures
Tg = 10 - 30 keV.
From equation (3.6), the microwave diminution effect is independent of
distance as long as the cluster can be resolved. In fact,
Birkinshaw et al.
(1981a)
have measured a diminution of
Tr
= -1.4 ± 0.3 mK from the distant
(z = 0.541) cluster 0016+16. Optically, this is a rich cluster
(Koo, 1981),
although the field is somewhat confused by a foreground cluster at
z = 0.30.
There is a strong X-ray source towards 0016+16, which would imply a very
high X-ray luminosity if it is associated with the more distant cluster
(White et al.,
1981b).
In some ways, microwave diminution observations of
distant clusters are more straightforward than observations of nearby
clusters, because the reference positions are further outside the cluster
core.
Recently, a new set of observations of the microwave diminution were
published by
Birkinshaw et al.
(1984)
(see also
Birkinshaw and Gull,
1984).
These observations used the Owens Valley Radio Observatory and are
apparently less subject to systematic effects than earlier observations.
They confirm the detections of 0016+16
(Tr
= -1.40 ± 0.17 mK), A665
(
Tr
= -0.69 ± 0.10 mK), and A2218
(
Tr
= -0.70 ± 0.10 mK). Several of
these detections have also been confirmed by
Uson and Wilkinson
(1985).
Since there are now several confirming observations of the microwave
diminution in these three clusters, it may be that the effect has finally
been observed unambiguously. However, in view of the disagreements
between different observers in the past, the withdrawal of previously
claimed detections, and the inconsistency of some of the radio results
with X-ray measurements of the amount of gas present, I do not feel
completely confident that the current microwave diminution results are
conclusive. It is clear that the major sources of errors in the
measurements are
not statistical but systematic. These include very low level systematic
problems with the response of the radio telescopes used
(Lake and Partridge,
1980).
One major source of problems is the possible presence of radio sources
in the cluster. If these are concentrated at the cluster core, they will
increase the radio
brightness of the cluster and mask the microwave diminution. All of the
observations are corrected for the presence of strong radio sources, and the
observers generally avoid observing clusters, such as Perseus, which
contain very strong radio sources. There is still the danger that a
larger number of harder
to detect, weaker radio sources will make a significant contribution to
the cluster radio brightness.
Birkinshaw (1978)
surveyed six clusters, including A576 and A2218, for weak radio source emission, and concluded
that it was unlikely to affect the microwave diminution measurements.
Schallwich and Wielebinski
(1978)
detected a weak radio source in the
direction of A2218, and corrected the microwave diminution
measurement of
Birkinshaw et al.
(1978)
for this cluster. Unfortunately, this correction would
destroy the agreement of this measurement with the shorter wavelength
measurement of
Perrenod and Lada
(1979),
because the radio source and
microwave diminution have different spectral variations.
Tarter (1978)
has suggested that if clusters contained a small amount of ionized gas at
a cooler temperature than the X-ray emitting gas, the free-free radio
emission from this gas could mask the microwave diminution. All of these
radio source problems would generally mask the microwave diminution
and might explain why some clusters that are predicted to have very
strong diminutions, such as A2319, are in fact observed to have
positive
Tr.
What about A576, in which a strong microwave diminution was
initially
observed, although very little gas is observed in X-rays? The microwave
diminution measurements are generally relative measurements in which one
compares the cosmic microwave brightness in the direction of the cluster
core
with the brightness at one or more positions away from the cluster core. A
negative
Tr
at the cluster core cannot be distinguished from a positive
Tr
in these reference positions, which are generally not far outside
the cluster core. Thus the observation of a negative
Tr
in A576 may
indicate that there is excess radio emission in the outer parts of the
cluster.
a href="Sarazin_refs.html#142" target="ads_dw">Cavallo and Mandolesi
(1982)
have suggested that this radio emission is
produced by the stripping of gas from spiral galaxies in the outer parts
of the cluster.
The microwave and X-ray observations of a cluster can be used to derive a
distance to the cluster which is independent of the redshift
(Cavaliere et al.,
1977,
1979;
Gunn, 1978;
Silk and White, 1978).
From equation (3.6),
Tr
depends on the electron density ne, the gas
temperature Tg, and the size of the
emitting region. The X-ray flux fx from the cluster
depends on all of these, but
also decreases with the inverse square of the distance to the
cluster. Thus the
distance can be determined by comparing the X-ray flux and the microwave
diminution:
![]() | (3.7) |
where DA is the angular diameter distance
(Weinberg, 1972),
z is the redshift,
c is the
angular radius of the cluster core
(Section 2.7),
Tg(0) is the gas temperature at the cluster center,
and the coefficient of
proportionality depends on the distribution of gas in the cluster and the
X-ray detector response
(Cavaliere et al.,
1979).
In fact, any assumptions
about the gas distribution can be avoided by mapping the variation of
both the X-ray surface brightness Ix and the microwave
diminution as a
function of the angle away from the cluster center
.
Silk and White (1978)
find
![]() | (3.8) |
where f is a known function of gas temperature, which for a hot solar
abundance plasma contains only atomic constants. This determination of the
distance to the cluster is independent of the distribution of the gas as
long as it is
spherically symmetric. Applying this method to nearby clusters and comparing
the distances with the redshift could allow the determination of the Hubble
constant h0. Mapping high redshift clusters (z
1) could give the
cosmological
deceleration parameter q0; together, these two
parameters determine the structure, dynamics, and age of the universe
(Weinberg, 1972),
yet remain very poorly determined after a half century of observational
cosmology research.
Unfortunately, the difficulty of obtaining reliable microwave diminution measurements has made it impossible to apply this method at the present time (Birkinshaw, 1979; Boynton et al., 1982). In general, cluster microwave diminutions have not been mapped with sufficient accuracy to allow the distance to be determined from equation (3.8). Even the optical data on clusters are not accurate enough to allow an accurate distance determination. In addition, the cause of false detections, such as A576, must be determined so that they can be weeded out of cluster samples. For example, if the detection of A576 were taken seriously, it would imply a distance to this cluster at least an order of magnitude more than its redshift distance (White and Silk, 1980).
Gould and Rephaeli
(1978)
suggested that it might be easier to detect the
Sunyaev-Zel'dovich effect unambiguously at high frequencies
( <
0) at which
Tr
is positive. Some observations have been attempted at
= 1 - 3 mm
(Meyer et al.,
1983),
but no cluster diminutions were detected, and this wavelength range
straddles
0.
Observations at shorter wavelengths must be made from satellites.
Sunyaev and Zel'dovich
(1981)
point out that although their effect is
often thought of as a small change in the cosmic microwave background,
at <
0 the
effect may also be considered as an enormous source of
submillimeter luminosity for the cluster. Because the surface brightness of
the submillimeter emission is proportional to
T
ne
l, where l
r is
the path length through the cluster and r is the radius of the
gas, and the surface area is proportional to r2, the
luminosity is proportional
to ne r3 or the mass
mg of the gas in the cluster. The submillimeter
luminosity at frequencies above the critical frequency
(
<
0) is given
by
![]() | (3.9) |