large scale structure (galaxy correlations) · overview • redshift surveys • theoretical...
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Large Scale Structure(Galaxy Correlations)
Bob Nichol (ICG,Portsmouth)Bob Nichol (ICG,Portsmouth)
“majority of its surface area is only about 10 feet above sea level”
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Overview
• Redshift Surveys• Theoretical expectations• Statistical measurements of LSS• Observations of galaxy clustering• Baryon Acoustic Oscillations (BAO)• ISW effect
I will borrow heavily from two recent reviews:1.Percival et al. 2006, astro-ph/06015382.Nichol et al. 2007 (see my webpage)
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P(k) models II[U
nits
of V
olum
e]
Suppressionof power
Stronger BAO
Lack of strong BAO means low baryon
fraction
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Measuring ξ(r) or P(k)
Data
Random
r
Simple estimator:ξ(r) = DD(r)/RR(r) - 1
Advanced estimator:ξ(r) = (DD-2DR+RR)/RR
The latter does a better job with edge effects, which cause a bias to the mean density of points
Usually 10x as many random points over SAME area / volume
Same techniques for P(k) - take Fourier transform of density field relative to a random catalog over same volume. Several techniques for this - see Tegmark et al.
and Pope et al. Also “weighted” and mark correlations
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Measuring ξ(r) IIEssential the random catalog looks like the real data!
HEALPix HEALPix & Mangle & & Mangle & SDSSPixSDSSPix
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ξ(r) for LRGs
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Errors on ξ(r)
On small scales, the errors are Poisson
On large scales, errors correlated and typically larger than Poisson
• Use mocks catalogs• PROS: True measure of cosmic variance• CONS: Hard to include all observational
effects and model clustering• Use jack-knifes (JK)
• PROS: Uses the data directly• CONS: Noisy and unstable matrices
Hardest part of estimating these statistics
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Jack-knife Errors
5 64
2 3
Real Data • Split data into N equal subregions• Remove each subregion in turn and compute ξ(r )• Measure variance betweenregions as function of scale
5 64
1 3
N=6
σ 2 =(N −1)
N(
i=1
N
∑ ξi −ξ)2
Note the (N-1) factor because there or N-1 estimates of mean
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Latest P(k) from SDSS
keq ≈ 0.075Ωmh2
Ωm=0.22±0.04
Ωm=0.32±0.01
No turn-over yet seen in data!
2σ difference
Depart from “linear”predictions at much lower k than expected
Strongest evidence yet for Ωm << 1 andtherefore, DE
Errors from mocks(correlated)
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Hindrances
There are two “hindrances” to the full interpretation of the P(k) or ξ(r)
• Redshift distortions: Helped using modeling & simulations
• Galaxy biasing: Helped through higher order correlations
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Redshift distortions
Therefore we usually quote ξ(s) as the “redshift-space” correlation function, and ξ(r) as the “real-space”correlation function.
We can compute the 2D correlation function ξ(π,rp), then
“Fingers of God”
Infall around clusters
Expected
We only measure redshifts not distances
w(rp ) = 2 ξ(rp0
π max∫ ,π )dπ
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Biasing
Maximal ignorance
However, we know it depends on color & L
Is there also a scale dependence?
We see galaxies not dark matter
δgal = bδdm
P(k)gal = b2P(k)dm
bb*
= 0.85 + 0.15 LL*
+ 0.04(M* − M 0.1r)
Swanson et al.
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Biasing II
All galaxies reside in a DM halo
Elegant model to decompose intra-halophysics (biasing) from inter-halo physics (DM clustering)
Halo model
2-haloterm
1-haloterm
P(k) = P1−halo + P2−halo
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Biasing III
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Higher order correlations
Biasing could be helped through use of higher order correlations e.g. 3-point correlation function (bispectrum)
s
qs
θ
1
2
3
Peebles “Hierarchical Ansatz”
P123 = n3(1+ξ23 +ξ13 +ξ12 +ξ123)dV 3
Q(s,q,θ) =ξ123
ξ23ξ13 +ξ12ξ13 +ξ12ξ23
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Higher order correlations II
Credit: Alex Szalay
Same 2pt, different 3pt
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Higher order correlations III
Credit: Alex Szalay
Qgalaxies = bQdarkmatter
FOG
Gaztanaga & Scoccimarro 2005
Filaments
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Halo ModelKulkarni et al. 2007
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BAO Measurements
SDSS DR5 520k galaxies
WMAP3
Ωm=0.24 best
fit WMAP model
Percival et al. 2006
Miller et al. 2001, Percival et al. 2001,Tegmark et al. 2006, Cole et al. 2005,Eisenstein et al. 2005, Hutsi 2006, Blake et al. 2006, Padmanabhan et al. 2006
Power spectrum of galaxy clustering. Smooth component removed
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Looking back in time in the Universe
FLAT GEOMETRYCREDIT: WMAP & SDSS websites
SD
SS
GA
LA
XIE
S
CM
B
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Looking back in time in the Universe
OPEN GEOMETRYCREDIT: WMAP & SDSS websites
SD
SS
GA
LA
XIE
S
CM
B
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Looking back in time in the Universe
CLOSED GEOMETRYCREDIT: WMAP & SDSS websites
SD
SS
GA
LA
XIE
S
CM
B
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Cosmological Constraints
Sullivan et al. (2003)
Standard ruler (flat,h=0.73,Ωb=0.17)
Best fit Ωm=0.26
99.74% detection
h=0.72±0.08 HSTΩm=0.256+0.049
-0.029
Ωmh2 WMAP3
Ωm=0.256+0.019-0.023
Ωm0.275h WMAP3
Ωm=0.256+0.029-0.024
Percival et al. (2006)
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BAO with Redshift
99.74% detection
Percival et al. (2006)
143k + 465k
79kz~0.35
z~0.2
Percival et al. 2007
Measure ratio of volume averaged distance
D0.35 /D0.2 = 1.812 ± 0.060
Flat ΛCDM = 1.67
Systematics (damping, BAO fitting) also ~1σ. Next set of measurements will need to worry about this
Dv(z) =(1+ z)2 czDA(z)2
H (z)⎡
⎣ ⎢
⎤
⎦ ⎥
13
>3σ detection (Hutsi et al., Percival et al)
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Cosmological Constraints
1σ
2σ
3σ
W
Ωm
Only D0.35 /D0.2
With CMB
Flatness assumed, constant w
Favors w<-1 at 1.4σ
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Cosmological Constraints
1σ
2σ
3σ
W
Ωm
Only D0.35 /D0.2
With CMB
Flatness assumed
W
Ωm
Ωm = 0.249 ± 0.018
w = -1.004 ± 0.089
D0.35 /D0.2 = 1.66 ± 0.01
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Discrepancy!What Discrepancy?
