Full-Data Results of Hubble Frontier Fields: UV Luminosity Functions at $z\sim6-10$ and a Consistent Picture of Cosmic Reionization

TL;DR

This study presents deep UV luminosity functions at redshifts 6-10 from Hubble Frontier Fields data, providing insights into galaxy evolution and cosmic reionization consistent with Planck observations.

Contribution

It offers the first comprehensive UV luminosity functions at z~6-10 including lensing effects, and explores reionization scenarios compatible with multiple observational constraints.

Findings

UV luminosity functions have steep faint-end slopes, α~ -2, at z~6-8.

Luminosity density decline is non-accelerated beyond z~8 for M_trunc=-15.

Reionization scenarios with specific escape fractions and faint limits are consistent with observations.

Abstract

We present UV luminosity functions of dropout galaxies at $z\sim6-10$ with the complete Hubble Frontier Fields data. We obtain a catalog of $\sim450$ dropout-galaxy candidates (350, 66, and 40 at $z\sim6-7$, 8, and 9, respectively), whose UV absolute magnitudes reach $\sim-14$ mag, $\sim2$ mag deeper than the Hubble Ultra Deep Field detection limits. We carefully evaluate number densities of the dropout galaxies by Monte-Carlo simulations, including all lensing effects such as magnification, distortion, and multiplication of images as well as detection completeness and contamination effects in a self-consistent manner. We find that UV luminosity functions at $z\sim6-8$ have steep faint-end slopes, $\alpha\sim-2$, and likely steeper slopes, $\alpha\lesssim-2$ at $z\sim9-10$. We also find that the evolution of UV luminosity densities shows a non-accelerated decline beyond $z\sim8$ in the case of $M_\mathrm{trunc}=-15$, while an accelerated in the case of $M_\mathrm{trunc}=-17$. We examine whether our results are consistent with the Thomson scattering optical depth from the Planck satellite and the ionized hydrogen fraction $Q_\mathrm{HII}$ at $z\lesssim7$ based on the standard analytic reionization model. We find that there exist reionizaiton scenarios that consistently explain all the observational measurements with the allowed parameters of $f_{\rm esc}=0.17^{+0.07}_{-0.03}$ and $M_\mathrm{trunc}>-14.0$ for $\log\xi_\mathrm{ion}/[\mathrm{erg}^{-1}\ \mathrm{Hz}]=25.34$, where $f_{\rm esc}$ is the escape fraction, $M_\mathrm{trunc}$ is the faint limit of the UV luminosity function, and $\xi_\mathrm{ion}$ is the conversion factor of the UV luminosity to the ionizing photon emission rate. The length of the reionization period is estimated to be $\Delta z=3.9^{+2.0}_{-1.6}$ (for $0.1<Q_\mathrm{HII}<0.99$), consistent with the recent estimate from Planck.

Tables

Table 1. Table 1 Observational properties and the numbers of high- z 𝑧 z galaxy candidates of the HFF Data

Field	Depth ($H_{160}$)aaThe depths are defined with a $0\stackrel{\prime \prime }{.}35$-diameter aperture.	AreabbThe area of each image is reduced by the masking near the bright stars.	Number of Galaxies
	($5\sigma$ limit mag)	(arcmin2)	$z\sim 6-7$	$z\sim 8$	$z\sim 9$	$z\sim 10$
Abell2744 Cluster	28.88	4.75 (1.52ccThe survey area in the source plane at $z=7$.)	22	10	3	0
Abell2744 Parallel	29.11	4.32	30	4	4	0
MACS0416 Cluster	28.84	4.73 (2.00ccThe survey area in the source plane at $z=7$.)	25	5	3	0
MACS0416 Parallel	29.30	4.78	23	9	6	0
MACS0717 Cluster	28.56	4.58 (0.75ccThe survey area in the source plane at $z=7$.)	22	0	0	0
MACS0717 Parallel	28.88	4.25	41	6	3	0
MACS1149 Cluster	28.87	4.66 (1.32ccThe survey area in the source plane at $z=7$.)	41	2	4	0
MACS1149 Parallel	29.04	4.72	37	10	3	0
AbellS1063 Cluster	28.85	4.25 (0.98ccThe survey area in the source plane at $z=7$.)	23	4	2	0
AbellS1063 Parallel	29.12	4.36	39	6	3	0
Abell370 Cluster	28.65	4.14 (0.73ccThe survey area in the source plane at $z=7$.)	7	6	2	0
Abell370 Parallel	29.14	4.31	40	3	7	0
Total			350	66	40	0

Table 2. Table 2 5 ​ σ 5 𝜎 5\sigma limiting magnitudes

Field	$B_{435}$	$V_{606}$	$i_{814}$	$Y_{105}$	$J_{125}$	$J{H}_{140}$	$H_{160}$
Abell2744 Cluster	28.72	28.83	28.94	29.20	28.87	28.92	28.88
Abell2744 Parallel	28.84	29.20	29.03	29.39	29.00	29.03	29.11
MACS0416 Cluster	28.74	29.08	28.96	29.11	28.85	28.87	28.84
MACS0416 Parallel	28.65	28.92	29.01	29.45	29.22	29.26	29.30
MACS0717 Cluster	28.70	28.74	28.76	28.91	28.61	28.70	28.56
MACS0717 Parallel	28.96	29.00	29.01	29.16	28.94	28.95	28.88
MACS1149 Cluster	28.57	28.89	28.94	29.17	28.81	28.73	28.87
MACS1149 Parallel	28.50	28.83	28.90	29.35	28.98	29.06	29.04
AbellS1063 Cluster	28.69	28.86	28.90	29.19	28.87	28.98	28.85
AbellS1063 Parallel	28.87	29.66	29.09	29.43	29.06	29.19	29.12
Abell370 Cluster	28.64	28.78	28.86	29.00	28.69	28.74	28.65
Abell370 Parallel	28.65	28.90	29.07	29.45	29.00	29.01	29.14

