B-mode and SZ experiments
SZ – overview
Mark Birkinshaw
University of Bristol
B-mode and SZ experiments
Thermal SZ effect
Photons gain energy, spectrum depressed at low 
I

Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
tSZ effect – Kompaneets spectrum
• for non-relativistic
electrons, effect is
independent of Te
• at Te > 5 keV enough
electrons relativistic that
spectrum varies at high :
relativistic corrections
measure mass-weighted Te
• Kompaneets form useful
approximation at low  for
all Te
Cambridge; 20 July 2009
5 keV
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Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
The ye parameter
The Comptonization parameter
At low frequency the tSZ effect has amplitude ΔTRJ = -2ye  10-4
for the centre of a rich cluster. CMB photons are far from
equilibrium with cluster gas after scattering.
ye defines the angular shape of the cluster SZ effect – it is a
function of position on the sky, measures line-of-sight averaged
pressure, and is redshift independent.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
The Ye parameter
A survey usually measures an integrated tSZE flux density,
proportional to the integrated Comptonization in the survey beam
An observation will measure only some fraction of the integrated
flux density because of the implicit spatial filtering.
Ye is redshift dependent but a strong indicator of cluster binding
energy (mass).
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Angular structure
X-ray (L), SZ effect (R) ellipsoidal models for Abell 665: note
difference in angular structures – tSZ effect is far more extended.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
The kSZ effect
If the cluster is moving along the line of sight, then in the cluster
frame the CMB is anisotropic. Scattering isotropizes it by an
amount  evz, giving kinematic SZE
This makes the kinematic effect hard to see against the brighter
thermal effect – it’s necessary to use spectral differences to separate
the effects.
Even then, the kinematic effect is heavily confused by primordial
CMB structures – has same spectrum.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
kSZ effect
• kinematic spectrum
related to temperature
gradient of CMB
spectrum
• no zero
• small compared to
thermal effect at low
frequency
• confused by
primordial structure
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
8
B-mode and SZ experiments
Polarization effects
There are three contributions to the polarization signal
•
•
•
scattering the quadrupole in the primordial CMB, effect ~ 0.1 K in either
the E or B modes and coherent shape across the cluster
multiple scatterings inside the cluster, effect ~ 0.1 K in a ring about the
cluster centre
transverse velocity of the cluster, effect ~ 10× smaller (easier to measure
through transverse lensing effect in intensity, ~ 0.1 K)
These effects are confused by the cluster lensing the primordial
CMB polarization, causing a signal ~ 3 K
Spectral and spatial structures of these effects differ, may allow
separation, though lensing effect dominates.
All effects beyond current capabilities.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Levels of study of SZ effect
• First level: detection of integrated effect
– Complete since mid 1980s
– 200+ clusters well detected
– Narrow band of cluster properties (selection effect imposed by
sensitivity, resolution)
– Cluster energy contents, mass measurements, baryon mass fractions,
Hubble constant
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
tSZE distribution: X-ray selected clusters
Lancaster et
al., in prep.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Scaling relations: tSZ/kTe
Close to selfsimilar slope.
Cluster scaling
relation at z ~
0.2. Mass probe
to z >
Lancaster et al., in
prep.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Cluster energy content
Total SZ flux density
S RJ  Ye   d  neTe dz  U thermal
Thermal energy content immediately measured in redshiftindependent way
Virial theorem then suggests SZ flux density is direct measure
of gravitational potential energy
Flux density indicates mass and degree of organization of
cluster atmosphere.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
13
B-mode and SZ experiments
Cluster energy content
S RJ  Ye   d  neTe dz  U thermal
Useful measurement requires absolute calibration of flux
density scale – still an issue in radio astronomy at 5% level.
Comparisons with galaxy kinematics at 5% level valuable but
little work so far.
