first predicted by the russian scientists sunayaev and zel’dovich in 1969

Giuseppina CoppolaGiuseppina Coppola 11

First predicted by the Russian scientists Sunayaev and Zel’dovich in 1969.

Galaxy Clusters have hot gas that produce electrons by bremsstahlung(Tgas ~10-100 Kelvin).

CMB photons are cold (TCMB ~ 2.7 Kelvin).

Inverse Compton scattering occurs between CMB photons and the hot electrons of clustrer atmosphere.

Energy will be transferred from the hot electrons to the low energy CMB photons changing the shape of their intensity vs. frequency plot :

• measuremnts made at low frequencies will have a lower intensity, since photons which originally had these energies were scattered to higher energies. This distorts the spectrum by ~0.1%.


SZ effect distorsion of the CMB signal

• Note the decrement on the low frequency side, and the increment at higher frequencies.•The amplitude of the distorsion is proportional to Te, although shape is indipendent of Te. The relativistic equation has a slightly more complicated shape.


Overview

1. CMB2. Radiation basic

3. Scattering by electron population4. Kompaneets approximation

5. SZ and galaxy cluster 6. Struments


The Cosmic Microwave Background Radiation

The CMBR is the dominant electromagnetic radiation field in the Universe.

• Isotropy

• Photon density:

• Peak brightness:

at

• Specific intensity of the radiation:

• Energy density:

Principal Properties

• Trad ~ 2.7K


Thermal history of the Universe and CMBR

The origins of the CMBR lie in an early hot phase of the expansion of the Universe.

Very high zVery high z: matter and radiation were in good thermal contact because of the abundance of free electrons.

z of recombinationz of recombination: most electrons have become bound to ions.

z of decouplingz of decoupling: the interaction lenght of photons and electrons exceeds the scale of the Universe.

z z ~1000-1500~1000-1500: the Universe was becoming neutral, matter-dominated and transaprent to radiation. Most of the photons that are now in the CMBR were scatterated by electrons for the last time.

After recombination……After recombination……

Potential fluctuations grow to form Large Scale Structure

• overdensities collapse to form galaxies and galaxy cluster;• underdensities expand into voids.


I. Radiation basicsreal space volume

momentum space volume

• Distribution function

• Specific intensity photon frequency

• Number density of photons in the Universe

• Energy density of the radiation field


II. Radiation basics

In the presence of absorption, emission and scattering processes, and in a flat spacetime, Iν obeys a transport equation:transport equation:

emissivity

absorption coefficient

scattering coefficient

scattering redistribution function

Specific intensity may be changed by:

• redistributing photons to different directions and frequencies (e.g. scattering);• absorbing or emitting radiation (e.g. thermal bremsstrahlung);• making photon distribution function anisotropic (Doppler effect);


I. Single photon-electron scattering

Compton scattering formula

For

classical Thomson cross-section formula

The probability of a scattering with angle θ: ve= βc and μ = cosθ

Redistribution function:


II. Single photon-electron scattering

The scattered photon frequency:

Introducing the logarithmic frequency shift: s=log(νʺ/ ν ), the probability that a single scattering of the photon causes a frequency shift s from an electron with speed βc is:


I. Photon Scattering by electron population

Averaging over the electron β distribution

If every photon is scattered once, then the resulting spectrum is given by:

Probability that a scattering occurs from ν0 to ν

Since


II. Photon Scattering by electron population

The probability of N scatterings:Optical depth

Probability that aphoton penetrates the electron cloud

The full redistribution function is given by Raphaeli formula:

In most situations the electron scattering medium is optically thin, then

and


I. The Kompaneets approximation

In the non-relativistic limit the scattering process may be described by the Kompaneets equation, which describes the change in the occupation number, by a diffusion process.

For small xe, we have:

Canonical form of the diffusion equation

Solution


II. The Kompaneets approximation


III. The Kompaneets approximation

At low y and for an incident photon spectrum of the form of CMBR, we can use the Approximation:

• The spectrum of the effect is given by a simple analytical function;• the location of the spectral maxima, minima and zeros are indipendent of Te in the Kompaneets approximation;• the amplitude of the intensity change depends only on y.

Kompaneets vs. Raphaeli formula


1. Useful to determine the intrinsic three-dimensional shape of the cluster;

2. Useful to extract information on thermal structure in the intracluster gas;

3. Useful to measure the projected mass of gas in the cluster on the line of sight if the temperature structure of the cluster is simple;

4. Useful to detect clusters;5. Useful to test the cosmology.


The Sunayaev-Zel’dovich effect from clusters of galaxies

If a cluster atmosphere contains gas with electron concentration ne(r), then the scattering optical depth, Comptonization parameter and X-ray surface brightness are:

There is no unique inversion of bx(E) to ne (r) and Te (r)


I. Parameterized model for gas cluster

They use a parameterized model for the properties of the scattering gas in the cluster and they fit the values of these parameters to the X-ray data.

