Cross-Correlation of 2MASS with WMAP3:

Implications for ISW

Anaïs Rassat (University College London)

Kate Land (Imperial College London)

Ofer Lahav (University College London)

Integrated Sachs-Wolfe Effect

2-3σ

SDSS,XRB,NVSS,APM,2MASS

WMAP1

WMAP3

~10 papers

2003-2006

TENTATIVEXRB/NVSSWMAP1Boughn & Crittenden

2003

NOXRB/NVSSCOBEBoughn & Crittenden

2002

CLAIMED

DETECTION

TRACERCMBAUTHORYEAR

2-3σ

SDSS,XRB,NVSS,APM,2MASS

WMAP1

WMAP3

~10 papers

2003-2006

TENTATIVEXRB/NVSSWMAP1Boughn & Crittenden

2003

NOXRB/NVSSCOBEBoughn & Crittenden

2002

CLAIMED

DETECTION

TRACERCMBAUTHORYEAR

2MASS Galaxy Survey

Publicly available eXtended Source Catalogue (XSC)J, H, K bands (Near Infrared)~1,650,000 Galaxies with magnitudes corrected for Galactic extinction.Analysis includes 69% sky & 1,250,000 GalaxiesCompare with Cabré et al. 2006 (SDSS DR4): ~16% (z ~ 1)

Scranton et al. 2003 (SDSS – LRGs) : ~ 8% (z ~ 0.45)Fosalba and Gaztañaga 2003 (APM): ~10% (z ~ 0.15)

2MASS ⊗ WMAP3

• Auto-Correlation

• Cross-Correlation

• AoE statistic

Auto-Correlation Function: ACF

22

2 )()(4

krjrDrdrfk

kdkbC kggg

)()(),( 2 zDkPzkP lin

)()(),( 2 zDkPzkP linnon

EXACT IN LINEAR THEORY

)(ggC

Constant linear bias b from Cgg(ℓ)

12 < K20 < 14

•Best fit 1.04.1025.04.175.08

gb

2MASS ⊗ WMAP3

• Auto-Correlation √

• Cross-Correlation

• AoE statistic

3rd Year WMAP Foreground reduced maps of Q,V and W bands

Q band (41 GHz) V band (61 GHz)

W band (94 GHz)

Images fromWMAP Science Team

Method:• Follow Afshordi et al. 2004 (WMAP1 2MASS)⊗• Perform Cross-Correlation in Harmonic Space:

• Cut Kp2 mask on WMAP3, Cut out 31% of 2MASS sky

m

Tlm

glmgT aa

lC *)(

)12(

1

ALL of 2MASS with ILC map

CORRELATION?

2MASS 4 Magnitude Bins with ILC map

POSITIVE CORRELATION TREND FOR LOW MULTIPOLES?

Four Magnitude Shells ⊗Q, V, W, ILC WMAP3 maps

AchromaticTrend

1σ from 500 simulations of CMB with 2MASS

WMAP3 / 2MASS

Changes between WMAP1 & WMAP3

■ WMAP3□ WMAP1

Why is there a difference?

Theory

Exact in linear theory:

Small angle approximation:

)()(4

2

kWkWk

kdkbC TgggT

rc

ggT PzfzDrnr

dzbC 21

]1)([)(

)()(2

21

22

Predicted Cross-Correlation: Exact & Small Angle Approximation:

ℓ ~ 11

Shells with

z ~ 0.067 (>2.105gal)

z ~ 0.084 (>4.105 gal)

∆χ2 = χ2 ISW - χ2NULL= 2

☼

OPEN COSMOLOGIES

Model Dependent Statistic

Assume there is Dark Energy in a Ωk=0 Universe• CgT [DATA] = h* CgT[ISW_fiducial]

• Without prior on σ8: h ~ 1.7 or 2σ detection• (Null detection corresponds to h < 0)

• With prior on σ8: h ~ 1.6• Etc.. Full Parameter Space needs to be investigated

ALTERNATIVE FIDUCIAL MODELS

h ~ 1.7

2σ Detection

2MASS ⊗ WMAP3

• Auto-Correlation √

• Cross-Correlation √

• AoE statistic

Axis of Evil

☼

ℓ=2 ℓ=3 ℓ=4 ℓ=5

WMAP3

2MASS

Summary: 2MASS ⊗ WMAP3

• WMAP3 ⊗ 2MASS : within 1σ [NULL] (Model Independent)

• ISW (fiducial) : within 1σ [NULL]

• CgTDATA ~ 1.7 CgT

FIDUCIAL (Model Dependent 2σ Detection)

• AoE(WMAP) ≠ AoE(2MASS)

Thanks to Filipe Abdalla, Niayesh Afshordi, Sarah Bridle, Carlo Contaldi, for comments, advice and assistance.