Kevin MacDermid- The Sunyaev-Zeldovich Effect

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The Sunyaev-Zeldovich Effect

Kevin MacDermid

December 14, 2006

1 Introduction

People love explosions. For this reason alone it is no surprise that the current model for

the beginning of the universe starts with a bang, like a Hollywood movie, but much muchbigger. This model is the well known Big Bang Cosmology, where the universe is saidto be expanding due to an explosion some 15 billion years ago. This begs some immediatequestions, such as when exactly did the big bang occur, how much total mass is there inthe universe, and will it continue to accelerate, eventually slow to a stop, or even comeback together in a Big Crunch. To answer these questions several parameters, such as thetotal mass in the universe and the Hubble constant, must be determined. Unfortunately,having but one viewpoint, on one planet, in one solar system, in one galaxy has not madethis a simple task. Many methods have been used to try to determine some of theseparameters, most consisting of tracking so called standard candles such as variable starsand supernovae to estimate distances; however, different methods provide different answers.Part of the problem is that the radiation from a luminous body will drop off as the squareof the distance, meaning that a celestial object twice as far away will be a four times moredifficult to see.

In 1980, the Russian physicists Sunyaev and Zeldovich 1 proposed that is may be possible todetect galaxy clusters by observing small fluctuations in the cosmic microwave backgroundradiation (CMB). The CMB will be further explained in the following section, for now letme simple state that the CMB is truly background radiation, in that it must pass throughall space in a given direction before reaching the Earth. As such, it will pass throughall intervening objects which is of particular interest for the most massive stellar objects,clusters of galaxies, gas between the galaxies will tend to increase the energy of the CMBphotons through inverse Compton scattering, a process which is now known as the Sunyaev

Zeldovich (SZ) effect.1This one of several Roman alphabet spellings of these two names, others include Siuniaev and Zeldovich.

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As the SZ effect relies on one of the major physical processes coupling matter and energy,as will be discussed shortly, it provides a strong cosmological probe. It can and has beenused to measure the properties of gas in galaxy clusters as well as the motion of theseclusters and thus the evolution of the universe as a whole.

Here I will attempt to present an overview of the reasons for studying the SZ effect, followedby an explanation of the physics. I will close with some of the methods of detection, andtheir respective difficulties.

2 The Cosmic Microwave Background Radiation

A logical place to begin is a discussion of the cosmic background radiation (CMB) itself.As mentioned in the previous section, the CMB is the light radiated by the surface of lastscattering. That is, it was the first light to radiate freely as the universe became transparent

to electromagnetic waves. This occurred when the universe had expanded enough to cool toabout 3000K. Earlier than this, matter and radiation remained in thermal contact, and thusequilibrium, because of the abundance of free electrons for scattering. At this temperature,however, matter became neutral, the number of free electrons decreased significantly, andradiation became decoupled from matter. As such, most of the photons that now make upthe CMB were scattered by electrons for the last time, which is why it is often called thesphere of last scattering or red-shift of last scattering [6]. As an aside, this decouplingof photons and electrons led to a drop in the length scale necessary for gravitational collapse,allowing the fluctuations present in mass density that had previously been stabilized by theradiation field to begin to fall together, becoming the large-scale objects visible today.

The CMB is perhaps the best cosmological probe known at present. First discovered over

thirty years ago it has been the strongest evidence for the inflation model of the universedue to its uniformity, which suggests thermal contact between all points at some time inthe past. In fact, its spectrum is characterized by a single temperature, Trad 2.7K whichimplies a specific intensity of

I =2h3

c2(eh/kBTrad 1)1. (1)

Corresponding to a peak brightness Imax 3.7W,2 Hz1sr1 at max 160GHz, a

photon density n 4 108 photons m3, a mass density of pgamma 5 10

31 kg m3

that is much less then the critical density to close the universe of

crit =

3H20

8G = 1.88 1026

h2

okgm3

.

where Ho is the Hubble constant and ho = Ho/100kms1M pc1 is the dimensionless

version, has been narrowed down to 0.5 ho 0.8 [5].

