Halo proﬁles from lensing
observations of clusters

Masamune Oguri (IPMU, Univ. of Tokyo)

2011/9/21, SZX HuntsvilleThis talk is based on:“Combined strong and weak lensing analysis of
28 clusters from Sloan Giant Arcs Survey”
arXiv:1109.2594
Collaborators:
Matt Bayliss (Chicago → Harvard)Håkon Dahle (Oslo)
Keren Sharon (Chicago)
Mike Gladders (Chicago)Priya Natarajan (Yale)
Joe Hennawi (MPIA)
Ben Koester (Chicago)Expected halo proﬁle in ΛCDM
Cuspy
so-called NFW proﬁle,slope gets shallower
toward the center
Concentrationcorrelated with mass,
more massive halos
are less concentrated
Triaxial
not spherical, highly
elongated

http://www.mpa-garching.mpg.de/galform/millennium/

Anomalously high concentration?
project surface density

Umetsu, Takada & Broadhurst (2007)

rsrvirlensing analysis of
Abell 1689
cvir ~ rvir/rs ~12much larger thantypical cvir (~4), may
be hard to reconcile
with ΛCDM
triaxiality?
other clusters?

distance from centerImpact of triaxiality on lensing(mass)

Oguri etal.
Oguri,Takada, Umetsu & Broadhurst (2005)

Convergence profiles of the triaxial halo with the virial massM⊙ , the concentration parameter ce = 1.15, and the triaxial/c = 0.4 and b/c = 0.7. The halo is placed at zl = 0.3, and we
rce redshift of zs = 1.0. We consider the projection along each
ncipal axes: from upper to lower the dashed lines show profiles
g z, y, and x (see eq. [1]), respectively. The convergence profile
onding spherical NFW halo is also plotted by the solid linen (see text for details). The vertical arrow indicates the virial(ﬁtting mock lens signals)(concentration)
F . 2.— Constraint contours in the virial mass and halo concentration
parameter space,obtainedconcentrations
by fitting the mock data of triaxial halos to thelensing-derived masses
andspherical NFW halo model. The contours show 68%, 95%, 99.7% confidence
limits (corresponding to ∆χ = 2.3, 6.17 and 11.8, respectively). From left to(assuming sphericalarefromsigniﬁcantly
right, halo)
the constraint contours
the convergence profiles of the triaxial halo
projected along the principal axes x, y, and z (as in Figure 1), respectively,
are shown. For comparison, the square symbol shows the best-fitting modelaﬀected by the orientation
ofobtained
theby projectingcluster!
for the convergence profile
the a priori sphericallyIG2averaged mass profile of the input triaxial halo.

High concentration controversy
High concentrations inconsistent with ΛCDM?

Yes

No

Broadhurst et al. (2005)
Oguri et al. (2005)
Comerford & Natarajan (2007)
Oguri & Blandford (2009)
Broadhurst & Barkana (2008)
Corless et al. (2009)
Broadhurst et al. (2008)
Okabe et al. (2010)
Oguri et al. (2009)
Richard et al. (2010)
Sereno et al. (2010)
Morandi et al. (2011)
Zitrin et al. (2011)
Sereno et al. (2011)
Umetsu et al. (2011)
Meneghetti et al. (2011)
Gralla et al. (2011) [talk by M. Gralla](blue: Iʼm involved)

Sloan Giant Arcs Survey (SGAS)
Hennawi et al. (2008), Bayliss et al. (2011)
Gladders et al., in prep.

based on optical (red-sequence) clusters from the
Sloan Digital Sky Survey
look for strong lenses by visual inspection of
SDSS or follow-up images>40 clusters with prominent giant arcs discovered,extensive arc spectroscopy w/ Gemini/GMOS

Subaru/Suprime-cam follow-up
world best telescopefor cluster weak lensing!
gri-band imaging(g ~ 20min, r ~ 40min, i ~ 30min)~7 nights allocated from2007 to 2011
(PI: M. Oguri)→ strong+weak lensing
analysis for ~30 clusters

Example: SDSS0851

22M. Oguri et al.

Example: SDSS1138

Combined strong
and weak lensing ana
Mass-concentration
relation
5STACKING ANALYS

