Transcript Clusters and groups of galaxies

Clusters of galaxies
The ICM, mass measurements
and statistical measures of
clustering
Plan of this class
The intracluster medium, its origin, dynamics and
general properties
Evidence of Dark Matter in clusters
Masses derived by the virial theorem, x-rays and
gravitational lensing
Results from studies of gravitational lensing in clusters
Statistical 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 the
Intracluster 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 Xray 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, Xray 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 highfrequencies that is characteristic of bremsstrahlung.
Coma Cluster
Hughes 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 and
Forman 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
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Globular clusters
Elliptical galaxies
Groups of galaxies
Rich clusters
1-2 M/L
5-10 h M/L
100-300 h M/L
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 another independent evidence for
DM in 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.
STRONG LENSING
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.
Gravitational lensing: the basic ideas
Observer
Strong lens
Weak lens
Galaxy cluster
Background
galaxy
 “Strong” lensing occurs when
Long arcs and multiple images are produced.
 “Weak” lensing occurs when
Small arclets and distortions are produced.
A 1451
Strong Lensing
z = 0,199

A 1451
z = 0,199

Weak Gravitational Lensing
Mellier 99
Why Weak Lensing ?
Classical techniques (dynamics of the galaxies
and X-ray emission of the hot intra-cluster gas)
are based of the assumption of dynamical
equilibrium
Allows the reconstruction of the surface mass
density
Measuring Faint Galaxy Shapes
Cypriano et
al. 2005
Mass  Light
A2029
In 77% of the cases the
center of light and mass
Light
Mass
distributions are consistent
with each other...
...but
there are
exceptions
Mass
Light
A3739
Mass
Light
Mass  Light
A4010
Mass
Light
Mass  Light
There is a strong alignment between the
BGC and the dark mater main axis
Comparison with X-Rays
A1451
A2163
A2744
TX ~ TSIS,SIE
Comparison with the Velocity Dispertion
A2163
A1451
σv ~ σSIS,SIE
A2744
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
σtotal = 1777 km/s
σA
= 1121 km/s
σB
= 682 km/s
Interpretation: There are two structures
along the line of sight
Girardi & Mezzetti (2001)
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
 Reconstruct the 2-D potencial
 Needs good seeing
 Cannot separate components along the
line of sight.
Which method is the best one ?
X-Rays
 Depend of thermal/dynamical state of
the ICM
 Cannot separate components along the
line of sight.
 All Sky Surveys (e.g. ROSAT) can
provide large and homogeneous samples
Which method is the best one ?
Dynamics of
galaxies
 Depend on the dynamical state of the
cluster galaxies (galaxies relaxes later than
the ICM)
 Reliable results depends on a large
number of galaxy velocities over a large
area (e.g. Czoske et al. 2002)
 Can separate structures along the line
of sight
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 Largescale 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
The Cfa Slice
Lei de
Hubble
d=v/Ho
De Lapparent et al. 1988
The Cfa Slice
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 twopoint 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 largescale structure of the universe.
 There is strong evidence of structure on scales of over
100 h-1 Mpc in the cluster distribution.