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Cosmological data is encoded in the CMB in two ways. First, the anisotropies presentin the sphere of last scattering are thought to be the blue print of the universe, as thedensity fluctuations led to gravitational collapse into the current state of the universe.Secondly, there is a great deal of data present in the CMB brightness and spectrum due to

matter interaction. The SZ effect is an example of such a matter interaction.

3 Physics of the Sunyaev-Zeldovich effect

Were the CMB undisturbed since decoupling of radiation it would a simple matter toextract information regarding inflation and the epoch of last scattering, however, therewould be no imprint, and thus no information, about present day structures. On the otherhand, if the reverse were true then its interactions with matter today would most likelyhave overwritten any available information from the early universe. In reality, the CMBlies somewhere between these two possibilities, its spectrum and intensity are affecteddirectly by high temperature stars and clusters as well as gravitationally lensed by anymassive object, or combination thereof. The thermal SZ effect, of which the distinctionwill be made later, is much more intense than gravitation lensing, though in measurementslensing must be accounted for [1].

The basic physics of the Sunyaev-Zeldovich effect are fairly simple. Clusters of galaxieshave masses that exceed 31014M with effective gravitational radii, Reff, on the order ofmega-parsecs. For a gas in hydrostatic equilibrium with its gravitation potential the virialtheorem states that the average kinetic energy will be half the average potential or

kBTe GMmp2Reff

7(M/3 1014M)(Reff/Mpc)1keV. (2)

which leads to thermal emission in the X-ray spectrum composed of bremsstrahlung andline radiation.

Around a quarter of the mass of these galaxy clusters are ionized intracluster gas [2]. Assuch there is an extremely high number of free electrons available to scatter CMB photonspassing through. The details of this interaction are covered in Ribicki and Lightman, andwill be discussed further in the next section but let me now mention simply that for lowenergies the cross-section is the Thomson scattering cross section, T, leading to an opticaldepth e = neTReff 10

2.

Due to the low energy of the CMB photons there is a greater probability of up-scattering,

as will be shown in the next section. Furthermore, an average scatter produces a changein mean photon energy (/) (kBTe/mec2) 102. Overall then, the SZ effect leads

to a change in brightness of about one part in 104, which is possible, though challenging,to measure.

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3.1 Single Photon-Electron Scattering

To begin with, recall that Compton scattering describes the interaction between photonsand unbound electrons. For electrons at rest, single photon electron scattering simply

follows the well known Compton energy formula,

f =

1 + mc2 (1 cos ). (3)

Where, f is the final photon energy, the initial and is the scattering angle.

The SZ effect is, in fact, simply a special case of Compton scattering where the photonis from the CMB and the electron belongs to the intracluster gas. In this situation theelectrons are much hotter, or higher energy, than the incident radiation and the Comptonscatter will tend to increase the photon energy, which is why this is often called inverseCompton scattering. This process is discussed in section seven of Ribicki and Lightman,

here an outline will be given [7].Basically, the Lorenz transforms between the lab and rest frame introduce an increase inphoton energy on the order of 2, for relativistic electrons with 21 h/mc2, that stillsatisfy the Thomson scattering condition mc2. While this process can greatly increasethe energy of a photon it should be noted that it will be partially countered by severalterms from the quantum mechanical treatment of this scattering. The exact equation iscalled the Klein-Nishina formula, and is beyond the scope of this paper.

For the clusters of galaxies that cause the SZ effect, the electrons can be considered mildlyrelativistic, mec2. This greatly simplifies the physics involved, though more carefulcalculations requires relaxing this assumption, see, for example Bernstien, 1990 [9]. So,while these are generally called inverse Compton, they could more accurately be calledThomson scattering.

