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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.