Large-scale Structure: Theory & Observations

1. Large-scale Structure:Theory & Observations Josh Frieman Structure Formation & Evolution, Santiago, October 2002

2. 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.

3. 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

4. Formation of Dark Halos (Virgo consortium)

5. 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

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

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

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

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

10. Constraints on the Baryon Density from 2dF Galaxy Redshift Survey Power Spectrum Increasing b suppresses power on small scales (and increases amplitude of wiggles) Percival, etal. Tegmark & Hamilton

11. 2dF GRS Power Spectrum m,tot < 2.2 eV --reasonable prior on m --BBN prior on b --simple model of bias & redshift distortions 0.05 0.01 =0  = m,tot 94 eV Elgaroy, etal

12. 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

13. Large-scale Structure, circa 1986 Center for Astrophysics Survey Filaments, Walls, Voids, Rich clusters 100 Mpc You Are Here `Pizza Slice’ 6 degrees thick containing 1060 galaxies: position of each galaxy represented by a single dot deLapparent, Geller, Huchra

14. Las Campanas Redshift Survey Shectman,etal

15. Colless, etal

16. SDSS Redshift Survey ~200,000 galaxy redshifts so far

18. APM Galaxy Survey (digitized plates) ~106 galaxy positions, magnitudes bJ < 20 Maddox,etal

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

20. 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

21. 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

22. Rescale Power by linear bias factor for 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

23. Galaxies are Biased tracers of the Dark Matter Tegmark, etal

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

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

27. Bias depends on Galaxy Luminosity Compare 2dF results of Norberg, etal SDSS Redshift Survey Intrinsically bright Intrinsically faint

28. 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

29. 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

30. Halo Occupation Distribution “Halo Occupation” Model for Bias Assume: • All galaxies live in dark matter halos. • Galaxy content of a halo is statistically independent of the • halo’s larger scale environment. Depends only on mass. The bias of a certain galaxy class (type, luminosity, etc) is fully defined by: • 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 Also see: semi-analytic models

31. Galaxy Clustering Cosmological Model Ω, P(k), etc. Galaxy Formation Gas cooling, Star formation, Feedback, Mergers, etc. Dark Halo Population n(M), ξ(r|M), v(r|M), ρ(r) Halo Occupation Distribution P(N|M) Spatial bias within halos Velocity bias within halos Galaxy-Mass Correlations

33. SLOAN DIGITAL SKY SURVEY http://www.sdss.org GOAL: 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 Max-Planck A and IA Johns Hopkins University Institute for Advanced Study U.S. Naval Observatory University of Washington Japan Participation Group Los Alamos National Lab Funding: Sloan Foundation, NSF, DOE, NASA, member institutions, Japan Ministry of Education University of Pittsburgh

34. SDSS 2.5 meter Telescope

35. 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

36. Projected to June 2005: 6600 sq deg imaging 600,000 spectra

37. 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

38. 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 Budavari,etal Zehavi, etal Tegmark, etal

39. SDSS Angular Clustering I Galaxy angular correlation function dP=n2[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 bright faint Scranton, etal Connolly, etal

40. Two-parameter fit of SDSS Angular KL Data to CDM Models Amplitude 8 = 0.92 ± 0.06 • Safe • Truncation • of KL modes • Orthogonal • Constraints • Probing Power Around the Peak Shape  ( mh) = 0.19 ± 0.04 Szalay, etal

41. 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

42. Photometric Camera filter response with and w/o atmospheric extinction of 1.2 airmasses

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

44. 343k 316k 254k 185k 280k 127k 326k 185k The Photo-z Samples All: 50M mr<21 : 15M 10 stripes: 10M 0.1<z<0.3 -20 > Mr 2.2M 0.1<z<0.5 -21.4 > Mr 3.1M -20 > Mr >-21 1182k -21 > Mr >-23 931k -21 > Mr >-22 662k -22 > Mr >-23 269k

45. Angular Correlations II. • Luminosity dependence: 3 cuts -20> M > -21 -21> M > -22 -22> M > -23

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

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

48. Redshift Distribution and Radial Selection Function for the Spectroscopic Sample -22 < Mr < -19 14.5 < r’ < 17.77 2000 sq. deg. ~140,000 galaxies 120,000 at z<0.15 N P cz (km/sec)

49. Redshift-Space Galaxy Correlation Function