Clusters of galaxies

The ICM, mass measurements and statistical measures of

clustering

Plan of this classThe intracluster medium, its origin, dynamics and

general propertiesEvidence of Dark Matter in clustersMasses derived by the virial theorem, x-rays and

gravitational lensingResults from studies of gravitational lensing in clustersStatistical measures of clustering

The intracluster medium

Clusters are among the most luminous X-ray sources in the sky. This X-ray emission comes from hot intracluster gas.

X-ray observations provide information on the amount, distribution, temperature and chemical composition of theIntracluster gas

For comparison,

Cataclismic variables Lx = 1032 – 1038 erg/s

Milky Way, M31 Lx = 1039 erg/s

Clusters of galaxies Lx = 1043– 1045 erg/s

Only Seyferts, QSOs, and other AGN rival clusters in X-ray output

Clusters may emit nearly as much energy at X-ray wavelengths as visible

L(optical) = 100 L* galaxies = 1045 erg/s

The Lx – σ correlation

What is the origin of cluster X-ray emission?

Answer: hot (107 – 108 K) low-density (10-3 cm-3) gas, mostly hydrogen and helium, that fills space between galaxies. At these high temperatures the gas is fully ionized.

Two emission mechanisms: 1) Thermal bremsstrahlung (important for T > 4 x 107 K) free electrons may be rapidly accelerated by the attractive

force of atomic nuclei, resulting in photon emission because the emission is due to Coulomb collisions, X-ray

luminosity is a function of gas density and temperature Lx = nelectron nion T1/2 = rho_gas2 T_gas1/2

2) Recombination of electrons with ions (important T < 4 x 107 K)

Dynamics of the intracluster gas

The intracluster gas can be treated as:

An ideal fluid

In hydrostatic equilibrium

At a uniform temperature

X-ray spectra

Spectroscopy of the intracluster gas provides information on its temperature and composition

Observed spectra show exponential decrease at high-frequencies that is characteristic of bremsstrahlung.

Coma ClusterHughes et al. 93

Emission lines due to Fe, Ni and other heavy elements are seen. This suggests that much of the intracluster gas must have been processed through stars.

Chemical abundance of the intracluster gas can be measured from the equivalent widths of these emission lines. It is found to be about 30-40% of solar abundance

If the galaxies and gas are both in thermal equilibrium in the cluster potential well, then one expects

m v(gal)2 = 3 kbTgas

Tgas proportional to v(gal) 2

What is the origin of the intracluster gas?

Two possibilities: The intracluster gas once resided in galaxies and was later

removed. - this would explain high metallicity of gas - galaxies in the cores of rich clusters are observed to be deficient in HI gas, which suggests that stripping has occurred. The gas is primordial, originating at the time of cluster formation. - but since Mgas >> Mgal it is difficult to understand how so much material could have been stripped from galaxies

How much gas is there in clusters?

Cluster Mass estimates: X-ray gas

The total gas mass in clusters exceeds the total galaxy mass. Gas contributes as much as 10-20% of

the total cluster mass.

David, Jones andForman 95

Evidence of Dark Matter (DM) in clusters

Dark Matter in Clusters

A more accurate name for “clusters of galaxies” would be “clusters of dark matter”

Observational evidence suggests that 80-90% of the mass in clusters is in an invisible form

1) What evidence is there for dark matter?2) How much dark matter is there?

3) What is the distribution within clusters?

Evidence of Dark Matter in clusters Virial mass estimates If a cluster is in virial equilibrium then its mass can be

estimated from Mvirial = R<v2>/G

Observations indicate that the total cluster mass exceeds the combined masses of all galaxies by factors of 10-20.

Example: the Coma Cluster Mvirial = 1 x 1015 h-1 solar masses Ltot = 4 x 1012 h-2 solar luminosities Assuming a typical galaxy with M/L = 10 Then Mvirial/Mgalaxies = 25

Typical mass to light ratios

Globular clusters 1-2 M/L Elliptical galaxies 5-10 h M/L Groups of galaxies 100-300 h M/L Rich clusters 300-500 h M/L

Mass to light ratio of Coma

Mass estimate using the Virial theorem

X-ray mass estimates If the intracluster gas is in hydrostatic euilibrium in the cluster potential, then the cluster

mass can be determined from

Gravitational lensing studies provide Gravitational lensing studies provide another independent evidence for DM another independent evidence for DM

in clustersin clusters

Gravitational Lensing – some history

1913 – Einstein predicted that the gravitational field of massive objects can deflect light rays.