Table 3. Table 3 Best-fit Schechter parameters of luminosity functions

Reference	$M_{\ast }$	$\log {\varphi }_{\ast }$ [Mpc-3]	$\alpha$
$z\sim 6-7$
This Work	$-{20.89}_{-0.13}^{+0.17}$	$-{3.78}_{-0.15}^{+0.15}$	$-{2.15}_{-0.06}^{+0.08}$
Atek et al. (2015a)	$-{20.89}_{-0.72}^{+0.60}$	$-{3.54}_{-0.45}^{+0.48}$	$-{2.04}_{-0.13}^{+0.17}$
Bouwens et al. (2015)	$-20.87\pm 0.26$	$-{3.53}_{-0.23}^{+0.24}$	$-2.06\pm 0.13$
Laporte et al. (2016)	$-{20.33}_{-0.47}^{+0.37}$	$-{3.43}_{-0.15}^{+0.12}$	$-{1.91}_{-0.27}^{+0.26}$
Livermore et al. (2017)	$-{20.800}_{-0.049}^{+0.058}$	$-{3.667}_{-0.041}^{+0.044}$	$-{2.07}_{-0.04}^{+0.04}$
Kawamata et al. (2017)	$-{20.73}_{-0.81}^{+0.46}$	—	$-{1.86}_{-0.18}^{+0.17}$
$z\sim 8$
This Work	$-{20.35}_{-0.30}^{+0.20}$	$-{3.60}_{-0.30}^{+0.15}$	$-{1.96}_{-0.15}^{+0.18}$
Bradley et al. (2012)	$-{20.26}_{-0.34}^{+0.29}$	$-{3.37}_{-0.29}^{+0.26}$	$-{1.98}_{-0.22}^{+0.23}$
Bouwens et al. (2015)	$-20.63\pm 0.36$	$-3.68\pm 0.32$	$-2.02\pm 0.23$
Laporte et al. (2016)	$-{20.32}_{-0.26}^{+0.49}$	$-{3.52}_{-0.44}^{+0.58}$	$-{1.95}_{-0.40}^{+0.43}$
Livermore et al. (2017)	$-{20.742}_{-0.152}^{+0.195}$	$-{3.784}_{-0.145}^{+0.145}$	$-{2.02}_{-0.07}^{+0.08}$
Kawamata et al. (2017)	$-20.73$ (fixed)	—	$-{1.80}_{-0.30}^{+0.22}$
$z\sim 9$
This Work	$-{51.39}_{-44.73}^{+18.51}$	$-{19.42}_{-24.15}^{+7.73}$	$-{2.22}_{-0.17}^{+0.26}$
This Work	$-20.35$ (fixed)	$-{3.88}_{-0.12}^{+0.08}$	$-1.96$ (fixed)
Oesch et al. (2013)	$-18.8\pm 0.3$	$-2.94$ (fixed)	$-1.73$ (fixed)
Laporte et al. (2016)	$-20.45$ (fixed)	$-{4.15}_{-0.24}^{+0.15}$	$-{2.17}_{-0.43}^{+0.41}$
McLeod et al. (2016)	$-20.1$ (fixed)	$-{3.62}_{-0.10}^{+0.08}$	$-2.02$ (fixed)
Kawamata et al. (2017)	$-20.73$ (fixed)	—	$-{1.59}_{-0.18}^{+0.19}$
$z\sim 10$
This Work	$-{59.71}_{-9.61}^{+29.90}$	$-{35.60}_{-5.93}^{+23.73}$	$-{2.93}_{-0.41}^{+0.83}$
This Work	$-20.35$ (fixed)	$-{4.60}_{-0.22}^{+0.14}$	$-1.96$ (fixed)
Oesch et al. (2014)	$-20.12$ (fixed)	$-4.27\pm 0.21$	$-2.02$ (fixed
Bouwens et al. (2015)	$-20.92$ (fixed)	$-{5.10}_{-0.20}^{+0.18}$	$-2.27$ (fixed)
McLeod et al. (2016)	$-20.1$ (fixed)	$-{3.90}_{-0.20}^{+0.13}$	$-2.02$ (fixed)

