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

2. 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?

3. 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’

4. 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

5. 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)

6. Gravitational instability: hierarchical collapse generates ever larger structures

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

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

9. 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 institutions

10. 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

11. 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, ~140, ~40,000

12. ‘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

13. The 2dF site
Prime Focus

14. The 2dF facility

15. 2dF on the AAT

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

17. Data pipeline: real-time X-corr z’s

18. Survey Progress 45% of nights allocated were usable
Now: 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

19. 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

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

21. 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).

22. 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.

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

24. 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.

25. Cone diagram: 4-degree wedge

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

27. 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

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

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

30. 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)

31. Tilt, COBE and cluster normalization

32. 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

33. Effects of baryons

34. 2dFGRS power spectrum - detail
nonlinearities, fingers of God, scale-dependent bias ...
Ratio to Wh=0.25CDM model (zero baryons)

35. 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

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

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

38. 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

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

40. Consistency with other constraints
Cluster baryon fraction
Nucleo-synthesis
CMB

41. Tests on mock data

42. Recovering LCDM

43. 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

44. 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

45. 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

46.  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 =  p =  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% 

47. 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)]

48. 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

49. 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 =  (for L=1.9L*)
+ b result  Wm = 0.27  entirely internal to 2dFGRS

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

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

52. 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

53. 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)

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

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

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

57. 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...

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

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

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

61. 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 for 100,000 redshift 2dFGRS data release