The CMB and the SZ Effect

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The CMB and the SZ Effect

• Current Topics 2008
• Dr. Katy Lancaster

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Course Content

• Introduction
• The Cosmic Microwave Background
• The Sunyaev Zeldovich Effect
• Science from the SZ effect
• The Hubble constant
• Gas fractions
• Number counts
• Practicalities
• Telescopes
• Issues

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Lecture 1

• A brief history
• Production of the CMB
• Production of primary anisotropies
• The Sunyaev Zeldovich effect

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Brief history lesson

• 1950s, two conflicting cosmological theories
• Steady State theory
• Universe always has been and always will be in a
  static, homogenous state.
• Expanding Universe
• Hubbles observations, 1929
• Gamov - realised that the Universe was once
  extremely dense and hot, thus must have since
  expanded and cooled

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Penzias and Wilson

• 1965, were making sensitive observations of
  microwave emission from the galaxy
• Detect annoying level of static in all
  directions
• At the same time, Dicke at Princeton predicted
  the existence of relic radiation from the Big
  Bang
• Nobel Prize, 1978

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COBE

• NASA satellite launched late 80s
• Cosmic Microwave Background radiation was found
  to have a perfect blackbody spectrum
• Implies Universe was once isothermal. Only Big
  Bang models predict this.
• For this (and other reasons), the COBE scientists
  won the Nobel prize in 2007

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Primordial Universe

• Early Universe Devoid of structure.
• T gt 4000K, entirely ionised - sea of electrons,
  protons, helium nuclei and photons
• Too hot for atoms to form
• Photons repeatedly Thomson scatter from
  electrons, unable to propagate freely
• Almost perfect thermal equilibrium due to the
  coupling of matter and radiation
• Predicted and required by Big Bang models
• Universe is opaque

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Thermalisation

• As COBE discovered, the CMB has a perfect
  blackbody spectrum.
• Two contributory processes during the first year
  after the Big Bang, each creates/destroys
  photons
• At very early times, thermal Bremstrahlung
  radiation / absorption ep?ep?. This ceased
  as the Universe cooled. Produces thermal
  spectrum
• Later, double Compton scattering e? ? e2?.
• Only effective while collision rate gt expansion
  rate
• Since then there has been no process capable of
  destroying the spectrum (although there may be
  tiny distortions)

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Recombination

• Early Universe filled with free electrons, photon
  mean-free path small (Universe in thermal
  equilbrium, opaque)
• Impossible for any information about this time to
  be communicated to us via radiation
• Temperature of Universe falls to 4000K, very few
  photons with energy gt Hydrogen binding energy,
  13.6eV
• Electrons and protons combine ep ? H?
• Vast majority of free electrons disappear.
  Universe now neutral, photons can free-stream
• In fact recombination happens over a time or
  redshift slice (1500 gt z gt 1200 ) rather than
  instantaneously.

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Surface of last scattering

• The CMB photons were emitted at the same time,
  and thus underwent their final scattering event
  at the same time
• All CMB photons move at the speed of light, have
  travelled the same distance since this time
• We can think of the CMB as being emitted from a
  fictitious spherical surface, of which we are at
  the centre
• Like observing the surface of the sun, although
  it is the outer reaches (or rather, the very
  early Universe) that we can not observe, rather
  than the inner workings
• Strictly speaking, recombination is not
  instantaneous, so we sometimes talk about the
  thickness of the surface

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Surface of last scattering
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The CMB today

• The CMB photons have been significantly
  redshifted by the Hubble expansion.
• Photon wavelengths have increased by
  R(t)1/(1z)
• CMB temperature falls as 1/R(t) a specific
  prediction of the Big Bang model
• Temperature of the CMB today T0 T/(1z) 2.73K
• Can test the relation at other redshifts by
  observing stellar line emission from CN molecules
• Actually first measured in circa 1940 but not
  identified as the CMB until much later!

