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Clusters in the perspective of CosmologyAndreas Reisenegger

Pontificia Universidad Católica de Chile, Santiago

International Workshop on

STRUCTURE FORMATION AND COSMOLOGY

Santiago, Chile, October 28-31, 2002

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This talk: what it is

An introduction to the role of clusters in constraining cosmological parameters.

A general discussion of the physical properties of clusters and their relations.

Point of view of a “pen-and-paper theorist”.

Somewhat idiosynchratic selection of topics.

Mostly aimed at students and non-experts.

Time for a nap for cluster experts.

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This talk: what it is NOT An exhaustive compilation and critical

discussion of the work done on the subject.

Interesting complement: Rosati et al. 2002, Annual Reviews of Astronomy & Astrophysics

A discussion of all the (fascinating!) physics going on in clusters (cooling flows, magnetic fields, shocks, galaxy stripping, etc.): hopefully not relevant to cosmology.

A contribution to the knowledge of cluster experts.

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Outline

What is a cluster?

A warning on physics in cosmology

Mass measurements and cosmology

A word on cluster searches.

Cluster formation and cosmology

Conclusions

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What is a cluster?

To the optical observer: A clump of galaxies

Coma cluster; López-Cruz

To the X-ray observer: A clump of hot gas. Chandra image of Virgo cluster; Young et al. 2002

To the theorist: A clump of mass (mostly dark) Simulation; Beisbart et al. 2001

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WARNING! Our laws of physics (particularly dynamics and gravity:

Newtonian or relativistic) have only been checked on Solar System scales (including binary pulsars and other binary stars), L < light-days.

In extragalactic astrophysics, the same laws are applied on L ~ 103 - 10 light-years, an extrapolation of 6 to 13 orders of magnitude, yielding extraordinary results: 95% of the energy in the Universe is evident only through this extrapolation!

So, why do we do this??

Simplicity. (We don’t know of a good alternative.)

It works! (Concordance of cosmological parameters from different arguments.)

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Mass measurements: virial

The virial theorem relates the average kinetic and potential energy of galaxies in a “virialized” cluster.

Measurement of galaxy velocity dispersion (along the line of sight) yields an estimate of the cluster mass, M ~ 2 R / G.

Assumptions: “Virialized” (equilibrium)

galaxy distribution in a static, spherically symmetric potential well.

A970: Sodré et al. 2001

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Mass measurements: gas

The hot gas observed in X-rays is expected to settle to hydrostatic equilibrium in the cluster’s gravitational potential.

Deproject gas density n(r) and temperature profile T(r) to obtain gravitating mass

Get both gravitating mass and gas mass profiles.

Assumptions: Hydrostatic equilibrium in spherical potential. Formerly also uniform temperature.

drnTd

rGmnr

rM)(

)()(

2

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Mass measurements: lensing Projected mass density determined

through:

Weak lensing (statistical average of galaxy ellipticities) on large scales: total cluster mass (talk by Refregier).

Strong distortions (arcs) and multiple imaging on small scales: cluster core mass distribution (talk by Kneib).

Limitations:

Mass sheet degeneracy (insensitivity to uniform mass distribution).

Strong lensing usually must use a parameterized mass distribution; uniqueness not guaranteed.

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Radial infall into a massive structure produces a characteristic pattern in redshift space (Kaiser 1987).

Amplitude of “caustics” (maximum radial velocity lines), A(r), is determined by the mass profile, M(r) (and the age of the Universe): can be inverted (Regös & Geller 1989).

Mass measurements: infall

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Mass measurements: infallCan be improved, trying to

account for random, nonradial peculiar velocities (Diaferio & Geller 1997, Diaferio 1999).

Applicable to non-virialized structures, even superclusters (Reisenegger et al. 2000).

Figure: Radius-redshift diagram for the Shapley Supercluster.Distance from supercluster center [deg]

Rec

essi

on v

eloc

ity

[km

/s]

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Mass measurements: Agreement?Reasonable

agreement between methods, although none is absolutely reliable or very precise.

Weak evidence for validity of General Relativity on cluster scales.

Here: Velocity dispersions predicted from weak lensing vs. measured values (Irgens et al. 2002).

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Mass measurements: M/L

Very high mass/light ratios, ~200 solar, in rich clusters.

“Virial” mass/light Girardi et al. 2002; H0=100h km/s/Mpc

“Hydrostatic” mass/lightHradecky et al. 2000; H0=50 km/s/Mpc

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Mass measurements & Assuming M/L in clusters is the same as elsewhere in the

Universe, M = 0.2 0.05 (Carlberg et al. 1997; CNOC survey).

Mgas0.15Mtotal; Mstars “negligible”: Extrapolation to the rest of the Universe (with baryon=0.045 from Big Bang nucleosynthesis + chemical abundances) yields low M0.3 (or less; Hradecky et al. 2000).

