Anisotropies in the CMB
Current Topics 2010
Katy Lancaster
http://www.star.bris.ac.uk/katy
The course• Today (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
General Resources
• CMB temperature anisotropies– Wayne Hu’s website and associated articles:
http://background.uchicago.edu/~whu/– Particularly ‘Ringing in the new cosmology’
• CMB polarisation– Angelica Oliviera-Costa’s website and links therein:
http://space.mit.edu/~angelica/polarization.html– Particularly her review article: http://xxx.lanl.gov/abs/astro-ph/0406358– And movies!
• WMAP / Planck websites, wikipedia….
Assessment• Case study of a CMB experiment:
– 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– Essay Format
• Lecture 5: an interactive case-study of WMAP
Assessment
• You could choose via topic:– CMB temperature anisotropies – CMB polarisation– Thermal SZ effect– Kinetic SZ effect
• Brain storm of possible experiments:CBI
DASI
Ryle Telescope
OVRO/BIMAACBAR
SPT
ACT
SuZIE II
BOOMERANG MAXIMA
EBEX
Some expts look at a combination
VSA
Today’s lectures
The Cosmic Microwave Background
Lecture 1: Production of the CMB and associated temperature anisotropies
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’
Discovery
Penzias & Wilson
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
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
Thermal spectrum
Proof that UniverseWas once in thermalequilibrium as requiredBy big bang models
Perfect black body
COBE
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+pe+p+– Double Compton scattering: e+ e+2
• Effective while collision rate > expansion rate• No process since has been capable of
destroying the spectrum
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
Last scattering surface
Last scattering surface
Observing the CMB today:Frequency spectrum
COBE
Observing the CMB today:Uniform glow across sky
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 Universe @ 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
Observing the CMB: Blackbody Temperature
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
Observing the CMB today:Turn up the contrast…..
• Dipole pattern due to motion of Earth/Sun relative to CMB
• Indicates a velocity of 400 km/s
WMAP
Observing the CMB today:Subtract dipole
• Snapshot of the Universe aged 380,000 years!
• Very beginnings of structure formation
WMAP
‘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
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’
< 20
2 < < 1000
> 9°
0.02° < < 90°
Characterising the CMB:Statistical properties
Amplitude of fluctuations as function of angular scale
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):
Analogy: Fourier series
• Sum sine waves of different frequencies to approximate any function
• Each has a coefficient, or amplitude
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!
Visualising the components
Multipoles
In practice
• Design experiment to measure
• Find component amplitudes
• Plot against
• is inverse of angular scale,
Plotting the power spectrum
Very small array (VSA), 2002
Double binnedNote third peak
Generating theoretical
OUTPUT
INPUTFavorite cosmological
Model: t0, , b, z*
PHYSICS
Via powerful Computer code
CMBFAST Or CAMB
Fit to data
??
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
Sachs-Wolfe Effect
• Gravitational potential well – 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
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
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
First peak
~200
~1º
Characteristicscale ~1º
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
Harmonic sequence
Sound waves in a pipe
Sound waves in the early Universe
Harmonic sequence
Modes with half the wavelength oscillate twice as fast, =c/
Peaks equally spaced
1
23
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
Doppler shifts
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
Power spectrum summary
Sachs-Wolfe Plateau
Acoustic Peaks
Damping tail
Many experiments…
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
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