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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”

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)

P(k) models II[U

nits

of V

olum

e]

Suppressionof power

Stronger BAO

Lack of strong BAO means low baryon

fraction

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

Measuring ξ(r) IIEssential the random catalog looks like the real data!

HEALPix HEALPix & Mangle & & Mangle & SDSSPixSDSSPix

ξ(r) for LRGs

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

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

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)

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

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

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.

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

Biasing III

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

Higher order correlations II

Credit: Alex Szalay

Same 2pt, different 3pt

Higher order correlations III

Credit: Alex Szalay

Qgalaxies = bQdarkmatter

FOG

Gaztanaga & Scoccimarro 2005

Filaments

Halo ModelKulkarni et al. 2007

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

Looking back in time in the Universe

FLAT GEOMETRYCREDIT: WMAP & SDSS websites

SD

SS

GA

LA

XIE

S

CM

B

Looking back in time in the Universe

OPEN GEOMETRYCREDIT: WMAP & SDSS websites

SD

SS

GA

LA

XIE

S

CM

B

Looking back in time in the Universe

CLOSED GEOMETRYCREDIT: WMAP & SDSS websites

SD

SS

GA

LA

XIE

S

CM

B

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)

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)

Cosmological Constraints

1σ

2σ

3σ

W

Ωm

Only D0.35 /D0.2

With CMB

Flatness assumed, constant w

Favors w<-1 at 1.4σ

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

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

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

ISW II

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.

WMAP-SDSS CorrelationNo signal in a flat, matter-dominated Universe

Luminous Red Galaxies (LRGs)

WMAP W band

ISW DetectedUpdate of the Scranton et al. (2003) paper

• 6300 sq degrees• Achromatic• 3σ detection

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

Evolution of DE

Consistent with Consistent with w=w=--11

RRules out modelsules out modelsΩΩDD��((z=1z=1.5).5) > 0.5> 0.5

Modified Gravity

LCDMDGP

Song et al. (2006)

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

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)

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

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)

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”

DE ScienceMeasure BAO at z~1 and z~3 to determine w(z)

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)