The Thomson cross section can accurately be used in this limit,

dTd

=1

2r20(1 + cos

2 ) (4)

where r0 is the electron radius and the angle the photon is deflected by the scattering. Ifthe geometry is similar to figure 1, then the probability of scattering with angle is

p()d =

24(1 )31

(5)

and the probability of scattering to angle is,

(; ) =3

8

1 + 22 +

1

2(1 2)(1 2)

d. (6)

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This change in direction causes the scattered photon to appear at frequency

= (1 + )(1 )1, (7)

where = cos .

Figure 1: The geometry of scattering in the rest frame of the electron before the interaction.

Typically, the scattering is expressed in terms of the logarithmic frequency shift,s = log(/). Which, when combined with the previous several equations leads to aprobability of scattering causing a frequency shift s from an electron with speed c is

P(s; ) =3

164

2

1

(1 + ) 1 + 22 + 1/2(1 2)(1 2) (1 )3d (8)Where the integral is performed over real angles so that, for up-scattering s > 0,

1 =1 es(1 + )

(9)

2 = 1 (10)

and for down-scattering (s < 0)1 = 1 (11)

2 =1 es(1 )

. (12)

This integration can be done numerically, see Figure 2 below.

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-.5 0 0.5 1 1.5

s

0

2

4

6

8

10

12

P(s;B)

Beta = 0.5

Beta = 0.1

Beta = 0.3

Beta = 0.7

Figure 2: The scattering probabilities function for several betas. Note that the functionbecomes increasingly asymmetric and broader as increases.

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3.2 Scattering of the CMB by an Electron Population

Above, the physics for a single photon scattering are described. This can be broadened toan electron population simply by averaging over the distribution of the electrons.

The probability distribution can be given by,

P1(s) =

1

lim

pe()P(s; )d, (13)

where pe() is the electron distribution and lim is the minimum beta capable of causinga frequency shift s,

lim =e|s| 1

e|s| + 1.

Of course, this is true only if the electron distribution does not extend to Lorenz factorsoutside the limit of the Thomson approximation. In the case of galaxy clusters typical

electron temperatures can be as high as 15 keV (1.8108K) but the corresponding Lorenzfactors will still be small, and the Thomson approximation will hold.

Furthermore, in the case of a galaxy cluster the electron velocities can be taken to bethermal, so they follow a relativistic Maxwell distribution,

pe()d =52exp(

)d

K2(1

)

, (14)

where is the dimensionless electron temperature

=

kBTemec2

.

The above integral, given by equation 13, can be performed numerically, the results forkBTe = 5.1 and 15.3keV is shown in figure 3. Notice that the distribution of scatteredphoton frequencies is asymmetric, with a stronger up-scattering tail (s > 1) than down-scattering region. Thus the effect is a mean frequency increase [4].

The next step is to use the frequency shift for single scattering that we have just calculatedon the spectrum of the CMB. This amounts to finding the intensity over the frequencyrange as well as including the possibility of multiple scattering. The detailed calculationwill not be included here, though it can be found in Birkinshaw, the result is,

I() =2h

c2e

P1(s)ds

30

eh0/kBTrad

3

eh/kBTrad1,

(15)

where 0 is our original frequency and the final. Note that this intensity change is red-shift independent, as it depends only on the conditions of the scattering gas. It is this factthat makes the SZ so useful for cosmology.

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Figure 3: Plots of the scattering kernel, equation 13. The solid line is as calculated byRephaeli (1995a) [11]. The dotted line is as calculated by Sunyaev 1980 [12]

3.3 The Kompaneets approximation

For completeness, a brief mention will be made here of the Kompaneets approximationas it has been used for most of the work on the SZ effect. The Kompaneets approxima-tion basically amounts to taking the non-relativistic limit, which simplifies the scatteringconsiderably leading to a spectral change of

I(x) = x3

n(x)I0, (16)

where n is the spectral change caused by scattering

n = xyex

(ex 1)2(xcoth(x/2) 4), (17)

and x = hkBTe . Also, y =kBTectmec2e

, where e = (neT)1, is a dimensionless measure of time

spent in the electron distribution, and I0 =2hc2

kBTrad

h

3. For the details of this derivation

see Kompaneets, 1957.