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Observing the CMB

• Uniform high energy glow - the sky is not dark at
  radio frequencies

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The Dipole

• Doppler shift introduces hot and cold regions
• The Local group is moving at 400km/s relative to
  the CMB!
• Also see annual modulation due to Earths orbit

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Primary Fluctuations

• The CMB appears isotropic (same temperature
  everywhere) unless we look very carefully
• Initial isotropy actually slightly distorted
  during / before recombination
• We observe temperature variations, referred to as
  primordial anisotropies or fluctuations (see
  pic)
• We measure the temperature difference in two
  directions separated by some angle ?.
• Take many measurements and find the mean value
  for a particular angular scale
• All CMB anisotropies are characterised in this
  way

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• WMAP, monopole, dipole and galactic emission
  removed
• ?K in the presence of 3K background

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Primary Fluctuations

• The CMB appears isotropic (same temperature
  everywhere) unless we look very carefully
• Initial isotropy actually slightly distorted
  during / before recombination
• We observe temperature variations, referred to as
  primordial anisotropies or fluctuations (see
  pic)
• We measure the temperature difference in two
  directions separated by some angle ?.
• Take many measurements and find the mean value
  for a particular angular scale
• All CMB anisotropies are characterised in this
  way

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• Measure size of temperature difference for a
  range of ?
• Plot against ? Power Spectrum

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Sources of anisotropy

• Sachs Wolfe Effect
• Acoustic Oscillations
• Doppler Shift
• Silk Damping
• Secondary processes

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Sachs Wolfe Effect

• Quantum fluctuations in the dark matter
  distribution led to density inhomogeneities
• These developed under gravity
• A CMB photon released from a region with a
  non-zero gravitational potential will experience
  an additional redshift
• It has to climb out of the potential well
• This creates power on the scales gt 1?

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Acoustic Oscillations

• Over-dense regions in dark matter amplified
  during inflation, collapse under gravity
• Baryons falls into the resulting potential wells
• Radiation pressure increases as the material
  collapses
• Eventually the pressure overcomes gravity and
  causes an expansion.
• ..expansion continues until gravity wins again

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Acoustic Oscillations

• This was taking place at recombination
• Oscillations were happening on all scales.
  Largest scale sound horizon. Other scales were
  not causally connected.
• Modes which had reached their extrema by
  recombination produced enhanced features in the
  CMB
• Compressions - hot spots. (Recombined slightly
  later, thus suffered less cosmological
  redshifting)
• Rarefactions - cold spots. (Recombined slightly
  earlier)

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Acoustic Oscillations

• Oscillating modes form harmonic sequence
  Largest regions had diameter of the sound
  horizon, next largest were half this size etc
• Oscillation frequencies corresponded to this
  largest region oscillates at half the speed of
  the next largest etc
• First peak region which had time to compress
  exactly once before recombination
• Second peak region which had time to compress
  and rarefy, ie one full oscillation before
  recombining
• Third peak, fourth peak.

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Doppler shifts

• Also related to the acoustic oscillations
• At times inbetween the extrema of expansion for
  each oscillation region, the motion of the fluid
  reached its maximum velocity
• This resulted in a Doppler shift of the photons
  released when the plasma recombined
• This contriubutes power inbetween the locations
  of the acoustic peaks the power spectrum does
  not go to zero

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Silk Damping

• On the smallest scales, the effect of photons
  escaping from the oscillating region becomes
  important
• The loss of these photons damps the power on
  the smallest angular scales

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What can we learn?

• The power spectrum is a complicated function
  which depends on the values of the various
  cosmological parameters H0, ?M, ?b, ??, ?k,
  zre, t0.and many more.
• We observe the CMB and then try fitting the
  powere spectrum to the data. We tweak the
  parameters to find the best fit.
• And hey presto, we have our very own measurement
  of the cosmological model

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What can we learn?
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Galaxy formation

• The anisotropies in the CMB are widely regarded
  as imprints of the seeds of structure formation
• That is, those oscillating regions from the early
  Universe grew and developed under gravity into
  the stars and galaxies we see today
• If we take the CMB and compare it to observations
  of large scale structure, we can constrain
  structure formation scenarios