• 2.4σ difference between SN & BAO. The BAO want more acceleration at z<0.3 than predicted by z>0.3 SNe (revisit with SDSS SNe)
• ~1σ possible from details of BAO damping -more complex then we thought
• Assumption of flatness and constant wneeds to be revisited
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Integrated Sachs-Wolfe EffectDark Energy effects the rate of growth of structure in Universe
• Poisson equation with dark energy:
• In a flat, matter-dominated universe (CMB tells us this), then density fluctuations grow as:
• Therefore, curvature or DE gives a change in the gravitational potential
k 2Φ'= −4πG ddη
a−1(δρm + δρDE )[ ]
δρm ∝ a ⇒ dΦ /dη = 0
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ISW II
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Experimental Set-up
Nolta Nolta et al, et al, Boughn Boughn & Crittenden, Myers et al, & Crittenden, Myers et al, Afshordi Afshordi et al, et al, Fosalba Fosalba et al., et al., Gaztanaga Gaztanaga et al., et al., Rassat Rassat et al.et al.
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WMAP-SDSS CorrelationNo signal in a flat, matter-dominated Universe
Luminous Red Galaxies (LRGs)
WMAP W band
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ISW DetectedUpdate of the Scranton et al. (2003) paper
• 6300 sq degrees• Achromatic• 3σ detection
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Giannantonio et al. (2006)Cross-correlation of WMAP3 and SDSS quasars
Detection of DE at z>1
0.075<0.075<ΩΩmm<0.45<0.45--1.15<1.15<ww<<--0.760.76
WMAP3 best fit
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Evolution of DE
Consistent with Consistent with w=w=--11
RRules out modelsules out modelsΩΩDD��((z=1z=1.5).5) > 0.5> 0.5
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Modified Gravity
LCDMDGP
Song et al. (2006)
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Future Dark Energy Survey
DETF Terminology
• Stage II are experiments going on now (most are still limited by statistics and systematics)• Stage III are next generation (before end of decade). Investigate systematics and gain factor of >3• Stage IV are next decade and gain factor of 10Trotta & Bower PPARC Report / Peacock et al. report from ESA/ESO WG
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After SDSSII (AS2)
• Measure distance to ~1% at z=0.35 and z=0.6
• 10000 deg2 with 1.5m LRGs to 0.2<z<0.8
• 160k quasars at 2.3<z<2.8• Starting 2009• h to 1% with SDSS SNe
Baryon Oscillation Spectroscopic Survey (BOSS)
2SLAQ (www.2slaq.info)
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Dark Energy Survey (DES)
• 5000 sq deg multiband (g,r,i,z) survey of SGP using CTIO Blanco with a new wide-field camera
• 9 sq deg time domain search for SNe
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ANNz: Collister & Lahav 2005, Abdalla et al.
DES Photo-z’sDES science relies on good photometric estimates
of the 300 million expected galaxies
Simulated DES
Simulated DES+VISTA
griz
grizJKu-band from VST could remove the low-z errors
(ugrizJK)
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WFMOS• Proposed MOS on Subaru via an
international collaboration of Gemini and Japanese astronomers
• 1.5deg FOV with 4500 fibres feeding 10 low-res spectrographs and 1 high-res spectrograph
• ~20000 spectra a night (2dfGRS at z~1 in 10 nights)
• DE science, Galactic archeology, galaxy formation studies and lots of ancillary science from database
• Design studies underway; on-sky by2013
• Next Generation VLT instruments; meetings in Garching
• Combine with an imager and do “SDSS at z=1”
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DE ScienceMeasure BAO at z~1 and z~3 to determine w(z)
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WFMOS LegacyFacility instrument
Galaxy Evolution: Every galaxy in Coma (Mr < -11)IGM and Quasars: Simultaneously observing QSOs and galaxies in the same fieldsCalibrate photo-z’s: LSST and DES require > a few 105 unbiased redshifts (Abdalla et al. 2007)
400400000GalaxyArcheology
100600000300124.52.3 - 3.3
10020000002000422.70.5 - 1.3
NightsNumberArea (sq degs)
Volume (h-
1 Gpc)R limit(AB)
z range
(Glazebrook et al. 2005)