Observational Constraints on Galaxy

Clusters and DM Dynamics

Doron Lemze

Tel-Aviv University / Johns Hopkins University

Collaborators:Tom Broadhurst, Yoel Rephaeli, Rennan Barkana, Keiichi

Umetsu,

Rick Wagner, & Mike Norman

21/9/10

Overview:

• Observational constraints on galaxy clusters.

Study case: the high-mass cluster A1689

• DM Dynamics

Lemze, Broadhurst, Rephaeli , Barkana, & Umetsu 2009

Lemze, Rephaeli , Barkana, Broadhurst, Wagner, & Norman 2010

Subaru/suprime-cam

VLT/VIMOS

The measuring instruments

Hubble

Strong lensing

Weak lensing Imaging of cluster galaxies

Cluster galaxies

spectroscopy

cD galaxy

0 0.5’Lemze, Barkana, Broadhurst & Rephaeli 2008

Galaxy surface number density

About 1900 cluster members.

Velocity-Space Diagram

Velocity caustics method:Diaferio & Geller 1997

Diaferio 1999

About 500 cluster members.

Methodology

2

22)()(

)()()(2

)()(r

rrGMrr

r

rrr

dr

d gal

rgalrgal

)(

)(1)(

2

2

r

rr

r

t

R

galgal

Rr

rdrrR

22

)(2)(

R

rgal

gal

pRr

rdrrR

rrr

RR

22

2

2

2

2

2

))(1)(()(

)(

2)(

Jeans eq.

Velocity anisotropy

Galaxy surface number density

Projected velocity dispersion

The unknowns: rgal M is taken from lensing

Galaxy surface number density

data points : 20

Projected velocity dispersion

data points : 10

The number of free

parameters : 5

---------------------------------------

dof : 25

Galaxy surface

number density fit

Projected velocity

dispersion fit

)530/(6.15/22 dofr

)210/(6.32 r

)320/(122 r

The fit results

Galaxy number density profile

Velocity anisotropy profile

Galaxy velocity anisotropy data vs. simulations

Arieli, Rephaeli, & Norman 2010

Mass profiles

r

caustics dxxFxAGrM0

2 )()(/1)( Here M is not taken from lensing!

The high concentration problem

Broadhurst et al. 2008

Zitrin et al. 2010

A1689 MS2137

Can we trust the high value found?

Comerford & Natarajan 2007

13virc

sunvirMhM 11510)4.03.1(

Virial mass vs. concentration parameter

Here M is not taken from lensing!

Comerford & Natarajan 2007

Hennawi et al. 2007

Bullock et al. 2007

62 clusters

Building statistical samples

Duffy et al. 2007

10 halos per data bin

N-body simulations using WMAP5 parameters

X-ray measurements

Building statistical samples

Johnston et al. 2007

Weak lensing measurements of stacked

SDSS groups and galaxy clusters

In agreement with Mandelbaum et al.

2006

Large samples

Conclusions

• We estimated for the first time

a detailed 3D velocity profile.

• We found that the caustic

mass is a good estimation for

the mass profile.

• Our three independent

estimates for the mass profile

are consistent with each

other.

• We constrained the virial

mass using galaxy positions

and velocities data.

• We deduced high values for

the concentration parameter

using two independent

methods.

DM dynamics

Question: how one can determine DM dynamics when

“DM spectroscopy” is hard to obtain?

Answer: by using a surrogate Measurement. The first

Choice should be other kind of collisionless particles - galaxies.

The orbit of a test particle in a collisionless gravitational system is

independent of the particle mass. This would presumably imply

that once hydrostatic equilibrium is attained, most likely as a result

mixing and mean field relaxation, DM and galaxies should have the

same mean specific kinetic energy, i.e., ,

where

)()( 2,

2, rr totgaltotDM

))(23)(()()()()( 2,

2,

2,

2,

2, rrrrrr iriiiritoti

Host et al. 2009

DM velocity anisotropy

Best-fit value:13.027.049.0

DM density

All other colors

DM density

Galaxy density

Total matter density

1])/1)(/[( ssDM rrrr12106061330

sr27.176.079.2

Best-fit values:

Model-dependent Model-independent

)(

)()( 2

,

2,

r

rrf

totgal

totDM

coll

The collisionless profile

Model-independentModel-dependent

colltotDM

totgalf

r

rrb /1

)(

)()(

,

,

The velocity bias profile

Conclusions

• We obtain the mean value of the

DM velocity anisotropy parameter,

and the DM density profile.

• r 1/3 r_vir seems to be a ∼transition region interior to which

collisional effects significantly modify

the dynamical properties of the

galaxy population with respect to

those of DM in A1689

Comerford & Natarajan 2007

Hennawi et al. 2007

Bullock et al. 2007

??C is measured using lensing and X-ray???

62 clusters

Building statistical samples

Duffy et al. 2007

10 halos per data bin

N-body simulation using WMAP5 parameters – lower sigma_8

X-ray measurements

X-ray data

dr

rd

dr

rd

rmG

Trk gasgas

gasp

B)()(

)(21

2 21 gasgasgas

Assuming

a gas density profile

Double model

Assuming

a temperature profile

Isothermal

Fitting a double

Surface brightness

model

Where a single model is

2

3

2

2

1)0()(

c

gasgas r

rnrn

For gas in hydrostatic equilibriumdr

d

dr

dPgas

gas

1

,2

)(

r

rGM

dr

d

, and Tk

mP

B

p

gas

gas

.

For the isothermal assumption:

where

For obtaining the mass profile:

Lensing data )(rM

What has been done previously?

)(rM

crit

Assuming

a DM profile

NFW

Doron Lemze

Tel-Aviv University

Collaborators:Tom Broadhurst , Rennan Barkana, Yoel Rephaeli, Keiich Umetsu

Collaborators:

Johnston et al. 2007

Weak lensing measurements of stacked

SDSS groups and galaxy clusters

In agreement with Mandelbaum et al.

2006

Large samples

Black points are from the shear profile

fits for the L200 luminosity bins and the

red points are from the N200 richness bins.

In

Rachel Mandelbaum, Uros Seljak, Christopher M. Hirata 2008

Astro-ph 0805.2552v2

FIG. 5: The best-fit c(M) relation at z = 0.22 with the 1

allowed region indicated. The red points with errorbars show

the best-fit masses and concentrations for each bin when we

fit them individually, without requiring a power-law c(M) relation.

The blue dotted lines show the predictions of [39] for

our mass definition and redshift, for theWMAP1 (higher) and

WMAP3 (lower) cosmologies. The prediction for theWMAP5

cosmology falls in between the two and is not shown here.

Their measurements are actually lower than the theoretical model

Eventhough they have used WMAP1 (which gives a lower curve see

Duffy et al. 2007). This indicate that they stack the clusters without

Exactly center them ontop of each other and didn’t separate the background

From the cluster galaxy good. These two effect lowers the concentration value.