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