Large-scale Structure: Theory & Observations Josh Frieman Structure 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 P i ~ k n 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 a Cold Dark Matter Model Features: Filamentary structure amplified 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) =  d 3 x e ik·x  (x)  (k 1 )  (k 2 )  = (2  ) 3 P(k 1 )  3 (k 1 +k 2 ) Evolution: P gal (k) = b 2 gal (k) P i (k) T(k;  j, n,  8 ) bias primordial spectrum Non-linear Transfer function

Cold Dark Matter Models Power Spectrum of the Mass Density Turnover due to delayed perturbation growth in radiation era SCDM  CDM Open CDM P ~ k P ~ k -3 k eq ~  m h =  h/Mpc Non-linearLinear Shape parameter

Power Spectrum in Cold Dark Matter Models Cold Dark Matter Models  m h=0.5 SCDM  m h=0.2  CDM (assumed biased) Amplitude  8 Rms Linear Mass Fluctuations in spheres of Radius 8h -1 Mpc

More Cold Dark Matter Less Cold Dark Matter (Open) Cold Dark Matter with 

Probing Neutrino Mass and Baryon Density SDSS + MAP: will constrain sum of stable neutrino masses as low as ~ 0.5 eV Wiggles Due to Non-zero Baryon Density

Constraints on the Baryon Density from 2dF Galaxy Redshift Survey Power Spectrum Percival, etal. Tegmark & Hamilton Increasing  b suppresses power on small scales (and increases amplitude 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  =  = 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, Rich clusters deLapparent, Geller, Huchra

Las Campanas Redshift Survey Shectman,etal

Colless, etal

SDSS Redshift Survey ~200,000 galaxy redshifts so far

APM Galaxy Survey (digitized plates) ~10 6 galaxy positions, magnitudes b J < 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 select different mixes of galaxy populations Evidence for type-dependent Bias Error bars not shown! Missing: PSCz, EDSGC, ESO Slice, 2dF, SDSS, … Vogeley

Galaxy Clustering varies with Galaxy Type How are each of them related 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 factor for each survey: different galaxy types cluster with different strengths P i (k) = b 2 i P m (k) Galaxies  Mass Best fit CDM Model:  h = Vogeley

Galaxies are Biased tracers of the Dark Matter Tegmark, etal

Cannot describe bias on scales smaller than smoothing scale. Choice of smoothing scale is arbitrary. δ m is generally unobservable. “Environmental” Bias

Bias Depends on Galaxy Color Cf. morphology- density relation Zehavi, etal SDSS Redshift Survey

Bias depends on Galaxy Luminosity Compare 2dF results of Norberg, etal Intrinsically bright Intrinsically faint 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 Ω m =0.4, Ω Λ =0.6, Ω b =0.02h -2 h=0.65, n=0.95, σ 8 = dm gas particles l=50 Mpc/h, m b =8.5x10 8 M sun 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 M P(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 Distribution P(N|M) Spatial bias within halos Velocity 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 GOAL GOAL: MAP THE UNIVERSE IN 3 DIMENSIONS OVER A LARGE VOLUME Photometric Survey: ~ band CCD images Spectroscopic Survey: ~10 6 galaxy and 10 5 QSO redshifts University of Chicago Fermilab Princeton University New Mexico State Johns Hopkins UniversityInstitute for Advanced Study U.S. Naval Observatory University of WashingtonJapan Participation Group Max-Planck A and IA Funding: Sloan Foundation, NSF, DOE, NASA, member institutions, Japan Ministry of Education Los Alamos National Lab University 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

Projected to June 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, etal Tegmark, etal Budavari,etal

SDSS Angular Clustering I Galaxy angular correlation function dP=n 2 [  w  d   d   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, etal Connolly, etal bright faint

Safe Truncation of KL modes Orthogonal Constraints  Probing Power Around the Peak Amplitude  8 = 0.92 ± 0.06 Shape  (   m h) = 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 Camera filter response with and w/o atmospheric extinction of 1.2 airmasses

Galaxy photometric redshift estimates Predicted redshift from 5-band SDSS Photometry Spectroscopic measured redshift Connolly, etal Csabai, etal

The Photo-z Samples 343k 254k185k 316k280k 326k185k 127k -20 > M r > k -21 > M r >-23931k 0.1<z< > M r2.2M -21 > M r >-22662k -22 > M r >-23269k 0.1<z< > M r3.1M 10M 10 stripes: 10M 15M m r <21 : 15M 50M All: 50M

Angular Correlations II. Luminosity dependence: 3 cuts -20> M > > M > > M > -23

Angular Correlations III. Color Dependence 4 bins by rest-frame SED type

Sky coverage of SDSS redshift survey (Aitoff projection, equatorial coordinates) (Dust map from Schlegel, Finkbeiner & Davis)

