1. Anisotropies in the CMB
Current Topics 2010
Katy Lancaster

2. The course Today (12pm, 4pm): This Thursday: Next Monday (12pm, 4pm):
The Cosmic Microwave Background (CMB)
This Thursday:
NO LECTURE
Next Monday (12pm, 4pm):
The Sunyaev Zel’dovich (SZ) Effect
Next Thursday (5pm)
Journal workshop with many hints for the assessment

3. General Resources CMB temperature anisotropies CMB polarisation
Wayne Hu’s website and associated articles:
Particularly ‘Ringing in the new cosmology’
CMB polarisation
Angelica Oliviera-Costa’s website and links therein:
Particularly her review article:
And movies!
WMAP / Planck websites, wikipedia….

4. Assessment Case study of a CMB experiment: Essay Format
Relevant scientific background
How it works and any unique features
Key science achieved / promised
Comparison with competitors (esp WMAP)
Essay Format
No strict word limit, ~1500 words
Hard copies to me by 5pm Thursday 18th March
Lecture 5: an interactive case-study of WMAP

5. Assessment You could choose via topic:
CMB temperature anisotropies
CMB polarisation
Thermal SZ effect
Kinetic SZ effect
Brain storm of possible experiments:
Some expts look at a combination
CBI
ACT
DASI
OVRO/BIMA
ACBAR
MAXIMA
BOOMERANG
SPT
EBEX
Ryle Telescope
VSA
SuZIE II

6. The Cosmic Microwave Background
Today’s lectures
The Cosmic Microwave Background
Lecture 1: Production of the CMB and associated temperature anisotropies

7. Why are we interested?
The CMB is the oldest and most distant ‘object’ we can observe
It provided definitive proof of the proposed Big Bang model
Its intrinsic features allow us to place tight constraints on the cosmological model
Opened up the era of ‘precision cosmology’

8. Discovery
Penzias &
Wilson

9. Primordial Universe Primordial (early) Universe hot and dense
Plasma of photons, electrons, baryons
T > 4000K
Hot, dense, devoid of structure, too hot for atoms to form
most photons had energies greater than the binding energy of Hydrogen
Photons and baryons tightly ‘coupled’ via Thomson scattering
Unable to propagate freely (opaque, like ‘fog’)
Perfect thermal equilibrium

10. Recombination and decoupling
Universe expands, cools
380,000 years after the big bang, T~4000K
Very few photons have E > 13.6 eV, binding energy of hydrogren (despite large photon-baryon ratio)
Electrons and protons combine: H
Very few charged particles (eg free electrons), Universe largely neutral
Photons no longer scattered, no longer coupled to the baryons
Escape and stream freely across the Universe
We observe these photons today: the CMB

11. Thermal spectrum COBE Perfect black body Proof that Universe
Was once in thermal
equilibrium as required
By big bang models

12. Thermal spectrum COBE: CMB has perfect blackbody spectrum
As required by the big bang model
ie, at some time, the Universe was in thermal equilibrium
How? Two processes:
Thermal Bremstrahlung: e+pe+p+
Double Compton scattering: e+  e+2
Effective while collision rate > expansion rate
No process since has been capable of destroying the spectrum

13. Last scattering surface
CMB photons have (mostly) not interacted with anything since they last scattered off electrons immediately before recombination
We are viewing the ‘surface of last scattering’
All photons have travelled the same distance since recombination
We can think of the CMB as being emitted from a spherical surface, we are at the centre
Behind the surface (ie further back in time) the universe was opaque like a dense fog: we can’t see into it
Strictly speaking, the surface has a thickness as recombination was not instantaneous
This is important for polarisation…..coming later

14. Last scattering surface

15. Last scattering surface

16. Observing the CMB today: Frequency spectrum
COBE

17. Observing the CMB today: Uniform glow across sky

18. Observing the CMB today: Uniform glow across sky
This presents us with the ‘Horizon problem’
Universe isotropic at z~1000? Must have been in causal contact!
Impossible!
Sound horizon size = speed of light x age of z=1000
We know this is ~1 degree
Universe was NOT in causal contact
Invoke inflationary theory to solve this
Universe in causal contact and thermal equilbrium, then experienced a period of rapid growth

19. Observing the CMB: Blackbody Temperature

20. Observing the CMB today
Photons released at recombination have travelled unimpeded to us today
Blackbody spectrum, T=2.73K
Much cooled via expansion of Universe
Observe at microwave frequencies
Highly isotropic (at low contrast)
Fills all of observeable space, makes up majority of Universe’s energy density
~5x10-5 of total density

21. Observing the CMB today: Turn up the contrast…..
WMAP
Dipole pattern due to motion of Earth/Sun relative to CMB
Indicates a velocity of 400 km/s

22. Observing the CMB today: Subtract dipole
WMAP
Snapshot of the Universe aged 380,000 years!
Very beginnings of structure formation

