Lecture 3 The Sunyaev Zel'dovich Effect

							        Lecture 3

The Sunyaev Zel’dovich Effect
                Lecture 3
• What is the Sunyaev Zel’dovich Effect?
• Why is SZ useful? Unique property, science we
  can derive from measurements
• Real examples, comparisons between
  experiments
• What improvements are required in order to
  progress with ‘traditional’ aims
• Current status (the truth behind the hype)
• Science prospects for the future
• Note… If I refer to ‘SZ’ without specifiying, I mean
  thermal!
   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
• Integrated Sachs-Wolfe effect, Rees-Sciama
  effect, Gravitational lensing (of the CMB), Cosmic
  strings, Sunyaev Zel’dovich effect - by far the
  largest, Ostriker-Vishniac effect, Others??
          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 cluster’s mass is in
  galaxies
• Most of the mass is in Dark Matter
• But a sizable fraction is found in baryonic
  gas......
                                X-rays - see hot gas
                                via Bremstrahlung
                                emission

                                10-30% of total mass




Chandra Image of the Coma cluster
            Cluster Gas
• Clusters have masses ~ 3x1014 M
• 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
Aside: Compton Scattering
• Compton scattering: Photon loses
  energy on interacting with matter
• Inverse Compton 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
                          SZ Effect basics
                                                 • CMB photons incident on a
                                                   galaxy cluster
                                                 • Scattering probability is
                                                   small
                                                 • Those which do collide
            Photons scattered to higher energy     receive energy boost due
                                                   to inverse Compton
                                                   scattering
Intensity




                                                 • Spectrum shifted to higher
                   SZ dip at radio                 frequency
                   frequencies
                                                 • Decrement - null -
                   Frequency                       increment
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)
             Optical Depth
• For a cluster atmosphere with electron
  density ne(r), the optical depth for scattering
  along a particular line of sight is:




• Where σT is the Thomson cross section
• The cluster gas is optically thin. τe<<1, ie the
  probability of scattering is small
          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):
         Aside:
 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:
 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:

                            with
• For the Rayleigh Jeans region:
      Intensity Change

• In units of specific intensity:

• With frequency dependence given
  by:
     Kinematic SZ Effect
• Additional spectral distortion caused by cluster
  velocity component along line of sight, βz
• Collective motion of cluster gas modifies CMB
  spectrum via Doppler shift
• Observe decrement:


• Where:
SZ Intensity Spectra

             • Shape of g(x), h(x)

             • Thermal:
               decrement, null,
               increment

             • Kinematic: Near
               maximum at the
               thermal null
          Thermal vs Kinematic
• Specific intensity changes:



• Spectral dependence similar at
  low freq.



• i.e for a typical cluster:

 The KSZ effect is < 10% of the thermal effect at low freq.
     A Brief History of SZ
• Postulated by Sunyaev and Zel’dovich in 1970
• Many observational attempts with little success
  until Birkinshaw 1978 - trustworthy measurement
  put the technique on the map (OVRO)
First SZ image - Jones 1993.
1990s, 2000s - plethora of SZ studies. 50+
  detections, unresolved images
2000s onwards - purpose built instruments,
  surveys, high resolution images, samples
     A Brief History of SZ
Postulated by Sunyaev and Zel’dovich in 1970
Many observational attempts with little success
  until Birkinshaw 1978 - trustworthy
  measurement put the technique on the map
• First SZ image - Jones 1993 (Ryle Tel.)
• 1990s, 2000s - plethora of SZ studies. 50+
  detections, unresolved images
• 2000s onwards - purpose built instruments,
  surveys, high resolution images, samples
Strength of decrement independent of redshift
        SZ Science Basics
• SZ can be exploited alone, or in combination
  with data from other wavebands
• Most astronomy relies on multi-frequency
  observations (i.e. optical, infrared, X-ray, radio)
• Can combine SZ with:
  • X-rays (discussed at length here)
  • Strong lensing (total mass)
  • Weak lensing
  • Velocity dispersions from optical spectra
        X-ray observations
• In these lectures, we will focus predominantly on how
  we combine SZ with X-ray data
• X-ray surface brightness is given by:



• More usual to remember that:



• So the X-ray emission has a different dependence on
  the cluster temperature and density
    SZ Redshift Independence
• Unique property of the SZ effect
• SZ is a spectral distortion rather than a process of
  emission. Recall:



• No redshift dependence
• For central measures, completely independent of
  redshift. Total flux density depends on angular size
• Extremely useful for surveys - currently detect
  clusters out to redshift ~1 (optical, IR, X-ray)
     Scientific Applications
• We can learn a great deal of science from SZ
  measurements:
  - Thermal SZ - Cosmology: Angular diameter
    distance, Hubble’s constant, Hubble diagrams
  - Thermal SZ - Cluster properties: Cluster gas
    fractions, Universal Baryon fraction
  - Number counts - Test cosmological models
  - Kinematic SZ - Cluster peculiar velocities
• We will also look at some major results found in
  the literature
      Distance Estimates
• Back to the equations for SZ and X-ray
  surface brightness. Approximate the
  temperature and density distribution as
  constants:

• Equate and eliminate the density term:
     Distance Estimates
• Relate the size of the cluster on the
  sky to the line-of-sight distance
  through it
  - If spherical, size on sky = l-o-s distance
  - Could also assume an elliptical model
  - In reality: fit a model to the X-ray data
• Simplest case:
      Distance Estimates
• More complicated than this really….
• Density is far from constant
• Assume a model for the density distribution, eg:




• And integrate….. Gets even more complicated!
• Well explained in Birkinshaw, Hughes and
  Arnaud 1991
               Literature....
• Mason et al. 2001: ‘A measurement of H0 from
  the S-Z effect’. ~7 clusters,

• Reese et al 2002: ‘Determing the cosmic
  distance scale from interferometric measurements
  of the S-Z Effect’. ~20 clusters,

• Jones et al. 2005: ‘H0 from an orientation
  unbiased sample of S-Z and X-ray clusters’, small
  sample but more sensible selection,
               Hubble Diagram
                       • Angular diameter
                         distances determined
                         from SZ
                         measurements,
                         plotted against redshift

                       • Lines correspond to
                         different cosmologies

                       • Clearly need higher
                         redshift data, higher
Reese et al 2002         precision
                         measurements
 Distance scale - future?

• Accuracy of distance estimates sensitive to
  calibration uncertainties
• Best SZ calibration accuracy ~2.5%
• ROSAT calibration ~10% (XMM and
  Chandra are better)
• SYSTEMATICS - uncertain about
  assumptions of isothermality, substructure,
  point source contaminations
   Need higher resolution information - purpose
    built instruments
 Distance scale - future?
• Also limited by sample size, and
  incomplete sample selection
• ‘Complete sample’ - e.g. all clusters
  above some flux limit, regardless of
  size, shape, radio source
  population......
• .....believed to more accurately
  represent the Universe, i.e. less bias
  SZ Surveys will produce more
   statistically robust samples, mass limited
Gas Properties and Ωb

• Have already seen that we can find the
  gas density from SZ if we know the
  temperature - take this from X-ray data.
• Fit cluster-density model to 2-D SZ signal,
  e.g. King model:



• Empirical relation, established for globular
  clusters (!) but works well here
..Gas mass, gas fraction..
• Integrate density distribution out to some
  radius to find the gas mass:


• Can find total mass from SZ by assuming
  hydrostatic equilibrium, otherwise use X-
  rays / lensing. Then:


• Compare with findings from e.g. X-rays to
  test models and assumptions
          Literature....

• For
• Grego et al 2001: ‘Galaxy cluster gas
  mass fractions from Sunyaev Zel’dovich
  measurements: Constraints on ΩM.’

• Lancaster et al 2005: ‘Very Small Array
  observations of the Sunyaev Zel’dovich
  effect in nearby galaxy clusters.’
    Cluster Evolution?




                       Grego et al 2001
Unable to constrain this well at the moment!
           Constraining ΩM
• Expect ~90% of cluster baryons to exist as ICM.
  Remaining ~10% in galaxies.
• Gas fraction is lower limit on Universal baryon
  fraction


• So, measure baryon fraction from SZ, take
  baryon fraction from eg BBN or primordial CMB,
  leads directly to an estimate of the matter
  density:


     VSA
ICM properties - future?

