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**Anisotropies in the CMB**

Current Topics 2010 Katy Lancaster

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**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

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**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….

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**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

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**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

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**The Cosmic Microwave Background**

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

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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’

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Discovery Penzias & Wilson

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**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

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**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

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**Thermal spectrum COBE Perfect black body Proof that Universe**

Was once in thermal equilibrium as required By big bang models

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**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

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**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

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**Last scattering surface**

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**Last scattering surface**

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**Observing the CMB today: Frequency spectrum**

COBE

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**Observing the CMB today: Uniform glow across sky**

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**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

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**Observing the CMB: Blackbody Temperature**

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**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

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**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

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**Observing the CMB today: Subtract dipole**

WMAP Snapshot of the Universe aged 380,000 years! Very beginnings of structure formation

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**‘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

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**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’

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< 20 > 9° 2 < < 1000 0.02° < < 90°

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**Characterising the CMB: Statistical properties**

Amplitude of fluctuations as function of angular scale

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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):

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**Analogy: Fourier series**

Sum sine waves of different frequencies to approximate any function Each has a coefficient, or amplitude

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**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!

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**Visualising the components**

Multipoles

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**In practice Design experiment to measure Find component amplitudes**

Plot against is inverse of angular scale,

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**Plotting the power spectrum**

Double binned Note third peak Very small array (VSA), 2002

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**Generating theoretical**

INPUT Favorite cosmological Model: t0, , b, z* ?? PHYSICS Via powerful Computer code CMBFAST Or CAMB OUTPUT Fit to data

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**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

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**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

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**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

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**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

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

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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

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**Harmonic sequence Sound waves in a pipe**

Sound waves in the early Universe

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Harmonic sequence Modes with half the wavelength oscillate twice as fast, =c/

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Peaks equally spaced 1 3 2

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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

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Doppler shifts

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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

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**Power spectrum summary**

Acoustic Peaks Sachs-Wolfe Plateau Damping tail

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Many experiments…

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**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

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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

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