John Peacock Garching December 2001 Measuring large-scale structure in the universe with the 2dF Galaxy Redshift Survey John Peacock Garching December 2001

The distribution of the galaxies Hubble proves galaxies have a non-random distribution 1950s: Shane & Wirtanen spend 10 years counting 1000,000 galaxies by eye - filamentary patterns?

Redshift surveys Inverting v = cz = Hd gives an approximate distance. Applied to galaxies on a strip on the sky, gives a ‘slice of the universe’

Las Campanas Redshift Survey Redshift surveys: v = cz = H0 d d = z x 3000 h-1 Mpc h = H0 / 100 km s-1 Mpc -1 CfA Survey ~15000 z’s Las Campanas Redshift Survey ~25000 z’s

Inflationary origin of structure? Assume early universe dominated by scalar-field V(f) at GUT energies Predicts small fluctuations in metric. Scalar fluctuations (= Newtonian potential) have nearly flat spectrum - also expect tensor modes (gravity waves)

Gravitational instability: hierarchical collapse generates ever larger structures

Nonlinear predictions of theory Bright galaxies today were assembled from fragments at high redshift

Results from the 2dF Galaxy Redshift Survey Target: 250,000 redshifts to B<19.45 (median z = 0.11) Current total: 213,000

33 people at 11 institutions The 2dFGRS Team Australia Joss Bland-Hawthorn Terry Bridges Russell Cannon Matthew Colless Warrick Couch Kathryn Deeley Roberto De Propris Karl Glazebrook Carole Jackson Ian Lewis Bruce Peterson Ian Price Keith Taylor Britain Carlton Baugh Shaun Cole Chris Collins Nick Cross Gavin Dalton Simon Driver George Efstathiou Richard Ellis Carlos Frenk Ofer Lahav Stuart Lumsden Darren Madgwick Steve Maddox Stephen Moody Peder Norberg John Peacock Will Percival Mark Seaborne Will Sutherland Helen Tadros 33 people at 11 institutions

2dFGRS input catalogue Galaxies: bJ  19.45 from revised APM Total area on sky ~ 2000 deg2 250,000 galaxies in total, 93% sampling rate Mean redshift <z> ~ 0.1, almost all with z < 0.3

2dFGRS geometry ~2000 sq.deg. 250,000 galaxies NGP SGP Strips+random fields ~ 1x108 h-3 Mpc3 Volume in strips ~ 3x107 h-3 Mpc3 NGP SGP NGP 75x7.5 SGP 75x15 Random 100x2Ø ~70,000 ~140,000 ~40,000

‘2dF’ = ‘two-degree field’ = 400 spectra Tiling strategy ‘2dF’ = ‘two-degree field’ = 400 spectra Efficient sky coverage, but variable completeness High completeness through adaptive tiling: multiple coverage of high-density regions

The 2dF site Prime Focus

The 2dF facility

2dF on the AAT

Configuring fibres >12 arcsec spacing; 15 degree bend <10 seconds to position each fibre Configuring fibres

Data pipeline: real-time X-corr z’s

Survey Progress 45% of nights allocated were usable Now: 213000 z’s 45% of nights allocated were usable Current rate 1000 redshifts per allocated night Survey will end in Jan 2002 after 250 nights total Expected final size: 230,000

Sky Coverage of Survey NGP SGP 62% of fields were observed up to July 2001 Final strips will be trimmed to finish early 2002. NGP SGP

Redshift distribution N(z) for 156000 galaxies. Still shows significant clustering. The median redshift of the survey is <z>=0.11 Almost all objects have z < 0.3.

Redshift yield The median redshift yield is 93%. 10% of fields have a yield less than 80%. 30% of fields have a yield less than 90%. After ADC s/w fix, good conditions routinely give yields >95%. Reliability: of 1404 z’s in overlap with LCRS, only 8 disagree (99.4% agree).

Completeness Redshift completeness is >90% for bJ<19 but drops to 80-85% at bJ=19.45. Completeness is similar in NGP and SGP strips. Completeness as a function of magnitude varies with the overall completeness of the field. Selection function depends on (at least) overall completeness and magnitude.

Cutouts are bright stars and satellite trails. NGP Survey mask SGP Cutouts are bright stars and satellite trails.

Sampling & Uniformity Adaptive tiling  efficient, uniform sampling… when done. At current stage of survey, sampling is highly variable. This limits applications requiring large contiguous volumes.

Cone diagram: 4-degree wedge

Fine detail: 2-deg NGP slices (1-deg steps) 2dFGRS: bJ < 19.45 SDSS: r < 17.8

Spectral classification by PCA Apply Principal Component analysis to spectra. PC1: emission lines correlate with blue continuum. PC2: strength of emission lines without continuum. PC3: strength of Balmer lines w.r.t. other emission. Define spectral types as sequence of increasing strength of emission lines Instrumentally robust Meaning: SFR sequence Early Late Mean spectrum PC1 PC2 PC3

LFs by spectral type From early to late types: M* gets fainter: -19.7  -19.2  gets steeper: -0.8  -1.7 Sum of Schechter fits to each type Overall STY Schechter fit

Infrared luminosity functions match 2MASS : 12,000 galaxies with J,K,z - gives stellar LF independent of dust Wstars = 0.0014 ± 0.00013 (Kennicutt) Wstars = 0.0029 ± 0.00027 (Salpeter) >95% of baryons are dark

The CDM power spectrum growth: d(a) = a f(W[a]) Break scale relates to W(density in units of critical density): In practice, get shape parameter G (almost = Wh)

