HSCWLWG (March 17, 2009)HSCWLWG (March 17, 2009)

Mass Density Profiles of Mass Density Profiles of Strong Lensing ClustersStrong Lensing Clusters

Keiichi Umetsu Keiichi Umetsu

(ASIAA, LeCosPA/NTU)(ASIAA, LeCosPA/NTU)

Radial Density Profiles ofRadial Density Profiles ofSelf-Gravitating DM HalosSelf-Gravitating DM Halos

Logarithmic density slope: Inner density slopeInner density slope, r@ r0 > Collisional nature of DM particles > DM equation-of-state (cold, warm) > Degree of velocity anisotropy: dynamics

> Affect the DM annihilation rate (DM2)

Outer density slopeOuter density slope, , r@ rRvir > Smooth accretion after early fast collapse > boundary condition (finite mass) Mass ConcentrationMass Concentration (e.g., Cvir=R-2/Rvir) > Imprints of structure formation > Growth of outskirts (Rvir, or Mvir) > Progenitor formation epoch (R-2): DE, Structure for

mation (8)

rd

rdr DM

ln

)(ln)(

Empirical NFW Profile for CDM HalosEmpirical NFW Profile for CDM Halos

Jing & Suto 99

svirvir

s

rrc

rrrr

/:

)/1()( 213D

r

Simulation based prediction for gravitationally-bound CDM halos: Universal density profile of CDM halos Universal density profile of CDM halos

Navaro,Frenk,& White (NFW) 96, 97

Equilibrium-state dln/dlnr, sensitive to DM nature

Outer: ρ∝ 　 r^ -3

Inner: ρ∝ 　 r^ -1

Galaxies Groups Clusters

N-body CDM halosN-body CDM halos

LCDM Predictions?LCDM Predictions?

Universal NFW profileUniversal NFW profile (Navarro, Frenk, White 1996, 1997)(Navarro, Frenk, White 1996, 1997)

N-body based empirical form:

DM “EntropyDM “Entropy” (Bertschinger 1985; Taylor & Navarro 01; Hansen 0

4), related to a proximity to the coarse-grained phase-space density, Q(r)

213D )/1()( srrrr

)()()( 32 rrKr DMr

N-body simulations show a power-law behavior in equilibrium regions: -profile-profile (Navarro+08; Lapi & Cavariere 08,09)

)()(/)()()(/)(:)( 2/333/22 rKrrrQrrrK rDMDMr

)CD(3.125.1with)( MrrK

-profile-profile + Jeans eqJeans eq. allows for an analytical modeling of equilibrium-state CDM halo profiles (Lapi & Cavariere 08,09) Range of density slope is constrained, with some correction by the velocity anisotropy, (r)

2

2

1)(r

tr

Mass and Velocity Structure Mass and Velocity Structure

of A1689 (z=0.183)of A1689 (z=0.183)

Weak and Strong LensingWeak and Strong Lensing

(Subaru/S-Cam + HST/ACS)(Subaru/S-Cam + HST/ACS)

o Broadhurst, Takada, KU et al. 05, ApJLo Oguri, Takada, KU, Broadhurst 05o Medezinski, Broadhurst, KU+07, ApJo Broadhurst, KU et al. 08, ApJLo KU & Broadhurst 08, ApJo KU+ 09, ApJ (AMiBA+Subaru)

Equilibrium-State DM Density ProfileEquilibrium-State DM Density Profile

NFW (CDM) consistent profiles

KU & Broadhurst 08, ApJ

A1689 Broadhurst,KU+08, ApJL

)()()( rrr mm )()( rr m1)( rr

Surface mass density profile

Tangential shear profile

ACS high-resolution imaging inner SL profile (<1’)

S-Cam wide-field imaging outer WL profile (1’<r<20’)

3)( rr

Observational evidence of the continuously steepening density profile, dln/dlnr(r), expected for collisionless, non-relativistic (Cold) DM

2)( rr

Weak/Strong Lensing and Weak/Strong Lensing and Cluster DynamicsCluster Dynamics

(Subaru/S-Cam, HST/ACS, (Subaru/S-Cam, HST/ACS, VLT/VIMOS)VLT/VIMOS)

o Lemze, Broadhurst, Rephaeli, Barkana, KU 09, ApJ accepted

Velocity Caustic StructureVelocity Caustic Structure

Lemze, Broadhurst, Rephaeli, Barkana, & KU 08, ApJ acceptd (arXiv:0810.3129)

Projected velocity distribution of ~500 members Projected velocity distribution of ~500 members from VLT/VIMOS spec dataVelocity Caustic DiagramVelocity Caustic Diagram (Diaferio 1999) -- Application to A1689

Zero escape-velocity meeting @ the lensing derived Rvir =2.1Mpc/h

Symmetric, smooth caustic curves steadily declining @ r>300kpc relaxed, no-prominent velocity substructure

