Formation hiérarchique des Formation hiérarchique des structures à grande échelle de structures à grande échelle de

l’Univers:l’Univers:

Les observations face aux modèlesLes observations face aux modèles

Sophie Maurogordato

En collaboration avec:

M. Arnaud, E. Belsole, F. Bernardeau, M.Lachièze-Rey, J.L. Sauvageot, R.Schaeffer, R. Teyssier (CEA-CEN Saclay)

F. Bouchet (IAP)

C. Benoist, A. Bijaoui, H. Bourdin, C.Ferrari, E. Slezak (OCA)

C. Balkowski, V. Cayatte, P. Felenbok, D. Proust (Obs. Paris- Meudon)

R. Pello, J.P. Kneib (OMP, Toulouse)

A.Cappi, P. Vettolani, L. Feretti (Obs. & CNR Bologna, I)

M. Plionis, S. Basilakos (Obs. Athenes, Gr)

D. Batuski, C. Miller, T. Beers, J. Kriessler (USA)

The ESP team

CfA2

SSRS2

9325 galaxies

mB<15.5

From da Costa et al. 1994

150 h-1Mpc

General Framework

Big Bang theory

General Relativity

Cosmological Principle

Primordial fluctuations (infinitesimal)

Growth by gravitational instability

Large scale structure of the Universe observed today

Cosmological Scenario

• Density parameters: m + + k = 1 (Einstein equations)

m: total matter

: dark energy

k: curvature

b: baryonic matter

• Hubble constant :

H0 = 100 h km/sec/Mpc

• Normalization:

8 mass fluctuations in 8h-1 Mpc spheres

+ Nature of dark matter

Cosmological parameters from observations

Large Scale

Structuresm

0.6/bb8mh

Peculiar velocity field

8m0.6

mh

SN Ia3-4m Clusters:

Baryon Fraction

b,m,h

ClusterAbundance

8m0.6

WeakLensing8m

0.6

CMBm

mh2

bh2

n,t0,

Big Bang Nucleosynthesis

bh2

CosmologicalScenario

Statistical Analysis of galaxy and cluster distribution

Cosmological Scenario

Scale-invariant relations:VPF, cumulants,…

2-pt indicatorsESP

Galaxy/matter « Bias »

Luminosity segregationSSRS, SSRS2, ESP

High order Moments of galaxies and clusters

How to constrain P(k) from LSS ? • Primordial P(k) matter Theoretical Predictions

Nature of density fluctuations (gaussian, non gaussian) Mechanism (inflation, texture, cosmic strings)

Linear evolution• Evolved P(k) matter

bias : relation galaxies/matter distributionlinear bias approximation: g m

• Evolved P(k)galaxies in real space

modelling the clustering distortion redshift space/real space

• Evolved P(k)galaxies in redshift space Observations

Modelling P(k)

P(k) = B k (1+{ak+(bk)3/2+(ck)2})2/

a,b,c functions of = h (Bond and Efstathiou 1984)

CMBNormalisation : B

LSS via and model of bias(variance in spheres of 8h-1 Mpc)and linear evolution

Coherence of large and small scales normalisation bias

Shape : characteristical of the nature and amount of dark matter

Standard CDM : = h = 0.5

The evolution of the clustering pattern with z for different cosmological scenarios

2nd order statistics on galaxy catalogs

2D APM:Shape of w() and P(k) disagrees with SCDM (=0.5)

3D catalogs:

Large uncertainty on normalisation (bias)

Problem of Fair Sample

From Maddox et al. 1990

From Efstathiou et al. 1992

The ESO Slice ProjectEuropean Project (Vettolani et al. 1998) at the ES0 3.6m telescope

Slice of 23 square degrees near SGP

bJ < 19.4

3342 redshifts

Large structure :

50 x 100 h-1 Mpc @z=0.1

From Vettolani et al. 1998

3D correlation function in 2000’s

The power excess at large scales detected by the 2D APM is confirmed

SCDM with =0.5 ruled out. Best agreement

= 0.2-0.3

From Guzzo et al. 1999

Scaling relations in the galaxy/matter distribution

Observations:

The distribution of galaxies today is highly non gaussian.

