Size—luminosity Relations and UV Luminosity Functionsat z~6—9 simultaneously derived
from the complete Hubble Frontier Fields data
Kawamata+17, arXiv:1710.07301

Ryota Kawamata
The University of Tokyo
With:
Masafumi Ishigaki, Kazuhiro Shimasaku, Masamune Oguri, Masami Ouchi, Shingo Tanigawa

1. Introduction

Galaxy Sizes Aﬀect the LF
Assumed galaxy sizes significantly affect detected fractions and the LF(e.g. Grazian+11, Bouwens+17)

z~6
w/ larger size
→low completeness→steeper LF

0.4(M ⇤ M )(↵+1)/ 10

w/ smaller size→high completeness→shallower LF
Bouwens+17

re-MUV Relations Assumed in LF Studies
Considerable difference between assumed re-MUV relations in LF studies

101z⇠67

re / kpc

Atek+15100

10Laporte+16
Livermore+16
Ishigaki+15
Bouwens+17
Ishigaki+17

110 2

re / L' 0 0.25
242220

18
MUV

16

14

12RK+17

re-MUV Relations Assumed in LF Studies
At bright magnitudes, the assumed re-MUV relations are consistent
with observations.

101z⇠6Shibuya+15

7re / kpc

Atek+15100

10Laporte+16
Livermore+16
Ishigaki+15Bouwens+17
Ishigaki+17

1

10 224222018
MUV

161412RK+17

re-MUV Relations Assumed in LF Studies
At faint magnitudes, re-MUV relation is suggested to be steeper.

101z⇠6

Shibuya+15
Kawamata+15

7re / kpc

Size measurements
at very faint magnitudes are needed
Atek+15100

10Laporte+16
Livermore+16
Ishigaki+15
Bouwens+17
Ishigaki+17

1

10 2

24222018
MUV

161412RK+17

2. Data

Hubble Frontier Fields

PI: J. Lotz

Deep and high-resolution observations by HST＋Strong gravitational lensing eﬀects by clusters
Abell 2744

MACS J0416

Abell S1063

MACS J1149

MACS J0717

Abell 370

STScI/NASA

3. Results & Discussion

re-MUV Relations at z~6-7
At faint magnitudes of MUV > -18:z⇠6101

8 → 91 galaxies
This Work (cluster)This Work (parallel)
Shibuya+15

7re / kpc

Shibuya+15
100

Cluster Fields(lensed)

10 1

10 2

Parallel Fields(non-lensed)
24

23

22

21

20

19

18 17
MUV

1615

14

13
RK+17

12

re-MUV Relations at z~8
At faint magnitudes of MUV > -18:

0 → 7 galaxies
This Work (cluster)This Work (parallel)
Shibuya+15z⇠8101

re / kpc

Shibuya+15
100

Cluster Fields(lensed)

10 1

10 2

Parallel Fields(non-lensed)
24

23

22

21

20

19

18 17
MUV

16

15

14

13RK+1712

re-MUV Relations at z~9
At faint magnitudes of MUV > -18:

This Work (cluster)This Work (parallel)
Holwerda+15

z⇠9101re / kpc

1 → 3 galaxies

Holwerda+15

100

Cluster Fields(lensed)

10 1

10 2

Parallel Fields(non-lensed)
24

23

22

21

20

19

18 17
MUV

1615

14

13RK+17

12

Incompleteness Eﬀectz⇠6re / kpc

1007Abell 2744
cluster field

Noin t D
th etis ec
ar teea d10 1

10 2
22

21

20

1918

17 16
MUV

151413

12

0.0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
2.4
2.7
3.0

log10 (Completeness)

Incompleteness effect: larger faint galaxies are not detected
Needs to be corrected for to obtain the intrinsic distribution

RK+17

Modeling the Intrinsic Distribution
Parametrize the intrinsic distribution using 5 parameters

Luminosity Function (M*, α)1011

Intrinsic Distr.
×Completeness1000
10erre // kpc
kpc

10re-MUV Relation(μ, σ, β)1010 111010 2224242322222120
20191818

MUVMUV17161615141413

Modeling the Observed Distribution
By multiplying the completeness, the observed distr. is modeled.

