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Anisotropies in the CMB

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)

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Anisotropies in the CMB

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  1. Anisotropies in the CMB Current Topics 2010 Katy Lancaster http://www.star.bris.ac.uk/katy

  2. 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 workshopwith many hints for the assessment

  3. 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….

  4. 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

  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. 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 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

  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….. • Dipole pattern due to motion of Earth/Sun relative to CMB • Indicates a velocity of 400 km/s WMAP

  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 Doublebinned 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 • 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

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