The Kompaneets approximation has three main advantages. First, the spectrum of the SZ

effect is given by a simple analytical function. Second, the location of the maxima, minimaand zeroes become independent of Te. And, finally, the amplitude of the intensity changesonly with the Compton y parameter, which itself is proportional only to the temperatureand optical depth of the electron cloud.

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A comparison of these two intensity functions, the full relativistic and the Kompaneets ap-proximation is given in figure 4. Note that while it is possible to get closer to the relativisticequation by taking further orders of this approximation relies on the assumptions thatthe cluster is optically thin and that the electron distribution function is that of a single

temperature gas. In practice, if results of greater than one percent accuracy are neededthe full relativistic expression must be used.

Figure 4: The spectral deformation caused by the SZ effect. The Kompaneets approxima-tion is shown as a dotted line. The left is for electrons at kBTe = 5.1keV and the right isfor electrons at kBTe = 15.3keV

4 Secondary SZ effects

What has been described above is more specifically called the thermal SZ effect. There aretwo important secondary effects related directly to thermal SZ. Each leads to different andcould, at least theoretically, be detected.

4.1 The non-thermal SZ effect

The first is the not so imaginatively named non-thermal SZ effect. This is simply the SZeffect produced by a non-thermally distributed group of electrons. Recall that equation 13

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allowed any distribution of electrons, and it is possible that a sufficiently dense relativisticelectron cloud could produce a similar SZ effect.

The math involved in calculations becomes quite involved, as the full relativistic treatment

is necessary. Here only qualitative properties will be discussed, see Birkinshaw for moredetail.

The optical depth to inverse Compton scattering depends on the low frequency limit of thestructure being observed for high frequencies. As such, the non-thermal SZ effect can bethought of as a test of the minimum energy of electrons that produce radio radiation.

Unfortunately, it is not easy to detect the SZ from non-thermal electron populations asthere is a great deal of synchrotron radio emission. At low frequencies the synchrotronemission will easily dominate over the non-thermal SZ. At high radio frequencies, however,there is more chance that the SZ effect could be detected, but there are still difficultiesseparating the SZ from the flatter section of the synchrotron radiation.

A further difficulty is that radio emitters are expected to be strongly in-homogeneous, sosingle dish measurements average over a variety of different radio source structures. Thisimplies that the data taken might actually be produced by small variations in the electronenergy distribution function. To get accurate results observations must be made with angu-lar resolution comparable with the small-scale structures, which will prove difficult.

4.2 The Kinematic SZ effect

The kinematic SZ effect is caused by the movement of the galaxy cluster responsible forthermal or non-thermal SZ relative to the Hubble flow. Thus, in the reference frame of thescattering gas the microwave background will appear anisotropic which inverse Comptonwill cause to become more isotropic again. Of course, in so doing it causes the radiationfield at the observer to become less isotropic, but instead to show a structure towardthe scattering atmosphere with amplitude proportional to evz/c, where vz is the peculiarvelocity along the line of sight [8]

The kinematic effect can be a problem when accurate measurements of the thermal SZare attempted; however, it also provides further information about the cluster itself. Ofcourse, to be capable of this it is necessary to separate the thermal and kinematic effects.This can be accomplished using their different spectral properties.

The derivation of the kinematic SZ effect can be found in Phillips 1995. As a basic outline,the assumption made is that both the kinematic and the thermal effects are small, allowing

cross terms to be omitted. It should be noted that this approximation is not correct forthe non-thermal effect, which will not be discussed here. With this assumption in place

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the occupation number in a given frame can be found to be

n = (exp(x1z(1 z1)) 1)1 (18)

where x1 =h1kBT1 is the dimensionless frequency of the photons in the frame of the scattering

medium. Using this with the typical radiative transfer equation it is possible to derive anequation for the scattered radiation intensity, the results are,

I = eI0x4ex

(ex 1)2, (19)

for the intensity and

TB = eTradx2ex

(ex 1)2, (20)

for the brightness temperature. This amounts to a decrease in the radiation tempera-ture.

