Large-scale Structure:Theory & Observations

Josh FriemanStructure Formation & Evolution, Santiago, October 2002

The Structure Formation Cookbook

1. Initial Conditions: A Theory for the Origin of Density Perturbations in the Early Universe Your favorite Inflation model: primordial spectrum Pi ~ kn

2. Cooking with Gravity: Growing Perturbations to Form Structure Set the Oven to Cold (or Hot or Warm) Dark Matter Season with a few Baryons and add Dark Energy

3. Let Cool for 13 Billion years

4. Tweak (1) and (2) until it tastes like the observed Universe.

N-body simulation:Evolution of Structure in aCold Dark Matter Model

Features:

Filamentary structureamplified by gravity

Hierarchical collapse, virialization, and merging of dark halos

See talks by Teyssier, Navarro

Virgo consortium

Formation of Dark Halos

(Virgo consortium)

Evolution of Structure

Density Power Spectrum:

(k) = d3x eik·x (x) (k1)(k2) = (2)3 P(k1)3(k1+k2)

Evolution:

Pgal(k) = b2gal(k) Pi(k) T(k; j, n, 8)

bias primordial spectrum Non-linear Transfer function

ColdDarkMatterModels

Power Spectrum of the Mass Density

Turnover dueto delayedperturbationgrowth in radiationera

SCDMCDMOpen CDM

P ~ k

P ~ k-3

keq ~ mh =

h/Mpc

Non-linearLinear

Shape parameter

Power Spectrum in Cold Dark Matter Models

Cold Dark Matter Models

mh=0.5SCDM

mh=0.2 CDM (assumed biased)

Amplitude

8

Rms Linear

Mass

Fluctuations

in spheres of

Radius

8h-1 Mpc

More ColdDarkMatter

Less ColdDarkMatter(Open)

ColdDarkMatterwith

Probing Neutrino Mass and Baryon Density

SDSS + MAP: will constrain sum of stable neutrino masses as low as ~ 0.5 eV

WigglesDue to Non-zeroBaryonDensity

Constraints on the Baryon Density from 2dF Galaxy Redshift Survey Power Spectrum

Percival, etal. Tegmark & Hamilton

Increasingb suppressespower on small scales(and increasesamplitude of wiggles)

2dF GRS Power Spectrum

m,tot < 2.2 eV

--reasonable prior on m

--BBN prior on b

--simple model of bias & redshift distortions

Elgaroy, etal

=00.01

0.05

= m,tot

94 eV

Probes of Structure Formation

Probing the Galaxy Distribution:

--Galaxy Photometric and Spectroscopic Surveys

Probing the Mass Distribution: --CMB anisotropy --Weak & Strong Gravitational Lensing --Peculiar velocities

Probing the High-redshift Universe:

--Constraining Dark Matter Properties via High-redshift Quasars & the Lyman-alpha forest (see talk by Petitjean)

Bias

Large-scale Structure, circa 1986

`Pizza Slice’ 6 degrees thick containing 1060 galaxies: position of each galaxy represented by a single dot

100 Mpc

You Are Here

Center for Astrophysics Survey

Filaments,Walls,Voids,Richclusters

deLapparent, Geller, Huchra

Las Campanas Redshift SurveyShectman,etal

Colless, etal

SDSS RedshiftSurvey

~200,000 galaxy redshifts so far

APM Galaxy Survey (digitized plates)

~106 galaxy positions, magnitudes bJ < 20 Maddox,etal

SDSS Imaging Survey

~3000 sq deg. covered so far (50 M objects) ~6600 sq. deg. by June 2005 r’ < 22

Determination of the galaxy Power spectrum c. 1990’s

Surveys selectdifferent mixes of galaxypopulations

Evidence for type-dependentBias

Error bars not shown!

Missing:PSCz, EDSGC,ESO Slice, 2dF,SDSS, …

Vogeley

Galaxy Clustering varies with Galaxy Type

How are each of themrelated to the underlying Mass distribution?