Requires integration over entire cluster – high level of
confusion for low-z clusters unless the cluster is mapped and
point sources (AGN at cm , star-forming or dusty galaxies at
mm ) and primordial CMB are removed
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Cluster baryonic content
Total SZ flux density
S RJ  Ye   d  neTe dz  N eTe
If have X-ray temperature, then SZ flux density measures
electron count, Ne (and hence baryon count)
Combine with X-ray derived mass to get fb
Redshift-independence of ye should allow baryon content to be
measured to large z.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Cluster baryonic content
S RJ   d  neTe dz  N eTe
Effective measurement of electron number in cluster requires
•
•
•
absolute calibration of SZ data and
adequacy of isothermal model over full SZ extent
accurate electron temperature from X-ray
Technique avoids assumptions on cluster shape, or hydrostatic
equilibrium. Compare with X-ray data to test cluster model.
Integral over cluster, subject to confusion problems at low z.
Much of SZ effect comes from outer gas where Te is poorly
measured in the X-ray.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Baryon mass fraction
Inside 250 kpc:
XMM +SZ
Mtot = (2.0  0.1)1014 M
Mgas = (2.6  0.2)  1013 M
Combine results:
fb = 0.13 ± 0.02
(distance-independent)
WMAP:
fb = 0.12 ± 0.02
Cambridge; 20 July 2009
CL 0016+16 with XMM
Worrall & Birkinshaw 2003
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Baryon mass fraction evolution
SRJ  Ne Te
Total SZ flux  total
electron count  total
baryon content.
b/m
Compare with total mass
(from X-ray or
gravitational lensing) 
baryon fraction
Figure from Carlstrom et al. 1999.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Cluster Hubble diagram
X  n T
X-ray surface brightness
2 1/ 2
e e
I  ne Te L
SZE intensity change
Eliminate unknown ne to get
cluster size L, and hence distance
or H0
Cambridge; 20 July 2009
L
1 3 / 2
X e
L  I  T
2
H 0   L I  X T
Mark Birkinshaw, U. Bristol
2
3/ 2
e
19
B-mode and SZ experiments
Cluster Hubble diagram
CL 0016+16
DA = 1.36  0.15 Gpc
H0 = 68  8  18 km s-1 Mpc-1
Worrall & Birkinshaw 2003
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Cluster Hubble diagram
• poor leverage for other
parameters
• need many clusters at z >
0.5
• need reduced random
errors
• ad hoc sample
• systematic errors
• cluster evolution should
not affect method, can
extend to higher z
Cambridge; 20 July 2009
From Carlstrom, Holder & Reese 2002
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Levels of study
• First level: detection of integrated effect
• Second level: structure of integrated effect
–
–
–
–
Still rudimentary (compare X-ray images)
Low dynamic range of data in contrast (20:1 about best)
Low dynamic range of data in angular scale (5:1 about best)
Astrophysics of cluster structure formation, thermalization of gas,
cluster mergers
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Cluster gas structures
Better measured in the X-ray, since higher
signal/noise. But in principle the ne
dependence of the SZ effect gives higher
sensitivity to cluster edges than ne2.
NFW

Gas structure poorly sampled by current
tSZ data: few map points (radiometer
arrays), poor angular dynamic range
(interferometers). New bolometer data
(MUSTANG, APEX-SZ) better.
