Fermi Summer School (July 22, 2008)

The The AMiBAAMiBA ProjectProject

Keiichi Keiichi UmetsuUmetsu, on behalf of , on behalf of

The The AMiBAAMiBA TeamTeam

OutlineOutline

1.1. CMB and InterferometersCMB and Interferometers2.2. Introduction: Introduction: AMiBAAMiBA3.3. Science GoalsScience Goals4.4. Progress OverviewProgress Overview5.5. First First AMiBAAMiBA Observations of 6 Observations of 6

ClustersClusters6.6. SummarySummary

1.1. Interferometers for CMB Interferometers for CMB ObservationsObservations

CMB vs. InterferometerCMB vs. Interferometer

To measure the weight of a frog which is attached to a Jumbo-Jet:

Single dish observations compare two measurements:

mMmM =−+ ')(

mM

M : weight of Jumbo with the frog'M : weight of Jumbo without a frog

5' 10

−<Mm

Interferometer measures directly m

Credit: Prof. Atsuto Suzuki;

Figure by Prof. Makoto Hattori Measurement of CMB anisotropy:

Observable: Observable: Complex Visibility, Complex Visibility, V(u,vV(u,v))

multipoleangular ||2

vectorbaseline

]2exp[)()()( 2

ul

du

xuixIxAxduV

r

rr

rrrrr

πλ

π

≈

=

⋅= ∫

I(x) : intensity map on the skyA(x) : antenna primary beam pattern

)]()([)( xIxAuV rrr FT=

Visibility is Fourier Transform of intensity pattern I(x) attenuated by A(x)d=

)()(| *2 uVuVC ullrr

≈= π

Angular power spectrum directly measured by interferometer!!

E-field measured by a pair of receivers, being cross-correlated to form a complex visibility

Fringes Fringes transitFringes in drift-scanning observations with

the 2-element AMiBA prototype (2002-2004)

CMB InterferometersCMB InterferometersTypical angular sizes ~ 1degree – 10 arcmin

small antennas, and/or, low frequency (10-100GHz) CMB anisotropy = diffuse, weak signal (10-100μK)

close-packed, or compact array to maximize sensitivityObserving strategies, different from traditional onese.g., no geometrical delay to creat fringes when tracking

CBI @ 26-36 GHz, 13 elements,Chile (1999~)

DASI @ 26-36 GHz, 13 elements,South Pole (1999~)

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛≈

Δ=Δ

−

mm3cm60'201

1 λθ du

Uniform UVUniform UV--CoverageCoverage

UV-track due to earth rotation while tracking a target

Traditional interferometer [2-axes: Azimuth, Elevation]

AMiBA with active platform rotations[3-rotation DoF: Az, El, Pol ]

)]([)( 1 uSxB sr −= FTSynthesized beam (PSF) is an Inverse FTInverse FT of the uv-sampling function:

12 sky-pol rotations done for Jupiter observations

2. Introduction2. Introduction

AArray for rray for MiMicrowave crowave BBackground ackground AAnisotropy nisotropy ––

AMiBAAMiBA

• Academia Sinica Institute of A&A (ASIAA)• National Taiwan University (NTU), Physics• NTU Department of Electrical Engineering• Australia National Telescope Facility• University of Carnegie Mellon• Jet Propulsion Laboratory/TRW• Major Contractors: ALONG, CoTech@Taiwan,

Vertex (hexapod), CMA (platform)

(I) (I) ““CMB Polarization Power SpectraCMB Polarization Power Spectra””

(II) (II) ““ClustersClusters’’ SunyaevSunyaev--ZeldovichZeldovich Effects (SZE)Effects (SZE)””

AMiBAAMiBA: CMB structure on l=800: CMB structure on l=800--10,00010,000

AMiBAAMiBA SpecificationSpecification

7x1.2m 13x1.2m

•• 7 / 13 / 197 / 13 / 19--element interferometerelement interferometer– Co-mounted on a 6m platform– 21 / 78 / 171-baseline– Cassegrain D=60,120cm antennas

•• Dual channel 84Dual channel 84--104GHz104GHz (3mm)– HEMT cooled to 15K– Tsys = 100K

•• Full polarization capabilityFull polarization capability– Dual polarizer: Linear X,Y

•• Complex 4Complex 4--lag lag correlatorcorrelator– N = 42 / 156 / 342 - correlators

•• Angular scales and sensitivitiesAngular scales and sensitivities– FoV = 22’ (D=60cm)– FoV = 11’ (D=120cm)– 2’ -6’ resolution– 60mJy/beam in 1hr (Point Source, DS)

Late 2008 Late 2008

Site: MaunaSite: Mauna--Loa (3400m)Loa (3400m)

Mauna Kea (4200m)Mauna Kea (4200m) Platform (6m)