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Secondary Anisotropies

• Majority of CMB photons have travelled through
  the unimpeded since last scattering
• Hence observed power spectrum
• Some have interacted with ionised matter on their
  path towards us
• This imprints structures on the observable CMB -
  Secondary Anisotropies
• Also contribute to the power spectrum

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Sources of anisotropy

• Integrated Sachs-Wolfe effect
• Gravitational lensing
• Rees-Sciama effect
• Ostriker-Vishniac effect
• Cosmic strings
• Sunyaev Zeldovich effect - by far the largest
• Many more postulated..

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Galaxy Clusters

• Rich Clusters - congregations of hundreds or even
  thousands of galaxies
• See cluster galaxies and lensing arcs in the
  optical
• But only around 5 of a clusters mass is in
  galaxies
• Most of the mass is in Dark Matter
• But a sizable fraction is found in baryonic
  gas......

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X-rays - see hot gas via Bremstrahlung
emission 10-30 of total mass
Chandra Image of the Coma cluster
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Cluster Gas

• Clusters of galaxies have masses 3x1014M?
• Deep potential wells, gas temperatures 7keV
• Ionised and energetic
• Constitutes 30 of the cluster mass
• Gas characteristics may reflect those of the
  Universe as a whole - interesting to study

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Compton Scattering

• Compton scattering Photon loses energy on
  interacting with matter
• Inverse Comptin scattering Photon gains energy
  on interacting with matter
• In the SZ effect low energy CMB photon scatters
  from high energy cluster electron
• Photon energy is boosted

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SZ Effect basics

• CMB photons incident on a galaxy cluster
• Scattering probability is small
• Those which do collide receive energy boost due
  to inverse Compton scattering
• Spectrum shifted to higher frequency
• Decrement - null - increment

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Optical Depth

• For a cluster atmosphere with electron density
  ne(r), the optical depth for scattering along a
  particular line of sight is
• Where ?Tis the Thomson cross section
• The cluster gas is optically thin????eltlt1, ie the
  probability of scattering is small

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Comptonisation

• The degree to which the CMB is affected by
  inverse Compton scattering is described by the
  Comptonisation parameter
• Or for the isothermal approximation (often
  employed in the past)

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Brightness Temperature

• Often used in Radio / CMB astronomy
• Defined as The temperature of a blackbody that
  would be observed with the same intensity as the
  observed source, at a particular frequency
• From the Planck law
• For the low frequency Rayleigh-Jeans region

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Temperature Decrement

• The change in the brightness temperature of the
  CMB due to the thermal SZ effect is given by
• Where the frequency dependence is given by
• For the Rayleigh Jeans region

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Intensity Change

• In units of specific intensity
• With frequency dependence given by

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Kinematic SZ Effect

• Additional spectral distortion caused by cluster
  velocity component along line of sight, ?z
• Collective motion of cluster gas modifies CMB
  spectrum via Doppler shift
• Observe decrement
• Frequency dependence

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SZ Intensity Spectra

• g(x), h(x)
• Thermal decrement, null, increment
• Kinematic Near maximum at the thermal null

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Thermal vs Kinematic

• Specific intensity changes
• Spectral dependence similar at low freq.
• i.e for a typical cluster

The KSZ effect is lt 10 of the thermal effect at
low freq.
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Decrement - Null - Increment

• ACBAR produced these nice images of a galaxy
  cluster at 150, 220 and 275 GHz
• Multi-frequency observations useful for
  eliminating primordial CMB contamination (as well
  as detecting the kinematic effect)

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Summary 1

• CMB - blackbody spectrum, primordial features
• Fit power spectrum to deduce values of the
  cosmological parameters
• CMB photons incident on a galaxy cluster may be
  inverse Compton scattered by hot gas
• This Sunyaev Zeldovich Effect manifests itself
  as a decrement - null - increment depending on
  observing frequency
• Cluster peculiar velocity also modifies the
  radiation via the smaller Kinematic effect