• Again, larger SZ samples will enable better
  determination of parameters for individual
  clusters
• High resolution observations will allow us
  to fit sophisticated models to the cluster
  gas - substructure
• SZ imaging needs to progress in order to
  keep up with developments in X-rays
Virgo - Rosat
Virgo - Chandra
         Peculiar Velocities
• Can only be derived from the kinematic SZ effect
• Observe at the thermal null, or use multi-
  frequency data
• Spectrally the same as primordial CMB - difficult
  to measure peculiar velocity for individual
  objects.
• Samples more promising - uncertainties average
  out
• Measure velocity fields at high redshift by finding
  peculiar velocities for many clusters
   Literature...
             Thermal + Kinematic
             SZ for Abell 2163



                    SuZIE

                   Diabolo + SuZIE

               Best-fit Thermal
BIMA           Best-fit Kinematic
               Best-fit Combined
   Literature...
             Thermal + Kinematic
             SZ for Abell 2163



                    SuZIE

                   Diabolo + SuZIE


BIMA
Why are peculiar velocities
         useful?
• Measure for a number of clusters in a
  particular redshift ‘bin’ and minimise errors
• Repeat for a range of redshift bins
• Can derive something about the formation
  of large scale structure - i.e. how quickly
  things are moving around at different
  redshifts
• Clusters move under gravity - learn about
  distribution of matter at different epochs
         The next big thing:
            SZ Surveys
• SZ selected samples will allow us to improve on
  ‘traditional’ SZ applications (Hubble const. etc)
• New frontier - cluster number density and its
  evolution with time
• The potential of this application will be realised
  with the release of cluster catalogues from SZ
  surveys
• One aim is simply to record how many clusters are
  found in e.g. different redshift bins
• Examine cluster evolution (e.g. mass functions)
  and the geometry of the Universe
         Cluster Abundance




                       Distinguish between
                       cosmological models
Carlstrom et al 2002
    SZ-selected samples
• Previous SZ samples are often chosen
  somewhat arbitrarily - i.e. clusters picked
  because they are easy to observe
• Some attempts to select representative
  samples from X-ray catalogues (e.g. Jones
  et al 2005, Lancaster et al 2005)
• Still subject to ‘selection effects’ (i.e. X-
  rays point preferentially to dense clusters)
• SZ catalogues will be mass-limited only
    SZ-selected samples
• X-ray catalogues are limited in numbers
  due to rapid fall off of detectable flux with
  distance
• SZ catalogues do not suffer from this
  limitation - will yield large numbers of new
  clusters, enabling studies of large scale
  structure via methods currently applied to
  galaxy catalogues e.g. 2DF
• Will also provide the first picture of the
  high-redshift Universe
     SZ Science to date
• Distance estimates to reasonable
  precision
  - Good agreement between different
    experiments
• ICM properties e.g. gas fractions
  - Large errors but consistent between
    experiements
      Surveys: South Pole
        Telescope (SPT)
• Staniszewski et al
  2008
• FIRST SZ SURVEY
  TO PUBLISH!
• Detect 4 clusters in
  their blind survey
• 3 (1!) previously
  unknown
• Larger dataset
  currently being
  analysed
    Surveys: Arcminute
  Microkelvin Imager (AMI)
• Barker et al 2006
• Imaged one cluster
• Many more pointed
  observations….will
  publish ‘soon’
• Blind survey underway
• My top tip for the best
  suppression of
  contaminants
    Surveys (?): Array for
Microwave Anisotropy (AMiBA)
• Wu et al 2009 etc
• Brand new CMB group,
  finding their feet
• Imaged 6 clusters at very
  high significance
• Blind survey capability…..
  But they may stick to
  imaging
     Surveys: One Centimetre
      Receiver Array (OCRA)
• Lancaster et al 2007
• Detect 4 well known
  clusters at high
  significance with
  prototype receiver
• Will publish larger sample
  imminently (scaling
  relations)
• Imaging / surveying
  capabilities with upgrade
       Surveys: Sunyaev
     Zel’dovich Array (SZA)
• Muchovej et al 2007
• Observe 3 high redshift
  clusters
• SZA has performed its
  blind survey….. Before
  the data were analysed,
  the telescope was re-
  configured as KARMA!
• Real experts, so
  perhaps it will be OK….
          Near future:
         what to expect
• Detailed images - physics of clusters as
  individuals, and Universal population
  (OCRA, AMiBA, AMI, SZA?)
• Large samples - more statistically robust
  estimates of cosmological parameters
• Blind surveys - direct view of the growth of
  large-scale structure over entire redshift
  range (SPT, AMI, SZA, OCRA?, AMiBA?)
• Note of caution: need good optical / X-ray
  observations for redshifts and science
                      Summary
• Sunyaev Zel’dovich: Inverse Compton scattering of
  CMB photons by the cluster gas
    – Decrement - null - increment
•   SZ probes the cluster gas differently to X-rays
•   Signal independent of redshift
•   Measure Hubble Constant, Gas fraction
•   Next big thing: SURVEYS
•   Mass limited catalogues, huge international effort