Aim: go beyond global models to
astrophysics of gas structures –
atmosphere assembly physics, feedback.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Cluster gas structures
Effective use of SZ to get gas structures requires
•
•
•
•
high sensitivity (long integrations/low systematic errors)
good beamshape knowledge (hard for arrays)
excellent angular dynamic range (hard for interferometers)
good avoidance of confusion and cluster AGN
Variety of cluster substructures (shocks, etc.) will also affect
interpretation of large-scale structure. Future of SZ effect may
be in finding pressure substructures.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Lensing and SZ effect
Weak lensing measures ellipticity field e, and so surface mass
density

1

crit  d θ  i (θ, θ) ei(θ)
2
Surface mass density map combined with SZ effect map gives a
map of fb  SRJ/, and shows distribution of baryons relative to
dark matter in clusters. Integrated over solid angle gives
measure of fb.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Lensing and SZ effect
Inside 250 kpc:
XMM +SZ
Mtot = (2.0  0.1)1014 M
Lensing
Mtot = (2.7  0.9)1014 M
XMM+SZ
Mgas = (2.6  0.2)  1013 M
CL 0016+16 with XMM
Worrall & Birkinshaw 2003
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Lensing and the tSZ effect
z=0.68
z=0.68
z=0.58
z=0.14
z=0.25
z=0.73
z=0.29
4.25
z=0.14
z=0.25
pixel data
from
simulations
clusters
× identified in
simulations
Noise dominated region
4.5
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Levels of study
• First level: detection of integrated effect
• Second level: structure of integrated effect
• Third level: use of integrated effect to find clusters
– Focus of most new instruments: SZA, SPT, APEX/LABOCA, AMI,
OCRA-F, AMiBA, …
– Extensive low-z sample from Planck
– Emphasis on cosmology via cluster counts: redshift distribution
sensitive to σ8 (or Λ)
– Generally rely on multi-band separation of SZ and primary CMB
signals
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Cluster surveys: X-ray
XMM-LSS field
Contains many
cluster candidates at
z>1
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Cluster counts
• SZ-selected samples
– almost mass limited and orientation independent
– potentially more sensitive than X-ray at high z
• Large area surveys
– 1-D interferometer surveys slow, 2-D arrays better
– radiometer arrays fast, but radio source issues
– bolometer arrays fast, good for multi-band work
• Survey in regions of existing surveys
• First large survey results starting to emerge (Bonn
meeting, last week)
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Cluster counts
Cluster counts
and redshift
distribution
provide strong
constraints on 8,
m, and cluster
heating.
dN/dz
m=1.0 L0 80.52
m=0.3 L0.7 80.93
m=0.3 L0 80.87
z
Figure from Fan &
Chiueh 2001
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Cluster counts
• SZ-selected samples limited by changing cluster linear size (and
temperature) and coherence at high z since selection is by
thermal energy content
• maximum detectable redshift probably  2
• evolution little constrained by SZ data – observations over a
wide range of redshift, but insufficient angular dynamic range;
need ye distribution at several z
• need for good follow-up SZ imaging of cluster samples,
including multi-band removal of CMB (10 arcsec or better
angular resolution; 10 μK or better noise; μJy sensitivities)
• beware Malmquist bias – flux density surveys
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
32
B-mode and SZ experiments
Levels of study
•
•
•
•
First level: detection of integrated effect
Second level: structure of integrated effect
Third level: use of integrated effect to find clusters
Fourth level: spectral studies
– Extend cluster surveys to lower temperatures
– Few attempts at cluster velocities, cluster velocity evolution
– No serious work on multi-phase plasmas and non-thermal SZ effect
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
33
B-mode and SZ experiments
Cluster radial velocity
• kinematic effect z-independent in I()
• separable from thermal SZ effect by spectrum
• confusion with primary CMB limits velocity accuracy to about
150 km s-1
• velocity substructure in atmospheres will reduce accuracy
further
• statistical measure of velocity distribution of clusters as a
function of redshift from cluster samples
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Cluster radial velocity
Need
• good SZ spectrum
• X-ray temperature
Confused by CMB
structure
Sample  vz2
Few clusters so far, vz 
1000 km s
A 2163; figure from LaRoque et al. 2002.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Cluster radial velocity
Extracting the kinematic SZ effect requires spectral separation, so
•
•
•
absolute calibration to high precision over range of wavelengths
excellent bandpass calibration to fit spectrum well
knowledge of cluster thermal structure – also requires precision calculation
of spectrum including relativistic and multiple-scattering effects
Expect velocity substructure in cluster gas from mergers and infall
– might be observable in future
If can detect statistically in samples of clusters at different
redshifts, can get measure of kinematic evolution of clustering
(new datum for cluster formation studies)
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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B-mode and SZ experiments
Cluster radial velocity
J0717.5+3745 at z = 0.548
Particularly interesting in
mergers such as this.
