1. AY202a Galaxies & Dynamics Lecture 19: Large Scale Structure

2. What is the object of the game?
Three questions + :
What is the distribution of matter in space now?
What was the distribution a long time ago?
How did the distribution evolve?
And 4. What can we learn about the Cosmological Model?
Routes:
Galaxy &Cluster & AGN (Redshift) Surveys
Luminosity Functions
Clustering Statistics
Comparison to Models
CMB

3. The Problem of LSS How did the Universe get its lumps?
We know that ~400,000 years after the big bang the Universe was really smooth - bumps and wiggles smaller than one part in 105.
Today the Universe is really lumpy. You and I are over densities of a factor of 1030.

4. We study structures by making maps. Topography/Topology

5. Election ’06 Congressional Districts

6. Its all in the display: Election ’04 By County R/B
By County color range
By state scaled by population

7. Its all in the display II
Election ’08
By County R/B
By County color range
By state scaled by population

8. History of LSS Studies Early Days ---- just 2-d Maps from Catalogs
Messier ~1771, 103 original objects, now 110
NGC (J. Dreyer + Herschels) ~1880
7840 Objects in the NGC
5326 in the Index Catalogs
Shapley & Ames Catalog 1932
1246 galaxies
mpg < 13.2

11. Revised Shapley Ames Catalog – Sandage & Tammann

12. Large Scale Structure LSS is the distribution of galaxies in space.
History:
A. Dawn of “time” (or of observational cosmology) --- The Universe is
“Sensibly Uniform” (E. Hubble 1936)
B. View Rapidly Evolved
Shapley-Ames Catalog (1936) Superclusters?
F. Zwicky ( ) Clusters Common

13. Zwicky vs Hubble --- the Field vs Clustering on all scales

14. C. Attempts to look at distortions Rubin 1952
D. Delineation of the “Local Supergalaxy” deVaucouleurs 1956
E. New Catalogs created from Photographic Surveys D only
Zwicky++ the CGCG;
Vorontosov-Velyaminov ++ the MCG 1960’s
Nilson = UGC (1974)
Lauberts & West = ESO (1970’s)

15. Zwicky and his Catalogue of Galaxies and of Clusters of Galaxies
(CGCG)

16. Catalogue of Galaxies & of Clusters of Galaxies –
Zwicky, Herzog, Kowal, Wild ~31,000 galaxies

17. Shane-Wirtanen Map
Lick ~1968

18. Nilson UGC + ESO + MCG 25,000 galaxies
From Nigel Sharp
1977

19. 3D Mapping the Local Universe
Not much progress until the mid 1970’s!
In 1972 the largest “complete” galaxy redshift sample had only ~250 galaxies
New theoretical drivers --- Peebles & students & friends
angular correlation functions w(θ) = P(θ)/PR(θ) - 1
Key was innovation in detector technology:
computers + digital detectors
sensitive radio receivers

20. First attempts at 3-D analysis
Turner & Gott CGCG w some v’s
Rubin, Ford, Thonnard & Roberts ’76 Flows?
Tifft & Gregory ’76 LSS around Coma
Sandage & Tammann RSA velocities (still w plates!)
Caltech Group (remain nameless but includes JH)
Davis, Geller & Huchra ’78 3-D statistics
Chincarini & Rood ’79 analysis of existing v’s
Kirshner, Oemler Schechter & Shectman ’81 Bootes Void
Giovanelli & Haynes ’80s Arecibo Surveys,
’82 Lynx - Ursa Major filament

21. Turner & Gott 1975-76 Isolated Galaxies Groups Systematic Analysis
of clustering in
the CGCG
LF & Omega
Binary Galaxies

22. Tifft & Gregory ’76 1. All galaxies in groups or clusters
2. Truly isolated galaxies don’t 
3. Coma < 3o
(#3 probably wrong)

23. Davis, Geller &
Huchra ’78
1st Spatial correlation function from a redshift survey
LF and Omega again

24. 1. Coma big, part of a 200 Mpc structure
Chincarini & Rood ’79
1. Coma big, part of a 200 Mpc structure
2.  chains, clumps & voids

