1. Large-scale structure from 2dFGRS John Peacock IAU 216 Sydney July 2003

2. 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?

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. The CDM power spectrum growth:  a  a f(  [a]) Break scale relates to  (density in units of critical density): In practice, get shape parameter  almost =  h 

5. The universe according to CDM Bright galaxies today were assembled from fragments at high redshift

6. Results from the 2dF Galaxy Redshift Survey Target: 250,000 redshifts to B<19.45 (median z = 0.11) 250 nights AAT 4m time 1997-2002

7. 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

8. 2dF on the AAT

9. 2dFGRS input catalogue  Galaxies: b J  19.45 from revised APM  Total area on sky ~ 2000 deg 2  250,000 galaxies in total, 93% sampling rate  Mean redshift ~ 0.1, almost all with z < 0.3

10. 2dFGRS geometry NGP SGP NGP 75  x7.5  SGP 75  x15  Random 100x2  Ø ~70,000 ~140,000 ~40,000 ~2000 sq.deg. 250,000 galaxies Strips+random fields ~ 1x10 8 h -3 Mpc 3 Volume in strips ~ 3x10 7 h -3 Mpc 3

12. The 2dF site Prime Focus

13. Final 2dFGRS Sky Coverage NGP SGP Final redshift total: 221,283

14. 2dFGRS Redshift distribution  N(z) Still shows significant clustering at z < 0.1  The median redshift of the survey is = 0.11  Almost all objects have z < 0.3.

15. Cone diagram: 4-degree wedge

17. Fine detail: 2-deg NGP slices (1-deg steps) 2dFGRS: b J < 19.45 SDSS: r < 17.8

18. Spectrum of inhomogeneities  x Primordial power-law spectrum (n=1?) Transfer function

19. Key scales: * Horizon at z eq : 16 (  m h 2 ) -1 Mpc (observe  m h) * Free-stream length : 80 (M/eV) -1 Mpc (  m h 2 = M / 93.5 eV) * Acoustic horizon : sound speed < c/3 1/2 * Silk damping M sets damping scale - reduced power rather than cutoff if DM is mixed Generally assume adiabatic Parameters:  d  b  v  neutrino h w n M

20. 2dFGRS power-spectrum results Dimensionless power: d (fractional variance in density) / d ln k Percival et al. MNRAS 327, 1279 (2001)

21. Effects of baryons

22. 2dFGRS power spectrum - detail Ratio to  h=0.25 CDM model (zero baryons) nonlinearities, fingers of God, scale-dependent bias...

23. Power spectrum and survey window  Window sets power resolution and maximum scale probed: P obs (k) = P(k) * |W(k)| 2  Full survey  more isotropic, compact window function.

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

25. Confidence limits ‘Prior’: h = 0.7 ± 10% & n = 1  m h = 0.20 ± 0.03 Baryon fraction = 0.15 ± 0.07

26. Consistency with other constraints Cluster baryon fraction Nucleo- synthesis

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

28. Power spectrum: Feb 2001 vs ‘final’

29. Model fits: Feb 2001 vs ‘final’  m h = 0.20 ± 0.03 Baryon fraction = 0.15 ± 0.07  m h = 0.18 ± 0.02 Baryon fraction = 0.17 ± 0.06 if n = 1: or  m h = 0.18 e 1.3(n-1)

30. Conclusions from P(k) Lack of oscillations. Must have collisionless component CDM models work Low density if n=1 and h=0.7 apply possibilities for error: Isocurvature?  =1 plus extra ‘radiation’? Massive neutrinos? Scale-dependent bias? (assumed  gals   mass )

31. Tests on mock data

32. Recovering  CDM

33. Redshift-space distortions (Kaiser 1987) z obs = z true +  v / c  v prop. to  0.6  0.6 b -1  n/n Apparent shape from below linearnonlinear (bias)

34. 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  

35.  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) Model fits to z- space distortions  = 0.3,0.4,0.5;  p = 400  = 0.4,  p = 300,500  99%

36. Photometric recalibration Start with SuperCosmos UKST scans SDSS overlap in 33 equatorial plates: rms  = 0.09 mag ( =  SDSS-MGC  Force uniform optical and opt-2MASS colours: rms linearity and ZP corrections 1.4% and 0.15 mag Calibration good to <1% and <0.03 mag  recalibrate APM (rms 0.14 mag)

37. 2dFGRS in COLOUR passive active R magnitudes from SuperCosmos Rest-frame colour gives same information as spectral type,  but to higher z