1919 – Eddington measured the deflection of starlight by the Sun, confirming Einstein’s prediction.

1937 – Zwicky suggested that galaxy clusters may produce observable lensing.

1987 – First evidence of “strong” gravitational lensing by clusters was found (Lynds/Petrosian, Soucail et al.)

1990 – “Weak” gravitational lensing by clusters was discovered (Tyson et a. 1990).

Today – Evidence of lensing has been found for several dozen clusters. New examples are being discovered all the time.

1986 – Lynds & Petrossian discover the first gravitational arcs in clusters of

galaxies

1987 – Soucail et al. determine the distance to the arc: twice the distance to the cluster that “contains” it.

STRONG LENSING

Gravitational lensing: the basic ideas

Galaxy cluster

Background galaxyObserver

Strong lens

Weak lens

“Strong” lensing occurs when

Long arcs and multiple images are produced.

“Weak” lensing occurs when

Small arclets and distortions are produced.

A 1451z = 0,199

Strong Lensing

A 1451z = 0,199

Weak Gravitational Lensing

Mellier 99

Why Weak Lensing ?

Allows the reconstruction of the surface mass density

Classical techniques (dynamics of the galaxies and X-ray emission of the hot intra-cluster gas) are based of the assumption of dynamical equilibrium

Measuring Faint Galaxy Shapes

Cypriano et al. 2005

Mass Light

Mass Light

A2029In 77% of the cases

the center of light and mass

distributions are consistent with each

other...

Mass Light...but there are exceptions

Mass Light

A3739

Mass Light

Mass Light

A4010

Mass Light

There is a strong alignment between the BGC and the dark

mater main axis

Comparison with X-Rays

TX ~ TSIS,SIE

A2744

A1451A2163

Comparison with the Velocity Dispertion

A1451

A2744A21

63

σv ~ σSIS,SIE

The dynamical state of the clusters

Most of the clusters appears to be relaxed (lensing dynamical methods)

Cluster with TX > 8 keV (σv >1120 km/s) shows signs of dynamical activity

The dynamical state of the clusters

A2744 – Virial mass> Lensing > X-rays

Girardi & Mezzetti (2001)

σσtotaltotal= 1777 = 1777 km/skm/sσσAA = 1121 = 1121 km/skm/sσσBB = 682 = 682 km/skm/s

Interpretation: There are two structures along the line of

sight

Chandra observations confirms fusion along the line of sight (Kempner & David 2004)

Which method is the best one ?

Weak Lensing

Independent of the dynamical state

Needs good seeing

Reconstruct the 2-D potencial

Cannot separate components along the line of sight.

Which method is the best one ?

X-Rays

All Sky Surveys (e.g. ROSAT) can provide large and homogeneous samples

Depend of thermal/dynamical state of the ICM

Cannot separate components along the line of sight.

Which method is the best one ?

Dynamics of

galaxies

Depend on the dynamical state of the cluster galaxies (galaxies relaxes later than the ICM)

Can separate structures along the line of sight

Reliable results depends on a large number of galaxy velocities over a large area (e.g. Czoske et al. 2002)

No single method is perfect !

What can we learn from gravitational lensing?

Gravitational lensing can be used to determine the amount and distribution of dark matter in clusters.

Unlike virial or X-ray mass determinations, lensing requires no assumptions about the dynamical state of the cluster!

The arc thickness is related to the cluster mass distribution. More concentrated mass distributions produce thinner arcs.

Modelling the positions and shapes of arcs and arclets allows the cluster potential to be mapped. Lensing models have become so good that in can predict the locations of faint additional arcs.

Gravitational lensing causes images to be magnified. Clusters of galaxies can be used as natural “telescopes”to study extremely distant galaxies that would be otherwise too faint to see.

Lensing can also be used to place cosmological constraints, because distances (Dos, Dol, Dls) depend on omega, Ho and lambda.

z = 5.6

Ellis, Santos, Kneib & Kuijken (2001)

What have we learned so far from gravitational lensing?

Samples of strong and weak gravitational lensing have been found in several dozen clusters.