Table 4. Table 4 Dropout candidates at z ∼ 6 − 7 similar-to 𝑧 6 7 z\sim 6-7

ID	R.A. (J2000)	Dec (J2000)	$i_{814}-Y_{105}$	$Y_{105}-J_{125}$	$J_{125}$aaTotal magnitudes $m_{\mathrm{tot}}$ estimated with the aperture correction $m_{\mathrm{tot}}=m_{\mathrm{AP}}-0.82$.	$\mu$bbMagnifications calculated with mass models in Kawamata et al. (2017).	Photo-$z$	ReferenceccReferences. (1)Atek et al. (2014), (2)Atek et al. (2015a), (3)Coe et al. (2015), (4)Laporte et al. (2014), (5)Laporte et al. (2015), (6)Laporte et al. (2016), (7)Livermore et al. (2017), (8)McLeod et al. (2016), (9)Oesch et al. (2015) (10)Zheng et al. (2014), (11)Zitrin et al. (2014)
Abell2744 Cluster
HFF1C-$2251$-$4556$	$3.593804$	$-30.415447$	$2.68\pm 0.36$	$0.05\pm 0.05$	$26.10\pm 0.04$	$3.64$	${6.62}_{-0.75}^{+0.75}$	(1), (2), (7)
HFF1C-$1695$-$4527$	$3.570654$	$-30.414659$	$1.33\pm 0.10$	$0.11\pm 0.05$	$26.22\pm 0.04$	$1.47$	${6.00}_{-0.69}^{+0.69}$	(1), (2)
HFF1C-$2549$-$3119$	$3.606222$	$-30.386644$	$1.07\pm 0.08$	$0.08\pm 0.05$	$26.26\pm 0.04$	$1.55$	${5.80}_{-0.67}^{+0.67}$	(1), (2), (7)
HFF1C-$1930$-$4181$	$3.580452$	$-30.405043$	$>2.36$	$0.17\pm 0.09$	$26.61\pm 0.07$	$4.47$	${6.79}_{-0.76}^{+0.76}$	(1), (2), (7)
HFF1C-$2516$-$4570$	$3.604865$	$-30.415839$	$0.92\pm 0.14$	$0.06\pm 0.08$	$26.67\pm 0.06$	$2.84$	${5.64}_{-0.65}^{+0.65}$	$\cdots$
HFF1C-$2348$-$3454$	$3.597834$	$-30.395961$	$>2.13$	$0.27\pm 0.11$	$26.79\pm 0.08$	$3.31$	${7.00}_{-0.78}^{+0.78}$	(2), (7)
HFF1C-$2178$-$2458$	$3.590761$	$-30.379408$	$0.96\pm 0.14$	$-0.16\pm 0.10$	$27.07\pm 0.08$	$1.68$	${5.84}_{-0.67}^{+0.67}$	(7)
HFF1C-$2047$-$3526$	$3.585321$	$-30.397958$	$>1.83$	$0.13\pm 0.15$	$27.19\pm 0.11$	$3.23$	${6.75}_{-0.76}^{+0.76}$	(2), (7), (10)
HFF1C-$2425$-$4143$	$3.601072$	$-30.403991$	$1.11\pm 0.24$	$0.00\pm 0.12$	$27.27\pm 0.10$	$3.74$	${5.95}_{-0.68}^{+0.68}$	(1), (2), (7)
HFF1C-$2414$-$4370$	$3.600619$	$-30.410296$	$>1.97$	$-0.06\pm 0.13$	$27.29\pm 0.10$	$11.88$	${6.39}_{-0.72}^{+0.72}$	(2), (7)
HFF1C-$2482$-$2595$	$3.603426$	$-30.383219$	$0.87\pm 0.14$	$-0.13\pm 0.12$	$27.30\pm 0.10$	$1.48$	${5.78}_{-0.66}^{+0.66}$	(2), (7)
HFF1C-$2477$-$4372$	$3.603214$	$-30.410350$	$>1.89$	$-0.03\pm 0.14$	$27.34\pm 0.11$	$4.02$	${6.29}_{-0.71}^{+0.71}$	(1), (2), (7), (10)
HFF1C-$2230$-$4479$	$3.592944$	$-30.413328$	$1.44\pm 0.33$	$-0.09\pm 0.14$	$27.36\pm 0.11$	$6.80$	${6.10}_{-0.70}^{+0.70}$	(2), (7)
HFF1C-$1845$-$3107$	$3.576889$	$-30.386329$	$>1.45$	$0.13\pm 0.19$	$27.46\pm 0.14$	$8.01$	${6.11}_{-0.70}^{+0.82}$	(2), (7)
HFF1C-$2040$-$4471$	$3.585016$	$-30.413084$	$0.86\pm 0.17$	$-0.24\pm 0.15$	$27.46\pm 0.13$	$2.95$	${5.68}_{-4.73}^{+0.65}$	$\cdots$
HFF1C-$1911$-$4242$	$3.579635$	$-30.406723$	$1.06\pm 0.37$	$0.08\pm 0.20$	$27.53\pm 0.16$	$3.45$	${5.58}_{-5.25}^{+0.64}$	$\cdots$
HFF1C-$2616$-$3070$	$3.609003$	$-30.385283$	$1.35\pm 0.29$	$-0.07\pm 0.15$	$27.57\pm 0.12$	$1.44$	${6.05}_{-0.69}^{+0.69}$	(2), (7)
HFF1C-$2509$-$4337$	$3.604563$	$-30.409364$	$1.43\pm 0.55$	$0.12\pm 0.19$	$27.63\pm 0.14$	$3.12$	${6.08}_{-0.75}^{+0.78}$	(2), (7)
HFF1C-$2274$-$2562$	$3.594752$	$-30.382305$	$0.84\pm 0.23$	$-0.17\pm 0.18$	$27.73\pm 0.15$	$1.85$	${0.06}_{-0.06}^{+3.53}$	$\cdots$
HFF1C-$2364$-$4454$	$3.598515$	$-30.412612$	$>1.18$	$0.16\pm 0.27$	$27.94\pm 0.19$	$15.56$	${6.58}_{-1.21}^{+0.80}$	(7)
HFF1C-$1991$-$3429$	$3.582960$	$-30.395262$	$>0.90$	$0.14\pm 0.28$	$27.97\pm 0.21$	$9.25$	${1.28}_{-1.07}^{+5.53}$	(7)
HFF1C-$2172$-$2471$	$3.590518$	$-30.379763$	$>1.36$	$-0.02\pm 0.26$	$28.10\pm 0.21$	$1.73$	${6.11}_{-1.11}^{+0.82}$	(2), (7)
Abell2744 Parallel
HFF1P-$5395$-$1452$	$3.474802$	$-30.362578$	$>2.36$	$0.44\pm 0.08$	$26.64\pm 0.06$	$\cdots$	${7.30}_{-0.81}^{+0.81}$	$\cdots$
HFF1P-$5292$-$4021$	$3.470509$	$-30.400605$	$0.83\pm 0.14$	$0.10\pm 0.09$	$26.96\pm 0.07$	$\cdots$	${5.76}_{-0.66}^{+0.66}$	$\cdots$
HFF1P-$5793$-$1536$	$3.491387$	$-30.364890$	$>2.19$	$0.42\pm 0.11$	$26.97\pm 0.07$	$\cdots$	${7.33}_{-0.82}^{+0.82}$	$\cdots$
HFF1P-$5398$-$1451$	$3.474918$	$-30.362542$	$>1.86$	$0.60\pm 0.12$	$26.98\pm 0.08$	$\cdots$	${7.50}_{-1.52}^{+0.83}$	$\cdots$
