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

MS2137-23 ResultsMS2137-23 Results

Best-fitting density profile: r - with = 0.57 0.11

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?

More radial arc More radial arc systemssystems

<> = 0.52 ~ 0.3

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

Multiple Image Interpretation

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.

The best mass models are centered around ~0.1 which translates to an ellipticity in the surface density of ~0.2

Histogram of ellipticity in the potential

Best-fitting density profile

=0.20; 2=21.2 for 16 degrees of

freedom