40. 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

41. Mean spectrum PC1 PC2 PC3 Early Late 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

42. Redshift-space distortions and galaxy type Passive:  =  m 0.6 /b = 0.46  0.13  p = 618  50 km s -1 Active:  =  m 0.6 /b = 0.54  0.15  p = 418  50 km s -1 Consistent with  m = 0.26, b passive = 1.2, b active = 0.9

43. Power spectrum and galaxy type shape independent of galaxy type within error on spectrum

44. Nonlinear evolution and bias Linear NL Benson et al. (2000): galaxies tend to be antibiased on small scales in numerical simulations  = autocorrelation = FT (power spectrum)

45. Radial luminosity bias high z  high L  high b  large-scale power too high? Extra radial weight:    X = 0.85 + 6 z 1.75 (factor 1.6 from z=0 to z=0.25)   new window function Effect is  n = 0.005

46. Meaning of clustering Neyman Scott & Shane (1953): random clump model  r  (r < R) ”  r  obs:  r   ”  = 2.4? Modern view: gravitational instability of (C)DM - sheets, pancakes, filaments, voids...

47. Dark-matter haloes and bias Moore et al:  = [ y 3/2 (1+y 3/2 ) ] -1 ; y = r/r c

48. Correlations from smooth haloes PS++ mass function and NFW++ halo profile gives correct clustering  CDM  CDM Lin NL APM

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

50. Relation to CMB results Combining LSS & CMB breaks degeneracies: LSS measures  m h only if power index n is known CMB measures n and  m h 3 (only if curvature is known) curvature total density baryons

51. The CMB geometrical degeneracy

52. 2dFGRS + CMB: Flatness CMB alone has a geometrical degeneracy: large curvature is not ruled out Adding 2dFGRS power spectrum forces flatness: | 1 -  tot | < 0.04 Efstathiou et al. MNRAS 330, L29 (2002)

53. The CMB peak degeneracy

54. Detailed constraints for flat models (CMB + 2dFGRS only: no priors) Preferred model is scalar-dominated and very nearly scale-invariant Percival et al. MNRAS 337, 1068 (2002)

55. 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

56. Impact of WMAP

57. likelihood contours pre-WMAP + 2dFGRS 147024 gals scalar only, flat models

58. likelihood contours post-WMAP + 2dFGRS 147024 gals scalar only, flat models - WMAP reduces errors by factor 1.5 to 2

59. likelihood contours post-WMAP + 2dFGRS 213947gals scalar only, flat models

60. Effect of neutrinos Free-stream length: 80 (M/eV) -1 Mpc (  m h 2 = M / 93.5 eV) M ~ 1 eV causes lower power at almost all scales, or a bump at the largest scales  =0.05

61. Neutrino mass limit Elgaroy et al. PRL 89, 061301 (2002) Degeneracy: higher neutrino mass resembles lower  h, so true  h can be higher Needs a prior: for  < 0.5, limit is f  < 0.13, or M < 0.6 eV (assuming degenerate mass hierarchy)

62. Vacuum equation of state (P = w  c 2 ) w shifts present horizon, so different  m needed to keep CMB peak location for given h w < - 0.54 similar limit from Supernovae: w < - 0.8 overall 2dFGRS

63. Extra relativistic components? Matter-radiation horizon scale depends on matter density (  m h 2 ) and relativistic density (=1.68  CMB for 3 light neutrinos). Suppose  rel = X (1.68  CMB ) so apparent  m h =  m h X -1/2 and  m =1 h=0.5 works if X=8 But extra radiation affects CMB too. Maintaining peak location needs h=0.5X 1/2 if  m =1 If w=-1, 2dFGRS+CMB measure h X -1/2 = 0.71 +- 5% with HST h = 0.72 +- 11%, hence 1.68X = 1.70 +- 0.24 (3.1 +- 1.1 neutrinos)

64. Summary  >10 Mpc clustering in good accord with  CDM –power spectrum favours  m h= 0.18 & 17% baryons  CMB + 2dFGRS implies flatness –CMB + Flatness measures  m h 3.4 = 0.078 – hence h = 0.71 ± 5%,  m = 0.26 ± 0.04  No evidence for tilt (n = 0.96 +- 0.04) or tensors –But large tensor fractions not yet strongly excluded  Neutrino mass <0.6 eV if  m =1 excluded  w < - 0.54 by adding HST data on h (agrees with SN)  Boosted relativistic density cannot save  m =1 –Neutrino background detected if w = -1  Data public: http://www.mso.anu.edu.au/2dFGRS/Public