HFF1P-$5535$-$2162$	$3.480642$	$-30.371175$	$1.79\pm 0.34$	$-0.05\pm 0.09$	$27.05\pm 0.07$	$\cdots$	${6.32}_{-0.72}^{+0.72}$	$\cdots$
HFF1P-$5701$-$1517$	$3.487575$	$-30.364380$	$1.25\pm 0.27$	$0.32\pm 0.13$	$27.19\pm 0.09$	$\cdots$	${5.65}_{-4.76}^{+0.65}$	$\cdots$
HFF1P-$5734$-$3406$	$3.488924$	$-30.394630$	$>1.63$	$0.26\pm 0.13$	$27.24\pm 0.09$	$\cdots$	${6.75}_{-0.79}^{+0.76}$	$\cdots$
HFF1P-$5581$-$2176$	$3.482550$	$-30.371559$	$1.19\pm 0.28$	$0.15\pm 0.11$	$27.25\pm 0.09$	$\cdots$	${5.77}_{-0.93}^{+0.66}$	$\cdots$
HFF1P-$5615$-$3497$	$3.483960$	$-30.397152$	$1.72\pm 0.42$	$-0.00\pm 0.12$	$27.32\pm 0.10$	$\cdots$	${6.26}_{-0.71}^{+0.71}$	$\cdots$
HFF1P-$5221$-$3488$	$3.467582$	$-30.396908$	$>2.01$	$0.13\pm 0.13$	$27.36\pm 0.10$	$\cdots$	${6.75}_{-0.76}^{+0.76}$	$\cdots$
HFF1P-$5748$-$3583$	$3.489520$	$-30.399528$	$>1.68$	$0.05\pm 0.14$	$27.39\pm 0.11$	$\cdots$	${6.64}_{-0.75}^{+0.75}$	$\cdots$
HFF1P-$5210$-$3156$	$3.467097$	$-30.387686$	$1.30\pm 0.25$	$-0.26\pm 0.12$	$27.41\pm 0.10$	$\cdots$	${6.06}_{-0.69}^{+0.69}$	$\cdots$
HFF1P-$5185$-$3398$	$3.466056$	$-30.394409$	$1.10\pm 0.26$	$-0.02\pm 0.15$	$27.54\pm 0.12$	$\cdots$	${5.93}_{-0.68}^{+0.68}$	$\cdots$
HFF1P-$5573$-$2343$	$3.482238$	$-30.376221$	$0.94\pm 0.33$	$0.15\pm 0.17$	$27.65\pm 0.13$	$\cdots$	${1.26}_{-1.08}^{+3.73}$	$\cdots$
HFF1P-$4940$-$1588$	$3.455844$	$-30.366359$	$1.04\pm 0.37$	$-0.03\pm 0.19$	$27.79\pm 0.15$	$\cdots$	${5.60}_{-4.69}^{+0.65}$	$\cdots$
HFF1P-$5327$-$2576$	$3.471985$	$-30.382683$	$>1.23$	$0.26\pm 0.21$	$27.84\pm 0.16$	$\cdots$	${6.66}_{-2.06}^{+0.82}$	$\cdots$
HFF1P-$5054$-$1587$	$3.460587$	$-30.366320$	$0.94\pm 0.39$	$0.03\pm 0.21$	$27.87\pm 0.16$	$\cdots$	${5.76}_{-1.30}^{+0.67}$	$\cdots$
HFF1P-$5587$-$3058$	$3.482833$	$-30.384961$	$0.97\pm 0.45$	$0.13\pm 0.20$	$27.87\pm 0.16$	$\cdots$	${1.08}_{-0.92}^{+5.09}$	$\cdots$
HFF1P-$5687$-$3584$	$3.486988$	$-30.399579$	$0.98\pm 0.41$	$-0.08\pm 0.21$	$27.88\pm 0.17$	$\cdots$	${5.89}_{-1.22}^{+0.68}$	$\cdots$
HFF1P-$5638$-$2369$	$3.484920$	$-30.376917$	$1.20\pm 0.50$	$0.11\pm 0.21$	$27.90\pm 0.16$	$\cdots$	${5.95}_{-0.74}^{+0.71}$	$\cdots$
HFF1P-$5691$-$3514$	$3.487148$	$-30.397615$	$1.04\pm 0.40$	$-0.19\pm 0.21$	$27.90\pm 0.17$	$\cdots$	${4.15}_{-4.04}^{+1.95}$	$\cdots$
HFF1P-$5429$-$2542$	$3.476220$	$-30.381741$	$>1.47$	$-0.12\pm 0.21$	$27.98\pm 0.17$	$\cdots$	${5.79}_{-5.54}^{+0.80}$	$\cdots$
HFF1P-$5509$-$1488$	$3.479545$	$-30.363580$	$>1.35$	$0.06\pm 0.25$	$28.03\pm 0.20$	$\cdots$	${4.68}_{-4.28}^{+0.92}$	$\cdots$
HFF1P-$5453$-$3095$	$3.477238$	$-30.385998$	$>1.33$	$-0.19\pm 0.22$	$28.08\pm 0.19$	$\cdots$	${6.46}_{-0.73}^{+0.73}$	$\cdots$
HFF1P-$4938$-$2422$	$3.455763$	$-30.378410$	$>1.18$	$0.08\pm 0.26$	$28.12\pm 0.20$	$\cdots$	${6.05}_{-5.19}^{+1.31}$	$\cdots$
HFF1P-$5381$-$3517$	$3.474216$	$-30.397703$	$>1.09$	$0.14\pm 0.27$	$28.12\pm 0.21$	$\cdots$	${6.30}_{-5.76}^{+0.92}$	$\cdots$
HFF1P-$5566$-$3224$	$3.481928$	$-30.389557$	$>1.36$	$-0.26\pm 0.23$	$28.12\pm 0.20$	$\cdots$	${6.17}_{-0.77}^{+0.70}$	$\cdots$
HFF1P-$5467$-$2421$	$3.477807$	$-30.378362$	$>1.05$	$0.15\pm 0.26$	$28.13\pm 0.20$	$\cdots$	${5.75}_{-5.13}^{+1.16}$	$\cdots$
HFF1P-$5445$-$2223$	$3.476915$	$-30.372888$	$>1.22$	$-0.04\pm 0.25$	$28.16\pm 0.20$	$\cdots$	${5.78}_{-5.17}^{+1.00}$	$\cdots$
HFF1P-$5588$-$2288$	$3.482859$	$-30.374682$	$0.91\pm 0.49$	$0.02\pm 0.27$	$28.24\pm 0.22$	$\cdots$	${1.09}_{-1.03}^{+3.70}$	$\cdots$
MACS0416 Cluster
HFF2C-$0949$-$5187$	$64.039545$	$-24.088540$	$1.08\pm 0.11$	$-0.01\pm 0.05$	$26.37\pm 0.04$	$1.54$	${5.88}_{-0.67}^{+0.67}$	(7)
HFF2C-$1148$-$3434$	$64.047846$	$-24.062066$	$1.63\pm 0.13$	$-0.16\pm 0.06$	$26.64\pm 0.05$	$12.31$	${6.23}_{-0.71}^{+0.71}$	(3), (7)
HFF2C-$1131$-$3400$	$64.047138$	$-24.061138$	$0.99\pm 0.11$	$-0.06\pm 0.08$	$26.93\pm 0.07$	$9.89$	${5.88}_{-0.67}^{+0.67}$	(7)
HFF2C-$0899$-$3404$	$64.037485$	$-24.061238$	$1.26\pm 0.22$	$-0.01\pm 0.11$	$27.05\pm 0.09$	$3.21$	${6.04}_{-0.69}^{+0.69}$	(3), (7)
HFF2C-$0828$-$5386$	$64.034514$	$-24.094074$	$1.08\pm 0.23$	$0.04\pm 0.15$	$27.22\pm 0.12$	$1.50$	${5.90}_{-0.68}^{+0.68}$	(7)
