The image plane approachto cosmic telescopes
Masamune Oguri(University of Tokyo)
Collaborators (alphabetical): Masafumi Ishigaki, Ryota Kawamata,
Yoshiaki Ono, Masami Ouchi, Kazuhiro Shimasaku

2015/8/4 IAU GA FM22 @ Hawaii

Oguri PASJ 62(2010)1017

Mass modeling with glafic• publicly available strong lens modeling code
(http://www.slac.stanford.edu/~oguri/glafic/)• parametric mass modeling with a variety oflens potentials (NFW, SIE, Hernquist, perturbations, ....)• can handle both point and extended sources• efficient algorithms to solve lens equationand optimize model parameterspoint source
extended source

3

image plane (θi) source plane (βi)

Recent glafic update: mapprior• now one can include constraints on various
lensing quantities (e.g., μ, κ, γ1, γ2, ...) at arbitrary
position on the sky• this allows one to add magnification constraints
from SNIa (Rodney et al. 2015) and (reduced) shear
constraints from weak lensingAn example from SDSS J1029+2623

Oguri et al. (2013)• 27 multiple images at z~2• HST weak lensing constraints
added (20” grid, 89 positions)Cluster as a cosmic telescope• two competing effects from lensing magnification− detection of intrinsically faint galaxies− decrease of the survey volume

image planesource planeLuminosity function?

• traditional (?) approach: source plane approach− derive un-lensed mags for all high-z galaxies− compute magnification-corrected volume− estimate luminosity function• some difficulties

Non-uniform survey depth
The Astrophysical Journal, 799:12 (21pp), 2015 January 20

Ishigaki et al.

• in a cluster field limiting
29.14

29.03

29.08

28.87

29.05

28.81

28.91

29.09

28.99

28.98

28.61

28.73

28.68

28.99

28.77

29.06

Ishigaki et al. (2015)

Figure 1. HST/WFC3-IR H160 image of the A2744 cluster field. The numbers
denote 5σ limiting magnitudes defined in a 0.′′ 4-diameter aperture, measured in
the 4 × 4 grid cells.

3.1. Photometric Catalog

mags are non-uniform
due to ICL etc.

• also limiting mags andmagnifications must be
correlated

Figure 2. Difference between the aperture-corrected total magnitudes (mtot )and the SExtractor’s AUTO magnitudes (mAUTO ) as a function of the aperturemagnitude mAP for our dropout candidates in the cluster (filled circles) andparallel (open circles) fields. The horizontal line corresponds to the case wheremAUTO is equal to mtot .

We adopt the diameters of 0.′′ 36 (0.′′ 38) and ∼0.′′ 2 for the PSFmatched images and for the PSF-unmatched blue-band images
in the cluster (parallel) field, respectively. The detection limits
are also defined with 0.′′ 36 (0.′′ 38) diameter apertures for the
PSF-matched images and ∼0.′′ 2 diameter apertures for the PSFunmatched images in the cluster (parallel) field.
We apply an aperture correction that is defined by thefollowing procedure. We create a median stacked J125 -band

Complex lensing effect• high-z galaxies are not point sources but
extended• selection function depends on not only

magnification but also shear, spatial variationof magnification, ... (see, e.g., Oesch et al. 2015)• also at high magnifications model error isvery large, making the estimate of unlensed
magnification inaccurateImage multiplicity
The Astrophysical Journal, 799:12 (21pp), 2015 January 20

YJ1-2
128

• high-z galaxies can often be

YJ1

z=4

• sometimes it’s not cleari5(19.1)

whether candidate multiple
imagesare real or not
12
z=4 12z=48

8i8(19.3)(e.g., Kawamata
et al. in prep.)