Bias depends upon Galaxy Type

Need large, carefully selected samples to study this: 2dF, SDSS

Rescale Power by linear bias factorfor each survey:different galaxy types cluster with different strengths

Pi(k) = b2i Pm(k)

Galaxies Mass

Best fit CDM Model:h = 0.2-0.3 Vogeley

Galaxiesare Biasedtracers of the Dark Matter

Tegmark, etal

• Cannot describe bias on scales smaller than smoothing scale.• Choice of smoothing scale is arbitrary.• δm is generally unobservable.

“Environmental” Bias

Bias Depends onGalaxyColor

Cf. morphology-density relation

Zehavi, etal

SDSS Redshift Survey

Bias depends on Galaxy Luminosity

Compare 2dF results of Norberg, etal

Intrinsically bright

Intrinsicallyfaint

SDSS Redshift Survey

Theoretical Models for Bias

Requires gas dynamics, star formation, dynamical Friction, mergers, feedback, etc.

Expectation:

Bias depends on type and scale, evolves with time, and is stochastic

Blanton, etal

SPH Simulation

• Ωm=0.4, ΩΛ=0.6, Ωb=0.02h-2

h=0.65, n=0.95, σ8=0.8

• 1443 dm + 1443 gas particles l=50 Mpc/h, mb=8.5x108Msun

• Gravity + gas dynamics radiative + Compton cooling photoionization heating star formation + feedback

• FoF halos, b=0.173 Davé, Katz, & Weinberg

• The probability distribution P(N|M) that a halo of mass M contains N galaxies

<N>M P(N|<N>)

• The relation between the galaxy and dark matter spatial distribution within halos

• The relation between the galaxy and dark matter velocity distribution within halos

Halo Occupation Distribution

1. All galaxies live in dark matter halos.2. Galaxy content of a halo is statistically independent of the halo’s larger scale environment. Depends only on mass.

Assume:

The bias of a certain galaxy class (type, luminosity, etc) is fully defined by:

“Halo Occupation” Model for Bias

Also see: semi-analytic models

Cosmological Model

Ω, P(k), etc.

Galaxy Formation

Gas cooling, Star formation, Feedback, Mergers, etc.

Halo Occupation DistributionP(N|M)

Spatial bias within halosVelocity bias within halos

Galaxy-Mass Correlations

Dark Halo Population

n(M), ξ(r|M), v(r|M), ρ(r)

Galaxy Clustering

SLOAN DIGITAL SKY SURVEY

GOALGOAL: MAP THE UNIVERSE IN 3 DIMENSIONS OVER A LARGE VOLUME

• Photometric Survey: ~108 5-band CCD images

• Spectroscopic Survey: ~106 galaxy and 105 QSO redshifts

University of Chicago Fermilab Princeton University New Mexico State

Johns Hopkins University Institute for Advanced Study

U.S. Naval Observatory University of Washington Japan Participation Group

Max-Planck A and IA

http://www.sdss.org

Funding: Sloan Foundation, NSF, DOE, NASA, member institutions, Japan Ministry of Education

Los Alamos National LabUniversity of Pittsburgh

SDSS 2.5 meter Telescope

SDSS Data

April 2000: Survey begins (commissioning ends)June 2005: Survey finishes

Data so far: ~3,264 unique square degrees of 5-band imaging (7/02) (~60 million objects) ~375,000 object spectra (G,Q,S redshifts)

Samples currently being analyzed (preliminary results today):

~2,500 sq. deg. imaging with photometric redshifts ~170,000 main galaxy (spectroscopic) redshifts ~30,000 QSO redshifts ~25,000 LRG redshifts

ProjectedtoJune 2005:

6600 sq deg imaging

600,000 spectra

SDSS Public Data Releases

•Series of Staged Data Releases (cf. COBE)

•June 2001: Early Data Release

~600 square degrees of 5-band imaging (~8 million galaxies to r* < 22.5)

~60,000 object spectra (redshifts)

•January 2003: First Data Release ~2,800 sq. deg. imaging ~200,000 spectra/redshifts

Large-scale Structure Results

•Results of the LSS Working Group

•Angular Clustering of Galaxies in the Photometric Survey

--incorporation of photometric redshifts

--clustering by galaxy type (color and luminosity) •Power spectrum and Two-point correlation of Galaxies in the Spectroscopic Survey --clustering by galaxy type

•In the works: clustering of LRGs, clusters, QSOs, Ly-a forest; higher order correlations of galaxies; clustering by spectroscopic type and stellar mass

Zehavi, etalTegmark, etal

Budavari,etal

SDSS Angular Clustering I

Galaxy angularcorrelation function

dP=n2[wdd

Check for systematics:correlate with dust, galactic latitude, seeing

Mask out regions of bad seeing, high dust obscuration, bright stars, etc.

