Measuring large-scale structure in the universe with the 2dF Galaxy Redshift Survey

John Peacock Garching December 2001

The distribution of the galaxies

1930s:

Hubble proves galaxies have a non-random distribution

1950s:

Shane & Wirtanen spend 10 years counting 1000,000 galaxies by eye

- filamentary patterns?

Redshift surveysInverting 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~25000 z’s

CfA Survey~15000 z’s

Redshift surveys: v = cz = H0 d d = z x 3000 h-1 Mpc

h = H0 / 100 km s-1 Mpc -1

Inflationary origin of

structure?

Assume early universe dominated by scalar-field V() 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

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

NGP

SGP

NGP 75x7.5 SGP 75x15 Random 100x2Ø ~70,000 ~140,000 ~40,000

~2000 sq.deg.250,000 galaxies

Strips+random fields ~ 1x108 h-3 Mpc3

Volume in strips ~ 3x107 h-3 Mpc3

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

2dF on the AAT

Survey Progress

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

Now: 213000 z’s

62% of fields were observed up to July 2001 Final strips will be trimmed to finish early 2002.

Sky Coverage of Survey

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.

Survey mask

NGP

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

The CDM power

spectrum

growth:

aa f([a])

Break scale relates to (density in units of critical density):

In practice, get shape parameter almost = h

2dFGRS power-spectrum results

APM deprojection: real space

2df: redshift space

result robust with respect to inclusion of random fields

Dimensionless power:

d (fractional variance in density) / d ln k

Effects of baryons

2dFGRS power spectrum - detail

Ratio to h=0.25CDM model (zero baryons)

nonlinearities, fingers of God, scale-dependent bias ...

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

‘Prior’:

h = 0.7 ± 10%

mh = 0.20 ± 0.03

Baryon fraction = 0.15 ± 0.07

Relation to CMB results

Geometrical degeneracy: need a value for h, even with no tensors

curvature

total density

baryons

Consistency with other constraints

Cluster baryon fraction

Nucleo-synthesis

CMB

Scalar fit to 2dFGRS + CMB

Joint likelihood removes need to assume parameters: mh2 from CMB and mh from LSS gives both m & h:

m = 0.27 ± 0.05

Redshift-space distortions (Kaiser 1987)

zobs = ztrue +v / c v prop. to 0.6 0.6 b-1

n/n

Apparent shape from below

linear nonlinear

(bias)

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

r

and Fit quadrupole/monopole ratio of

(,) as a function of r with model having 0.6/b and p (pairwise velocity dispersion) as parameters.

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.

Model fits to z-space distortions

= 0.3,0.4,0.5; p= 400

= 0.4, p= 300,500

99%

Measuring bias - 1: CMB

The problem: do galaxies trace mass? n/n = b r/r

Take mass 8 from CMB (scalar fit) and apparent (redshift-space) 8 from 2dFGRS P(k):

b(1.9L*) = (1.00 ± 0.09) exp[- + 0.5(n-1)]

Measuring bias - 2: Bispectrum(with Verde, Heavens, Matarrese)

1

2

1

2

3

Two-point correlations:

< 1 2 > = : FT = P(k) power spectrum

Three-point correlations:

< 1 2 3 > = : FT = B(k1,k2,k3) bispectrum

= 0 for Gaussian field. Measure of gravitational nonlinearity

Bispectrum resultsAssume local nonlinear bias: g = b1 m + b2 (m)2

Nonlinear bias can mimic some aspects of gravitational evolution (e.g. skewness) - but full bispectrum contains shape information: bias doesn’t form filaments

CDM

CDM

Results for NGP + SGP: b1 b2 (for L=1.9L*)

+ result m = 0.27 - entirely internal to 2dFGRS

data match unbiased predictions

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

The tensor CMB degeneracy

Degeneracy: compensate for high tensors with high n and high baryon density

scalar

plus tensors

tilt to n = 1.2

raise b to 0.03

Constraining tensors with Dimensionless power:

d (fractional variance in density) / d ln k

Scalar only: 8 = 0.75.

Predicts (L*) = 0.39

High tensor: 8 = 0.64.

Predicts (L*) = 0.29

(also fails to match cluster abundance)

Summary

>10 Mpc clustering in good accord with LCDM– power spectrum favours m h= 0.20 & 15% baryons

• With h = 0.7 ± 10%, gives m = 0.27 ± 0.05

No significant large-scale bias (3 arguments):– redshift-space distortions with m from P(k)

– comparing CMB 8 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