25. KOSS ’81
133 redshifts in
three fields to
R ~ 16.3

26. Giovanelli & Haynes ’82
Lynx-Ursa Major Filament

27. Why & How Redshift Surveys?

29. Larson wasn’t quite right…

30. CfA Surveys (1) DHLT (1982). (2) dLGH++ (1985-1995)

31. FL Whipple Obs

32. The Little Telescope That Could
The FLWO 60-inch

33. Davis, Tonry, Latham & Huchra
The Z Machine
Davis, Tonry, Latham & Huchra
Based on a concept by Shectman & Gunn

36. Spectral features in galaxies

37. Cross correlation
Techniques:
DFT’s of spectra
Schechter ’76
Tonry & Davis ’78
Kurtz & Mink ‘98

39. Giovanelli & Haynes Pisces-Perseus Survey (Arecibo)

40. Zwicky Catalogue and the first CfA Slice
Why Strips?

41. Zwicky C and the first CfA Slice
Why Strips? (1) Optimal Observing Strategy (2) Good mapping strategy

42. 1985 deLapparent, Geller & Huchra

43. CfA2 LF by Type

46. CfA2 1995

47. 300 – 400 M lyr
400 – 500 M lyr

48. Las Campanas Redshift Survey 1998
Shectman et al.
Fibers + Plug Plates on the
100” Dupont

49. 2 Degree Field Redshift Survey

50. 2dF Sky Coverage

52. Sloan DSS

53. SDSS Sky Coverage 2003
SDSS DR6
Spectroscopic
Sky Coverage
(2006)

54. Local Large Scale Structures
Fairall

56. Cosmology from LSS
Compare the observed distribution of galaxies with those predicted by models:
Tools:
Correlation functions
Topology
Power Spectrum
Count Statistics (counts-in-cells, …)
Void Probability Function
Genus GS Wavelets Fractals Filling Factor etc.

57. Correlation Functions
Angular correlation function ω(θ) is defined by δPθ = N [1 + ω(θ)] δΩ where N is the number of objects per steradian and δPθ is the probability of finding an object with solid angle δΩ at an angular distance θ from a randomly chosen object. (draw rings around each galaxy and count its neighbors as a function of angular radius)

59. and observationally γ ~ 1.8
The Spatial Correlation Function ξ(r) or ξ(s)
is defined by
δPr = n [1 + ξ(r)] δV
where n is the volume number density of objects and δPr is the probability of finding an object within volume element δV at a distance r from a randomly chosen object.
Peebles (and everyone since) found roughly
ξ(r) ~ B r-γ = (r/r0) -γ
and observationally γ ~ 1.8

60. Correlation Function Estimation
<DD> <RR>
Hamilton ξ =
or = <DD>/<DR>
Landy & Szalay
ξ = (<DD> - 2<DR> + <RR>)/<RR>
<DR>2

62. SDSS ‘05

64. for a homogeneous model (ApJ 117, 134 (1953)
Angular and Spatial Correlation functions are related by Limber’s Equation
ω(θ) =
for a homogeneous model (ApJ 117, 134 (1953)
(r1,r2)2 dr1 dr Ψ1 Ψ2 ξ(r12/r0)
[  r2 dr Ψ ]2

65. The Power Spectrum
Suppose the Universe is periodic on a volume VU. Consider the Simplest case, a volume limited sample with equal weight galaxies, N galaxies. Measure fluctuations on different scales in volume V:
P(k) = (<|δk|2> - 1/N) (Σ |wk|2)-1 (1-|wk|2)-1
where δk = 1/N Σ e ik.xj - wk
And w(x) is the window function for the survey
= 1 inside and = 0 outside the boundaries k j

66. wk is the Fourier Transform of w(x)
So w(x) = V/VU Σ wk e-ik.x
wk is the Fourier Transform of w(x)
This derives from
<|δk|2> = δk0D /N + P(k)
variance
sample Poisson Fluctuations Real Power
mean due to finite sampling per mode
(see Peacock & Dodds; Park et al 1994)
Kronecker delta

68. LCRS vs CfA2+SSRS2

69. SDSS
Tegmark et al. 2004

71. SDSS vs and plus other measures
Red line are from a Monte Carlo Markov chain analysis of the WMAP for simple flat scalar
adiabatic models parameterized by the densities of dark energy, dark matter, and baryronic matter, the spectral index and amplitude, and the reionization optical depth.

73. Counts in Cells Analysis

74. Simulations
Industry started by S. Aarseth followed by Efstathiou, White, Frenk & Davis and now
many others. (c.f. Virgo Consortium)
Big groups at MPI, NCSA, Chicago.
N-Body codes or N-body Hydro codes
(PP, PPM, Grid, SPH)

75. Constrained Model (V. Springel)

76. LCDM simulation Filaments are warm Hydrogen (~10^5 K) 250 Mpc Cube Hernquist 2003

77. SCDM
VIRGO Consortium

78. OCDM

79. LCDM

80. Current best simulations don’t reproduce the observations.
We still only have a rudimentary theory of galaxy and star formation. (semi-analytic models –arrgh!)
We are just beginning to observe the evolution of LSS
It appears that most of the “stuff” in the Universe is invisible (Dark Matter, Dark Energy, even most baryons).
We don’t know what Dark Matter is!

81. Baryon Acoustic Oscillations
Eisenstein et al ’05
noted that LRG
sample had large
effective volume

82. SDSS LRG Correlation Function

83. Simulations from D. Eisenstein
based on Seljak & Zaldarriaga
(CMBfast code)
Evolution of Fluctuations of different Stuff

85. Today

86. Large Synoptic Survey Telescope
8.4-m
7 degree FOV

87. Hectospec Positioner on MMT
300 Fibers
covering a
1 degree field
of view
D. Fabricant

89. Paper for next week:
Detection of Baryon Acoustic Peak in the Large Scale Correlation Function of the SDSS Luminous Red Galaxies
Eisenstein et al. 2005, ApJ 633, 560.