12

z=4

YJ1-3

Ishigaki et al. (2015)

Figure 8. Predicted positions of multiple images of HFF1C-YJ1 using our massmodel. The red circles show the positions of HFF1C-YJ1 and its multiple images
with IDs HFF1C-YJ1-2 and HFF1C-YJ1-3. The radius of each circle is 0.′′ 3.
The white crosses in the upper (lower) panel indicate the predicted position ofimage HFF1C-YJ1-2 (HFF1C-YJ1-3) at z = 4, 6, 8, 10, and 12 with the tracks
over a redshift range 4 < z < 12. Our mass model predicts that the redshift of
YJ1 is z > 6, as discussed in Zitrin et al. (2014).

[see also Zitrin et al. 2014]z=4

i6(19.2)
128multiply
imaged
8
12
z=4

z=4

Y9

Ishigaki et al.

6 8 12
Y9-2• not all multiple images are
i5-2

detected (above mag limit)

Figure 10. Same as Figure 8, but for HFF1C-i5, HFF1C-i6, and HFF1C-i8. The
cyan circles show the positions of HFF1C-i5, HFF1C-i6, HFF1C-i8 and theirmultiple images. The green circle presents the position of HFF1C-i5-2 predicted
by Jauzac et al. (2014).

(2014b). In our paper, we refer to Image 5.4 as HFF1C-i5-2. In
Figure 10, we plot the predicted positions of these four multiple
images. The predicted position of HFF1C-i5-2 is about 8′′ awayfrom the images reported by Atek et al. (2014b). Instead, it isclose to the position predicted by Jauzac et al. (2014), shownwith the green circle in Figure 10. The observed images of theother three multiple images lie near the predicted positions at
z = 6 and 8. Our mass model predicts that the best-fit value ofIshigaki et al. ApJ 799(2015)12

Our approach: Image plane approach• compare number counts of galaxies in theimage plane• full Monte Carlo simulations including all

lensing selection effects to predict observed
number counts for each input LF model

（Φ*, L*, α)z ∼ 6–7

This work

number densities

observation∗∗−3(Mpc )−20.45+0.1
−0.2
+0.69
−20.63−0.56−3.30+0.10−0.20

Ishigaki et al. ApJ 799(2015)12

derive&the&mock−2.06best&ﬁt&parameter&± 0.12
observation−2.01 ± 0.21
−1.94+0.09−0.10−1.88+0.17−0.20

Our approach: Image plane approachmock
et al. (2014b)
catalog Bouwens
Bouwens et al. (2011)
Atek et al. (2014a)−21.04 ± 0.26

or
LFanalysis
analysislensingr LF
Ouchi et al. (2009)

Schenker et al. (2013)−20.14 ± 0.26
−20.10 ± 0.76
−20.14+0.36−0.48

effectsz∼8This work
Bouwens et al. (2014b)
Bouwens et al. (2011)−20.45+0.3−0.2−19.97 ± 0.34

−3.34 ± 0.36
−3.65+0.27−0.17−3.07 ± 0.26
−3.16 ± 0.68
−3.19+0.27−0.24−3.65+0.15−0.25−3.19 ± 0.30

−1.72 ± 0.65
−1.87+0.18−0.17−2.08+0.21−0.12−1.86 ± 0.27

outputoutput−3.22 ± 0.43
−1.91
± 0.32
Schechterparam−20.10 ± 0.52

apparent
surface
Schenker
et al. (2013)−20.44 apparent
−3.50
−1.94
(Φ*,surface
M*,α)comparewithcomparewithz∼9numberdensities
densities
numberobservation
observation
populate
This work−20.45 (fixed)−4.00 ± 0.15
−2.08 (fixed)
galaxies
Oesch et al. (2013)−18.8 ± 0.3−2.94 (fixed)−1.73 (fixed)
Bouwens et al. (2014a)−20.04 (fixed)−3.95−2.06 (fixed)
derive&the&derive&the&
mock
mock
best&ﬁt&parameter&
best&ﬁt&parameter&
Schechter parameters,
fit both the observed
lensing we simultaneously
source&plane
observation
observation
image&plane
HFF number counts and the UV luminosity function
data points
effectw/
glaficobtained in the previous studies. For our dropouts at z ∼ 6–7,
Bradley et al. (2012)−20.26+0.29
−0.34
+0.47
−0.35

−3.37+0.26
−0.29
+0.35
−0.32

−1.98+0.23
−0.22
+0.21
−0.24

fitting to observed
number counts→ best-fit param＋

Figure 13. 68% and 95% confidence level contours of Schechter parameteM∗ and α, for the UV luminosity functions at z ∼ 6–7 (black) and z ∼ 8 (rerespectively. The contours indicate our best-estimate results with our H
data and all of the previous measurements. The crosses denote the bestparameter values.