Reaching the zero velocity @~2Mpc/h, matching the lensing-derived virial radius clear boundary at Rvir, well-isolated cluster

Caustics clearly separate cluster and field galaxies, allowing for an accurate measurement, 1D= (1400 +/- 60) km/s

)()(1

)(0

2 rFRdRAG

rMr

A(R): ~escape velocity

)CL%68(4.13,10)4.03.1( 115 virsunvir CMhM

A1689 (z=0.18)

Multi-Wavelength Dynamical Analysis Multi-Wavelength Dynamical Analysis for the 3D Velocity Anisotropyfor the 3D Velocity Anisotropy

2

22 )()(

)(2)()(

)(

1

r

rGMr

r

rrrn

dr

d

rn rrgalgal

Jeans equationJeans equation with “static”, “spherically symmetric” spatial distributions, but including 3D velocity anisotropy

ADA

galprojgal

Dr

rdrrnn

22

)(

)(

)(2)(

ADA

galArproj

galproj

Dr

rdrrn

r

Drr

n 222

22

)(2

)()(

)()()(1)(

)(

2)(

Projected galaxy distribution as measured from S-Cam (Vi’) imaging

Projected velocity dispersion profile from 500 caustic-identified member galaxies

from strong/weak lensing

Solve J.Eq. for (1) the 3D galaxy density Solve J.Eq. for (1) the 3D galaxy density profile (nprofile (ngalgal(r)) and (2) the 3D velocity (r)) and (2) the 3D velocity

anisotropy profile (anisotropy profile ((r)) constrained by (r)) constrained by observed projected profiles:observed projected profiles:

2

2

1)(r

tr

Inner/Outer Density SlopesInner/Outer Density Slopes

With the analytic DM “entropy” model in the framework of LCDM, L+C09 showed that the standard LCDM can explain simultaneously the observed flatter inner density slope and the steeper outer slope, assuming a central velocity-anisotropy dominated by tangential orbits ((0)=-0.15).

(Lapi & Cavaliere 09, ApJL accepted)

Radial Mass Density Profile of the Radial Mass Density Profile of the Strong Lensing Cluster Strong Lensing Cluster

CL0024 (z=0.395)CL0024 (z=0.395)

o Zitrin, Broadhurst, KU et al. 09, ApJ submittedo KU+09, ApJ in prep.

HST ACS+NIC3 BVgriJH imaging for accurate photo-z of background galaxies

33 multiply lensed images (11 BG galaxies) in 8”<r<48”

ACS vs. Subaru DataACS vs. Subaru Data

Cluster virial radius (8’)

HST/ACS (2’x2’ region)HST/ACS (2’x2’ region)

33 multiply lensed images (11 BG galaxies) in 8”<r<48”

CL0024: Luminosity vs. Mass MapsCL0024: Luminosity vs. Mass Maps

Subaru Distortion g+ MeasurmentSubaru Distortion g+ Measurment

)()()( rrr mm

Comparison of g+ ProfilesComparison of g+ Profiles

Joint ACS+Subaru ConstraintsJoint ACS+Subaru Constraints

Weak Lensing and SZEWeak Lensing and SZE

(Subaru/S-Cam + AMiBA)(Subaru/S-Cam + AMiBA)

Mass and Hot Baryons in a Merging ClusterMass and Hot Baryons in a Merging Cluster

First AMiBA7 papers:First AMiBA7 papers:

Ho et al. 2009, ApJ in press (arXiv:0810.1871)

Nishioka et al. 2009, ApJ in press (arXiv:0811.1675)

Umetsu et al. 2009, ApJ in press (arXiv:0810.0969)

Wu et al. 2009, ApJ in press (arXiv:0810.1015)

Koch et al., ApJS, submitted

Lin et al., ApJ, submitted

A few more science/instrumentation papers to be submitted to ApJ soon

Color: AMiBA SZE decrement (Wu+09) electron pressure

Contours: Subaru WL (Okabe & Umetsu 08; Umetsu+09) mass (~DM)

A2142 (z=0.09)

Ho+09

Weak/Strong Lensing, Weak/Strong Lensing,

SZE, and X-raySZE, and X-ray

(Subaru/S-Cam + HST/ACS + (Subaru/S-Cam + HST/ACS + AMiBA + TAMiBA + TXX))

Cluster Hot-Baryon FractionsCluster Hot-Baryon Fractions

Umetsu+09, ApJ in press (arXiv:0810.0969)

Averaged fAveraged fgasgas profile of 4 profile of 4

AMiBA-lensing clusters AMiBA-lensing clusters with <Mwith <Mvirvir>=1.2e15 M>=1.2e15 Msunsun/h/h (A1689,A2142,A2261,A2390)

(22 +/- 16)% of the baryons are missing from the “hot” cluster environment (~5% accounted for by cold baryons)

First WL+SZE based fgas measurements on large scales (up to r200) without the hydrostatic-equilibrium assumption

Consistent with X-ray based measurements with the hydro-equilibrium assumption