1. The CMB and the SZ Effect
Current Topics 2008
Dr. Katy Lancaster

2. Course Content Introduction Science from the SZ effect Practicalities
The Cosmic Microwave Background
The Sunyaev Zel’dovich Effect
Science from the SZ effect
The Hubble constant
Gas fractions
Number counts
Practicalities
Telescopes
Issues

3. Lecture 1 A brief history Production of the CMB
Production of primary anisotropies
The Sunyaev Zel’dovich effect

4. Brief history lesson 1950s, two conflicting cosmological theories
Steady State theory
Universe always has been and always will be in a static, homogenous state.
Expanding Universe
Hubble’s observations, 1929
Gamov - realised that the Universe was once extremely dense and hot, thus must have since expanded and cooled

5. Penzias and Wilson
1965, were making sensitive observations of microwave emission from the galaxy
Detect ‘annoying level of static’ in all directions
At the same time, Dicke at Princeton predicted the existence of ‘relic’ radiation from the Big Bang
Nobel Prize, 1978

6. COBE NASA satellite launched late 80s
‘Cosmic Microwave Background radiation’ was found to have a perfect blackbody spectrum
Implies Universe was once isothermal. Only Big Bang models predict this.
For this (and other reasons), the COBE scientists won the Nobel prize in 2007

7. Primordial Universe Early Universe: Devoid of structure.
T > 4000K, entirely ionised - ‘sea’ of electrons, protons, helium nuclei and photons
Too hot for atoms to form
Photons repeatedly Thomson scatter from electrons, unable to propagate freely
Almost perfect thermal equilibrium due to the ‘coupling’ of matter and radiation
Predicted and required by Big Bang models
Universe is ‘opaque’

8. Thermalisation
As COBE discovered, the CMB has a perfect blackbody spectrum.
Two contributory processes during the first year after the Big Bang, each creates/destroys photons:
At very early times, thermal Bremstrahlung radiation / absorption: e+pe+p+. This ceased as the Universe cooled. Produces thermal spectrum
Later, double Compton scattering: e+  e+2.
Only effective while collision rate > expansion rate
Since then there has been no process capable of destroying the spectrum (although there may be tiny distortions)

9. Recombination
Early Universe filled with free electrons, photon mean- free path small (Universe in thermal equilbrium, ‘opaque’)
Impossible for any information about this time to be communicated to us via radiation
Temperature of Universe falls to ~4000K, very few photons with energy > Hydrogen binding energy, 13.6eV
Electrons and protons combine: e+p  H+
Vast majority of free electrons disappear. Universe now neutral, photons can free-stream
In fact recombination happens over a time or redshift ‘slice’ (1500 > z > 1200 ) rather than instantaneously.

10. Surface of last scattering
The CMB photons were emitted at the same time, and thus underwent their final scattering event at the same time
All CMB photons move at the speed of light, have travelled the same distance since this time
We can think of the CMB as being emitted from a fictitious spherical surface, of which we are at the centre
Like observing the surface of the sun, although it is the outer reaches (or rather, the very early Universe) that we can not observe, rather than the inner workings
Strictly speaking, recombination is not instantaneous, so we sometimes talk about the ‘thickness’ of the surface

11. Surface of last scattering

12. The CMB today
The CMB photons have been significantly redshifted by the Hubble expansion.
Photon wavelengths have increased by R(t)=1/(1+z)
CMB temperature falls as 1/R(t): a specific prediction of the Big Bang model
Temperature of the CMB today T0= T/(1+z) = 2.73K
Can test the relation at other redshifts by observing stellar line emission from CN molecules
Actually first measured in circa 1940 but not identified as the CMB until much later!

13. Observing the CMB
Uniform high energy glow - the sky is not dark at radio frequencies

14. The Dipole Doppler shift introduces ‘hot’ and ‘cold’ regions
The Local group is moving at 400km/s relative to the CMB!
Also see annual modulation due to Earth’s orbit

15. Primary Fluctuations
The CMB appears isotropic (same temperature everywhere) unless we look very carefully
Initial isotropy actually slightly distorted during / before recombination
We observe temperature variations, referred to as ‘primordial anisotropies’ or ‘fluctuations’ (see pic)
We measure the temperature difference in two directions separated by some angle .
Take many measurements and find the mean value for a particular angular scale
All CMB anisotropies are characterised in this way

16. WMAP, monopole, dipole and galactic emission removed
K in the presence of 3K background

17. Primary Fluctuations
The CMB appears isotropic (same temperature everywhere) unless we look very carefully
Initial isotropy actually slightly distorted during / before recombination
We observe temperature variations, referred to as ‘primordial anisotropies’ or ‘fluctuations’ (see pic)
We measure the temperature difference in two directions separated by some angle .
Take many measurements and find the mean value for a particular angular scale
All CMB anisotropies are characterised in this way

18. Measure size of temperature difference for a range of 
Plot against  : ‘Power Spectrum’

20. Sources of anisotropy Sachs Wolfe Effect Acoustic Oscillations
Doppler Shift
Silk Damping
Secondary processes

21. Sachs Wolfe Effect
Quantum fluctuations in the dark matter distribution led to density inhomogeneities
These developed under gravity
A CMB photon released from a region with a non-zero gravitational potential will experience an additional redshift
It has to ‘climb out’ of the potential well
This creates ‘power’ on the scales > 1

22. Acoustic Oscillations
Over-dense regions in dark matter amplified during inflation, collapse under gravity
Baryons falls into the resulting potential wells
Radiation pressure increases as the material collapses
Eventually the pressure overcomes gravity and causes an expansion….
…..expansion continues until gravity wins again

23. Acoustic Oscillations
This was taking place at recombination
Oscillations were happening on all scales. Largest scale: sound horizon. Other scales were not ‘causally connected’.
Modes which had reached their extrema by recombination produced enhanced features in the CMB
Compressions - hot spots. (Recombined slightly later, thus suffered less cosmological redshifting)
Rarefactions - cold spots. (Recombined slightly earlier)

24. Acoustic Oscillations
Oscillating modes form harmonic sequence: Largest regions had diameter of the sound horizon, next largest were half this size etc
Oscillation frequencies corresponded to this: largest region oscillates at half the speed of the next largest etc
First peak: region which had time to compress exactly once before recombination
Second peak: region which had time to compress and rarefy, ie one full oscillation before recombining
Third peak, fourth peak….