While the kinematic SZ effect is much smaller than the thermal effect at low frequenciesit can be detected at higher frequencies due to the difference between the two spectra. Infact, using the Kompaneets approximation it is possible to show that the kinematic effectpeaks (in intensity change) where the thermal effect is null, see Figure 5

Figure 5: Spectral distortion of CMB due to Sunyaev-Zeldovich effect. The left panelshows the intensity while the right shows the brightness temperature. The solid line is thethermal SZ effect, while the dashed line represents the kinematic effect [10]

Thus observations are possible near x = 2.83 (218 GHz) though for these observations to

be accurate the thermal SZ effect must be carefully accounted for. Also, although thistechnique only provides the peculiar velocity along the line of sight the other componentscan be determined using the specific intensity changes caused by gravitational lensing.Basically this amounts to a very slight dipole-like term apparent in the SZ effect from the

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movement of the mass. This term can be an order of magnitude smaller than the kinematicSZ effect, and thus would not be easy to measure. Further reading on the physics behindthis can be found in Rees & Sciama 1968 and Pyne & Birkinshaw 1993.

5 Applications of the Sunyaev Zeldovich Effect

Before proceeding the to the applications of the SZ effect a summary of the most importantfeatures of the thermal effect are in order. First, it is a slight spectral distortion, on theorder of 1mK proportional to the cluster pressure along the line of sight. Second, andperhaps most importantly, it is independent of redshift. In fact, the SZ effect is proportionalto the total thermal energy, and is only limited by the size of the cluster. This will beextremely important in the cosmology section to follow.

As an quick aside, note that the existence of the SZ effect proves that the CMB is not a

local effect inside our own galaxy. Though there was little debate about this it is obviousthat the SZ can only function if the CMB passes through the cluster, thus it must beradiated from a higher red-shift.

Of much greater interest however are the insights into galaxy cluster properties and cos-mology as whole described in the following section.

5.1 Cosmology

The most exciting potential application of the SZ effect are the high red-shift surveys itallows. It is possible to scan a fairly large section of the sky and discover the locations of

galaxy clusters by detecting slight changes in intensity. These clusters can then be usedto trace the evolution of the universe through time up to red-shifts of about three. Whilebeing able to track the evolution of galaxy clusters is compelling on its own the data fromthese surveys, as well as supporting measurements possible once the location of the clusteris well-known, allows the determination of several cosmological parameters.

For instance, the SZ effect allows an independent measurement of the Hubble constant,as the distance to a given cluster can be calculated by making use of the different densitydependencies of the SZ effect and X-ray emission. Specifically, the SZ effect depends ondensity to the first power while X-ray emission has second order density dependence. Whilethe calculation will not be given here (see Carlstrom, Holder, Reese [10]), it relies on onecritical assumption, namely, that the scale of the cluster along the line of sight is directly

related to the scale on the plane of the sky. Typically, spherical symmetry is assumed, andthese are taken to be equal.

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Furthermore, since the thermal SZ effect relies directly on the line of sight cluster pressure,it will be proportional to the number of free electrons available in the cluster. As such, ifthe temperature of the cluster can be obtained by other means (such as spectroscopy), thegas fraction can be determined directly. This leads to an estimate of the total gravitating

mass, by assuming hydrostatic equilibrium. The amount of gas present in clusters is vitalas it allows a better estimate of the total mass of a cluster, thus placing constraints on thedark matter.

Finally, the kinematic SZ effect is potentially a powerful cosmological tool as it providesthe only way to measure the peculiar velocity at high red-shift. Unfortunately, it is a veryweak effect making it extremely difficult to measure. Measurements should best be doneat around 218 GHz, as this is the null of the thermal effect, however even here the CMBfluctuations and background sources provide significant noise.

