The shape of cluster-scale
dark matter halos
Masamune Oguri(Kavli IPMU, University of Tokyo)

2013/4/16 Cluster Lensing @ STScIExpected halo shape in ΛCDM

• Cuspy

NFW radial profile• Concentration

more massive halos
less concentrated• Triaxial

highly non-sphericalwith axis ratio ~1:2
http://www.mpa-garching.mpg.de/galform/millennium/Oguri, Bayliss, Dahle, et al. MNRAS 420(2012)3213

Strong+weak lensing with SGAS

• Subaru/S-cam weak lensing analysis of 28 strong

lensing clusters from Sloan Giant Arcs Survey
Combined strong and[also talks by Keren Sharon, Matt Bayliss, Mike Gladders]• stacked radial profile

consistent with NFW(also Umetsu+11, Newman+13, Okabe+13)• stacked 2D shape

Figure 11. The two-dimensional weak lensing shear maps obtained from sta
directions and strengths of weak lensing shear distortion. Colour contours are t
using the standard inversion technique (Kaiser & Squires 1993). Both the shea
Left: The result when the position angle of each cluster is aligned to the Nortmeasured in strong lens modelling. The resulting stacked density distribution isThe result without any alignment of the position angle when stacking. The res〈e〉= 0.47±0.06

Oguri, Bayliss, Dahle, et al. MNRAS 420(2012)3213

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

our5.1
sampleStacked tangential
from
Weliterature
can study the average p(Umetsu+11;stackingZitrin+11)
lensing signals. Th
been successful for constrai
butions of cluster samples (Johnston et al. 2007; Leaut
2010). Herewe conduct sta
ΛCDM
prediction
shear profile for our lensing
w/triaxiality andconcentration relation fromlensing
bias eﬀect, whthe oﬀ-centreingof theselection
most significantsysteeffect[also talks/papersanalysis (e.g., Johnston et aby CLASH team]
Hirata 2008; Oguri & Takad
our analysis, because of the dFigure 5. The mass-concentration relation obtained from comfor individual clusters and tbined strong and weak lensing analysis. Filled triangles show ourassure that selected centres (results presented in this paper, whereas filled squares show reies in the strong lensing reg
sults from literature; A1689, A370,
CL0024,
RXJ1347 (Umetsu(e.g.,Fedeli 2012)of the mass distribution.
et al. 2011b), and A383 (Zitrin et al. 2011b). The black shaded
We perform stacking in• consistent with ΛCDM for high-mass clusters• excess at low-mass due to baryon cooling andcentral galaxy

Measured halo shape• shape of cluster-scale halos measured withgravitational lensing on average agrees very
well with ΛCDM model prediction• however, sometimes the structure of clusters
is much more complicated than this simplepicture

SDSS J1029+2623 (“the Hidden Fortress”)• largest-separation (θ=22.5″) lensed quasar
among ~150 lensed quasars known(Inada+2006; Oguri+2008)• rare example of three images “naked cusp”
configuration, which has been predicted tobe common among large-separation lenses(Oguri & Keeton 2004)

Image separations of quasar lenses
SDSS J1029+2623(Inada, Oguri et al. 2006)

SDSS J2222+2745(Dahle et al. 2013)

SDSS J1004+4112(Inada, Oguri et al. 2003)

SDSS J1029+2623(HST ACS/WFC3)

SDSS J1029+2623(HST ACS/WFC3)
quasar image B
quasar hostgalaxy
quasar image CG1quasar image A

G2

SDSS J1029+2623(HST ACS/WFC3)

modeling with glafichttp://www.slac.stanford.edu/~oguri/glafic/

image plane (θi) source plane (βi)

glafic• public software for lensinganalysis• adaptive grid for efficientlens equation solving• efficient mass modelingfor observed strong lenssystems• feel free to contact me
if you are interested!

Oguri, Schrabback, Jullo, et al. MNRAS 429(2013)482

Combined lensing analysis

The complex cluster SDSS J1029+2623

7Figure 6. Similar to Figure 4, but the surface mass density profile from the weak lensing analysis of the HST ACS/F814W image(blue) as compared to the Chandra X-ray surface brightness profile (red). The mass map is Gaussian-smoothed with σ = 8′′ .

[zcl= 0.58]• accurate and robust mass profile from three lensing
Figure 8. The tangential shear profile of the best-fit NFW model(solid line) as compared to the HST (filled squares) and Subaru (open circles) shear profiles and the reduced tangential shear
predicted by the best-fit strong lens model (filled triangles) forzs = 1.1. The best-fit shear profile is computed for zs = 1.1,
which is close to the eﬀective source redshifts of zs = 1.06 and1.19 for the HST and Subaru weak lensing data. The shaded region indicates the 1σ range. The lower panel shows the radial

Figure 7. Constraints on the virial mass Mvir and the concentration parameter cvir from the HST strong lensing analysis, HST
weak lensing, and Subaru weak lensing. For each constraint, weshow 1σ and 2σ ranges in this parameter space. The innermostcontours show the combined constraints.

observations, revealing its steep profile (cvir~20)

Fig(solaru
predzswhi
1.19
gion
proThebuttighfindfromram
wit
clus
eﬀe
How
intetwowit
clea
comtenNF
in r

tenof sOguri, Schrabback, Jullo, et al. MNRAS 429(2013)482

Lensing/X-ray
8 M. mass
Oguri et al.discrepancy• Compare with

X-ray mass from
Chandra• MX/Mlens~2-3• hard to explain

by non-thermalpressure, halo
triaxiality, ...
Figure 9. The enclosed mass within a sphere of radius r from theSuggested solution: Merger6boost of X-ray signals~1Gyr after merger• merger can enhanceline-of-sight

Simulation byNelson et al. (2012)

X-ray temperature and luminosity, as aFig. derived
3.— Top: Thetime evolutionof the mass
bias (top) for three cluste
result X-raymass
is biasedhigh(black, solid), and r200 (blue, dashed). Bottom: The mass accretion his
The vertical gray line marks the beginning of the latest major merger fcorresponding to the panels in Figures 1 and 2.

• line-of-sight merger can also explain thehigh cvir (King& Corless2007) to a small number of early forming obnecessarily
biasedSummary• average dark matter distribution in a large

sample of galaxy clusters measured withgravitational lensing is in excellent agreementwith ΛCDM prediction• on the other hand, sometimes the structureof clusters is highly complicated, showing ahuge (a factor of 2-3) discrepancy between
X-ray and lensing mass measurements,
presumably caused by merger• understanding these peculiar “outliers” will
be important for cosmology