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On the Distribution of On the Distribution of Dark Matter in Clusters Dark Matter in Clusters
of Galaxiesof Galaxies
David J SandDavid J Sand
Chandra Fellows Symposium 2005
Cold Dark Matter Cold Dark Matter SimulationsSimulations
Inner profile: r - NFW: 1.0 Moore: 1.5
log ()
Moore simulationlog (radius)
CDM is: non-relativistic (cold); collisionless; well motivated theoretically and observationally
Galaxy cluster scaleGalaxy cluster scaleStrong and Weak Strong and Weak
Gravitational LensingGravitational Lensing
Smith et al. (2001); tot ~ 1.3
Kneib et al. 2003; found outer slope out > 2.4
Strength: Total mass constraints without assumptions about dynamical state of cluster.
Weakness: Need more info to separate dark and luminous components.
Galaxy cluster Galaxy cluster dynamicsdynamics
Extended velocity Extended velocity dispersion profile dispersion profile of the brightest of the brightest cluster galaxycluster galaxy (e.g. (e.g. Kelson et al. 2002)Kelson et al. 2002)
Velocity Dispersion Velocity Dispersion profile of the profile of the galaxies in the galaxies in the clustercluster (e.g. Carlberg (e.g. Carlberg et al. 1997; Katgert et et al. 1997; Katgert et al. 2003)al. 2003)
Strength: Can probe to high cluster radii.
Weakness: Must assume orbital properties of stars/galaxies.
NFW profiles require unrealistic stellar M/L (Kelson et al. 2002)
X-ray Observations of the X-ray Observations of the ICMICM
Wide range of Wide range of inner slope inner slope values have values have been found: been found: ≈ ≈ 0.6 0.6 (Ettori et al. (Ettori et al.
2002)2002) to ≈1.2 to ≈1.2 (Lewis et al. 2003; (Lewis et al. 2003;
Buote & Lewis 2003)Buote & Lewis 2003) to ≈1.9 to ≈1.9 (Arabadjis (Arabadjis et al. 2002).et al. 2002).
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
Lensing + BCG DynamicsLensing + BCG Dynamics
GOAL: Combine constraints from dynamics of BCG/cD galaxies with lensing to measure the mass density profile of the inner regions of clusters.
MS2137-23MS2137-23
zclus=0.313
zarc=1.50
Two component, spherically symmetric
mass model representing BCG and cluster DM halo. We
utilize 3 free parameters: M*/L, , c. . Scale radius fixed at 400 kpc.
ESI spectrum
Issues to ExploreIssues to Explore
One object cannot be used to One object cannot be used to understand the DM density understand the DM density profile of clusters!profile of clusters!
What effects could ellipticity What effects could ellipticity and substructure have on our and substructure have on our results (see e.g. Dalal & Keeton results (see e.g. Dalal & Keeton 2003; Meneghetti et al. 2005)?2003; Meneghetti et al. 2005)?
Should scale radius be a free Should scale radius be a free parameter?parameter?
Tangential Arc Tangential Arc SystemsSystems
CONCLUSION: Radial arc systems are not biased toward shallower profiles.
Upper limit: < 0.57 (99% CL)
Full 2D modeling of MS2137Full 2D modeling of MS2137•We have upgraded J.P. Kneib’s LENSTOOL software to include generalized NFW mass profiles.
•LENSTOOL accounts for ellipticity (both in luminous and dark matter components) and substructure (e.g. associated with visible galaxies).
•Can take into account the full multiple imaging constraints
Two background sources associated with the tangential and radial arcs
Multiple images determined from spectroscopy, surface brightness conservation and iterative lens modeling.
Two features on the tangential arc and one on the radial arc are identified.
Constraints on inner slope with CDM motivated prior on rsc
The inner slope is =0.25+0.35-0.12 - in agreement
with work of Sand et al. 2004 (=0.57+0.11-0.08) .
However, the best-fitting rsc is poorly constrained.
Summary & ConclusionsSummary & ConclusionsWhat constraints do we get on the
inner slope?
Other issues remain: How do we constrain the scale radius? What effect does triaxiality have on our results?
Would dark matter models that have undergone adiabatic contraction better
fit the data?
Ellipticity of MS2137
Our inner slope constraints are robust if the DM halos are nearly round, as in MS2137. At least some cluster DM halos appear to have shallow inner slopes.
Meneghetti et al. 2005
obs/sim
Combine & Compare Combine & Compare Lensing, X-ray and Lensing, X-ray and
DynamicsDynamicsWill partially remove inherent
degeneracies and account for all major cluster mass components
Weak + Strong lensing data
X-ray surface brightness and temperature
K-band data and/or galaxy
velocity dispersion profile
+ +
Kelson et al. 2002
Best-fitting Density Profile Best-fitting Density Profile in Axially symmetric casein Axially symmetric case
Lensing critical lines• Critical lines are those places in the image plane where the magnification formally diverges.
• Radial arcs are presumably often obscured by bright, central galaxies in clusters.
Critical curves occur at the roots of the eigenvalues of the Jacobian that describes the lensing transformation.
Narayan & Bartelmann 1997
Measuring and Modeling Measuring and Modeling Velocity dispersion profilesVelocity dispersion profiles
• Stellar spectra are used as Stellar spectra are used as templates. They are templates. They are smoothed and redshifted to smoothed and redshifted to match the BCG. match the BCG.
• The Gauss-Hermite pixel-The Gauss-Hermite pixel-fitting software (van der fitting software (van der Marel 1994) was used. In Marel 1994) was used. In practice, it convolves a practice, it convolves a template with a line-of-sight template with a line-of-sight velocity profile and velocity profile and compares it with the BCG compares it with the BCG spectrum.spectrum.
Ellipticals are Ellipticals are pressure supported pressure supported (no/slow rotation).(no/slow rotation).
Expect Expect 22 rr2 2 from from integrating integrating spherical Jeans spherical Jeans eqn.eqn.
Measuring Modeling
Kelson et al. 2002
Constraints on the inner slope with rsc=400 kpc fixed
Direct Comparison with Sand et al. 2004
Lensing Only
Lensing + Dynamics
Same M/L range as Sand et al.
Lower values of cannot fit the
angular structure of the lens model.
More complex Modelling?More complex Modelling?Dalal & Keeton (2003); Bartelmann & Meneghetti Dalal & Keeton (2003); Bartelmann & Meneghetti
(2004); Meneghetti et al. 2005(2004); Meneghetti et al. 2005
Despite systematic Despite systematic check with LENSTOOL; check with LENSTOOL; concern remains concern remains about 1D modeling about 1D modeling performed in Sand et performed in Sand et al. (2004;2002)al. (2004;2002)
Suggest that by Suggest that by including including ellipticity NFW ellipticity NFW profiles are not profiles are not ruled out!ruled out!
Fixed scale radius Fixed scale radius of 400 kpc may also of 400 kpc may also bias results.bias results.
Estimated range of systematic <> from Sand et al.
2003
Dalal & Keeton 2003
Multiple Image Interpretation
Perturber
Two background sources associated with the tangential and radial arcs
Multiple images determined from spectroscopy, surface brightness conservation and iterative lens modeling.
Two features on the tangential arc and one on the radial arc are identified.
Comparison with 2D Comparison with 2D resultsresults
Using LENSTOOL allows the effects of substructure and ellipticity to be taken into account.
CONCLUSION: Neglect of substructure and ellipticity leads to at most a ~ 0.2 systematic.