For further information on the cosmological implications of the SZ effect, see the annualreview by Carlstrom, Holder and Reese [10].

6 Detection Techniques

Let us close with a discussion of the three methods used to detect the SZ effect completewith their respective strengths and weaknesses. Only an outline of the measurement proce-dure will be included here are there is little use reproducing data available in outer sources.In particular, see Birkinshaw 1999 [4] and Carlstrom et al. 2000 [13] for relatively recentreviews of the observations.

6.1 Single-Dish radiometer measurements

The first method used to detect the SZ effect makes use of existing radio telescopes on whichlarge periods of observing time are available. These telescopes tend to have beam-sizes ofa few arcminutes at microwave frequencies, which is about the angular size of moderatelydistant clusters of galaxies.

While relatively little customization is needed for this, making it relatively inexpensive, tomake accurate measurements long observation times are needed. For example, to make ameasurement with an accuracy of 10 K (brightness temperature) would take in excess offive hours.

The main problem encountered is emission from the Earths atmosphere, which varies withboth space and time. To account for this telescopes will tend to use difference measurementsby quickly switching from one location on the sky to another. It is also possible to use

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what is called drift-scanning, in which the sky is allowed to drift through the beam ofthe telescope, and the average baseline is removed from the signal.

Unfortunately, these differencing schemes limit the range of red-shifts for which the tele-

scope is useful. If the observations are of a cluster of galaxies at low red-shift, then theangular size of the clusters SZ effects may be comparable to the beam switching angle,thus reducing the observable signal. Alternatively, if the cluster is at high red-shift, thenits angular size in the SZ effects may be smaller than the telescope is able to measure (itsFWHM), so that beam dilution reduces the signal.

Another problem encountered is the difficulty relating the measured signal from the ra-diometer to the brightness temperature of the SZ effect. That is, there is a problem ofcalibration. Generally, the absolute calibration of the telescope will be tied to the obser-vation of planets, which can lead to a source of error.

6.2 Bolometric methods

Bolometric systems are quite similar to the radiometer measurements described in theprevious section, with greatly increased sensitivity. Furthermore, bolometric measurementsare of interest as they are sensitive outside the Rayleigh-Jeans part of the spectrum, thusproviding the possibility of separating the thermal and kinematic SZ effects.

Bolometers themselves are simply small absorbers connected to a heat sink through a thininsulating link. When incident radiation strikes the absorber it raises its temperature,which is then measured to extract the initial power. As each absorber is often on the orderof millimeters, an array is needed to obtain useful data.

A bolometer such as SCUBA has sensitivity at a wavelength of 850 m of 80 MJyHz1/2,with a 13-arcsec pixel size. A few hours of observation should suffice to detect the thermalSZ effect at high sensitivity, this is considerably better than the radiometric measurementsdescribed earlier.

However, a problem with this technique is the high sky brightness over which the observa-tions must be made. This implies that telescopes on high, dry sites or balloon experimentsare necessary for efficient observation.

Also, as in radiometric work, there is the problem of calibrating the data into absolutetemperature. Again, the calibration is typically made through reference to the brightness ofplanets, which limits the accuracy of intensity measurements to about 6 per cent. Includingthe error from the beam-pattern of the detectors, the bandpasses of the detector elements

and the opacity of the atmosphere increase this to about 8 per cent.

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6.3 Interferometric methods

The two previous techniques are best suited for large-scale surveys searching for or ex-amining galaxy clusters for only moderate angular resolutions. Radio interferometry, on

the other hand, is a powerful method for making images of SZ effects. These images canmostly be used in comparison with X-ray emission images. Also radio interferometry op-erates differently from the previous two, thus it suffers from other systematic difficultiesand can provide an independent view.

Radio interferometry is aptly named, it uses the correlation of signals from a pair of radioantennas. This correlation produces a response which is roughly proportional to a singleFourier component of the brightness of the source.