Recall White et al. 1993, Nature: “The baryon content of galaxy clusters – A challenge to cosmological orthodoxy”.

No doubt we have now reached a different orthodoxy! (tutorial by Frieman + most of this conference)

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Correlations of cluster properties: virial

Spherical collapse model: virialization at 182crit.

Define fiducial “virial radius” R=r200 as the radius containing <(<r200)> = 200 crit.

Characteristic cluster density (1+z)3.

“Virial relations” 2 T GM/R M2/3(1+z)1/3: agree well with observations.

Rosati et al. 2002, Ann. Rev. A&A

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Lx - T relation X-ray luminosity more

easily measured than mass: interesting to use as “surrogate”.

Emission predominantly bremsstrahlung (electron scattering by ions), LX n2T1/2R3.

If gas traces mass, n ~ same for all clusters at given z, get LX T 2: too flat compared to

observations!

Rosati et al. 2002

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Preheating: massive clustersThe shape of the LX-T relation can be brought into closer

agreement with observations if we assume that the gas is “preheated” by some source (supernovae? early star formation?) which increases its specific entropy, S log(T/n2/3) (Kaiser 1991).

If all the gas is heated to the same S, clusters will have a near-isentropic core with n T3/2, surrounded by an outer part where preheating is unimportant, and where (from virial and n ) n T/r2. The transition is at the “core radius” rc T-1/4.

So, the luminosity of a pre-heated cluster scales as LX n2T1/2rc

3 T11/4, close to the slope observed at high T, and

independent of redshift, in agreement with observations.

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Preheating: low-mass clustersFor low-mass clusters, the core radius can become

comparable to the virial radius, R T1/2(1+z)-1/2.

At lower mass (or T), the whole cluster could become dominated by preheating, with LX n2T1/2R3 T5 (1+z)-3/2.

Again roughly in agreement with observed slope.

“Break” at Tb (1+z)2/3: “high-mass” range restricted to higher temperatures at higher redshifts. On the other hand, the maximum cluster temperature is expected to be smaller at higher redshift.

Very naive “model”, but may indicate an “alarming” trend: little X-ray emission from high-z clusters.

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Searching for clusters For statistical studies (e.g., tracing large-scale structure),

well-defined samples of clusters with well-understood selection effects are essential. Ideal: Mass-limited sample.

Search methods so far: Galaxy overdensities, great help from color information: “red

sequence” (talk by F. Barrientos) X-ray emission: extended, thermal sources: e.g. XMM-LSS

Survey (talk by M. Pierre) Both rely on identification of “observer’s clusters” (red

galaxies, x-ray gas) with “theorist’s clusters” (mass): Is this identification applicable at all relevant redshifts?

New, promising methods: Sunyaev-Zel’dovich: scattering of CMB photons by hot electrons (talk by M.

Birkinshaw) Weak lensing (talk by A. Refregier)

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Cluster formation: “theory” Initially small (“linear”), gaussian perturbations,

characterized by a power spectrum P(k) kn, with n-1.5 on cluster scales. At given z, fractional mass fluctuations on scale M are

M M-(n+3)/6M-0.25.

“Linear” growth rate after recombination determined purely by gravity; independent of k. In Einstein-de Sitter Universe(M=1; good approximation at z0.8), M (1+z)-1.

A structure “collapses” (i.e., forms a virialized “halo”) when the linear-theory overdensity is ~1.7.

Expect mass of largest clusters Mmax(z) (1+z)-4: very strong evolution.

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Cluster formation: application Present-day abundance of

clusters constrains M

0.58=0.450.05 (van Waerbecke et al. 2001)

(see talk by A. Refregier).

More recent cluster formation in high-density Universe: Ratio of cluster abundance at z=0 and z=1 (say) strongly constrains M: a task for the XMM-LSS survey (talk by M. Pierre)

Rosati et al. 2002

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Mass profiles

Simulations predict characteristic mass density profile for relaxed clusters: “NFW profile” (Navarro et al. 1997).

Roughly confirmed by observations, though discrepancies in detail in central cores of clusters.

Suggestions of “self-interacting cold dark matter” (Spergel & Steinhardt 2000).

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Conclusions

Clusters of galaxies can be used in several different ways to constrain cosmological parameters, particularly M.

Generally yield low M, in agreement with the current “orthodoxy”.

Observational properties of clusters depend partly on still unresolved issues regarding gas heating/cooling processes.

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Acknowledgements

Felipe Barrientos: for useful suggestions regarding references and figures

Julio Navarro: for constructive criticism regarding scaling relations and preheating

David Valls-Gabaud: for useful comments regarding tests of Newtonian gravity in binaries