Careful error analysis:covariance

Scranton, etalConnolly, etal

bright

faint

SafeTruncationof KL modes

OrthogonalConstraintsProbing Power Around the Peak

Amplitude

8 =

0.92 ± 0.06

Shape ( mh) = 0.19 ± 0.04

Two-parameter fit of SDSS Angular KL Data to CDM Models

Szalay, etal

Angular Clustering with Photometric Redshifts

T. Budavari, A. Connolly, I. Csabai, I. Szapudi, A. Szalay, S. Dodelson,

J. Frieman, R. Scranton, D. Johnston and the SDSS Collaboration

Sample selection based on rest-frame quantities Strictly volume limited samples Largest angular correlation study to date Very clear detection of

Luminosity dependence Color dependence

Results consistent with 3D clustering

Photometric Camerafilter response

with and w/oatmosphericextinction of 1.2 airmasses

Galaxy photometricredshiftestimates

Predictedredshiftfrom 5-bandSDSSPhotometry

Spectroscopic measured redshiftConnolly, etalCsabai, etal

The Photo-z Samples

343k343k 254k254k 185k185k 316k316k 280k280k 326k326k 185k185k 127k127k

-20 > Mr >-21

1182k1182k

-21 > Mr >-23

931k931k

0.1<z<0.3-20 > Mr

2.2M2.2M

-21 > Mr >-22

662k662k

-22 > Mr >-23

269k269k

0.1<z<0.5-21.4 > Mr

3.1M3.1M

10 stripes: 10M10M

mr<21 : 15M15M

All: 50M50M

Angular Correlations II.

Luminosity dependence: 3 cuts-20> M > -21 -21> M > -22 -22> M > -23

Angular Correlations III.

Color Dependence4 bins by rest-frame SED type

Sky coverage of SDSS redshift survey

(Aitoff projection, equatorial coordinates)

(Dust map from Schlegel, Finkbeiner & Davis)

Redshift DistributionandRadialSelectionFunctionfor theSpectroscopicSample

-22 < Mr < -1914.5 < r’ < 17.77

2000 sq. deg.~140,000 galaxies

120,000 at z<0.15cz (km/sec)

N

P

Redshift-Space Galaxy Correlation Function

CorrelationAmplitudeContours

RadialRedshiftDistortionsdue topeculiarvelocities

,pr

1

1212 d(P,r

llpl

Q

)ˆˆcos( zr

4.0~6.0

bm

2dF: = 0.430.07

Forecast Constraints From SDSSLuminousRed GalaxyClustering:

GeometricTest for Dark Energy

Matsubara & Szalay

ProjectedCorrelationFunction

m

0

2)(

d,rrw ppp

Lum funcs & sel funcs by Michael Blanton (NYU)

Divide GalaxiesbyIntrinsicLuminosity:

Volume-limitedsubsamples

Clustering as a function of Galaxy Luminosity

Amplitude & Scaling consistent with angular photo-z results

bright

faint

Large scales: All pairs come from separate halos:

Small scales: All pairs come from same halo:

Halo Modeling

Berlind,Zehavi,Zheng, Weinberg

N~M

M1

N ~Mβ

Rescalebias

k=3

k=0.3k=0.1

k=0.03

k=1

Cmbgg OmOlLSS

SDSSClusteringCorrectedFor LuminosityBias

Finding GroupsIn SDSS

Berlind

SDSS Group Identification

Identify groups using:Friends-of-friends algorithmFixed tangential linking lengthVariable line-of-sight linking length

Group catalog:2,143 galaxy groups (N>2)