our5.1
sampleStacked tangential sWe canstudy the average pfromliterature

stackinglensing(Umetsuet al.
2011;signals. Thi
been successful for constrain
Zitrin et al. 2011)
butions of cluster samples (e[talkJohnstonby K. etUmetsu]
al. 2007; Leauth2010). Here we conduct stac
shear profile for our lensingΛCDM
prediction
concentration
relation fromoﬀ-centreingeﬀect, whic
w/thelensing
biasof the most significant systemanalysis (e.g., Johnston et al.
Hirata 2008; Oguri & Takada
our analysis, because of the dmass dependence of cvir detected
Figure 5. The mass-concentration relation obtained from comfor individual clusters and th­0.59
0.12slope
tooweaksteep?
(cvirFilledM
Okabeal. 2010)
vir
bined
strong andlensing analysis.
triangles
show our ) (cf.
assurethatetselected
centres (presults presented in this paper, whereas filled squares show reies atin thestrong
lensing regicconsistentw/
theoreticalprediction
highmassvir
sults from literature; A1689, A370, CL0024, RXJ1347 (Umetsuof the mass distribution.
et al. 2011b), and A383 (Zitrin et al. 2011b). The black shaded
low mass excess probably due to baryonWe
cooling
perform stacking in t
region indicates the predicted concentration parameters as a funcically, we compute the diﬀer

Stacked lensing analysis+
cluster 1+cluster 2cluster 3

combine weak lensing shear
measurements for many clusters
higher S/N, leading to accuratemean proﬁle measurement
stackedStacked lensing analysis
M.
Oguri
etal.
strong lens constraint

high S/N lensing
shear proﬁleby stacking 25
clusters

stacked tangential shear

12

follow NFW well

NFW ﬁtdistance from center
Figure 6. The stacked tangential shear profile obtained by com-Figure 7. Similar to Figure 6, bStacked lensing analysis

Combined strong and weak lensing ana

consistent with individual analysis

Figure 9. The mass-concentration relation obtained from thestacked lensing analysis. We show stacking results of 3 θE bins
(filled squares) and 3 Mvir bins (open circles). The mass and concentration measured from stacked strong and weak lensing analysis of 4 massive clusters at z ∼ 0.32 (Umetsu et al. 2011b) aretest the mass dependence ofbest-ﬁtM-cto θE bins
we relationconsider 3 Mvclustersfor the mass bin anafromindividual
Results of our stacking aanalysis
clusters
bins are ofshownin Figures 7
summarized in Table 5. We fi
θE bin are indeed most mas
third θE bins have similar mference of the Einstein radiΛCDM
diﬀerent prediction
concentrations. On
have similar
Einstein ra
w/binslensing
bias
clearly larger for smaller mas
These results can beconcentration relation inferr
clusters. Figure 9 shows th
similar to Figure 5, but thfrom stacked lensing analy
concentration relation fromable agreement with the bes
individual analysis of strong aShape: 2D stacking analysis
strong lens modelingθPAθrotate­θPAPA

stacked weaklensing analysis(No assumption on mass-light alignment!)

4stacked 2D weak lensing map
M. Oguri et al.

stacking w/ PA aligned

stacking w/ random PA

gure 11. The two-dimensional weak lensing shear maps obtained from stacking analysis of 25 clusters. The sticks shows observed
rections and strengths of weak lensing shear distortion. Colour contours are the surface density map reconstructed from the shear map
ing the standard inversion technique (Kaiser & Squires 1993). Both the shear and density maps are smoothed for illustrative purpose.
ft: The result when the position angle of each cluster is aligned to the North-South axis before stacking, by using the position angle
easured in strong lens modelling. The resulting stacked density distribution is clearly elongated along the North-South direction. Right:

Constraint on mean ellipticity
ΛCDM prediction(Jing & Suto 2002)

Aligned PA:
e = 0.47 0.06
Random PA:
e < 0.19
ellipticity detected
at 5σ levelmean ellipticity
consistent w/ ΛCDM
(cf. Oguri et al. 2010)

Summary: testing halo proﬁles­ NFW-like radial density proﬁle (r­1 inner, r­3 outer)observed proﬁle consistent with NFW­ concentration (low, correlated with mass)
steep mass dependence
consistent with ΛCDM at high masslarger cvir at small mass, due to baryon cooling?
­ large non-sphericity (axis ratio a/c ~ 0.4)
excellent agreement with ΛCDM!

Importance of multiband imaging
cluster member galaxies dilute
weak lensing signals(e.g., Medezinski et al. 2007)

eﬃcient background galaxy
selection in color-color space
use COSMOS photo-z catalog
for determining cut, selectingz > 0.7 galaxies onlyglaﬁc

URL: http://www.slac.stanford.edu/~oguri/glaﬁc/

fast lens equation solver w/ adaptive gridmodel optimization from observations
support various mass models
software is publicly available [Oguri (2010)]

image planesource planeEﬀect of ﬁtting
region15

ng and weak lensing analysis of 28 clusters

best-ﬁt for ﬁducial
ﬁtting box size

Figure 13. The mean ellipticities measured in stacked 2D shear
map as a function of the box size for fitting. Our fiducial result andits 1σ range adopting half the box size of 3h−1 Mpc are indicatedby the horizontal line with shading.

constraints do not change for smaller box sizes→ ellipticity does not change very much with radius

Table 6. Summary of the two-dimensional stacking analysis