Dark Matter Properties of Groups and Clusters ofGalaxies via Weak Gravitational Lensing
Alexie Leauthaud
LBNL & Berkeley Center for Cosmological Physics

With the COSMOS Weak Lensing team:Jean-Paul Kneib, Alexie Leauthaud (OAMP-Marseille)
Richard Ellis, Richard Massey (CalTech)
Catherine Heymans, Ludovic Van Waerbeke (UBC)
James Taylor (Waterloo), Cecile Faure (ARI)
Yannick Mellier (IAP), Alexandre Refregier (CEA-Saclay)
Jason Rhodes, David Johnston (JPL)& the COSMOS Collaboration

OUTLINEI.

THE COSMOS-HST SURVEYII.

WEAK LENSING WITH THE
HUBBLE SPACE TELESCOPE

III.

MOTIVATION FOR THIS
STUDY

IV.

GROUPS & CLUSTERS OFGALAXIES

THE COSMOSSURVEYACSThe largest contiguous
image ever taken withthe Hubble Space
Telescope (HST)HST ACS
Cycles 12 & 13590 orbits

1.4deg

NICMOS-3
1.6 µm -- 24mag~7% of area

I.

COSMOS: A panchromatic survey
HST-ACS
I814W
XMM
0.5 -10 keV

Magellan - IMAX

Spitzer MIPS
160, 70, 24 µm

VLT-VIRMOS
Spitzer IRAC
8, 6, 5, 4, 3 µm

CHANDRAGALEX
FUV, NUVVLA20 cm

CFHT Megacamu*, i*Subaru SCamB,V,r’,i,z’, NB816

CFHT Wircam
KNOAO
Ks

IRAM -30m
1.2 mmCSO Bolocam
1.1 mmI.

The cosmos xmm group sample

 ~ 180 groups detected throughextended XMM emission
Finoguenov et al. 2007
 1.67 deg 2 of contiguous ACS data high background number density (60gals/arcmin2) - no issues with the mass
sheet degeneracy
Leauthaud et al. 2007, Rhodes et al. 2007
 State of the art photometric redshifts(30 bands of data including IR and u band)
Ilbert et al. 2008
1.3 deg2
COSMOS survey
CHANDRA + XMMA. Finoguenov et al. 2007

~ 10 000 spectroscopic redshifts forphotoz calibration
Lilly et al. 2007

I.

The third dimension: photoz’s
The Z-COSMOS bright sample is magnitude limited at i+AB < 22.5 :A comparison to the Z-COSMSO bright sample shows that in this magnitude range,
the COSMOS photometric redshifts reach an accuracy of:

PHOTO-Zσz/(1+z) = 0.007 , catastrophic failures < 1 %SPECZ

Ilbert et al. 2008

I.

errors as a function of magnitude

Old COSMOS

68% ERROR

New COSMOSCFHTLS Deep
COMBO - 17i+ABIlbert et al. 2008

Cosmos redshift distribution
Note: Photometric redshifts are akey element to weak lensing
studies because the strength ofthe lensing signal depends on theangular diameter distances DOS
DOL DLS in particular through aquantity known as the criticalsurface mass density:

N/deg2/104

I.

Cumulative n(z)c2DOS" crit =4 #G DOL DLS!
Photo-zIlbert et al. 2008

DOS: distance Observer-Source
DOL: distance Observer-Lens
DLS: distance Lens-Source(more details soon …)

I.

Shear: space versus groundOUTLINEI.

THE COSMOS-HST SURVEYII.

WEAK LENSING WITH THE
HUBBLE SPACE TELESCOPE

III.

MOTIVATION FOR THISSTUDYIV.

GROUPS & CLUSTERS OFGALAXIES

Clumpy Dark Matter distribution ⇒ Curves spacetime.
Photon following curved spacetime

Springel et al. 2005

II.

Weak gravitational lensing

Simulation of the gravitational lens effect created by amassive object that passes in front of the Hubble Deep
Field (HDF)
L. L. Christensen (ESA)II.

