The Density Profile of Galaxy Clusters

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The Density Profile of Galaxy Clusters

• Lensing, Dark Matter and Dark Energy Meeting -
  Ohio, 2005
• Dave Sand -- Caltech

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Talk Outline

• Current state of simulations - both DM-only and
  with baryons
• Current state of observations at cluster scale
• -Results from strong weak lensing, X-ray,
  cluster dynamics
• -Attempts to use multiple mass measurement
  techniques simultaneously
• The future - constraining all of the major mass
  components in clusters
• Observers and simulators should cooperate.

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Cold Dark Matter Simulations
log (?)
log (radius)
Moore simulation
Inner profile ??r -? NFW ??1.0 Moore ??1.5
many others
What is the inner slope of cluster DM
profiles? What is the TOTAL density profile?
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Latest CDM-only Simulations (e.g. Navarro et al.
2004 Diemand et al. 2004 Tasitsiomi et al. 2004
others)

• Convergence achieved down to 0.003rvirroughly
  the size of massive galaxies. Baryons are
  important for progress!!
• Density profiles obtained using different codes
  and initial conditions agree.
• The generalized NFW density profile is a good fit
  to simulations with ? between 1.0 1.5. There
  is significant scatter.
• Avoid simple fitting formulastry to compare with
  simulations directly!

Generalized NFW
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CDM simulations with Baryons
e.g. Gnedin et al. 2004, Nagai et al. 2004
Borgani et al. 2004 others

• Cosmological simulations with gas dynamics,
  radiative cooling star formation
• Suffer from overcooling problem
• Dissipation of gas increases density of DM and
  steepens its radial profileis the standard gNFW
  profile not valid?? (Gnedin et al. 2004)
• Radial distribution of subhalos is in rough
  agreement with the observed radial distribution
  of galaxies (Nagai et al. 2004).

Illustration of adiabatic contraction (Gnedin et
al. 2004)
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Dwarf Galaxy Normal Galaxy Scale
Rotation curves of dwarf spirals and normal
spirals indicate flat DM density cores (e.g.
Simon et al. 2003) although this is still being
debated (e.g. Swaters et al. 2003 Hayashi et al.
2004).
Rotation curve of DD047 Salucci Boriello (2003)
Elliptical galaxies are more ambiguous dominance
of stellar mass at small radii makes measurements
difficult (e.g. Koopmans and Treu 2003).
G0047 Koopmans Treu (2003)
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Observational Constraints on Cluster Density
Profiles

• The ultimate observational goal is to measure the
  typical density profile (and its scatter) of all
  three major mass components in clusters stellar
  mass, hot gas of the ICM and Dark Matter
• To measure and separate all mass components,
  multiple techniques must be employed
  simultaneously.
• The cluster scale is great because there are
  multiple mass measurement techniques, each with
  its own strengths and weaknesses.

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Strong and Weak Gravitational Lensing
Strength Total mass constraints without
assumptions about dynamical state of
cluster. Weakness Difficult to separate luminous
from dark matter.
Smith et al. (2001) ?tot 1.3
Kneib et al. 2003 found outer slope ?out gt 2.4
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Galaxy cluster dynamics
Strength Can probe to high cluster
radii. Weakness Must assume orbital properties
of stars/galaxies.

• Extended velocity dispersion profile of the
  brightest cluster galaxy (e.g. Kelson et al.
  2002)
• Velocity Dispersion profile of the galaxies in
  the cluster (e.g. Carlberg et al. 1997 Katgert
  et al. 2003)

NFW profiles require unrealistic stellar M/L
(Kelson et al. 2002)
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X-ray Observations of the ICM
Strength Can probe to high cluster
radii Weakness Must assume the cluster is in
hydrostatic equilibrium difficult to account for
central BCG!
From Lewis et al. 2002 note the BCG component
can dominate on 10kpc scales

• Wide range of inner slope values have been found
  ? 0.35 (Sanderson et al. 2004) to 0.6 (Ettori
  et al. 2002) to 1.2 (Lewis et al. 2003 Buote
  Lewis 2004) to 1.9 (Arabadjis et al. 2002).
• Many studies have only compared NFW with an
  isothermal sphere (e.g. Schmidt et al. 2001
  Allen et al. 2002).

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Strong Lensing Abell 1689Parametric and
Nonparametric
Broadhurst et al. 2004

• 4-band ACS imaging ground based data
• 106 multiple images from 30 background sources
• Most distant arc has an Einstein radius of 50,
  allowing for reliable mass constraints out to
  150 kpc.
• Quality of data make it excellent for testing new
  mass measurement techniques

ACS image of Abell 1689
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Abell 1689 - Strong lensing Results (Broadhurst
et al. 2004)

• Finds ??r -0.550.1 in the inner regions for the
  total surface mass profile and that the profile
  matches a NFW profile with concentration c8
• Light is more concentrated than mass within 50
  kpc
• Softened isothermal sphere not completely ruled
  out
• Assigned a power-law profile to all cluster
  galaxies along with a low frequency component
  representing the DM of the cluster.

Best-fitting NFW (solid line) vs. data. Dashed
line is SIS with correct mass inside Einstein
radius
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Abell 1689 - Strong lensing Results -
Non-parametric
Diego et al. 2004

• Analyzed the Abell 1689 strong lensing
  observations using SLAP, a non-parametric lensing
  code.
• Results are in broad agreement with the
  Broadhurst analysis, within the Einstein radius
• Non-parametric technique a good check on standard
  parametric approaches
• How many other clusters have enough arcs to use
  this technique??