Clearly disturbed, shocklike structure, filament.
Hot!
Structure on few arcsec
scale, large field map
needed.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
37
B-mode and SZ experiments
SZ effect confusion on CMB
thermal SZ
kinematic SZ
RS effect
Figure from Molnar & Birkinshaw 2000
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
38
B-mode and SZ experiments
SZ effect confusion on CMB
SZ sky predicted using structure
formation code (few deg2, y = 0
– 10-4)
Primordial fluctuations ignored
Cluster counts strong function
of cosmological parameters and
cluster formation physics.
Need new technology to
perform surveys to low-mass,
high-z clusters.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
39
B-mode and SZ experiments
CMB properties
• Ratio of SZ effects at two
ν is a function of TCMB
(some dependence on Te
and cluster velocity)
• Use SZ effect spectrum to
measure CMB
temperature at distant
locations and over range
of redshifts
• Test Trad  (1 + z)
• SZ results plus molecular
excitation
Battistelli et al. (2002)
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
40
B-mode and SZ experiments
Levels of study
•
•
•
•
•
First level: detection of integrated effect
Second level: structure of integrated effect
Third level: use of integrated effect to find clusters
Fourth level: spectral studies
Fifth level: polarization
– No useful work to date
– Access to 3-D velocity field, remote measure of Q
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
41
B-mode and SZ experiments
CMB properties
• CMB power spectrum shows low quadrupolar power r
• Measure quadrupole at other places in Universe
• SZ effect polarization, important term is conversion of CMB
quadrupole to linear polarization
• Polarization signal small, confused by larger effect of cluster
lensing CMB polarization
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
42
B-mode and SZ experiments
Requirements on observations
Use
Size (mK) Critical issues
Energetics
0.50
Absolute calibration
Baryon count
0.50
Absolute calibration; isothermal/spherical
cluster; gross model
Gas structure
0.50
Beamshape; confusion
Mass distribution
0.50
Absolute calibration; isothermal/spherical
cluster
Hubble diagram
0.50
Absolute calibration; gross model;
clumping; axial ratio selection bias
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
43
B-mode and SZ experiments
Requirements on observations
Use
Size (mK) Critical issues
Blind surveys
0.10
Gross model; confusion
Baryon fraction
evolution
CMB
temperature
Radial velocity
0.10
Absolute calibration; isothermal/spherical
cluster; gross model
0.10
Absolute calibration; substructure
0.05
Absolute calibration; gross model;
bandpass calibration; velocity
substructure
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
44
B-mode and SZ experiments
Requirements on observations
Use
Size (mK) Critical issues
Cluster formation
0.02
Absolute calibration
Transverse
velocity
0.01
Confusion; polarization calibration
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
45
B-mode and SZ experiments
Things to shoot for
• First level: detection of integrated effect.
– Simple for high-temperature clusters
• Second level: structure of integrated effects.
– Depends on noise characteristics, sensitivity, CMB removal
• Third level: use integrated effect to find clusters.
– Similar requirements to structure, but on large sky areas
• Fourth level: spectral studies.
– Essentially new contribution of current and next generation
– Velocity information requires significant cluster sample
– Multi-component study requires high signal/noise
• Fifth level: polarization.
– Would be completely new
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
46
B-mode and SZ experiments
Possible SZ unique studies
• Fast hot outflows around ionizing objects at recombination (or
later) may show kinematic SZ with little thermal SZ.
• Information on multiple components in cluster atmospheres via
spectral studies. Inversion of spectrum into electron distribution
function.
• Information on developing cluster velocity field.
• Non-thermal SZ effect in large-scale radio sources to test
equipartition (c.f., X-ray inverse-Compton studies). Also issue
of non-standard electron populations seen in hot spots and jets.
Cambridge; 20 July 2009
Mark Birkinshaw, U. Bristol
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