Lensing mass estimates indicate large quantities of dark matter in clusters Lensing mass estimates agree with virial and X-ray masses (with a few

exceptions). The exceptions are probably clusters which are not in equilibrium. Hot clusters tend to present dynamical activity (major concern for

experiments designed to constrain cosmological parameters). Mass follows light in most cases. Cluster dark matter has a very steep radial distribution. Models of the cluster potential provide strong evidence of substructure in

the dark matter distribution. Gravitational lensing has been seen in clusters at z>1

Clusters as Tracers of Large-scale Structure

Why use clusters to map the large-scale structure of the universe?

Advantages

Clusters provide an efficient way of surveying a large volume of space

Cluster distribution provides information about conditions in the early universe

Clusters can be seen at great distances

Disadvantages

Their low space density makes clusters sparse tracers of the large scale structure

Results may depend on the chosen cluster sample

Redshifts of many clusters are still unmeasured

Velocidade

De Lapparent et al. 1988

Velocidade

d=v/Ho

Lei de Hubble

The Cfa Slice

Velocidade

The Cfa Slice

Velocidade

The Cfa Slice

Large scale structure – 2dF

Some history 1933 – Shapley noticed several binary and triple systems among

the 25 clusters that he catalogued “it is possible that clusters are but nuclei or concentrations in a very extensive canopy of galaxies”.

1954 – Shane and Wirtanen’s galaxy maps showed “a strong tendency for clusters to occur in groups of two or more”.

1956 – Neyman, Scott and Shane’s pioneering statistical models of galaxy clustering included “second-order clusters”, I.e., superclusters.

1957 – Zwicky declared that “there is no evidence at all for any systematic clustering of clusters… clusters are distributed entirely at random.”

1958 – Abell examined the distribution of clusters in his catalogue, and concluded that “clusters of clusters of galaxies exist”

Today – No doubt that galaxy clusters are clustered. Instead, debate is about the SCALE of this clustering.

Statistical measures of clustering

1) The two-point correlation function

2) The power-spectrum

3) Cluster alignments

Probability of finding objects in dV1 and dV2 separated by distance r

Two-point correlation function for Abell clusters

Abell cluster correlation function has the same power-law form as that for galaxies

ξ (r) = A rγ =1 (r/r0) γ ξ (r) = 1 at r= r0

γ = - 1.8

r0 = 20-25 h-1 Mpc Richer clusters are more strongly clustered than poorer clusters The Abell cluster correlation function has the same power-law

form as the galaxy correlation function, but with a 15 times greater amplitude (r0 = 5 h-1 Mpc for galaxies r0 = 20 h-1 Mpc for Abell clusters

Why is ξ (r) different for galaxies and clusters? Biasing! If Abell clusters have formed from rare high-density peaks (ν > 3σ) in the matter distribution, then their clustering tendency

will be enhanced by an amount ξcluster= ν2 ξmatter (Kaiser 1984).

Two-point correlation function for other cluster samples

APM and EDCC clusters show a weaker clustering tendency than Abell clusters

r0 = 13-16 h-1 Mpc for both samples ROSAT X-ray selected clusters

r0 = 14 h-1 Mpc Why do different cluster samples give different results? Three possibilities: (a) The Abell catalogue is unreliable (b) Richness-dependence of the cluster correlation function.

Abell, APM and EDCC clusters are fundamentally different types of objects.

(c) X-ray selected samples are flux-limited rather than volume-limited. This means that any X-ray selected sample will contain a mixture of nearby poor clusters and distant rich clusters.

Statistical measures: the power spectrum

Statistical measures: the power spectrum

Although P(k) is more complicated to measure than the two-point correlation function it has two big advantages:

1) it can be more directly compared with theory 2) it is a more robust measure

ξ (r) + 1 = Npairs/Nrandom = Npairs/(n 4/3 π r3) which is proportional to 1/n

Uncertainties in n produce large uncertainties in ξ when ξ << 1.

For P(k), each δk is proportional to n. Hence the shape of the power-spectrum is unaffected.

Statistical measures: cluster alignments

Clusters are often embedded in large-scale filamentary features in the galaxy distribution.

Cluster major axes tend to point along these filaments towards neighbouring clusters, over scales of about 15 h-1 Mpc, perhaps up to 50 h-1 Mpc.

These cluster alignments may provide important clues about cluster formation and cosmology

Clusters as LSS tracers

Clusters of galaxies are efficient tracers of the large-scale structure of the universe.

There is strong evidence of structure on scales of over 100 h-1 Mpc in the cluster distribution.