Mass map overlaid on image of A1689
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Strong Weak Lensing
Abell 1689 - Broadhurst et al. 2004
Combine ACS strong lensing Subaru weak
lensing Total mass profile well fit by an NFW
with a high concentration parameter c14 Could
this be because the cluster is undergoing a
merger along the line of sightor the effects of
baryon condensation?
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Strong Weak LensingCl0024 (Kneib et al. 2003)
??r-2
??r-3
With sparsely-sampled WFPC2 pointings, Kneib et
al have measured the shear out to 5 Mpc. A
combined weakstrong lensing analysis indicates
the density profile falls off like ??r-n with
ngt2.4. Found a relatively high concentration
parameter c22
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Strong Weak Lensing
MS2137-23 (Gavazzi et al. 2003)
?

• Reanalyzed deep HST/WFPC2 strong lensing data
  along with weak lensing using the VLT
• Inner slope well fit with 0.7lt?lt1.2 c12 for NFW

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Lensing Dynamics
GOAL Combine constraints from dynamics of BCG/cD
galaxies with lensing to measure the mass density
profile of the inner regions of clusters. (see
Sand et al. 2002Sand et al. 2004)
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Final Results
Radial Arc Systems
Tangential Arc Systems
Sand, Treu, Smith Ellis 2004
PDFs include random errors only!
Systematics on ? of 0.1-0.2 cluster
substructure ellipticity stellar template
mismatch orbital anisotropies projection
effectseach! (See also Bartelmann Meneghetti
2004 Dalal Keeton 2003)
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Comparing Weak Lensing with X-ray Mass profiles

• Comparing weak-lensing results with an X-ray
  analysis assuming hydro equilibrium has been done
  only rarely Abell 2390
• Chandra data ground-based weak lensing
• Results are consistent at 1-sigma level, despite
  the fact the cluster is bimodal in the optical
  (see also Squires et al. 1996 for A2218).

Abell 2390 Allen et al. 2001
Points lensing X-ray 68 confidence band
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Galaxy Velocity Dispersion Hot Gas in ICM
Lokas Mamon 2003
Studied the velocity moments of 1000 ellipticals
in the Coma cluster out to 3Mpc, while taking
into account the hot gas density distribution
from ROSAT data and the stellar mass from the
galaxy distribution.
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The number ratio of radial to tangential arcs
The number ratio of radial to tangential arcs is
a relatively robust measure of the average
density profile in your cluster sample (Molikawa
Hattori 2001 Oguri 2002)

• The Numbers
• 57 HST proposals
• 129 galaxy clusters
• 104 tangential, 12 radial arcs with L/Wgt7

Arcs were identified by eye both with and without
brightest cluster galaxies subtracted.
MS 1455 bogus radial arc
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Constraints on the DM Slope

• Constraints on inner DM slope depend strongly on
  mass of typical brightest cluster galaxy.
• Brightest cluster galaxies as massive as 1013
  Msun seem to be ruled out by arc number ratio.

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Combine Compare Lensing, X-ray and Dynamics
A simple 3 step prescription


X-ray surface brightness (no need to assume
hydrostatic eq.)
K-band data and/or galaxy velocity dispersion
profile
Weak Strong lensing data
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Why arent observers simulators cooperating
more??
The latest generation of CDM simulations warn
direct comparison with simulations rather than
with fitting formulae should be attempted
whenever possible. (Navarro et al.
2004) Diverse and complex nature of simulated
haloes is not done justice with simple
circularized fitting formulaeespecially in the
inner regions of clusters.
Simulated cluster with the HUDF ray-traced
through it (Meneghetti)
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Some work at dwarf galaxy scale..Hayashi et al.
2004
How accurate is the dark matter distribution
inferred from rotations curves derived from
simulated long-slit spectra?
Normally, LSB rotation curves are compared with
spherically averaged circular velocity curves of
CDM halos. Rotation curves which would be
interpreted as indicating a constant density core
are recovered 25 of the time. This is due to
the complicated effects of halo triaxiality on
the dynamics of the gas.
Too many free parameters?
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At the cluster scale
Simple questions that could be addressed by
ray-tracing strong lensing and weak lensing
features through simulations For example
Clowe et al. 2004 have studied the systematics of
fitting circular NFW profiles to simulated weak
lensing data.

• How well can the inner slope of a CDM halo be
  constrained with strong lensing alone? How many
  arcs do you need to measure the inner slope
  accurately?
• What does a strong weak lensing analysis buy
  you?
• Can you recover the triaxial nature of DM haloes
  with strong lensing observations?

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Summary Conclusions

• The detailed measurement of the density profile
  in individual galaxy clusters is advancing along
  several fronts with new methods being tested and
  systematics explored.
• New data sets from ACS in particular will provide
  a wealth of strong lensing data.
• Measuring and comparing the mass profile of
  clusters using lensing, X-rays and cluster
  dynamics should be able to account for all of the
  major cluster mass components and help understand
  the dynamical state of clusters as well.
• It should be possible to learn something about
  how to study the density profile of clusters
  observationally by simulating observations
  through CDM clusters.

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Systematics Future Work Ellipticity
Substructure!
Employing full 2D lens modeling with DM
ellipticity scale radius as free parameters
In process of implementing MCMC parameter
estimation (w/ P. Marshall)
Dalal Keeton 2003 Bartelmann Meneghetti 2004