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First predicted by the Russian scientists Sunayaev and Zel’dovich in 1969. Galaxy Clusters have hot gas that produce electrons by bremsstahlung (T gas ~10-100 Kelvin ). CMB photons are cold (T CMB ~ 2.7 Kelvin ). - PowerPoint PPT Presentation
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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%.
Giuseppina CoppolaGiuseppina Coppola 22
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.
Giuseppina CoppolaGiuseppina Coppola 33
Overview
1. CMB2. Radiation basic
3. Scattering by electron population4. Kompaneets approximation
5. SZ and galaxy cluster 6. Struments
Giuseppina CoppolaGiuseppina Coppola 44
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
Giuseppina CoppolaGiuseppina Coppola 55
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.
Giuseppina CoppolaGiuseppina Coppola 66
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
Giuseppina CoppolaGiuseppina Coppola 77
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);
Giuseppina CoppolaGiuseppina Coppola 88
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:
Giuseppina CoppolaGiuseppina Coppola 99
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:
Giuseppina CoppolaGiuseppina Coppola 1010
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
Giuseppina CoppolaGiuseppina Coppola 1111
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
Giuseppina CoppolaGiuseppina Coppola 1212
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
Giuseppina CoppolaGiuseppina Coppola 1313
II. The Kompaneets approximation
Giuseppina CoppolaGiuseppina Coppola 1414
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
Giuseppina CoppolaGiuseppina Coppola 1515
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.
Giuseppina CoppolaGiuseppina Coppola 1616
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)
Giuseppina CoppolaGiuseppina Coppola 1717
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
Giuseppina CoppolaGiuseppina Coppola 1818
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
Giuseppina CoppolaGiuseppina Coppola 1919
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
Giuseppina CoppolaGiuseppina Coppola 2020
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
Giuseppina CoppolaGiuseppina Coppola 2121
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.
Giuseppina CoppolaGiuseppina Coppola 2222
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
Giuseppina CoppolaGiuseppina Coppola 2323
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
Giuseppina CoppolaGiuseppina Coppola 2424
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
Giuseppina CoppolaGiuseppina Coppola 2525
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
Giuseppina CoppolaGiuseppina Coppola 2626
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
Giuseppina CoppolaGiuseppina Coppola 2727
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))
Giuseppina CoppolaGiuseppina Coppola 2828
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
Giuseppina CoppolaGiuseppina Coppola 2929
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)
Giuseppina CoppolaGiuseppina Coppola 3030
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.
Giuseppina CoppolaGiuseppina Coppola 3131
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
Giuseppina CoppolaGiuseppina Coppola 3232
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
Giuseppina CoppolaGiuseppina Coppola 3333
CL 0016+16
H0 = 68 km s-1 Mpc-1
if the cluster is modeled with a sphere isothermal