HFF2C-$0960$-$3425$	$64.040012$	$-24.061830$	$1.74\pm 0.43$	$0.00\pm 0.14$	$27.32\pm 0.11$	$9.53$	${6.28}_{-0.71}^{+0.71}$	(3), (7)
HFF2C-$1147$-$4580$	$64.047818$	$-24.082801$	$>1.85$	$0.23\pm 0.13$	$27.38\pm 0.10$	$1.41$	${6.75}_{-0.76}^{+0.76}$	(3), (7)
HFF2C-$1220$-$3595$	$64.050865$	$-24.066531$	$1.04\pm 0.19$	$-0.07\pm 0.12$	$27.38\pm 0.09$	$3.63$	${5.92}_{-0.68}^{+0.68}$	(3), (7)
HFF2C-$1156$-$3446$	$64.048176$	$-24.062404$	$1.55\pm 0.24$	$-0.18\pm 0.12$	$27.41\pm 0.10$	$15.60$	${6.16}_{-0.70}^{+0.70}$	(7)
HFF2C-$1181$-$3480$	$64.049226$	$-24.063349$	$1.76\pm 0.29$	$-0.22\pm 0.13$	$27.46\pm 0.11$	$26.13$	${6.27}_{-0.71}^{+0.71}$	(7)
HFF2C-$0768$-$5032$	$64.032020$	$-24.084227$	$0.82\pm 0.26$	$-0.01\pm 0.20$	$27.47\pm 0.16$	$7.55$	${5.47}_{-5.10}^{+0.63}$	$\cdots$
HFF2C-$0743$-$3348$	$64.030960$	$-24.059683$	$>1.49$	$0.32\pm 0.16$	$27.52\pm 0.11$	$1.75$	${1.39}_{-0.62}^{+5.98}$	$\cdots$
HFF2C-$1030$-$3258$	$64.042941$	$-24.057182$	$0.87\pm 0.21$	$-0.16\pm 0.16$	$27.52\pm 0.14$	$2.77$	${5.69}_{-0.66}^{+0.66}$	(7)
HFF2C-$0778$-$3204$	$64.032450$	$-24.055671$	$1.14\pm 0.31$	$0.03\pm 0.14$	$27.53\pm 0.11$	$1.67$	${5.97}_{-0.68}^{+0.68}$	(7)
HFF2C-$1105$-$5392$	$64.046063$	$-24.094241$	$>1.71$	$0.03\pm 0.15$	$27.53\pm 0.11$	$1.23$	${6.50}_{-0.74}^{+0.74}$	(7)
HFF2C-$0829$-$5229$	$64.034556$	$-24.089700$	$1.22\pm 0.32$	$-0.03\pm 0.20$	$27.54\pm 0.16$	$1.79$	${5.96}_{-0.91}^{+0.68}$	(3), (7)
HFF2C-$0856$-$4435$	$64.035702$	$-24.078765$	$1.07\pm 0.42$	$0.16\pm 0.24$	$27.59\pm 0.18$	$14.19$	${1.09}_{-0.83}^{+5.11}$	$\cdots$
HFF2C-$1045$-$3324$	$64.043574$	$-24.059001$	$1.36\pm 0.33$	$-0.19\pm 0.17$	$27.59\pm 0.15$	$4.86$	${6.06}_{-0.69}^{+0.69}$	$\cdots$
HFF2C-$0933$-$3382$	$64.038890$	$-24.060637$	$>1.68$	$0.00\pm 0.20$	$27.66\pm 0.16$	$3.72$	${6.41}_{-0.73}^{+0.73}$	(7)
HFF2C-$1051$-$5500$	$64.043800$	$-24.097245$	$1.07\pm 0.42$	$0.17\pm 0.18$	$27.71\pm 0.13$	$1.23$	${1.29}_{-0.85}^{+5.05}$	(7)
HFF2C-$1330$-$3565$	$64.055425$	$-24.065698$	$0.90\pm 0.26$	$0.00\pm 0.17$	$27.77\pm 0.13$	$2.30$	${5.75}_{-1.07}^{+0.66}$	$\cdots$
HFF2C-$1225$-$3594$	$64.051077$	$-24.066512$	$1.29\pm 0.36$	$0.02\pm 0.17$	$27.78\pm 0.13$	$3.53$	${6.03}_{-0.69}^{+0.69}$	(7)
HFF2C-$1308$-$3431$	$64.054524$	$-24.061998$	$0.96\pm 0.21$	$-0.28\pm 0.19$	$27.89\pm 0.16$	$4.17$	${5.75}_{-0.66}^{+0.66}$	(7)
HFF2C-$0771$-$3205$	$64.032155$	$-24.055706$	$1.03\pm 0.32$	$-0.31\pm 0.20$	$27.99\pm 0.18$	$1.69$	${5.82}_{-0.92}^{+0.67}$	(7)
HFF2C-$0924$-$5133$	$64.038512$	$-24.087045$	$>1.47$	$-0.36\pm 0.23$	$28.16\pm 0.20$	$1.71$	${6.24}_{-0.95}^{+0.71}$	(7)
MACS0416 Parallel
HFF2P-$3165$-$7300$	$64.131878$	$-24.125007$	$>2.46$	$0.61\pm 0.06$	$26.34\pm 0.03$	$\cdots$	${7.52}_{-0.84}^{+0.84}$	$\cdots$
HFF2P-$2773$-$7107$	$64.115583$	$-24.119644$	$2.28\pm 0.27$	$0.11\pm 0.04$	$26.38\pm 0.03$	$\cdots$	${6.43}_{-0.73}^{+0.73}$	$\cdots$
HFF2P-$3552$-$5571$	$64.148027$	$-24.099201$	$>2.41$	$0.51\pm 0.06$	$26.52\pm 0.04$	$\cdots$	${6.32}_{-0.72}^{+0.98}$	$\cdots$
HFF2P-$2912$-$7330$	$64.121367$	$-24.125856$	$>2.02$	$0.69\pm 0.11$	$26.93\pm 0.06$	$\cdots$	${7.62}_{-0.84}^{+0.84}$	$\cdots$
HFF2P-$3660$-$5583$	$64.152506$	$-24.099529$	$0.91\pm 0.12$	$-0.09\pm 0.09$	$27.01\pm 0.07$	$\cdots$	${5.81}_{-0.67}^{+0.67}$	$\cdots$
HFF2P-$3011$-$7264$	$64.125486$	$-24.124020$	$1.07\pm 0.20$	$-0.02\pm 0.08$	$27.13\pm 0.07$	$\cdots$	${5.92}_{-0.68}^{+0.68}$	$\cdots$
HFF2P-$3514$-$6214$	$64.146433$	$-24.105965$	$2.18\pm 0.54$	$0.00\pm 0.09$	$27.15\pm 0.07$	$\cdots$	${6.36}_{-0.72}^{+0.72}$	$\cdots$
HFF2P-$3809$-$6184$	$64.158736$	$-24.105133$	$0.92\pm 0.15$	$0.01\pm 0.10$	$27.16\pm 0.08$	$\cdots$	${5.77}_{-0.66}^{+0.66}$	$\cdots$
HFF2P-$3597$-$6014$	$64.149901$	$-24.100414$	$>1.80$	$0.38\pm 0.12$	$27.25\pm 0.08$	$\cdots$	${7.20}_{-0.80}^{+0.80}$	$\cdots$
HFF2P-$2796$-$7156$	$64.116513$	$-24.121026$	$1.17\pm 0.31$	$0.07\pm 0.14$	$27.64\pm 0.11$	$\cdots$	${5.99}_{-0.69}^{+0.68}$	$\cdots$
HFF2P-$3378$-$6338$	$64.140776$	$-24.109396$	$0.82\pm 0.28$	$0.10\pm 0.14$	$27.64\pm 0.11$	$\cdots$	${5.41}_{-5.07}^{+0.63}$	$\cdots$