Weak gravitational lensing

Weak gravitational
lensing

Strong gravitational
lensing

Z~0.5

Simulation of the gravitational lens effect created by amassive object that passes in front of the Hubble Deep
Field (HDF)II.

galaxy-galaxy lensing

Source Plane

We study the tangential component of the shear incircular annuli around a set of galaxies ( ~ 500 ).
The quantity that we seek to measure is Delta Sigma
which is the product of the shear and Sigma Crit :SDIS"#(r) $ #(< r) % #(r) = # crit & ' t (r)αDOSLens

IL!

ΘSc2
DOS
" crit =4 #G DOL DLS

DOI

ΘIOObserver

In this equation, Sigma represents the surface massdensity of the central lens. In order to calculate
Delta Sigma, we must calculate Sigma Crit for eachlens-source pair :!

Photo-ZTo calculate Sigma Crit we must know the angular
diameter distances between the observer, the source
and lens ( DOS, DOL, et DLS ). These distances are
given by the COSMOS photometric redshifts.

II.

The scientific promise ofgravitational lensing
I.

Weak lensing by large-scale structure (‘Cosmic shear’) → evolution of
the non-linear power spectrum & constraints on cosmological parametersΩM, σ8, w, w’…complementing and breaking degeneracies present inother methods (SN, CMB).

II.

Direct mapping of the dark matter distribution

III. Weak shear around galaxy clusters → estimate of total cluster massand mass reconstruction of low redshift clusters.
IV.

The average weak lensing shear of distant galaxies and groups(‘galaxy-galaxy lensing’) → ensemble average properties of dark matter
halos → connecting mass and light.

II.

A map of the dark matter
Massey et al. 2007

BLUEMass of the stars

YELLOW Galaxy density
REDX-rays

OUTLINEI.

THE COSMOS-HST SURVEYII.

WEAK LENSING WITH THE
HUBBLE SPACE TELESCOPE

III.

MOTIVATION FOR THISSTUDYIV.

GROUPS & CLUSTERS OFGALAXIESIII.

Aim of this work

 Study the Dark Matter properties of asample of ~150 groups/clusters detected
via extended XMM emission in theCOSMOS survey
 This is one of the largest samples of it’skind and is comprised of groups with halo
masses M200 ~ 5.1013 h-1 Msun.
 Together with the SDSS, this is one of
the first studies to probe the dark matter
halos of low mass groups via weaklensing.
1.3 deg2
COSMOS survey
CHANDRA + XMM
A. Finoguenov et al. 2007

iII.

Motivations for pushing down to
the low end of the mass function
I.

Constraints on cosmologicalparameters can be improved byextending measurements down to
the low end of the mass function (oncondition that masses can bemeasured correctly for groups).

Cosmological volume element, dV/dz

Growth function

The growth of the Dark Matter Mass Function overcosmic time - Heitmann et al. 2006

Most massive systems:- low numbers- mergers/ non relaxed- triaxiality

iII.

Motivations for pushing down to
the low end of the mass function

The growth of the Dark Matter Mass Function overcosmic time - Heitmann et al. 2006

I.

Constraints on cosmologicalparameters can be improved byextending measurements down to
the low end of the mass function (oncondition that masses can bemeasured correctly for groups).

II.

Understanding the scaling relationsof galaxy groups will lead to a better
handle on the slope and amplitude of
the scaling relations of more massivesystems.

iII.

Motivations for pushing down to
the low end of the mass function
I.

Constraints on cosmologicalparameters can be improved byextending measurements down to
the low end of the mass function (oncondition that masses can bemeasured correctly for groups).

II.

Understanding the scaling relationsof galaxy groups will lead to a better
handle on the slope and amplitude of
the scaling relations of more massivesystems.