25. Doppler shifts Also related to the acoustic oscillations
At times inbetween the extrema of expansion for each oscillation region, the motion of the fluid reached its maximum velocity
This resulted in a Doppler shift of the photons released when the plasma recombined
This contriubutes power inbetween the locations of the acoustic peaks: the power spectrum does not go to zero

26. Silk Damping
On the smallest scales, the effect of photons ‘escaping’ from the oscillating region becomes important
The loss of these photons ‘damps’ the power on the smallest angular scales

27. What can we learn?
The power spectrum is a complicated function which depends on the values of the various cosmological parameters: H0, ΩM, Ωb, Ω, Ωk, zre, t0….and many more.
We observe the CMB and then try fitting the powere spectrum to the data. We tweak the parameters to find the best fit.
And hey presto, we have our very own measurement of the cosmological model

28. What can we learn?

29. Galaxy formation
The anisotropies in the CMB are widely regarded as imprints of the ‘seeds’ of structure formation
That is, those oscillating regions from the early Universe grew and developed under gravity into the stars and galaxies we see today
If we take the CMB and compare it to observations of large scale structure, we can constrain structure formation scenarios

31. Secondary Anisotropies
Majority of CMB photons have travelled through the unimpeded since last scattering
Hence observed power spectrum
Some have interacted with ionised matter on their path towards us
This imprints structures on the observable CMB - ‘Secondary Anisotropies’
Also contribute to the power spectrum

32. Sources of anisotropy Integrated Sachs-Wolfe effect
Gravitational lensing
Rees-Sciama effect
Ostriker-Vishniac effect
Cosmic strings
Sunyaev Zel’dovich effect - by far the largest
Many more postulated…..

34. Galaxy Clusters
Rich Clusters - congregations of hundreds or even thousands of galaxies
See cluster galaxies and lensing arcs in the optical
But only around 5% of a cluster’s mass is in galaxies
Most of the mass is in Dark Matter
But a sizable fraction is found in baryonic gas......

35. Chandra Image of the Coma cluster
X-rays - see hot gas
via Bremstrahlung emission
10-30% of total mass
Chandra Image of the Coma cluster

36. Cluster Gas Clusters of galaxies have masses ~ 3x1014M
Deep potential wells, gas temperatures ~7keV
Ionised and energetic
Constitutes ~30% of the cluster mass
Gas characteristics may reflect those of the Universe as a whole - interesting to study

37. Compton Scattering
Compton scattering: Photon loses energy on interacting with matter
Inverse Comptin scattering: Photon gains energy on interacting with matter
In the SZ effect: low energy CMB photon scatters from high energy cluster electron
Photon energy is boosted

38. SZ Effect basics CMB photons incident on a galaxy cluster
Scattering probability is small
Those which do collide receive energy boost due to inverse Compton scattering
Spectrum shifted to higher frequency
Decrement - null - increment
Need a new name for this?

39. Optical Depth
For a cluster atmosphere with electron density ne(r), the optical depth for scattering along a particular line of sight is:
Where Tis the Thomson cross section
The cluster gas is optically thine<<1, ie the probability of scattering is small

40. Comptonisation
The degree to which the CMB is affected by inverse Compton scattering is described by the Comptonisation parameter:
Or for the isothermal approximation (often employed in the past):

41. Brightness Temperature
Often used in Radio / CMB astronomy
Defined as: ‘The temperature of a blackbody that would be observed with the same intensity as the observed source, at a particular frequency’
From the Planck law:
For the low frequency Rayleigh-Jeans region:

42. Temperature Decrement
The change in the brightness temperature of the CMB due to the thermal SZ effect is given by:
Where the frequency dependence is given by:
For the Rayleigh Jeans region:

43. Intensity Change In units of specific intensity:
With frequency dependence given by:

45. Kinematic SZ Effect
Additional spectral distortion caused by cluster velocity component along line of sight, z
Collective motion of cluster gas modifies CMB spectrum via Doppler shift
Observe decrement:
Frequency dependence:

46. SZ Intensity Spectra g(x), h(x) Thermal: decrement, null, increment
Kinematic: Near maximum at the thermal null

47. The KSZ effect is < 10% of the thermal effect at low freq.
Thermal vs Kinematic
Specific intensity changes:
Spectral dependence similar at low freq.
i.e for a typical cluster:
Proportionalities, typical values. Highlight this!
The KSZ effect is < 10% of the thermal effect at low freq.

48. Decrement - Null - Increment
ACBAR produced these nice images of a galaxy cluster at 150, 220 and 275 GHz
Multi-frequency observations useful for eliminating primordial CMB contamination (as well as detecting the kinematic effect)

49. Summary 1 CMB - blackbody spectrum, primordial features
Fit ‘power spectrum’ to deduce values of the cosmological parameters
CMB photons incident on a galaxy cluster may be inverse Compton scattered by hot gas
This ‘Sunyaev Zel’dovich Effect’ manifests itself as a decrement - null - increment depending on observing frequency
Cluster peculiar velocity also modifies the radiation via the smaller ‘Kinematic’ effect