SDSS Group Multiplicity Function

Preliminary HOD Constraints

Detecting Galaxy ClustersMaxBcg algorithm: Animation of process for single galaxy Perform step for all galaxies Build a 3-d map Locate maxima

Strengths Works to high z Very good photo-z

Weaknesses Assumes clusters contain Bright red galaxies

Annis, etalMiller, etalKim, etalGoto, etal

MaxBcg Photo-z’s

SDSS Cluster Abundance as a CosmologicalProbe

Non-Gaussian structure: beyond Two-point statistics

Identical Power spectra Szalay

JF, Gaztanaga

Angular 3-pointCorrelationFunction

N-body vs.NonlinearPerturbationTheory (PT)

q3 = z(12, 13, 23) -------------------------- w(12)w(13)+ cyc.

12

13

deg

Data

Model

Scoccimarro, Feldman, Fry, JF

Bispectrum of IRAS Redshift Surveys: PSCz Survey (~15,000 galaxies)

Q = B(k1,k2,k3) ------------------------- P(k)P(k2)+ cyc.

k2/k1=0.4-0.6

Perturbation Theory

PT withredshiftdistortions

biasedmodels

Collinearconfigurations

Collinearconfigurations

~Equilateral

Constraints on Bias Parametersfrom IRAS Bispectra

Local, deterministicBias model:

g = f() = b + b22/2

Qg = Q/b1 + b2/b12

Feldman, etal

PDF of the Evolved Density Field on Scales of ~ few Mpc

Cold Dark Matter simulation Bernardeau & Kofman

Higher Order AngularCorrelationsin early SDSSimaging data

SN =

‹N ›/‹ 2()›N-

Higher order Correlations probeBias & initialNon-Gaussianity

Szapudi, etal

S3

S4

Comparison with Biased CDM model

Higher Order Correlations consistent with Non-linear evolution from Gaussian Initial Conditions

Constrain models of Inflation S3

S4

Simulated Halowith Dwarf GalaxySatellites: does CDM predict too much substructure?

What are the Shapes of Dark Matter halos?

SDSS Probes Distribution of Stars in the Milky Way

Yanny, etalNewberg, etal

F turnoff stars on the celestial equator from SDSS: Halo clumps

Debris FromSagittariusDwarf Galaxy

New structures

A

C

Gravitational Lensing

•Strong lensing: (see talk by Kneib)Multiply imaged QSOs: fraction of lensed objects probes dark energy and halo DM profiles

•Weak lensing: Galaxy-Galaxy lensing: Probing Dark Matter Halos and bias

Large-area, low-z lensing: Stebbins, McKay, JF 96

Foregroundgalaxy

Lensing of intrinsically spherical galaxies: induced ellipticities exaggerated

BackgroundSourceshape

Galaxy-Galaxylensing

Foregroundgalaxy

Lensing of real (elliptically shaped) galaxies

Must co-add signal from a large number of foreground galaxies

BackgroundSourceshape

Galaxy-Galaxy Lensing in earlySDSS Data

Galaxy-massCorrelation function

~31,000 foreground galaxies with measuredredshifts

~106 background galaxy shapes (18<r’<22)

Fischer, etalMcKay, etal

g’

r’

i’

from foreground galaxy

December 14, 1999SDSSGalaxy-Galaxy Lensing

Galaxy Halos are Extendedand Massive

Measurement of the Galaxy-Mass correlation function: the GMCF

Galaxy-Mass: measured by SDSS lensing

Galaxy-Galaxy: directly measured by SDSS LSS

Mass-Mass: directly predictable by N-body simulations

Encoded in their relationship is the ‘bias’ between light and mass

wg mbg dk (k/)P (k) dw(w) Gb(w)Wf(w)J0(wk)

Infer mbg ≈ 1/4 to 1/3 from shear and bg

≈ from foreground clustering

Consistent with low-density universe and modest bias

Scaling of Lensing Mass with Galaxy Luminosity

Determine Mass to Light ratios

Combine with Galaxy LuminosityDensity

Infer Cosmic Mass Density

SheldonSheldon

• On-going: extend analysis to ~10 times larger dataset