Direct detection
via lensing

III.
The growth of the Dark Matter Mass Function overcosmic time - Heitmann et al. 2006

Galaxy groups also play in key rolein processes of galaxy formation(low velocity dispersions ⇒ galaxiesare more likely to merge)

III. Recommendations of the dark energy
task force
 We recommend that the Dark Energy program have multiple techniques at every
stage, at least one of which is a probe sensitive to the growth of cosmological structurein the form of galaxies and clusters of galaxies.
 Among the projects that can contribute to this goal are:F) Better characterization of cluster-mass observable relations through joint X-ray, SZ,
and weak lensing studies and also via numerical simulations including the effects ofcooling, star-formation, and active galactic nuclei.
In this project, we have looked into the calibration of the X-ray Luminosity (Lx) - Halomass (M200) relation. Nevertheless, the method outlined here can be applied to other mass
proxies such as Temperature, Richness, Velocity Dispersion, etc.
Lx - M200

T - M200

N200 - M200

σdyn - M200

MSZ - M200

A better understanding of each of these scaling relations is necessary for DE studies but
will also shed light on the the underlying physical processes within groups & clusters.

III.

The physics of cluster formation

OUTLINEI.

THE COSMOS-HST SURVEYII.

WEAK LENSING WITH THE
HUBBLE SPACE TELESCOPE

III.

MOTIVATION FOR THIS
STUDY

IV.

GROUPS & CLUSTERS OFGALAXIESIV.

The three main lensing techniques

I. Strong Lensing - Probes the mass within the Einstein Radius- Limited number of systems - Representative sample?

II. Weak lensing on an object by object basis - Only works forthe most massive systems - Limited by the shape of the lensing
weight function - Projection effects.

III. Stacked weak lensing - Can measure the mass forpotentially ANY systems - Can reduce the statistical noise - Not
affected by projection effects - Need to know center - No longer
access to the scatter.

IV.

Probing structures beyond the limitsof direct lensing detections• If you are interested in Dark
Energy you will want to probe:z = [0 , 1]

COSMOS lensing• You will also want toconsistently calibrate scaling
relations over z = [0 , 1]
(redshift evolution?)• For magnitude limited
observations, the lensing
detection significance is limitedby the lensing weight function.
• Stacking techniques can gowell below this limit techniques(all you need is a centre and amass proxy for the structures toprobe)

COSMOS XMM

Dark Energy

Plot from James Taylor

Log10( Lx.Ez-1 )TIV. Cosmos group sample

REDSHIFTTΛΣ [Msun pc-2 h72-1]T

IV. Results: Stacked weak lensing signals

R [Mpc h72-1]TLeauthaud et al 2008 in prep

Iv.

The M200 - Lx relation
 Form of the M200 - LXrelation:*Log10( M200.E(z)-1 h72-1 Msun)T$ LX " E(z)#1 'M 200 " E(z)= A "&)
M0L0%(!

 We find a slope : α ~ 0.62
in good agreement with
Stanek et al. 2007 and Rykoff
et al. 2008.
 Cluster data alone can bemisleading : Bardeau et al.
2007 find α ~ 1.2!

Log10( Lx.E(z)-1 h72-2 ergs s-1)T Current relation is limitedby measurement of cluster
masses.

 In addition to the determination of the slope and normalization, a better
understanding of the scatter in the Lx-M200 relation is also necessary. One could
measure this scatter with weak lensing for Lx E(z)-1 =[44,45].

Discussion & conclusions
 We observe a striking relation between Lx and halo mass over several decades inmass and luminosity. These are encouraging results in view of calibrating massobservable relations for DE studies and to gain a better understanding of cluster andgalaxy physics.
 The slope that we measure (α ~ 0.62 ) is inconsistent with simple models of selfsimilar evolution which predict α = 0.75. Additional physics beyond simple gravitational
collapse are necessary (e.g pre-heating, AGN & galaxy feed-back, etc.).
 Extending halo mass measurements down to the group regime is necessary inorder to obtain an accurate determination of the slope.
 The current measurement of the Lx-M200 relation is limited by systematic errors in
the determination of individual cluster masses via weak lensing.
 This work will enable studies of baryonic physics as a function of halo mass:⇒ determination of the baryon fraction in groups (Giodini et al. in prep)⇒ galaxy properties within groups as a function of halo mass
⇒ the assembly of the most massive galaxies, the central BCG’s.

The end
Domo arigato !