Hexapod MountControl Control ContainerContainer

AMiBAAMiBA –– A Hexapod TelescopeA Hexapod Telescope

6060cm antennacm antenna

CarboCarbon n fiberfiber platfoplatformrm

RReceieceiverver

HexHexapod apod jackjack

(June, 2006)

Optical telescope

Correlator boxCorrelator box

http://amiba.asiaa.sinica.edu.tw

0

Why at 3mm? Why at 3mm? Dust/Synchrotron foreground minimizedDust/Synchrotron foreground minimized

SynchrotronDust

Typical SEDs of Galaxies

Other CMB interferometers:

CBI (@30GHz)

AMI (@15GHz)

SZA (@30/94GHz)

3. Science Objectives3. Science Objectives

AMiBAAMiBA Data Analysis FlowchartData Analysis FlowchartSimulated or observed CMB signals:

Inflationary Cosmic stringsSZ effects Lensing effects

Fringe/lag data to visibilities

Data Taking(with AMiBA configuration)

1. SZ Effects2. CMB Polarizations3. Cosmological Parameters

(Ωtot Ωb Ωcdm ΩDE H0σ8 w nS nTτc etc.)

Power-SpectrumEstimation(maximum-likelihood analysis)

Map Making(maximum-entropy method, etc.)

Science Goal (I): Science Goal (I): Primary CMB Temperature AnisotropyPrimary CMB Temperature Anisotropy

3000 50002000500

Forecasts for the 7-element AMiBA

(l = 800 – 3000)

JHP Wu et al. 2004

3mon)

(2-patch)

Science Goal (II): Science Goal (II): SS--Z Effect by Clusters of GalaxiesZ Effect by Clusters of Galaxies

1010'' 1010'' 66''

X-rayX-ray X-ray

(Carlstrom+ 1999)SZE brightness independent of distance (z), SZE brightness independent of distance (z), while Xwhile X--ray/Optical/ray/Optical/LensingLensing signal of clusters gets faintersignal of clusters gets fainter

What we seek for is a 10-100 μK weak signal!!

AMiBAAMiBA -- Probing SmallProbing Small--Scale AnisotropyScale AnisotropyInput Primary (CMB) + Secondary (SZE) sky @ 94GHz

2’ FWHM beam

14‘ FWHM beam

AMiBAAMiBA will target angular scales smaller than WMAPto study “Cluster-Sized”structures (λ~1Mpc) via the SZ Effects.SZ Effects.

Simulated Simulated AMiBAAMiBA Deep SurveyDeep Survey

++ ==

Primary CMBPrimary CMB TT--SZE SZE ((ΛΛCDM, preheating)CDM, preheating) CMB+TSZE sky CMB+TSZE sky @94GHz@94GHz

Simulated Simulated AMiBAAMiBA surveysurvey

• 400ks integration over 1deg^2 (14 nights14 nights)

• 20cm gap between adjacent dishes filters out primary CMB primary CMB contaminationcontamination

• SensitivitySensitivity: 1.1mJy per 2’ beam: 0.5mJy primary contribution included

Umetsu et al. 2004

Late 2008

SZE SZE –– Probing HighProbing High--z Clustersz Clusters

The 13-element AMiBA will detect ~100 clusters (Ω=10deg^2) in 1 year

Limiting mass: Mlim =~ 1.5 x 1014 Msun/hN(z) peaked at z~0.9

Umetsu et al. 2004

Late 2008

Forecasts: Redshift distribution of AMiBA clusters:

4. 4. AMiBAAMiBA Progress Overview Progress Overview (2002(2002--2007)2007)

Site Development: Site Development: April 2004April 2004--August 2006August 2006

Mount commissioning: started in jan 2005Receiver and correlator on-site testing since late 2005

August 2006 Feb 2005

October 2004April 2004

Nov 2004

August 2005

Dedication and First Images (2006)Dedication and First Images (2006)

Dedication: Oct. 3, 2006Dedication: Oct. 3, 2006

0.5 Jy

7.3 Jy

850 Jy

AMiBAAMiBA First ImageFirst Image -- JupiterJupiter (Sep 8, 2006)(Sep 8, 2006)

Noise rms =~ 1Jy/beam (in 12s12s, 2x212x21 baselines)

Or 60mJy/beam in 1hr

Synthesized beam FWHM (6’)

)]()([)( 1 uVuSxI rrr −= FTDirty Image:Dirty Image:

Jupiter - 850Jy850Jy point source

First end-to-end verification of hardware + software (calibration, analysis pipelines)

First SZE DetectionFirst SZE Detection –– A2142 A2142 (April 2007)(April 2007)

2-P tracking for a long integration & DC/ground subtraction

Power of AMiBA to detect a 1% signal against DC/ground em.

Peak flux is -310mJy consistent with 30GHz VSA result.