• Isothermal beta-modelIsothermal beta-model: Te is constant and ne follows the spherical distribution


II. Parameterized model for gas cluster

Hughes et al. (1998), on the basis of observations of the Coma cluster, indroduced a useful variation on beta-model

Useful to describe the decrease of gas temperature at large radius


z=0.5455;

DA=760 h-1 Mpc

X-ray emission mapped by ROSAT PSPC

Structural parameters by isothermal beta-model

β = 0.73 ∓ 0.02Θc = 0.69 0.04 arcmin∓

rc = (150 10) h-1 kpc∓b0 = 0.047 0.002 counts s∓ -1 arcmin-2

ΔT0c≈ -0.82 h-1 mK at low frequency

These values are consistent with the results obtained using X-ray spectrum


III. Parameterized model for gas cluster

• Ellipsoidal modelEllipsoidal model:

M encodes the orientation and relative sizes of semi-major axes of the cluster.

β = 0.751 ∓ 0.025Θc = 0.763 0.045 arcmin∓

ΔT0c≈ -0.84 h-1 mK

SZ modelX-ray surface brightness model


Mass of the gas

For an isothermal model, the surface mass density in gas is:

Mean mass of gas per electron

If the electron temperature of the gas is constant:

This quantity can be compared with mas estimates produced by lensing studies.


Sz effect in cosmological terms

MethodMethod: comparison of SZ effect predicted from the model with the measured effect by X-ray data.

Since the predicted effect is proportional to h-1/2 via the dependence on DA, this comparison measures the value of H0 and other cosmological parameters

1. Measuring the CMB decrement from a cluster2. Mesuring X-ray emission from a cluster

Measuring the size of a cluster


Measuring the CMB decrement from a cluster

• Consider simplest model of cluster

Spherical with radius R Constant gas number density n Constant temperature Te

• SZ effect decrement ΔT

Directly related to density Directly related to the cluster path length Directly related to the temperature of the gas, Te

R

nTe

Temperature Decrement

ΔT = -Trad 2y or ΔT ≈ Trad 2Rn


Measuring X-ray emission from a cluster

• Model of cluster

Sphere of radius R Central number density of electron gas, n Temperature of the gas, Te

• X-ray surface brightness bX

Directly related to square of density Directly related to the cluster path length Temperature of the gas, Te

X-ray brightness bX ≈2Rn2

R

nTe


Measuring Size and Distance of the cluster

• Combined observations of bX and ΔT measure the path length along the line of sight• Use the radius of the cluster and the angular size to make an estimate at the cluster distance. Remember, we assumed that cluster was spherical

ΔT/Trad = 2RnbX ≈ 2Rn2

R = (ΔT/Trad )2 /2bX

DA ≈ R/θ

• H0 is obtained from the measured z of the cluster and the value of DA under some assumption about q0.

RDAθ


Result of SZ Distance Measurements

SZ distance vs. z

• SZ effect distances are direct (rather than relative);• SZ effect distances possible ar very large lookback times;• can see the theoretical angular diameter distance relation;

• Comments

H0 = 63 ∓ 3 km/s/Mpc for ΩM=0.3 and ΩΛ=0.7

But….

• selection effect, which caues the value of H0 to be biased low• the value of H0 depends by cluster model• unknown intrinsic shape of cluster atmospheres• uncertainties in the parameters of the model


Cluster Detectability

The total flux from the cluster that is requested:

Angular position on the sky

Any SZE clusters survey has some fixed angular resolution, which will not allow to spatially resolve low mass cluster. Therefore a background yb parameter will be present.If the gas temperature profile is isothermal, the integrated flux SZE cay be related to the cluster temperature weighted mass divided by DA

2:

If the temperature profile is isothermal only in the inner regions (Cardone, Piedipalumbo, Tortora (2005))


Interferometers used to measure the SZ effect

Cosmic Background Imager (CBI)• Located at the ALMA cite in Chajantor, Chile. These 13 antennae operate at 26-36 GHz

Degree Angular Scale Interferometer (DASI)• A sister project to CBI, located at South Pole.

These interferometers are suited to measure nearby clusters


X-ray telescopes used to measure the SZ effect

ROSAT• X-ray satellite in operation between 1990 and 1999. Mainly, its data has been used in conjunction with the radio observations to make estimates of H0 and Ωb. Uncertainties of the X-ray intensity are ~ 10%.

Chandra X-ray Observatory• Provides X-ray observations of the clusters to make etimates of the gas temperature. Chandra currently has the best resolution of all X-ray observatories.

XMM-Newton• ESA’s X-ray telescope. Has 3 European Photon Imaging Cameras (EPIC)


All-sky project used to measure SZ effect

Microwave Anisotropy Probe• Measures temperature fluctuations in the CMB.

Planck satellite• ESA project designed to image the entire sky at CMB wavelengths. Its wide frequency coverage will be used to measure the SZ decrement and increment to the CMB photons.


Systematic Uncertainties in current SZ effect measurements

• SZ effect calibration (∓8%)• X-ray calibration ( 10%∓ )• galactic absorption column density ( 5%∓ )• unresoved point sources still contaminate measurement of the temperature decrement ( 16%)∓•Clusters that are prolate or oblate along the line of sight will be affected.

Reese et al. 2001


References

1. Birkinshaw astro-ph/98080502. Bernstein & Dodelson Physical Review, 41, 2 19903. Cardone et al. A&A 429, 49-64 (2005)4. Carlstrom et al. astro-ph/9905255


CL 0016+16

H0 = 68 km s-1 Mpc-1

if the cluster is modeled with a sphere isothermal

first predicted by the russian scientists sunayaev and zel’dovich in 1969

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