Hierarchical relation between correlation functions which can be modelized by:

Hierarchical model

Schaeffer 1984, Fry 1984

Sum over graphes Sum over labelling of graphes

More generally: Scale invariant models (Balian and Schaeffer 1989)

SJ are independent of scale

Predictions for the matter distribution:SJ’s:

Mildly non linear regime: Perturbation theory (Juskiewicz, Bouchet and Colombi 1993, Bernardeau 1994)

Case of power laws: SJ are constants

Highly non linear regime: numerical simulations (Baugh, Gaztanaga and Efstathiou 1995)

Scale invariance of the Void Probability function:

SJ = f(1,…,J-1)

Scaling relations in 3D galaxy catalogsVoid probability function

Counts probabilities

Maurogordato, Schaeffer and da Costa 1992

Correlation functions

Benoist et al. 1999

SSRS

SSRS

SSRS2

Galaxy/Mass distributions• Does light trace mass ?

• Linear bias hypothesis:

gbm

• Biased galaxy Formation (Kaiser 1984, Bardeen et al. 1986)galaxies form at the location of high density peaks in an initial gaussian random field:

rr

more massive objects more clustered

Bias relation at small scales: more complicated (gaz cooling, supernovaefeedback, galaxy fusions within halos)

Distribution of galaxies within the halos: Semi-analytical models (Mo and White 1996, Benson et al. 2000, …)

Luminosity bias in the SSRS2

From Benoist et al. 1996

Strong enhancement of correlation amplitude for very bright galaxies:

M > -20.0

Luminosity bias in the ESP

redshift space

Real space (projected)

From Guzzo et al. 1999

The next generation catalogs:

Colless et al. 2002

106688 galaxies 2dF Galaxy Redshift Survey

Luminosity bias in 3D galaxy catalogs in the 2000’s

From Norberg et al. 2001

Test of the linear bias hypothesis

g(x)= bg m(x) gJ(r)=bg

JmJ(r) Sg

J = SmJ bg

J-2

Expected from luminosity segregation on (r)

Observed

Inconsistence between 2nd order and high order moments results for linear bias hypothesis at small scales.

From Benoist et al. 1999Second-order term for high luminosities

Cluster clustering3D (r)

ACO North and South with bII > 40

z<0.08

3D: Correlation function: power law with large correlation radius:

(r)=(r/r0)g - 19.3 < r0 < 20.6 h-1 Mpc

Good agreement with Postman et al. 1992

Power up to 40-50 h-1 Mpc

2D: Scale-invariance of cumulants : hierarchical relation for clusters

S3 cl ~ S3 gal inconsistent with r0 and linear bias hypothesis.

2D: ACO Projected high order correlation functions and cumulants

Cappi and Maurogordato 1992

Cappi and Maurogordato 1995

AQUARIUS

SUPERCLUSTER

American-French program

Percolation on the ACO catalog: dcc < 25 h-1 Mpc

supercluster candidates

From Batuski et al. 1999

Aquarius supercluster:

Exceptionally dense and extended !

n=8<n> over 110 h-1 Mpc

n=150<n> in the core (6 clusters)

110 h-1 Mpc

Conclusions• Galaxy distribution: hierarchical relations of high order correlations

(cumulants, VPF, count probabilities)

• Predicted in the frame of models with hierarchical formation of structures

• Success of gravity to form the structure pattern observed today from initial gaussian fluctuations

• Luminosity bias constant with scale (analysis of SSRS, SSRS2 and ESP, confirmed now by 2dFGRS and SDSS)

Problems with the linear bias hypothesis at small scales from the combined analysis of cumulants/ 2pt correlation function (galaxy and cluster distribution)

Today: multiple evidences for a «concordant » CDM hierarchical model:

m = 1 – = 0.3, b=0.02, h=0.70, n=1.Combining CMB and LSS analysis gives a better determination of the parameters

From Lahav et al. 2002

New generation of 3D surveys (SDSS, 2dFGRS, …) + CMB experiments at different angular scales (COBE, Boomerang, WMAP, Planck,…)

Soon : good knowledge of cosmological parametersBut still need to improve our understanding of the bias relation and physics of galaxy formation

Analysis of currently forming clusters

In the hierarchical model, galaxy clusters form by merging of smaller mass units

Irregular, morphologically complex clusters are still forming.

Insights on the formation process before virialisation

Cosmological interest: n(z) is dependant

Combined X-Ray/ Optical analysis allows to follow separately the distribution of gas and of galaxies.

