SZ – overview

B-mode and SZ experiments

SZ – overview

Mark BirkinshawUniversity of Bristol

Cambridge; 20 July 2009 Mark Birkinshaw, U. Bristol 2


Thermal SZ effect

I

Photons gain energy, spectrum depressed at low



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

5 keV15 keV



The ye parameterThe 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.



The Ye parameterA 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).



Angular structure

X-ray (L), SZ effect (R) ellipsoidal models for Abell 665: note difference in angular structures – tSZ effect is far more extended.



The kSZ effectIf 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.



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



Polarization effectsThere 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.



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



tSZE distribution: X-ray selected clusters

Lancaster et al., in prep.



Scaling relations: tSZ/kTe

Close to self-similar slope.

Cluster scaling relation at z ~ 0.2. Mass probe to z >

Lancaster et al., in prep.



Cluster energy contentTotal SZ flux density

thermaleeeRJ UdzTndYS Thermal energy content immediately measured in redshift-independent wayVirial theorem then suggests SZ flux density is direct measure of gravitational potential energy Flux density indicates mass and degree of organization of cluster atmosphere.



Cluster energy content

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

thermaleeeRJ UdzTndYS



Cluster baryonic contentTotal SZ flux density

eeeeeRJ TNdzTndYS 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.



Cluster baryonic content

eeeeRJ TNdzTndS 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-rayTechnique 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.



Baryon mass fractionInside 250 kpc:

XMM +SZMtot = (2.0 0.1)1014 MMgas = (2.6 0.2) 1013 M

Combine results:fb = 0.13 ± 0.02(distance-independent)

WMAP:fb = 0.12 ± 0.02

CL 0016+16 with XMMWorrall & Birkinshaw 2003



Baryon mass fraction evolutionSRJ Ne Te

Total SZ flux total electron count total baryon content.

Compare with total mass (from X-ray or gravitational lensing) baryon fraction Figure from Carlstrom et al. 1999.

b/m



Cluster Hubble diagramX-ray surface brightness

SZE intensity change

Eliminate unknown ne to get cluster size L, and hence distance or H0

LTn eeX2/12

LTnI ee

2/320

2/312

eXL

eX

TIH

TIL



Cluster Hubble diagramCL 0016+16

DA = 1.36 0.15 Gpc

H0 = 68 8 18 km s-1 Mpc-1

Worrall & Birkinshaw 2003



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 From Carlstrom, Holder & Reese 2002



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



Cluster gas structuresBetter 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 ne

2.

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.

NFW



Cluster gas structuresEffective 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 AGNVariety of cluster substructures (shocks, etc.) will also affect

interpretation of large-scale structure. Future of SZ effect may be in finding pressure substructures.



Lensing and SZ effectWeak lensing measures ellipticity field e, and so surface mass density

)(),(1 2crit θθθθ ii ed

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.



Lensing and SZ effectInside 250 kpc:

XMM +SZMtot = (2.0 0.1)1014 M

LensingMtot = (2.7 0.9)1014 M

XMM+SZMgas = (2.6 0.2) 1013 M

CL 0016+16 with XMMWorrall & Birkinshaw 2003



z=0.68z=0.68z=0.58

z=0.73

z=0.14

z=0.14

z=0.29

z=0.25

z=0.25

Noise dominated region

××

4.5

4.25

pixel data from simulations

clusters identified in simulations

Lensing and the tSZ effect



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



Cluster surveys: X-ray

XMM-LSS field

Contains many cluster candidates at z > 1



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)



Cluster countsCluster counts and redshift distribution provide strong constraints on 8, m, and cluster heating.

z

dN/dzm=1.0

m=0.3

m=0.3

Figure from Fan & Chiueh 2001



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



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



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



Cluster radial velocityNeed• 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.



Cluster radial velocityExtracting 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 futureIf can detect statistically in samples of clusters at different

redshifts, can get measure of kinematic evolution of clustering (new datum for cluster formation studies)



Cluster radial velocityJ0717.5+3745 at z = 0.548

Particularly interesting in mergers such as this.

Clearly disturbed, shock-like structure, filament. Hot!

Structure on few arcsec scale, large field map needed.



SZ effect confusion on CMB

Figure from Molnar & Birkinshaw 2000

thermal SZ

kinematic SZ

RS effect



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.

SZ effect confusion on CMB



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)



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



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



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





Blind surveys 0.10 Gross model; confusion

Baryon fraction evolution

0.10 Absolute calibration; isothermal/spherical cluster; gross model

CMB temperature

0.10 Absolute calibration; substructure

Radial velocity 0.05 Absolute calibration; gross model; bandpass calibration; velocity substructure





Cluster formation 0.02 Absolute calibration

Transverse velocity

0.01 Confusion; polarization calibration



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



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.

Documents

SZ – overview