HFF2P-$3253$-$6121$	$64.135552$	$-24.103380$	$>1.41$	$0.12\pm 0.15$	$27.68\pm 0.11$	$\cdots$	${6.63}_{-0.75}^{+0.75}$	$\cdots$
HFF2P-$3316$-$7571$	$64.138174$	$-24.132532$	$0.81\pm 0.25$	$-0.25\pm 0.15$	$27.75\pm 0.12$	$\cdots$	${5.27}_{-4.78}^{+0.61}$	$\cdots$
HFF2P-$3241$-$7291$	$64.135067$	$-24.124757$	$>1.27$	$0.26\pm 0.18$	$27.81\pm 0.12$	$\cdots$	${1.36}_{-1.21}^{+4.94}$	$\cdots$
HFF2P-$3084$-$7172$	$64.128511$	$-24.121451$	$1.00\pm 0.30$	$-0.22\pm 0.15$	$27.85\pm 0.13$	$\cdots$	${5.81}_{-0.67}^{+0.67}$	$\cdots$
HFF2P-$2909$-$7142$	$64.121231$	$-24.120634$	$>1.48$	$0.18\pm 0.18$	$27.89\pm 0.13$	$\cdots$	${6.11}_{-0.78}^{+0.88}$	$\cdots$
HFF2P-$3088$-$5573$	$64.128687$	$-24.099262$	$0.91\pm 0.41$	$-0.02\pm 0.18$	$27.92\pm 0.14$	$\cdots$	${5.81}_{-0.74}^{+0.67}$	$\cdots$
HFF2P-$3151$-$6300$	$64.131331$	$-24.108356$	$1.40\pm 0.51$	$-0.21\pm 0.16$	$27.94\pm 0.14$	$\cdots$	${6.12}_{-0.70}^{+0.70}$	$\cdots$
HFF2P-$3216$-$6167$	$64.134030$	$-24.104666$	$>1.05$	$0.22\pm 0.19$	$27.96\pm 0.14$	$\cdots$	${6.46}_{-5.40}^{+0.92}$	$\cdots$
HFF2P-$3429$-$6045$	$64.142896$	$-24.101277$	$>1.42$	$-0.03\pm 0.18$	$27.96\pm 0.14$	$\cdots$	${6.61}_{-0.75}^{+0.75}$	$\cdots$
HFF2P-$3441$-$8018$	$64.143391$	$-24.133838$	$>1.02$	$0.19\pm 0.23$	$28.01\pm 0.16$	$\cdots$	${1.28}_{-1.10}^{+5.17}$	$\cdots$
HFF2P-$3602$-$7428$	$64.150087$	$-24.128579$	$>1.18$	$-0.07\pm 0.22$	$28.10\pm 0.17$	$\cdots$	${6.01}_{-1.36}^{+0.79}$	$\cdots$
HFF2P-$3418$-$6426$	$64.142432$	$-24.111851$	$>1.12$	$-0.15\pm 0.26$	$28.37\pm 0.21$	$\cdots$	${1.35}_{-1.26}^{+5.41}$	$\cdots$
MACS0717 Cluster
HFF3C-$3377$-$4319$	$109.390738$	$37.742218$	$1.09\pm 0.08$	$-0.07\pm 0.05$	$25.82\pm 0.04$	$62.36$	${5.97}_{-0.68}^{+0.68}$	$\cdots$
HFF3C-$3817$-$5168$	$109.409066$	$37.754681$	$1.52\pm 0.10$	$-0.05\pm 0.04$	$25.96\pm 0.04$	$4.88$	${6.20}_{-0.71}^{+0.71}$	(6)
HFF3C-$3785$-$4338$	$109.407728$	$37.742740$	$1.48\pm 0.11$	$-0.07\pm 0.05$	$26.06\pm 0.04$	$8.66$	${6.18}_{-0.70}^{+0.70}$	(6)
HFF3C-$3928$-$4047$	$109.413667$	$37.734645$	$2.13\pm 0.29$	$0.03\pm 0.07$	$26.45\pm 0.06$	$14.22$	${6.47}_{-0.73}^{+0.73}$	(6)
HFF3C-$3578$-$5538$	$109.399102$	$37.764959$	$1.57\pm 0.21$	$-0.00\pm 0.07$	$26.52\pm 0.06$	$6.79$	${6.18}_{-0.70}^{+0.70}$	(6)
HFF3C-$3908$-$4016$	$109.412846$	$37.733795$	$2.09\pm 0.33$	$0.12\pm 0.08$	$26.55\pm 0.06$	$22.49$	${6.50}_{-0.74}^{+0.74}$	(6)
HFF3C-$3269$-$5069$	$109.386219$	$37.751924$	$1.73\pm 0.33$	$0.10\pm 0.09$	$26.66\pm 0.07$	$3.10$	${6.22}_{-0.71}^{+0.71}$	(6)
HFF3C-$3342$-$3294$	$109.389277$	$37.724858$	$1.31\pm 0.27$	$0.12\pm 0.10$	$26.84\pm 0.07$	$2.35$	${6.03}_{-0.69}^{+0.69}$	(6)
HFF3C-$3145$-$3537$	$109.381053$	$37.731611$	$1.43\pm 0.26$	$-0.05\pm 0.09$	$26.87\pm 0.08$	$3.54$	${6.13}_{-0.70}^{+0.70}$	(6)
HFF3C-$3047$-$4112$	$109.376996$	$37.736450$	$1.31\pm 0.22$	$0.08\pm 0.10$	$26.96\pm 0.08$	$4.22$	${6.03}_{-0.69}^{+0.69}$	(6)
HFF3C-$3389$-$4210$	$109.391220$	$37.739172$	$1.17\pm 0.49$	$0.22\pm 0.21$	$27.38\pm 0.16$	$26.64$	${5.86}_{-5.06}^{+0.98}$	(6)
HFF3C-$3096$-$5100$	$109.379016$	$37.752792$	$1.04\pm 0.23$	$-0.17\pm 0.17$	$27.41\pm 0.15$	$5.04$	${5.87}_{-0.67}^{+0.67}$	$\cdots$
HFF3C-$3318$-$5132$	$109.388269$	$37.753667$	$0.82\pm 0.29$	$0.04\pm 0.18$	$27.42\pm 0.14$	$5.61$	${5.49}_{-4.77}^{+0.64}$	$\cdots$
HFF3C-$4047$-$4196$	$109.418650$	$37.738793$	$1.19\pm 0.30$	$-0.15\pm 0.18$	$27.48\pm 0.15$	$9.18$	${5.97}_{-0.68}^{+0.68}$	(6)
HFF3C-$3810$-$4541$	$109.408780$	$37.748379$	$1.15\pm 0.33$	$-0.01\pm 0.19$	$27.53\pm 0.15$	$58.57$	${5.95}_{-0.68}^{+0.68}$	$\cdots$
HFF3C-$3585$-$5491$	$109.399393$	$37.763654$	$1.17\pm 0.46$	$0.18\pm 0.21$	$27.55\pm 0.16$	$7.31$	${5.74}_{-5.10}^{+0.90}$	$\cdots$
HFF3C-$3411$-$4573$	$109.392135$	$37.749271$	$0.97\pm 0.36$	$-0.02\pm 0.21$	$27.60\pm 0.17$	$9.14$	${5.60}_{-5.19}^{+0.65}$	$\cdots$
HFF3C-$2777$-$4506$	$109.365722$	$37.747409$	$>1.44$	$0.20\pm 0.24$	$27.64\pm 0.18$	$4.63$	${6.15}_{-4.99}^{+0.98}$	(6)
HFF3C-$3981$-$4481$	$109.415897$	$37.746722$	$>1.67$	$-0.08\pm 0.22$	$27.70\pm 0.18$	$15.12$	${6.51}_{-0.74}^{+0.74}$	(6)