Redshift Distribution and Radial Selection Function for the Spectroscopic Sample -22 < M r < < r’ < sq. deg. ~140,000 galaxies 120,000 at z<0.15 cz (km/sec) N P

Redshift-Space Galaxy Correlation Function

Correlation Amplitude Contours Radial Redshift Distortions due to peculiar velocities

2dF:  = 0.43  0.07

Forecast Constraints From SDSS Luminous Red Galaxy Clustering: Geometric Test for Dark Energy Matsubara & Szalay

Projected Correlation Function

Lum funcs & sel funcs by Michael Blanton (NYU) Divide Galaxies by Intrinsic Luminosity: Volume- limited subsamples

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  M1M1 N ~M β

Rescale bias

k=3 k=0.3 k=0.1 k=0.03 k=1

Cmbgg OmOl LSS

SDSS Clustering Corrected For Luminosity Bias

Finding Groups In SDSS Berlind

SDSS Group Identification Identify groups using: Friends-of-friends algorithm Fixed tangential linking length Variable line-of-sight linking length Group catalog: 2,143 galaxy groups (N>2)

SDSS Group Multiplicity Function

Preliminary HOD Constraints

Detecting Galaxy Clusters MaxBcg 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, etal Miller, etal Kim, etal Goto, etal

MaxBcg Photo-z’s

SDSS Cluster Abundance as a Cosmological Probe

Non-Gaussian structure: beyond Two-point statistics Identical Power spectra Szalay

JF, Gaztanaga Angular 3-point Correlation Function N-body vs. Nonlinear Perturbation Theory (PT) q 3 = z(  12,  13,  23 ) w(  12 )w(  13 )+ cyc.  12  13  deg Data Model

APM Results Solid: Perturbation Theory (PT) Open triangles: N-body Circles and Closed squares: APM Data biased models SCDM Local, deterministic Bias model:  g = f(  ) = b   + b 2  2 /2 Q g = Q/b 1 + b 2 /b 1 2

Scoccimarro, Feldman, Fry, JF Bispectrum of IRAS Redshift Surveys: PSCz Survey (~15,000 galaxies) Q = B(k 1,k 2,k 3 ) P(k  )P(k 2 )+ cyc. k 2 /k 1 = Perturbation Theory PT with redshift distortions biased models Collinear configurations Collinear configurations ~Equilateral

Constraints on Bias Parameters from IRAS Bispectra Local, deterministic Bias model:  g = f(  ) = b   + b 2  2 /2 Q g = Q/b 1 + b 2 /b 1 2 Feldman, etal

PDF of the Evolved Density Field on Scales of ~ few Mpc Cold Dark Matter simulation Bernardeau & Kofman

Higher Order Angular Correlations in early SDSS imaging data S N = ‹  N ›/‹  2 (  )› N-  Higher order Correlations probe Bias & initial Non-Gaussianity Szapudi, etal S3S3 S4S4

Comparison with Biased  CDM model Higher Order Correlations consistent with Non-linear evolution from Gaussian Initial Conditions  Constrain models of Inflation S3S3 S4S4

Simulated Halo with Dwarf Galaxy Satellites: does CDM predict too much substructure? What are the Shapes of Dark Matter halos? SDSS Probes Distribution of Stars in the Milky Way Yanny, etal Newberg, etal

F turnoff stars on the celestial equator from SDSS: Halo clumps Debris From Sagittarius Dwarf 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

SDSS: 2nd Candidate (Strongly) Gravitationally Lensed QSO SDSS image in 5 bands Magellan follow-up image: I band Inada, etal Keck spectra

Foreground galaxy Lensing of intrinsically spherical galaxies: induced ellipticities exaggerated Background Source shape Galaxy- Galaxy lensing

Foreground galaxy Lensing of real (elliptically shaped) galaxies Must co-add signal from a large number of foreground galaxies Background Source shape

Galaxy-Galaxy Lensing in early SDSS Data Galaxy-mass Correlation function ~31,000 foreground galaxies with measured redshifts ~10 6 background galaxy shapes (18<r’<22) Fischer, etal McKay, etal g’ r’ i’ from foreground galaxy

December 14, 1999 SDSS Galaxy- Galaxy Lensing Galaxy Halos are Extended and 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 w g     m b g  dk (k/  )P  (k)  dw(  w)  G b (w)W f (w)J 0 (wk  ) Infer  m b g    ≈ 1/4 to 1/3 from shear and b g   ≈  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 Luminosity Density  Infer Cosmic Mass Density

Sheldon

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