+0.39
−0.56

we compare our number counts of z ∼ 6–7 with the luminosity
function data points of z ∼ 7 in previous studies, assuming that
the UV luminosity function does not rapidly change in z ∼ 6–7.
We take the previous blank-field survey results from the studies
of CANDELS, HUDF09, HUDF12, ERS, and BORG/HIPPIES(Bouwens et al. 2014b), UltraVISTA+UKIDSS UDS (Bowler
et al. 2014), BoRG (Bradley et al. 2012), SDF+GOODS-N(Ouchi et al. 2009), and HUDF12/XDF+CANDELS (Oeschet al. 2013). We regard, φ∗ , and α as free parameters for
addM∗tothe fitting of number counts
at z ∼ 6–7 and z ∼ 8. Because theHFFstatistics of the z ∼ 9 luminosity function is poor, we choose
imageφ∗ for a free parameterand M∗ and α to be fixed to thebest-fit values of z ∼ 8. Maximizing the Poisson likelihood,
we obtain the best-fit parameters of (M∗ , log φ∗ (Mpc−3 ), α) =
+0.09
+0.10
(−20.45+0.1−0.2 , −3.30−0.20 , −1.94−0.10 ) for the z ∼ 6–7 dropout
+0.15
+0.21
candidates, (−20.45+0.3−0.2 , −3.65−0.25 , −2.08−0.12 ) for the z ∼ 8

HFF&image&Include all lensing effects!

＋＋

Number count(N vs mobs)

mock
observation

image&plane
image&plane
HFF&image&
HFF&image&complex lensing/selection
effects fully included!

Ishigaki et al. ApJ 799(2015)12

Implication for cosmic reionizationuminosity Densities ρUVrnal, 799:12 (21pp), 2015 January 20

Ishigak

PlanckSupport the rapid decrease of ρUV at z>8• confirm rapid decrease of ρUV at z>8• in tension with large τ from WMAP, butthough the rapid decrease of ρUV at z~9 is modest;see Derek’s talk)tension decreased in PlanckKawamata et al. ApJ 804(2015)103

Image plane approach to galaxy size
• traditional approach has been to measure galaxy
sizes by fitting normal (unlensed) Sersic profile
to lensed galaxy image and then correct for
magnification• we directly fit lensed and distorted Sersic profile
to observed galaxy image

Fit galaxy light profiles withfiles with
SIZEsize
MEA
plane approach
todistorted
galaxylensed andSérsicedImage
Sérsic profiles.
Kawamata et al. ApJ 804(2015)103

Plane

Source Plane
sourceplane

Our Method

Image Plane
image
plane
Fit galaxy light p

lensed and dist

Sersic param Observed Image(M, re, e, PA)
Profilelens effect
Lensed by
w/ glafic
Distorted
Undistorted
fittingorted
the mass map
Our Method
Sérsic profile

profileorted
profileSérsic profile

Observed Image
image
fitting
ProfileProfilefitting
Correct the fitting
galaxy inbest-fit
outputre & MUVHFF image
parameters
for magnification
Ordinary
ProfileUndistorted
Sérsic profile
fitting
Method