HFF3C-$3096$-$4181$	$109.379034$	$37.738386$	$1.27\pm 0.39$	$-0.01\pm 0.18$	$27.73\pm 0.15$	$6.22$	${6.02}_{-0.76}^{+0.69}$	(6)
HFF3C-$3510$-$5294$	$109.396250$	$37.758188$	$>1.38$	$-0.12\pm 0.25$	$27.88\pm 0.21$	$8.62$	${6.21}_{-1.17}^{+0.71}$	$\cdots$
HFF3C-$3091$-$4467$	$109.378815$	$37.746314$	$>1.72$	$-0.43\pm 0.24$	$28.11\pm 0.22$	$10.29$	${6.41}_{-0.73}^{+0.73}$	$\cdots$
MACS0717 Parallel
HFF3P-$2342$-$9539$	$109.347598$	$37.831665$	$2.27\pm 0.25$	$0.13\pm 0.05$	$26.15\pm 0.04$	$\cdots$	${6.48}_{-0.73}^{+0.73}$	(6)
HFF3P-$2252$-$9555$	$109.343857$	$37.832091$	$1.61\pm 0.18$	$-0.04\pm 0.06$	$26.57\pm 0.05$	$\cdots$	${6.22}_{-0.71}^{+0.71}$	(6)
HFF3P-$1410$-$0378$	$109.308788$	$37.843848$	$>2.06$	$0.41\pm 0.11$	$26.72\pm 0.07$	$\cdots$	${7.14}_{-0.87}^{+0.80}$	(6)
HFF3P-$2427$-$9379$	$109.351141$	$37.827197$	$2.37\pm 0.45$	$0.07\pm 0.08$	$26.72\pm 0.06$	$\cdots$	${6.57}_{-0.74}^{+0.74}$	(6)
HFF3P-$1604$-$9275$	$109.316835$	$37.824319$	$>2.25$	$0.14\pm 0.09$	$26.84\pm 0.07$	$\cdots$	${6.82}_{-0.77}^{+0.77}$	(6)
HFF3P-$1906$-$8524$	$109.329441$	$37.814580$	$>1.95$	$0.37\pm 0.10$	$26.86\pm 0.07$	$\cdots$	${7.17}_{-0.80}^{+0.80}$	$\cdots$
HFF3P-$1778$-$9084$	$109.324122$	$37.819016$	$0.84\pm 0.14$	$-0.10\pm 0.08$	$26.90\pm 0.07$	$\cdots$	${5.79}_{-0.67}^{+0.67}$	(6)
HFF3P-$1705$-$9266$	$109.321068$	$37.824061$	$1.41\pm 0.36$	$0.39\pm 0.10$	$26.91\pm 0.07$	$\cdots$	${5.90}_{-0.75}^{+1.14}$	(6)
HFF3P-$1519$-$8364$	$109.313303$	$37.810113$	$>2.23$	$0.14\pm 0.09$	$26.96\pm 0.07$	$\cdots$	${6.77}_{-0.76}^{+0.76}$	(6)
HFF3P-$1837$-$9275$	$109.326543$	$37.824306$	$1.39\pm 0.24$	$-0.06\pm 0.09$	$26.97\pm 0.07$	$\cdots$	${6.10}_{-0.70}^{+0.70}$	(6)
HFF3P-$1881$-$1103$	$109.328390$	$37.852862$	$1.64\pm 0.26$	$-0.17\pm 0.09$	$26.98\pm 0.07$	$\cdots$	${6.22}_{-0.71}^{+0.71}$	$\cdots$
HFF3P-$1844$-$9166$	$109.326863$	$37.821291$	$0.83\pm 0.19$	$0.10\pm 0.10$	$27.02\pm 0.08$	$\cdots$	${4.58}_{-3.88}^{+1.11}$	$\cdots$
HFF3P-$1855$-$8526$	$109.327331$	$37.814632$	$0.85\pm 0.16$	$-0.06\pm 0.10$	$27.03\pm 0.08$	$\cdots$	${5.78}_{-0.66}^{+0.66}$	(6)
HFF3P-$1977$-$9392$	$109.332397$	$37.827567$	$>2.18$	$0.12\pm 0.11$	$27.08\pm 0.08$	$\cdots$	${6.52}_{-0.74}^{+0.74}$	(6)
HFF3P-$2364$-$9356$	$109.348503$	$37.826577$	$>1.74$	$0.44\pm 0.14$	$27.19\pm 0.09$	$\cdots$	${7.31}_{-1.22}^{+0.81}$	(6)
HFF3P-$1762$-$0355$	$109.323430$	$37.843220$	$>1.70$	$0.36\pm 0.13$	$27.22\pm 0.09$	$\cdots$	${6.38}_{-5.23}^{+0.87}$	(6)
HFF3P-$1696$-$0348$	$109.320698$	$37.843017$	$1.16\pm 0.27$	$0.07\pm 0.12$	$27.23\pm 0.09$	$\cdots$	${5.87}_{-0.67}^{+0.67}$	$\cdots$
HFF3P-$1892$-$9418$	$109.328836$	$37.828302$	$>2.00$	$-0.05\pm 0.12$	$27.24\pm 0.09$	$\cdots$	${6.46}_{-0.73}^{+0.73}$	(6)
HFF3P-$1188$-$9165$	$109.299505$	$37.821260$	$0.96\pm 0.19$	$-0.04\pm 0.12$	$27.31\pm 0.10$	$\cdots$	${5.84}_{-0.67}^{+0.67}$	$\cdots$
HFF3P-$1399$-$9233$	$109.308292$	$37.823146$	$0.82\pm 0.19$	$-0.06\pm 0.14$	$27.45\pm 0.11$	$\cdots$	${5.71}_{-0.66}^{+0.66}$	(6)
HFF3P-$1527$-$9304$	$109.313633$	$37.825128$	$1.38\pm 0.36$	$-0.10\pm 0.15$	$27.46\pm 0.12$	$\cdots$	${6.09}_{-0.70}^{+0.70}$	$\cdots$
HFF3P-$1840$-$9281$	$109.326706$	$37.824478$	$0.90\pm 0.28$	$0.03\pm 0.15$	$27.46\pm 0.12$	$\cdots$	${5.65}_{-1.21}^{+0.65}$	(6)
HFF3P-$1263$-$9215$	$109.302636$	$37.822653$	$>1.96$	$0.03\pm 0.15$	$27.51\pm 0.12$	$\cdots$	${6.53}_{-0.74}^{+0.74}$	(6)
HFF3P-$1949$-$0448$	$109.331212$	$37.845804$	$1.40\pm 0.53$	$0.26\pm 0.18$	$27.55\pm 0.12$	$\cdots$	${5.96}_{-5.02}^{+1.12}$	(6)
HFF3P-$1319$-$0277$	$109.304963$	$37.841038$	$1.38\pm 0.46$	$0.17\pm 0.21$	$27.56\pm 0.16$	$\cdots$	${5.82}_{-5.24}^{+0.81}$	$\cdots$
HFF3P-$2208$-$9465$	$109.342009$	$37.829592$	$1.03\pm 0.31$	$0.08\pm 0.17$	$27.59\pm 0.13$	$\cdots$	${5.58}_{-4.94}^{+0.64}$	(6)
HFF3P-$1307$-$9251$	$109.304485$	$37.823649$	$1.07\pm 0.23$	$-0.19\pm 0.15$	$27.61\pm 0.13$	$\cdots$	${1.20}_{-1.06}^{+4.68}$	$\cdots$
HFF3P-$1477$-$9449$	$109.311563$	$37.829163$	$1.34\pm 0.56$	$0.27\pm 0.20$	$27.62\pm 0.14$	$\cdots$	${6.05}_{-1.18}^{+0.99}$	(6)