23. ‘Seeds’ of structure formation
At recombination, when the CMB was released, structures had started to form
This created ‘hot’ and ‘cold spots’ in the CMB
K in the presence of 3K background: difficult to see!
These were the seeds of the structures we see today

24. Characterising the CMB: Statistical properties
Other astronomy: observe individual star / galaxy / cluster in some direction
CMB astronomy: concerned with overall properties
Quantify the fluctuation amplitude on different scales
Qualitatively:
Measure temperature difference on sky on some angular separation…..many times….find mean
Plot as a function of angular scale
Higher resolution doesn’t mean better in this context
‘Power spectrum’

25. < 20
> 9°
2 < < 1000
0.02° < < 90°

26. Characterising the CMB: Statistical properties
Amplitude of fluctuations as function of angular scale

27. More rigorously
Measure temperature of CMB in a given direction on sky,
Subtract mean temperature and normalise to give dimensionless anisotropy:
Expand anisotropies in spherical harmonics (analogue of Fourier series for surface of sphere):

28. Analogy: Fourier series
Sum sine waves of different frequencies to approximate any function
Each has a coefficient, or amplitude

29. Back to the CMB… Use spherical harmonics in the place of sine waves
Calculate coefficients, and then the statistical average:
Amplitude of fluctations
on each scale.
This is what we plot!

30. Visualising the components
Multipoles

31. In practice Design experiment to measure Find component amplitudes
Plot against
is inverse of angular scale,

32. Plotting the power spectrum
Double binned
Note third peak
Very small array (VSA), 2002

33. Generating theoretical
INPUT
Favorite cosmological
Model: t0, , b, z* ??
PHYSICS
Via powerful
Computer code
CMBFAST
Or CAMB
OUTPUT
Fit to data

34. Primordial Anisotropies
As we have seen, the CMB exhibits fluctuations in brightness temperature (hot and cold spots)
Quantum density fluctuations in the dark matter were amplified by inflation
Gravitational potential wells (and ‘hills’) develop, baryons fall in (or away)
Various related physical processes which affect the CMB photons:
Sachs-Wolfe effect, acoustic oscillations, Doppler shifts, Silk damping
Signatures observeable on different scales

35. Sachs-Wolfe Effect Gravitational potential well No net energy change
Photon falls in, gains energy
Climbs out, loses energy
No net energy change
UNLESS the potential increases / decreases while the photon is inside it
Additional effect of time dilation as potential evolves
Most important at low multipoles
Probes initial conditions
Also: integrated Sachs-Wolfe

36. Acoustic Oscillations
Baryons fall into dark matter potential wells,
Photon baryon fluid heats up
Radation pressure from photons resists collapse, overcomes gravity, expands
Photon-baryon fluid cools down
Oscillating cycle on all scales
Springs:
Photon
pressure
Balls:
Baryon
mass

37. Acoustic peaks Oscillations took place on all scales
We see temperature features from modes which had reached the extrema
Maximally compressed regions were hotter than the average
Recombination happened later than average, corresponding photons experience less red-shifting by Hubble expansion: HOT SPOT
Maximally rarified regions were cooler than the average
Recombination happened earlier than average, corresponding photons experience more red-shifting by Hubble expansion: COLD SPOT

38. First peak
~200
~1º
Characteristic
scale ~1º

39. Other peaks
Harmonic sequence, just like waves in pipes / on strings: ‘overtones’
Same physics, 2nd, 3rd, 4th peaks….
2nd harmonic: mode compresses and rarifies by recombination
3rd harmonic: mode compresses, rarifies, compresses
4th harmonic: 2 complete cycles
Peaks are equally spaced in

40. Harmonic sequence Sound waves in a pipe
Sound waves in the early Universe

41. Harmonic sequence
Modes with half the wavelength oscillate twice as fast, =c/

42. Peaks equally spaced 1 3 2

43. Doppler shifts
Times inbetween maximum compression / rarefaction, modes reached maximum velocity
Produced temperature enhancements via the Doppler effect
Power contributed inbetween the peaks
Power spectrum does not go to zero

44. Doppler shifts

45. Silk Damping
On the smallest scales, easier for photons to escape from oscillating regions
This ‘damps’ the power at high multipoles
Referred to as the ‘damping tail’
Power falls off

46. Power spectrum summary
Acoustic Peaks
Sachs-Wolfe Plateau
Damping tail

47. Many experiments…

48. Many experiments… Broadly fall into three categories: Ground based:
VSA, CBI, DASI, ACBAR
Balloons
Boomerang, MAXIMA, Archeops
Satellites
COBE, WMAP, Planck
Listen out for mentions of these and their most significant results

49. Summary
The cosmic microwave background (CMB) radiation is left over from the big bang
It was released at ‘recombination’, when the Universe became neutral and Thomson scattering ceased
Structure formation processes were already underway, and are imprinted on the CMB as temperature anisotropies
Next lecture: what we can learn from the anisotropies, and polarisation in the CMB