Im
Lense
the m

et al. (2012); and the brown open hexagons for z _ 9 – 10 LBGs by Holwerda
et al. (2014). The blue and green lines show the average relations for LBGs atz _ 4 and z _ 5 by Huang et al. (2013), and the yellow dashed line theaverage relation for Lyα emitters and LBGs at z ∼ 5.7–6.5 by Jiang et al.
(2013). The black dots represent the average relation for local spiral galaxies
by de Jong & Lacey (2000) and the black dotted line is for z _ 0.5 irregulargalaxies by Roche et al. (1996). The error bars in re are the 1σ standard
deviations while those in MUV correspond to the bin widths.
Astrophysical Journal, 804:103 (13pp), 2015 May 10

Kawamata et al. ApJ 804(2015)103

Evolution of galaxy sizes

Kawamata et al.

he variances in magniﬁcation among the eight public masss at the positions of the sample galaxies. This uncertainty isconverted into the uncertainty in radius and is quadally added to the statistical error in the average radius forsample, thus resulting in a reduction of the weightpared with the parallel-ﬁeld and Ono et al.’s (2013)
ples for which only the statistical error is considered. We
ude the z _ 12 object given in Ono et al. (2013). The data
erguson et al. (2004) are not included because their sample
udes brighter (5L z*3) galaxies. We ﬁnd that the averageof bright galaxies decreases from z _ 2.5 to 6–7, inement with previous results (e.g., Bouwens et al. 2004;
hi et al. 2008; Oesch et al. 2010; Grazian et al. 2012; Huangl. 2013; Ono et al. 2013), while the evolution between
6–7 and ∼8 is insigniﬁcant. We note that the average
us of our z ∼ 6–7 combined sample may be underestimated*Redshiftof the ofaveragesize of Lbrightgalaxies. The red
Figure 7. Redshift evolution of the half-light radius to virial radius ratio. The
auseFigure
all but6. one
are evolution
in the range(0.3–0.5)z=3.
−1.24
circles open
show theweighted-averageof our samples
combinedhe smallcirclesin Figure 6radii
indicate
the modeof thewith Onoerror bars show the 1σ standard error of the half-light radius. The shaded bands
et al. (2013)ʼs, while the black circles are for Ono et al.’s (2013). The data ofare predictions from the model by Mo et al. (1998) changing jd m d and m d
for
–8
LBGs
over
the
same
normaldistribution
of
r
z
_
4
e
Curtis-Lake et al. (2014) are taken from the arXiv version of their paper. The
within the range of 0.05–0.1. The red, green, and blue bands correspond toerror range
bars show
the 1σ standard
error.
inosityobtainedby Curtis-Lakeet al. (2014), who
jd m d  1.5, 1.0, 0.5. The upper edge of each band corresponds to m d  0.05
e adopted a non-parametric, curve-of-growth method toand the lower to m d  0.1.
suretwosizes.
valuesare populations,slightly but irregularsystematically) galaxygalaxies have
localTheir(z 1 0.5
er thantheslope
other similarly
measurements
exceptfor6z–8_galaxies.
4, leadinga steep
to thoseof z _
m to Plotted
concludethat thegalaxysize doesin Figure6 istypicalthe averagehalf-lightradiusnotof brightThen, the virial radius is calculated by
The reason
for this In theiﬁcantlyz _ as
4–8.a function((0.3 –evolvegalaxiesof redshift.
1) L z*3) over13
¬
ematicdifferenceis average
not clear,although
we ﬁndsamples
in our of thiscalculationof theradii
for the merged
2GM
vir
­­


• galaxy sizes evolve with ∝(1+z)• ratio of galaxy size to virial radius of host halo
is almost constant (~3.3%) over wide z range[host halo mass from abundance matching]Current status:
mass modelingof 4 clusters
are ongoingaccuracy:
image position
RMS ≲ 0.4”
(Kawamata et al. in
prep)Current status:
mass modelingof 4 clusters
are ongoing

38 sources
111 images

65 sources
173 images

accuracy:
image position
RMS ≲ 0.4”
(Kawamata et al. in
prep)Summary• image plane approach offers a robust route to
extract high-z info from cosmic telescopes• the publicly available software glafic provides
useful tools for this• interesting results on reionization and galaxy
sizes (from the analysis of A2744 only!)• analysis of more HFF clusters ongoing