Cluster mass distributions(lessons from HFF)
Masamune Oguri
RESCEU/Physics/Kavli IPMU
University of Tokyo

2018/9/3 The Universe as a Telescope@Milan

Lotz, Koekemoer, Coe+ ApJ 837(2017)97

HST Frontier Fields (HFF)• >100 multiple images for each cluster led tosignificant progress in cluster strong lens study!

http://hubblesite.org

Spec-z revolutions
Strong lensing analysis on Abell 2744 - MUSE

VLT MUSE

3

HST WFC3 grism

ntrtsseceaee.
s)nMahler+2018• spec-z’s for many multiple images

Figure 1. Full MUSE mosaic overlaid on the HFF F814W image. The shaded colour regions highlight our observing strategy,
showing the total exposure time devoted to each section of thecluster. The region where multiple images are expected is marked
by the white countour, and the red region shows the outline of
the HFF WFC3 image mosaic.

Treu+2015→ secure identifications & more constraints!

https://archive.stsci.edu/prepds/frontier/lensmodels/

LENSTOOLLTM

CATS
SharonCaminhaZitrinGLAFICGLAFICLENSMODEL

Keeton(also GLEE by Grillo, Suyu+)

WSLAP+Diego Bernstein
GraleWilliams
SWUnited

Bradac

Non-ParametricParametric

HFF mass models (v3, v4)http://www.slac.stanford.edu/~oguri/glafic/

image plane (θi) source plane (βi)

GLAFIC• public software for strong
lensing analysis(“parametric” modeling)• adaptive grid to solve lensequation efficiently• support many kind of lenspotentials• see Kawamata, MO+ ApJ

819(2016)114 for detailsof our HFF mass modelingIshigaki, Kawamata, Ouchi, MO+ ApJ 854(2018)73

Some high-z galaxy results

The Astrophysical Journal, 854:73 (20pp), 2018 February 10UV
luminosity
densityThomsonscattering
opticaldepth
Ishigaki et al.

• analysis of all 6 HFF

Figure 9. Left panel: r UV calculated with Mtrunc = -11.0 . The black circles represent r UV from the best-ﬁt luminosity functions atz ~ 4–6 (Bouwens et al. 2015). The blue line and the light blue shade denote the best-ﬁt function of r UV and the 1s error, respectiv(see the text for the best-ﬁt parameters). The up-scattering r UV (z ) at z ~ 10 due to the large uncertainty in α does not affect the ﬁttinr UV (z ) is also large. Middle panel: te integrating from z=0 to a redshift z. The red line and the magenta shade represent te (z ) andconsistent with r UV (z ) shown with the blue line in the left panel. The black line and the gray region show the values of te and its
Planck Collaboration et al. (2016). Right panel: evolution of QH II. The green line and the light green shading represent QH II and thwith r UV (z ) shown with the blue line in the left panel based on Equation (16). The symbols denote constraints of QH II from Ota et a(2014; open diamond), Carilli et al. (2010; ﬁlled square), Bolton et al. (2011; ﬁlled star), McQuinn et al. (2008; open circle), OMcQuinn et al. (2007; ﬁlled pentagon), Mesinger (2010; open triangle), McGreer et al. (2011; open star), McQuinn et al. (200Dijkstra et al. (2011; open pentagon), Chornock et al. (2013, 2014; ﬁlled hexagons), Totani et al. (2014; open hexagon), and Pa

ionizedhydrogenfractionclusters• a simple galaxy reion

model can explain allobservations
et al. (2016) is smaller than the one obtained in previous
observations by the nine-year WMAP (te = 0.088[also0.013;talks by D. Coe, R. Bouwens]