8.6σ detection in 5hr x 2-Patch observations (2-3 nights)

P2P1 P1 - P2S + N(P1) + DC N(P2) + DC S + N(P1) – N(P2)

5. First 5. First AMiBAAMiBA Observations Observations of Six Nearby Clusters of of Six Nearby Clusters of Galaxies (Galaxies (AMiBAAMiBA 2007)2007)

Dish Configuration and UVDish Configuration and UV--CoverageCoverage

l=800-3000

Fourier-space samplingFourierFourier--space space sensitivity regionsensitivity region

•• Hexagonal closeHexagonal close--packedpacked– Sensitive to larger angular scales

• 21 baselines per polarization (instantaneous)• 3 independent baseline-lengths: 60, 100, 120cm• Angular scales: 6 to 22 arcmin

cluster z T [keV] Obs. Hours

S/NRatio

AMiBA[mJy]

A1689 0.183 9.7 11.7 7.6 -190

A1995 0.322 8.6 6.5 3.5 -130

A2142 0.091 9.7 5.5 8.6 -310

A2163 0.202 12.2 7.5 10.5 -330

A2261 0.224 8.8 9.9 5.2 -140

A2390 0.228 11.1 13.4 6.5 -150

SZE Decrement Observed SZE Decrement Observed in 6 Nearby Clustersin 6 Nearby Clusters

AMiBA Cluster Sample (0.09

Azimuthally Averaged Visibility FluxAzimuthally Averaged Visibility Flux

Interferometer observable is the complex visibility, where the error covariance for the measurements is (close-to) diagonal:

vectorbaseline

]2exp[)()()]()([)( 2

λ

π

du

xuixIxAxdxIxAuVr

r

rrrrrrr

=

⋅== ∫FT

0|)(|

)||2()()(2|)(| 00>=ℑ<

>=ℜ< ∫∞

uV

xuJxIxAdxxuVr

rr ππ

If the spatial distributions of A(x) and I(x) have circular-symmetry about the cluster center,

The primary CMB signal as well as instrumental noise (random Gaussian) will give an equal contribution to the REAL and IMAGINARY part The imaginary flux can be used as a monitor of the primary CMB contribution (and departure from symmetry)

Visibility Flux Profiles,

A1689 A1995

A2163 A2261

A2142

A2390

AMiBAAMiBA SZE + Subaru WL for Probing SZE + Subaru WL for Probing Cluster Gas Mass FractionsCluster Gas Mass Fractions

High-quality Subaru imaging data available from the Subaru archive (SMOKA) for 4 (/6) of AMiBA clusters with high X-ray temperatures (>8keV)

Umetsu et al. 2008ab (to be submitted to ApJL AMiBA issue)In collaboration with the AMiBA team,

T. Broadhurst, E. Medezinski, M. BirkinshawIncluding preliminary results

AMiBAAMiBA/Subaru Cluster Sample/Subaru Cluster Sample

Color imageColor image:

2D mass map (Subaru)

ContoursContours:

SZE (AMiBA@94GHz)

AMiBA:

FoV = 22’

PSF = 6’

Objectives: Cluster Gas Mass FractionsObjectives: Cluster Gas Mass Fractions

)()(

)(rMrM

rftot

gasgas <

<=<

Cosmological testCosmological test using the X-ray derived gas fractions via its distance dependence (e.g., Sasaki 96; Pen 97; Allen+04,08)

Measure (good lower bound) of the cosmic baryon fractioncosmic baryon fraction (e.g., White+93)

Cluster physicsCluster physics: non-gravitational physics (e.g., AGN feedback) breaking self-similarities, yielding mass dependence of gas fractions (e.g., Kravtsov+05; Bialek+01; Ettori+06)

2/3rayX ),;()z( −Λ− ΩΩ∝ mgas zDf

bm

bgas ff ≡Ω

Ω

MethodMethod

gasgasTMy ∝Ω=∝ ∫ )(dYFluxSZE 2 θ

totM∝Ω=∝ ∫ )(dKMass WL 2 θκ

SZE flux is a measure of the thermal energy content in the ICM (in projection)

Xtot

gasgas

Xgas TM

TMT

f 1)(

)(~

KY1~

Integrated convergence measures the total cluster mass (in projection)

Estimate of the gas fraction with X-ray temperature information without the hydrostatic equilibrium assumption (e.g., Myers+1997)

Here we will adopt a model-dependentdependent approach, using parameterized cluster models, to derive the 3D gas mass fractions.

