Clusters of galaxies The ICM, mass measurements and statistical measures of clustering

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Clusters of galaxiesThe ICM, mass measurements
and statistical measures of clustering
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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

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

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The Lx s correlation
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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 gt 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 lt 4 x 107 K)

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Dynamics of the intracluster gas

• The intracluster gas can be treated as
• An ideal fluid
• In hydrostatic equilibrium
• At a uniform temperature

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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 Cluster Hughes et al. 93
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• 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

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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 gtgt Mgal
  it is difficult to
• understand how so much
  material could
• have been stripped
  from galaxies

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How much gas is there in clusters?
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Cluster Mass estimates X-ray gas
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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
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Evidence of Dark Matter (DM) in clusters
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Dark Matter in ClustersA more accurate name for
clusters of galaxies would be clusters of dark
matterObservational evidence suggests that
80-90 of the mass in clusters is in an invisible
form1) What evidence is there for dark
matter?2) How much dark matter is there?3) What
is the distribution within clusters?
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Evidence of Dark Matter in clusters

• Virial mass estimates
• If a cluster is in virial equilibrium then
  its mass can be estimated from Mvirial Rltv2gt/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

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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

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Mass to light ratio of Coma
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Galaxy Dynamics
Mass estimate using the Virial theorem
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X-ray mass estimates

• If the intracluster gas is in hydrostatic
  euilibrium in the cluster potential, then the
  cluster mass can be determined from

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Gravitational lensing studies provide another
independent evidence for DM in clusters
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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 Einsteins
  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.

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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.
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Gravitational lensing the basic ideas
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Galaxy cluster
Background galaxy
Observer
Strong lens
Weak lens
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• Strong lensing occurs when
• Long arcs and multiple images are produced.
  
• Weak lensing occurs when
• Small arclets and distortions are produced.

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Strong Lensing
A 1451
z 0,199
?
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A 1451
z 0,199
?
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Weak Gravitational Lensing
Mellier 99
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Why Weak Lensing ?
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Measuring Faint Galaxy Shapes
Cypriano et al. 2005
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Mass ? Light
A2029
In 77 of the cases the center of light and mass
distributions are consistent with each other...
Light
Mass
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Mass ? Light
...but there are exceptions
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Mass ? Light
A4010
Light
Mass
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Mass ? Light
There is a strong alignment between the BGC and
the dark mater main axis
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Comparison with X-Rays
A1451
A2163
A2744
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Comparison with the Velocity Dispertion
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The dynamical state of the clusters
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The dynamical state of the clusters
Interpretation There are two structures along
the line of sight
Chandra observations confirms fusion along the
line of sight (Kempner David 2004)
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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.
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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
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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 !
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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 telescopesto 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.

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z 5.6
Ellis, Santos, Kneib Kuijken (2001)
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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 zgt1

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Clusters as Tracers of Large-scale Structure
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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

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Large scale structure 2dF
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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 Wirtanens galaxy maps showed a
  strong tendency for clusters to occur in groups
  of two or more.
• 1956 Neyman, Scott and Shanes 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.

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Statistical measures of clustering

• 1) The two-point correlation function
• 2) The power-spectrum
• 3) Cluster alignments

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Probability of finding objects in dV1 and dV2
separated by distance r
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Two-point correlation function for Abell clusters

• Abell cluster correlation function has the same
  power-law form as that for galaxies
• ? (r) A r? 1 (r/r0) ?
  ? (r) 1 at r r0
• ? - 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 ? (r) different for galaxies and clusters?
  Biasing!
• If Abell clusters have formed from rare
  high-density peaks
• (? gt 3s) in the matter distribution, then
  their clustering tendency will be enhanced by an
  amount ?cluster ?2 ?matter (Kaiser 1984).

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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.

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Statistical measures the power spectrum
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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
• ? (r) 1 Npairs/Nrandom Npairs/(n 4/3
  p r3)
• which is proportional to 1/n
• Uncertainties in n produce large
  uncertainties in ? when ? ltlt 1.
• For P(k), each dk is proportional to n.
  Hence the shape of the power-spectrum is
  unaffected.

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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

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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.