Evolution with time of the density and velocity distribution of galaxies during the merger event

From Schindler and Bohringer 1993

Evolution of the density and temperature of the gas with time during the merging event

From Takizawa 1999

Abell 521: a cluster forming at the crossing

of LSS filaments? - Severe gas-galaxy segregation

- X-Ray: well fitted by a 2-component -model: cluster + group

- Privilegiated axes

- Huge velocity dispersion: 1450 km/s (40 z)

- BCG offset from the main cluster, in the group region

From Arnaud, Maurogordato, Slezak and Rho, 2000

W

W

N

The Brightest Cluster GalaxyExtremely bright: L = 13 L*

Arc structure embedding knots at z cluster

Located near the X-Ray group center

Profile: de Vaucouleurs without the cD tail

BCG in formation within a group, by cannibalism of merging galaxies

From Maurogordato et al. 2000

Dynamical Analysis

New observational data: 150 zVariation of v and along the general axis of the cluster:

In the central ridge: very high velocity dispersion, low mean velocity. Signatures of an « old » collision.

In the X-Ray group: low velocity dispersion, higher mean velocity. Probably infalling group towards the main cluster.

Velocity distribution: non gaussian.

Well fitted by a mixture of three gaussian distributions.

From Ferrari et al. 2003

<v>

v

Witnessing the collision of the Northern group with the main cluster

Compression of the gas by the colliding group: Increase of Temperature in between the colliding units (detected by Chandra)Triggering of star-formation (excess of younger population in the compression region)

From Ferrari et al. 2003From Arnaud et al. 2003

MUSIC: the program

MUlti-wavelength Sample of Interacting Clusters

S. Maurogordato, C. Ferrari, C.Benoist, E. Slezak, H. Bourdin, A. Bijaoui (OCA)J.L. Sauvageot, E. Belsole, R. Teyssier, M. Arnaud (CEA-CEN Saclay)L.Feretti, G.Giovannini (IRA Bologne)

10 clusters at different stages of the merging process, 0.05 < z < 0.1

X-Ray: XMM/EPIC

Optical: 3-bands (V,R,I) wide-field imaging (ESO: Wfi@2.2m, CFHT: Cfh12K@3.6m) Multi-Object Spectroscopy (ESO: Efosc2@3.6m, next VIMOS@UT2, CFHT: MOS@3.6m)

Radio: VLA

MUSIC: Scientific Objectives

• Characterize the merging process: velocity field and mass ratio of the components, axis and epoch of collision. Reconstruction of the merging scenario by numerical simulation.

• Compare the respective distribution of galaxies, gas and dark matter according to the dynamical stage of the merging process.

• Test for correlation between Star Formation Rate and gas compression

• Large scale environnement. Do merging clusters preferentially occur at the crossing of filaments as predicted by hierarchical scenarios of structure formation ?

MUSIC: the targets

A 2933Pre

A 2440Pre

A 1750PreXMM/ESO

A 3921MidXMM/ESO

A 2384Mid

A 2142PostXMM/CFH

A 2065PostXMM/CFH

A 4038Post

Alignments effects in galaxy clusters

PAI Platon: OCA (S.Maurogordato), NOA (M. Plionis)

300 Abell clusters

Strong alignment effect for clusters within superclusters:

BCG / cluster

10 brightest galaxies / cluster

The case of Abell 521

Strong alignment of groups with the main orientation of the cluster

The fundamental plane of galaxy clusters: another evidence for hierarchical clustering

From Schaeffer, Maurogordato,

Cappi and Bernardeau 1993

Galaxy clusters

Elliptical galaxies

Dwarfs galaxies

Globular clusters

Galaxy clusters:

L = K R 2

Future: Analysis of the cluster distribution in the CFHTLS

Galaxy catalog

Cluster catalog

by identification of the Red Sequence of ellipticals

Constraining the hierarchical model:

I: Evolution of cluster counts with redshift:

From Evrard et al. 2003

Slice of 10°x10°

II- Evolution of correlation length with

richness

From Colberg et al. 2000

CONCLUSIONSCONCLUSIONS

Multiple evidences for the hierarchical model:

Scale invariance in the galaxy and cluster distribution,Fundamental plane for structures of very different masses,Properties of merging clusters.

« Concordant model »: CDM with m=0.3, =0.7 agrees with most results of observational cosmology but still room for other alternatives…

Next future:

Theory + Numerical simulations + Observations:

Which hierarchical model ?Better understanding of the bias relationNature of primordial fluctuationsTest of the Cosmological Principle