Since radio interferometers are typically designed to maximize the angular resolution thereis some maximum angular scale of structure that can be imaged by interferometers. TheSZ effect for clusters of galaxies has angular scales of several arcminutes, which will not be

visible using an interferometer. As such a radio interferometer has difficulty detecting theSZ effect, so a smaller interferometer is needed.

Using a smaller interferometer it should be noted that the effect of structures in the at-mosphere are significantly reduced. Emission from the atmosphere contributes to the totalnoise power entering the antennas which will not show up in the correlated data. So, ainterferometers do not respond to constant atmospheric signals, the uniform component ofthe CMB, or any other form of constant emission.

While the interferometric technique is very powerful it does suffer from some new difficultiesof its own. First, the range of frequency may be highly restricted so that a map cannottruly be formed. Furthermore, one must be careful to avoid correlation errors, which can

produce large and spurious signals. Further information on this can be seen in Partridgeet al. 1987.

7 Conclusion

I have here tried to provide a concise overview of the Sunyaev-Zeldovich effect; howeverthis is by no means an complete review on what has become a broad subject. For mypart, I recommend the review by Birkinshaw that has been cited throughout this paper forfurther reading.

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References

[1] Loeb Abraham and Refregier, Alexandres. Effect of gravitational lensing on mea-

surements of Sunyaev-Zeldovich effect Astrophysical Journal Letters, vol. 476, n 2,pt.2, 20 Feb. 1997, p L59-62

[2] White, D. A, Fabian, A. C Einstein Observatory evidence for the widespread baryonoverdensity in clusters of galaxies Mon. Not. R. Astron. Soc. (UK). vol 273, 1. pp72-84. March, 1995.

[3] Zeldovich, Ia.B and Siuniaev, R. A. Intergalactic gas in galactic clusters, the mi-crowave background radiation and cosmology Astrophysics and cosmic physics. (A83-01838 01-90), pp. 9-65, Nov. 1982,

[4] Birkinshaw, Mark. The Sunyaev-ZelDovich Effect Physics Reports, vol. 310, 2-3,p. 97-195, 1999.

[5] Sandage, A.R., Tammann, G. In Critical Dialogs in Cosmology ed. Turok, N.;World Scientific

[6] Dodelson, Scott. Cosmic Microwave Background: Past, Future, and Present. Inter-national Journal of Modern Physics, vol. 15, Suppl 1B. pp. 765-783, 2000.

[7] George B. Rybicki and Alan P. Lightman Radiative Processes in AstrophysicsStrauss GmbH, Morlenbach, Germany: Wiley-Vch, 2004.

[8] Rephaeli, Y. and Lahav O. Peculiar cluster velocities from measurements of thekinematic Sunyaev-Zeldovich effect Astrophys. J. (USA). vol 372, 1. pp 21-4. May,1991.

[9] Jeremy Bernstein and Scott Dodelson Aspects of the Zeldovich-Sunyaev mechanismPhysical Review D, vol. 41, n 2, Jan. 1990.

[10] John E. Carlstrom, Gilbert P. Holder, and Erik D. Reese Cosmology with theSunyaev-Zeldovich Effect Annu. Rev. Astron. Astrophy. vol 40. p 643-80. 2002.

[11] Rephaeli, Y. Comptonization of the cosmic microwave background: the Sunyaev-Zeldovich effect Annu. Rev. Astron. Astrophy. vol 33. p 541-79. 1995.

[12] Sunyaev, R. A. and Zeldovich Y. Microwave background radiation as a probe of thecontemporary structure and history of the universe Annu. Rev. Astron. Astrophy.vol 18. p 537-560. 1980.

[13] Carlstrom, J. E and Joy, M. and Holder, G and Holzapfel, W. and Laroque, S. andMohr, J. and Reese, E. The Sunyaev-Zeldovich Effect Constructing the Universewith Clusters of Galaxies. 2000.

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Kevin MacDermid- The Sunyaev-Zeldovich Effect