The parameters of the size–luminosity relation strongly
correlate with those of the luminosity function. The mostimportant may be the correlation between α and β, which has
been pointed out by several works, including Grazian et al.
(2011) and Bouwens et al. (2017a, 2017b). The top panel ofFigure 10 shows the correlation between α and β obtained inKawamata
this work together with the previous measurements ofthese et al.
parameters presented in Table 2. We ﬁnd that the steeper α inAtek et al. (2015a) and Ishigaki et al. (2017) will become
further consistent with ours if steeper size–luminosity relations
are assumed. Even with our large and deep sample, at z∼6–7
there still remains a moderate uncertainty in α due to theuncertainty in the size–luminosity relation. This uncertainty in
α is propagated to the UV luminosity density, a key quantity tocalculating the number density of ionizing photons, although
no previous studies on cosmic reionization have considered thisuncertainty. We note that although the values of α obtained in
Laporte et al. (2016) and Livermore et al. (2017) are consistent
with our value, their α–β combinations are outside (with alarge margin) of the 95% conﬁdence ellipse obtained in thisstudy. This demonstrates that these parameters must not bedetermined independently.
We also compare our α and β measurements with the resultsof the semi-analytical model of galaxy formation L-GALAXIES(Henriques et al. 2015). We run the L-GALAXIES code on twoN-body dark matter simulations of different resolutions, the eMillennium (Springel et al. 2005) and Millennium-II (BoylanKolchin et al. 2009), and combine the two galaxy catalogs toprobe a wide halo mass range. Applying Equation (12) to thecombined catalog ﬁnds that L-GALAXIES predicts an α
consistent with our value but a signiﬁcantly ﬂatter β. Resultsof the semi-analytical model of galaxy formation MERAXES(Mutch et al. 2016; Liu et al. 2017) are also compared. We ﬁnda good agreement with our results for z∼6–7 and 8 and anacceptable agreement for z∼9. Note that the values of βobtained here are different from those obtained in Liu et al.
(2017) because of different ﬁtting methods.

Kawamata, Ishigaki, Shimasaku, MO+ ApJ 855(2018)4

LF faint end slope

Some high-z galaxy results

βr∝
Lgalaxy size

• galaxy size important for galaxy LF measurements!
• degeneracy between LF and size parameters[also talks by D. Coe, R. Bouwens]Quantify goodness of mass models• blind test from mass modeling of simulated
strong lensing clusters (e.g., Meneghetti+2017)[talks by M. Meneghetti, C. Giocoli]• blind test from magnifications and time delaysof lensed SNe (e.g., Rodney+2015; Kelly+2015, 2016)[talks by N. Lyskova, P. Kelly, S. Rodney, T. Petrushevska]• root-mean-square (RMS) of differences ofmultiple image positions btw obs and model[talks by G. Caminha, L. Williams]

RMS of multiple image positions• typically 0.3”−0.7” for HFF|θ −θ|
imagecluster mass modeling(worse than meas. error)• many caveats:− smaller RMS does notnecessarily mean better− overfitting? use training
and test samples(e.g., Remolina Gonzalez+2018)− beware of misidentificationof multiple images

obs

modelplanemodelobs

sourceplane|βobs−βmodel|

2
How should we define RMS or χ ?

(1) ∑(2) ∑(3) ∑(4) ∑|θ⃗obs− θ⃗σ2| M( β ⃗−1M

obs|β⃗model |∂β ⃗=∂θ ⃗− β⃗

σ2|β⃗

2− β⃗

2

σ22

estimate RMS in the source planewith mag tensor, very similar to (1)(see MO PASJ 62(2010)1017)− β⃗obs

estimate RMS in the image plane,robust but time-consumingmodel) |model |
μ −1σ 2obs

2model |

approximated version of (2)can be biased toward higher
magnifications (flatter profiles)

choose proper one!

Improvements of RMS• mass modelingnot complete• RMS getting
better….

180

3160
140
2120Nimg• plotted data

image plane RMS [arcsec]

of clusters w/≳50 multiple
images

200

100
80

160
400

2005

2010

year

2015

2020

Improvements of RMS• mass modelingnot complete• RMS getting
better….

180

3160
140
2120Nimg• plotted data

image plane RMS [arcsec]

of clusters w/≳50 multiple
images20010080

160
4002005

2010year

20152020

zero by ~2020?

Open (?) questions• can we improve (no-overfitting) RMS further,and if yes, down to what value?

• does RMS contain any useful cosmologicalinformation such as small scale power ofdensity fluctuations?

• how well can we understand/model line-ofsight contributions?

Cluster lensing and dark matter• strong lensing allows us to accurately

measure dark matter (DM) distribution near
the cluster center• it provides useful constraints on DM models!

