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Observing the Clustering of Matter and Galaxies

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Lick Galaxy Map

CfA Slice with Great Wall

History:

1920- : galaxies in and around the local group are not distributed randomly

1950-1970: Shane and Wirtanen

- made maps of the (projected) galaxy distribution
- Non-random distribution on small to large scales
1980-1990: Geller, Huchra and many others

- made maps of the 3D galaxy distribution
- Depth variable redshift (not quite distance)
2000+: 2DF Redshift Survey / SDSS

- 100,000 galaxies with spectra
(Literature: e.g. Peacock: Cosmological Physics, p500-509)

Vatican 2003 Lecture 20 HWR

Star-Forming Galaxies

Red Galaxies

Vatican 2003 Lecture 20 HWR

- There is no unique way to describe clustering!
- Need to describe the degree of clustering not the particular configuration.
- Isotropy: clustering = f(x,y,z) f(r)

- Often-used measures are:
- Angular or real-space correlation function
- Genus curve
- Smooth galaxies on different scales
- Which fraction of the volume is filled by curves of a given over-/under-density

- Counts-in cells
- Main practical problems/issues:
- Complicated search volumes
- Finite number of tracers
- Redshift space distortion

Vatican 2003 Lecture 20 HWR

- Excess probability of finding one galaxy (mass element) “near” another galaxy:
- for a random (uniform) distribution: dP = n dV

n: mean number density

- a clustered distribution can be (incompletely) described by:

dP(r) = n [1 + (r)] dV, where dP is the probability of finding a second object near an object at r = 0

(r): two-point (or, auto-) correlation function

Note: (r) = < (x) (x+r) >, where (x) is the fractional over/under-density

- to account for translation and rotation invariance (cosmological principle) often the Fourier transform is used

P(k) | k|2 = (r) eikr d3r P(k): power spectrum

- practical estimation:

Vatican 2003 Lecture 20 HWR

- If no redshifts (distances) are available, one can define the angular correlation function dP () = n (1 + w() ) d
- Note:
- understanding the sampling window function of a survey is crucial
- usually one is measuring the correlation of tracers

Vatican 2003 Lecture 20 HWR

Red galaxies

Blue galaxies

„Redshift“ Distance

Angle on the sky

- Redshift-space correlation

Vatican 2003 Lecture 20 HWR

Axis ratio of the correlation in the space-velocity plane as a function of scale

Infall

Finger-of-God

- pairwise velocity dispersion from “finger-of-god”: 400km/s
- Cosmic density estimate from inflow: b = W0.6/b = 0.43 0.07

Vatican 2003 Lecture 20 HWR

From Peacock et al 2002

More luminous/massive galaxies are more strongly clustered

- Galaxies with little star-formation (~ “early types”) are much more strongly clustered on small scales
- A.k.a. morphology-density relation
- Presumably:dense environments lead to rapid/early completion of the main star-formation

Vatican 2003 Lecture 20 HWR

Baryon wiggles?

Galaxy correlation now reflects:

- initial fluctuations
- growth rate (enter W and L)
- transfer-function
- Galaxy bias
Comparison most straightforward in the linear regime >5-10 Mpc

Vatican 2003 Lecture 20 HWR

- Can one observe the growth of mass fluctuation and galaxy clustering directly?
- Put a “point” between the CMB and the present epoch.

- Two possible probes at z~3:
- Galaxies (Ly-break galaxies)
- The fluctuation inter-galactic medium (IGM): Ly-alpha forest

- Galaxies:from Adelberger, Steidel and collaborators:
- Ly-break galaxies at z~3 are nearly as clustered as L* galaxies now
- (massive) galaxies were more biased tracers of the mass fluctuations than they are now.

Vatican 2003 Lecture 20 HWR

- What causes the fluctuation Ly-alpha absorption?
- Collapsed objects (mini halos)
- General density (+velocity) fluctuations

Vatican 2003 Lecture 20 HWR

Vatican 2003 Lecture 20 HWR

- Much of the Ly-alpha forest arises from modest density fluctuations and convergent velocity flows!!

Vatican 2003 Lecture 20 HWR

From Croft et al 1998

Vatican 2003 Lecture 20 HWR

- This probes the mass between galaxies
- One can follow the evolution of structure with redshift

Vatican 2003 Lecture 20 HWR

z=1100

z=0-3

Verde 2003

- Until the last few years (BOOMERANG, MAXIMA, WMAP), the CMB fluctuations were measured on larger (co-moving) scales than the fluctuations measured in the low-z universe
- Only joint extrapolation in redshift and scale possible!

With new generation of z<5 LSS measurements and CMB experiments, a much more direct comparison is possible.

Impressive confirmation of structure growth prediction!!

Vatican 2003 Lecture 20 HWR

- Note:
- this is pre-WMAP, I.e. data from COBE + ground-based and baloon experiments!
(from Peacock et al 2003)

- h H0=100

- this is pre-WMAP, I.e. data from COBE + ground-based and baloon experiments!

Vatican 2003 Lecture 20 HWR

Vatican 2003 Lecture 20 HWR

Theory

Big Bang

Inflation

FRW/cosmological parameters

WM=0.27,L=0.7,H0=70

(Non-baryonic) dark matter dominates

(small) initial fluctuations

Growth of density fluctuations

Linear

Observations

Expansion,CMB,BBN

Space is flat, CMB is uniform, fluctuations are scale free

SN Ia, Galaxy Clustering, CMB

Dynamics,lensing,BBN,CMB

CMB

CMB vs large-scale structure

IGM fluctuations

Galaxy large scale struture

Vatican 2003 Lecture 20 HWR

Theory

Non-linear growth of densities

N-body,Press-Schechter

(dark matter) halo profiles

Hierarchical build-up of Structures

Successive conversion of gas into stars

Cooling, Feed-back

Enrichment

Remaining hot gas in clusters and IGM

Observations

Abundance, stellar mass and clustering of galaxies

dynamics, lensing

Observed merging, fewer massive galaxies at high-z(?)

Vatican 2003 Lecture 20 HWR

Observations

Global star-formation history and QSO evolution(z>6 to now)

Galaxy luminosity function and colors (as function of z)

Morphologies, Bulge/Disk, etc f(z)

vs. mass

vs. environment

Typical Sizes

Global Scaling Relations

Fundamental plane, Tully-Fisher

MBH – s relation

Theory

Hierarchical merging and gas supply

Gas cooling, feed-back, cold gas supply

Gas Disks Merging Spheroids

Hierarchical picture

Hierarchical picture

Angular momentum (but is it lost?)

Constant star fraction; similar ang.mom.

Good thing to work on…

Vatican 2003 Lecture 20 HWR