Observation

This Work“Observed”
Luminosity Function (M*, α)re / kpc

101“Observed”
re-MUV Relation
MLE (MCMC)
Observed Distr.
(μ, σ, β)101re / kpc

100

10 1

10 2

100

24

23

2120

1918

MUV

10 1

10 2

22242220

18

MUV1614171615

1413

Obtained re-MUV Relations at z~6-7The re-MUV relation is steeper than those at bright magnitudes.

z⇠6re / kpc

101This Work
This Work
Shibuya+15

7100

10 1

10 2

24232221201918 17MUV

1615

14

13RK+1712

Obtained re-MUV Relations at z~8The re-MUV relation is not well determined due to the small sample.

re / kpc

This WorkThis Work
Shibuya+15z⇠8101

100

10 1

10 2

2423222120

1918 17MUV

1615

1413RK+1712

Obtained re-MUV Relations at z~9The re-MUV relation is not well determined due to the small sample.

re / kpc

This Work
This Work
Holwerda+15z⇠9101100

10 1

10 2

24232221

201918 17MUV

1615

1413RK+1712

α—β Correlation at z~6–7
Strongly correlated slopes of the re-MUV relation and luminosity function
A steeper re-MUV relation and a shallower LF.
Shallower LF
1.2

L-Galaxies
Meraxes
Atek+15
Bouwens+15

1.4

Laporte+16
Livermore+16
Ishigaki+17
Bouwens+17

1.8This Work

95%

2.0

68%

↵

1.6

2.2
2.4

0.0

0.1

0.2

0.3

0.4

z⇠6

0.5

0.6

7
0.7

RK+17

Steeper re-MUV relation

α—β Correlation at z~8These two parameters are not well constrained.
Previous studies are within our 95% confidence contour.
Shallower LF
0.5

L-Galaxies
Meraxes
Bouwens+15
Laporte+16
Livermore+16
Ishigaki+17

1.0
1.5
↵

68%

2.0

95%

2.5

This Work%
5
9

3.0
3.5
4.0

1.0

0.5

0.0

0.5z⇠81.0RK+17

Steeper re-MUV relation

α—β Correlation at z~9These two parameters are not well constrained.
Previous studies are within our 95% confidence contour.
Shallower LF
0.0

L-Galaxies
Meraxes

Laporte+16
Ishigaki+170.568%

1.568%↵1.0This Work2.095%

2.5
0.0

0.5

1.0

1.5z⇠92.0

2.5RK+17

Steeper re-MUV relation

α—β Correlation at z~9These two parameters are not well constrained.
Previous studies are within our 95% confidence contour.

Large uncertainties in UV luminosity densities
Shallower
LF discussions of cosmic reionization!
and hence
0.0
0.5

L-Galaxies
Meraxes

100

Laporte+16
Ishigaki+17

Luminosity Function at z~6–7

10 1
N / Mpc3/ mag

α = -2.0468%

10 2

1.5 10 3

α = -1.69

10 4This WorkUV luminosity
95%density

2.068%↵1.010 5

2.5 10 6 24
0.0

220.5

2018
MUV

1.0161.514z⇠92.02.5

Steeper re-MUV relation

Modeling the Steep re-MUV Relation at z~6–7

re ∝ Lβ31+3γ
re ∝ Mhalo

Mstar

Analytical Model

Abundance Matching

Mo+98

Behroozi+13✓◆
1.678 jdrvir
re = pmd2
jd/ Mhalo
md
jd/md: disk-to-halo ratioof specific angularmomentumL
Mstar—L relation
Gonzalez+11

Mstar = f(Mhalo)

log10=✓

MstarM◆

39.6 + 1.7 ⇥ log10✓L1500erg s 1 Hz 1

◆Modeling the Steep re-MUV Relation at z~6–7
The model reproduces the slope when γ=0.15．
The fraction of specific angular momentum in the disk may be smaller infainter galaxies.

re / kpc

101

z⇠6This WorkRL Model

71.678re = p2

100

10 2

20

18

MUV

16

◆

rvir

jd/md: disk-to-halo ratioof specific angularmomentum= 0.1522

jd
md

jd/ Mhalo
md=010 1✓

14

12RK+17

Summary
We measure the sizes of ~334, 61, and 37 faint galaxies atz~6–7, 8, and 9.
Simultaneously derive the size–luminosity (RL) relations andUV luminosity functions (LF) corrected for incompletenessA steep RL relation and shallow LF at z~6-7, while those atz~8 and 9 are not well determined
The RL relations assumed in previous studies are too shallow.
The steep RL relation can be reproduced by a model in whichsmaller galaxies have lower specific angular momenta.