Less model-dependent “deprojection” can be done if detailed 2D profiles of X-ray, SZE, and WL data are available, assuming spherical/triaxialsymmetry (cf. Zaroubi+01; Sereno+07; Mahdavi+07)

Basic idea:

Cluster ModelingCluster ModelingTo better constrain the cluster models, we adopt the following

prior assumptions:(1) gas density traces the underlying total mass density @ large radii(2) constant polytropic relation between P and ρ(3) spherical symmetry

)()(

.)(/)(

rrP

constrr

gasgas

totgas

γρ

ρρ

∝

=

Two representative, physically-motivated cluster models:[A] isothermal beta modelisothermal beta model (β=2/3)

[B] NFWNFW--consistent universal pressure profileconsistent universal pressure profile (Komatsu & Seljak 01,02).)(@)( 2

constrTrrrr c

=>>∝ −ρ

20.115.1~),()(

@)(1

3

−∝

>>∝−

−

γρ

ργ rrT

rrrr

gas

s

At r>>rc, the total mass profile can be represented well by the Singular Isothermal Sphere (SIS) model

For both cases, T(r) is normalized to the X-ray cluster temperature.

WMAP3 Stacked SZE Profile WMAP3 Stacked SZE Profile (Afshordi+08)(Afshordi+08)

C_vir = 15C_vir=8

z3e44 erg/s subsampleIsothermal beta (upper)

NFW-consistent (lower)

Isothermal beta model yields a flat pressure profile, overestimating the power on large scales

Weak Weak LensingLensing Distortion ProfilesDistortion ProfilesTopTop: tangential (E-mode) shear, g+

BottomBottom: 45-deg rotated (B-mode) shear, gx

g+ profiles are compared with the NFW (ρ ~ r^-3) and the SIS (ρ ~ r^-2) models: SIS for A2142 (chi2/dof>3) is disfavored; NFW gives better fits for all clusters.

Slight perturbation in the gx-profile is seen due to substructure and/or elongation of the projected potential

Effects of substructures in the g-profiles are NON-LOCAL

Weak Weak LensingLensing 1D Mass Reconstruction1D Mass Reconstruction

Method by Umetsu & Broadhurst 08

Effects of substructure are local in the κ-profile

g+ fit for A2261 is likely to be affected by projection effects of mass structures @r=4’and 12’

GassGass Mass and Fraction ProfilesMass and Fraction Profiles

A1689

A2142

A2390

A2261

SampleSample--Averaged Gas Fraction Profiles Averaged Gas Fraction Profiles (>8keV (>8keV AMiBAAMiBA/Subaru Sample)/Subaru Sample)

)(018.0)(023.0123.0)KS01(200, samplestatfgas ±±=

For A2142, isothermal model is rejected @2sigma (w.r.t. NFW) for both of Subaru and AMiBA data The gas fractions also exceed the cosmic baryon fraction at all r>>r2500.

The two models are roughly consistent with the current statistical uncertainties.

For KS01 model, the sample averaged gas fraction @r200 is 0.123 +/- 0.03, which is about 1 sigma below the WMAP5 cosmic baryon fraction, fb=0.171+/-0.01.

SummarySummary

• After 6 years of efforts, AMiBA has made a first detection towards the SZ Effect by a galaxy cluster, and has observed 6 massive clusters in total for Cluster and Cosmology studies.

• Primary CMB observations with the 7-element AMiBA is ongoing.

• A further expansion to 13 1.2m dishes will start in this year, improving the sensitivity, angular-resolution, and dynamic range in UV-sampling.

• 13-element AMiBA +X-ray+WL observations will allow for a model-independent cluster de-projection

Fermi Summer School (July 22, 2008)OutlineCMB vs. InterferometerObservable: Complex Visibility, V(u,v)Fringes CMB InterferometersUniform UV-CoverageAMiBA: CMB structure on l=800-10,000AMiBA SpecificationSite: Mauna-Loa (3400m)AMiBA – A Hexapod TelescopeWhy at 3mm? �Dust/Synchrotron foreground minimizedAMiBA Data Analysis FlowchartScience Goal (I): �Primary CMB Temperature AnisotropyScience Goal (II): �S-Z Effect by Clusters of GalaxiesAMiBA - Probing Small-Scale AnisotropySimulated AMiBA Deep SurveySZE – Probing High-z ClustersSite Development: April 2004-August 2006Dedication and First Images (2006)AMiBA First Image - Jupiter (Sep 8, 2006)First SZE Detection – A2142 (April 2007)Dish Configuration and UV-CoverageAzimuthally Averaged Visibility FluxVisibility Flux Profiles, AMiBA SZE + Subaru WL for Probing Cluster Gas Mass FractionsAMiBA/Subaru Cluster SampleObjectives: Cluster Gas Mass FractionsMethodCluster ModelingWMAP3 Stacked SZE Profile (Afshordi+08)Weak Lensing Distortion ProfilesWeak Lensing 1D Mass ReconstructionGass Mass and Fraction ProfilesSample-Averaged Gas Fraction Profiles (>8keV AMiBA/Subaru Sample)Summary