Tilt, COBE and cluster normalization

2dFGRS power-spectrum results Dimensionless power: d (fractional variance in density) / d ln k APM deprojection: real space 2df: redshift space result robust with respect to inclusion of random fields

Effects of baryons

2dFGRS power spectrum - detail nonlinearities, fingers of God, scale-dependent bias ... Ratio to Wh=0.25CDM model (zero baryons)

Power spectrum and survey window Window sets power resolution and maximum scale probed: Pobs(k) = P(k) * |W(k)|2 Full survey  more isotropic, compact window function. Gain x2.3 in P(k) range

Model fitting Essential to include window convolution and full data covariance matrix

Confidence limits Wmh = 0.20 ± 0.03 Baryon fraction = 0.15 ± 0.07 ‘Prior’: h = 0.7 ± 10%

Comparison with other data All-sky PSCz: G = 0.20  0.05 SDSS EDR: G = 0.19  0.04 2dFGRS: G = 0.16  0.03

Relation to CMB results curvature Relation to CMB results baryons total density Geometrical degeneracy: need a value for h, even with no tensors

Consistency with other constraints Cluster baryon fraction Nucleo-synthesis CMB

Tests on mock data

Recovering LCDM

Scalar fit to 2dFGRS + CMB Joint likelihood removes need to assume parameters: Wmh2 from CMB and Wmh from LSS gives both Wm & h: Wm = 0.27 ± 0.05

Redshift-space distortions (Kaiser 1987) zobs = ztrue + dv / c dv prop. to 0.6 dr/r = 0.6 b-1 dn/n (bias) Apparent shape from below linear nonlinear

Redshift-space clustering z-space distortions due to peculiar velocities are quantified by correlation fn (,). Two effects visible: Small separations on sky: ‘Finger-of-God’; Large separations on sky: flattening along line of sight

 and   Model fits to z-space distortions Fit quadrupole/monopole ratio of (,) as a function of r with model having   0.6/b and p (pairwise velocity dispersion) as parameters.  = 0.4, p= 300,500 Best fit for r > 8 h-1 Mpc (allowing for correlated errors) gives:  = 0.6/b = 0.43  0.07 p = 385  50 km s-1 Applies at z = 0.17, L =1.9 L* (significant corrections) Full survey will reduce random errors in  to 0.03.  = 0.3,0.4,0.5; p= 400 99% 

Measuring bias - 1: CMB The problem: do galaxies trace mass? dn/n = b dr/r Take mass s8 from CMB (scalar fit) and apparent (redshift-space) s8 from 2dFGRS P(k): b(1.9L*) = (1.00 ± 0.09) exp[-t + 0.5(n-1)]

Measuring bias - 2: Bispectrum (with Verde, Heavens, Matarrese) 1 2 Two-point correlations: < d1 d2 > = x : FT = P(k) power spectrum 1 2 3 Three-point correlations: < d1 d2 d3 > = z : FT = B(k1,k2,k3) bispectrum = 0 for Gaussian field. Measure of gravitational nonlinearity

Bispectrum results Assume local nonlinear bias: dg = b1 dm + b2 (dm)2 Nonlinear bias can mimic some aspects of gravitational evolution (e.g. skewness) - but full bispectrum contains shape information: bias doesn’t form filaments data match unbiased predictions tCDM LCDM Results for NGP + SGP: b1 = 1.04  0.11, b2 = -0.05  0.08 (for L=1.9L*) + b result  Wm = 0.27  0.06 - entirely internal to 2dFGRS

Clustering as f(L) Clustering increases at high luminosity: b(L) / b(L*) = 0.85 + 0.15(L/L*) suggests << L* galaxies are slightly antibiased - and IRAS g’s even more so: b = 0.8

Robustness of r0 No change over 2 mag. increase in distance modulus

The tensor CMB degeneracy scalar plus tensors tilt to n = 1.2 raise wb to 0.03 Degeneracy: compensate for high tensors with high n and high baryon density

Constraining tensors with b Dimensionless power: d (fractional variance in density) / d ln k Scalar only: s8 = 0.75. Predicts b(L*) = 0.39 High tensor: s8 = 0.64. Predicts b(L*) = 0.29 (also fails to match cluster abundance)

The CDM clustering problem Non-monotonic scale-dependent bias LCDM tCDM b2 = xg /xm Jenkins et al. 1998 ApJ 499, 20

Numerical galaxy formation Follow halo merger histories: Recipes for cooling, star formation and feedback give predicted galaxy populations

Antibias in LCDM Benson et al. astro-ph/9903343

Meaning of clustering Neyman Scott & Shane (1953): random clump model r ~ r-a (r < R) ” x ~ r-(2a-3) obs: x ~ r-1.8 ” a = 2.4? Modern view: gravitational instability of (C)DM - sheets, pancakes, filaments, voids...

Dark-matter haloes and bias Moore et al: r = [ y3/2(1+y3/2) ]-1; y = r/rc

Correlations from smooth haloes LCDM NL APM Lin tCDM PS++ mass function and NFW++ halo profile gives correct clustering

Halo occupation numbers depend on mass PS++ mass function wrong shape for cluster/group LF LCDM Correct weighting of low-mass haloes predicts antibias

Summary >10 Mpc clustering in good accord with LCDM power spectrum favours Wm h= 0.20 & 15% baryons With h = 0.7 ± 10%, gives Wm = 0.27 ± 0.05 No significant large-scale bias (3 arguments): redshift-space distortions with Wm from P(k) comparing CMB s8 with P(k) amplitude direct internal bispectrum analysis Matches no-tilt no-tensor vanilla CMB tensor-dominated models excluded See http://www.mso.anu.edu.au/2dFGRS/ for 100,000 redshift 2dFGRS data release