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Anisotropies in the CMB Current Topics 2010 Katy Lancaster

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

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General Resources CMB temperature anisotropies –Wayne Hus website and associated articles: –Particularly Ringing in the new cosmology CMB polarisation –Angelica Oliviera-Costas 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: –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

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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: CBI DASI Ryle Telescope OVRO/BIMA ACBAR SPT ACT SuZIE II BOOMERANG MAXIMA EBEX Some expts look at a combination VSA

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Todays 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 Proof that Universe Was once in thermal equilibrium as required By big bang models Perfect black body COBE

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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+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

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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 cant 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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Observing the CMB today: Frequency spectrum COBE

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Observing the CMB today: Uniform glow across sky

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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 Universes energy density –~5x10 -5 of total density

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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

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

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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 doesnt mean better in this context Power spectrum

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< 20 2 < < 1000 > 9° 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 Very small array (VSA), 2002 Double binned Note third peak

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Generating theoretical OUTPUT INPUT Favorite cosmological Model: t 0,, b, z* PHYSICS Via powerful Computer code CMBFAST Or CAMB 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 –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 2 3

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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 Sachs-Wolfe Plateau Acoustic Peaks Damping tail

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Many experiments…

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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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