Things to check• central density profile (e.g., Newman+2013;Caminha+2017)• ellipticity (e.g., Richard+2009; MO+2012)• (mis-)alignment between DM andselfinteracting
DMstellar dist. (e.g., Donahue+2016; Jauzac+2018)• offset between centroids of DM andstellar dist. (e.g., Harvey+2017; Massey+2018)• subhalos/substructures (e.g., Jauzac+2016;Mohammed+2016; Natarajan+2017)

warm DM
fuzzy DM

et al.

Okabe, Nishimichi, MO+ MNRAS 478(2018)1141

pFigure 7. The mean ellipticities of di↵erent components against ab of the fitted ellipses. The quoted erroring standard deviation. Symbols of DM (filled circles), star (crosses), XSB (diamonds), and SZ (openp trianby 0.01, 0.02, 0.01, and 0.02 Mpc, respectively just for illustration purpose. A red star symbol at ab = 20of the ellipticity of the CG.

Prediction based on ΛCDM
ellipticityPA alignment• detailed prediction based on the Horizon-AGN

pFigure
8.
The
rmsof
thepositionangle
di↵erencefordi↵erent
components
againstab of the fitted elicities of di↵erent components against ab of the fitted ellipses. The quoted error-bars indicate the correspondfilled squares, open diamonds, and open triangles correspond to the rms values of DM, star, gas, XSB, anymbols of DM (filled circles), star (crosses), XSB (diamonds),and SZ (openare shifted horizontallyp triangles)
dashed lines indicate
the rms of position angle relative to the CG and total surface matter density, respectp

cosmological hydrodynamical simulation

0.02 Mpc, respectively just for illustration purpose. A red star symbol atG.

ab = 20 kpc represents a mean value

Although the satellite distribution is a better prior than theBCG, one should keep in mind that there is a non-negligible
scatter between position angles of stellar components andtotal matter distribution,✓ ⇠ 15 , which must be taken
into account when interpreting the stacking analysis results.

• star, gas and DM reasonably well aligned

6COMPARISON WITH O

Although the Horizon-AGN simu
cosmological hydrodynamical sim
reproduce the real universe. The rtions are thus valid only for theeverything is very preliminary

Quick check with HFF+• HFF clusters and some other clusters withaccurate GLAFIC mass models• compare halo ellipticity from strong lensmodeling with ellipticity of BCG light profile• also check the alignment of position angles

everything is very preliminary

Quick check with HFF+
0.8

eDM

0.6

0.4

0.2

0.0
0

0.2

0.4

eBCG

0.6

0.8

DM distribution ismore elongated than BCG

position angles arealigned well

8

Taizo Okabe et al.

8

Taizo Okabe et al.

everything is very preliminaryComparison with Horizon-AGN
observation

0.8

Horizon-AGN (Okabe+2018)(100kpc)eDM

0.6

0.4

0.2

0.000.2

0.4

eBCG

0.60.8• ellipticities of DM and BCG are similar in

Horizon-AGN, but different in observation (?)

Figure 4. Correlation of ellipticities of di↵erent components evaluated atpab = 0.1 Mpc against that of the CG. Red and blMore dark matter studies• caustic crossing near the critical curve canconstrain compact DM (primordial black holes)(Kelly+2018; Diego+2018;Venumadhav+2018; MO+2018)“Icarus”
found inMACS1149
seeP. Kelly’stalk!
(NASA/ESA/P. Kelly)MO, Diego, Kaiser+ PRD 97(2018)023518

Constraint on compact DM

mass fraction ofcompact DM• due to saturation

the robust interpretation
clue may be obtained bycurves before and after t
in order to obtain robus
matter from observations
ray-tracing simulations thcompact dark matter, astracing simulations are hekind light curves such com

high μ found inIcarus cannot be
explained incompact DM
scenario

excluded by“Icarus” obs• close window
VII.

SUMMARY

at 10-100 Msun

mass of compact DMFIG. 7: Constraints on the mass (M ) and abundance (fp ) ofcompact dark matter. Shaded regions show excluded regions

In this paper, we have amodel that consists of aconvergence and shear fie
ing properties of a point
magnification regions dueSummary• significant advance of cluster strong lensing
mass modeling after HFF• further improvement possible? note that wewant to get “accurate” mass models rather
than “precise” ones

• a lot of room to explore dark matter fromcluster strong lensing