HFF3P-$1538$-$9217$	$109.314090$	$37.822717$	$>1.30$	$0.33\pm 0.20$	$27.70\pm 0.14$	$\cdots$	${6.61}_{-5.17}^{+0.83}$	$\cdots$
HFF3P-$1375$-$9505$	$109.307304$	$37.830722$	$1.01\pm 0.30$	$0.03\pm 0.18$	$27.71\pm 0.14$	$\cdots$	${1.34}_{-1.29}^{+2.40}$	$\cdots$
HFF3P-$1373$-$9422$	$109.307223$	$37.828402$	$>1.66$	$0.06\pm 0.19$	$27.77\pm 0.15$	$\cdots$	${6.48}_{-0.73}^{+0.73}$	(6)
HFF3P-$1489$-$0326$	$109.312054$	$37.842390$	$>1.29$	$0.30\pm 0.21$	$27.77\pm 0.15$	$\cdots$	${6.92}_{-5.84}^{+0.78}$	(6)
HFF3P-$1810$-$0535$	$109.325457$	$37.848216$	$>1.35$	$0.14\pm 0.20$	$27.79\pm 0.15$	$\cdots$	${6.83}_{-1.43}^{+0.77}$	(6)
HFF3P-$1151$-$9291$	$109.297969$	$37.824773$	$>1.31$	$0.31\pm 0.23$	$27.86\pm 0.16$	$\cdots$	${1.36}_{-1.19}^{+5.38}$	$\cdots$
HFF3P-$1813$-$0035$	$109.325574$	$37.834310$	$0.90\pm 0.40$	$0.04\pm 0.22$	$27.87\pm 0.17$	$\cdots$	${5.58}_{-5.43}^{+0.64}$	$\cdots$
HFF3P-$1776$-$8528$	$109.324017$	$37.814689$	$1.15\pm 0.51$	$-0.05\pm 0.23$	$27.97\pm 0.18$	$\cdots$	${5.72}_{-5.30}^{+0.84}$	$\cdots$
HFF3P-$1853$-$9354$	$109.327214$	$37.826505$	$0.90\pm 0.34$	$-0.25\pm 0.22$	$27.97\pm 0.18$	$\cdots$	${5.60}_{-5.27}^{+0.65}$	$\cdots$
HFF3P-$2010$-$0108$	$109.333783$	$37.836334$	$0.87\pm 0.35$	$-0.04\pm 0.23$	$28.01\pm 0.18$	$\cdots$	${5.63}_{-5.06}^{+0.65}$	(6)
HFF3P-$1628$-$9029$	$109.317874$	$37.817496$	$0.87\pm 0.42$	$0.00\pm 0.25$	$28.08\pm 0.19$	$\cdots$	${5.64}_{-5.28}^{+0.69}$	$\cdots$
HFF3P-$1936$-$9052$	$109.330679$	$37.818119$	$0.84\pm 0.40$	$-0.04\pm 0.25$	$28.14\pm 0.20$	$\cdots$	${5.60}_{-5.23}^{+0.67}$	$\cdots$
HFF3P-$1494$-$9162$	$109.312291$	$37.821185$	$>1.14$	$0.01\pm 0.27$	$28.18\pm 0.21$	$\cdots$	${6.30}_{-4.99}^{+0.96}$	$\cdots$
MACS1149 Cluster
HFF4C-$4025$-$5027$	$177.417749$	$22.417435$	$>3.48$	$0.57\pm 0.03$	$25.21\pm 0.02$	$1.57$	${7.50}_{-0.83}^{+0.83}$	$\cdots$
HFF4C-$3888$-$4567$	$177.412018$	$22.415777$	$1.11\pm 0.05$	$0.12\pm 0.03$	$25.52\pm 0.02$	$1.94$	${5.81}_{-0.67}^{+0.67}$	$\cdots$
HFF4C-$3321$-$2566$	$177.388388$	$22.382390$	$1.67\pm 0.15$	$-0.07\pm 0.05$	$26.21\pm 0.04$	$1.74$	${6.27}_{-0.71}^{+0.71}$	$\cdots$
HFF4C-$3180$-$3434$	$177.382540$	$22.395401$	$0.86\pm 0.09$	$0.07\pm 0.06$	$26.30\pm 0.04$	$2.28$	${5.72}_{-0.66}^{+0.66}$	$\cdots$
HFF4C-$3911$-$5079$	$177.412999$	$22.418864$	$2.42\pm 0.36$	$0.03\pm 0.06$	$26.34\pm 0.05$	$1.70$	${6.47}_{-0.73}^{+0.73}$	$\cdots$
HFF4C-$3672$-$4342$	$177.403011$	$22.409501$	$1.07\pm 0.10$	$-0.07\pm 0.06$	$26.49\pm 0.05$	$3.68$	${5.96}_{-0.68}^{+0.68}$	$\cdots$
HFF4C-$4042$-$4205$	$177.418441$	$22.405696$	$0.91\pm 0.10$	$-0.09\pm 0.06$	$26.58\pm 0.05$	$1.77$	${5.84}_{-0.67}^{+0.67}$	$\cdots$
HFF4C-$3910$-$4491$	$177.412935$	$22.413642$	$2.26\pm 0.36$	$-0.19\pm 0.08$	$26.72\pm 0.07$	$1.87$	${6.41}_{-0.73}^{+0.73}$	$\cdots$
HFF4C-$4042$-$4207$	$177.418456$	$22.405770$	$0.97\pm 0.12$	$-0.11\pm 0.08$	$26.77\pm 0.06$	$1.77$	${5.87}_{-0.67}^{+0.67}$	$\cdots$
HFF4C-$4046$-$4231$	$177.418619$	$22.406430$	$1.06\pm 0.15$	$0.05\pm 0.08$	$26.81\pm 0.07$	$1.73$	${5.94}_{-0.68}^{+0.68}$	$\cdots$
HFF4C-$3952$-$5014$	$177.414690$	$22.417060$	$>2.16$	$0.07\pm 0.11$	$27.04\pm 0.09$	$1.71$	${6.44}_{-0.73}^{+0.73}$	$\cdots$
HFF4C-$3906$-$4324$	$177.412777$	$22.409016$	$>1.76$	$0.42\pm 0.12$	$27.09\pm 0.08$	$1.95$	${7.31}_{-1.09}^{+0.81}$	$\cdots$
HFF4C-$4047$-$4228$	$177.418635$	$22.406343$	$1.13\pm 0.19$	$-0.04\pm 0.10$	$27.09\pm 0.09$	$1.73$	${5.94}_{-0.68}^{+0.68}$	$\cdots$
HFF4C-$3705$-$4446$	$177.404410$	$22.412396$	$>1.88$	$0.33\pm 0.13$	$27.14\pm 0.09$	$3.50$	${6.60}_{-0.83}^{+0.75}$	$\cdots$
HFF4C-$3830$-$3120$	$177.409606$	$22.386668$	$1.77\pm 0.45$	$0.11\pm 0.13$	$27.20\pm 0.10$	$6.20$	${6.27}_{-0.71}^{+0.71}$	$\cdots$
HFF4C-$3765$-$3173$	$177.406897$	$22.388148$	$0.98\pm 0.23$	$0.13\pm 0.13$	$27.21\pm 0.10$	$5.16$	${5.71}_{-4.82}^{+0.66}$	$\cdots$
HFF4C-$3889$-$3206$	$177.412079$	$22.389059$	$>1.97$	$0.02\pm 0.14$	$27.31\pm 0.11$	$8.53$	${6.66}_{-0.75}^{+0.75}$	$\cdots$
HFF4C-$3433$-$2527$	$177.393042$	$22.381320$	$0.91\pm 0.26$	$0.08\pm 0.13$	$27.33\pm 0.10$	$1.76$	${5.83}_{-0.67}^{+0.67}$	$\cdots$
HFF4C-$4026$-$3382$	$177.417760$	$22.393947$	$1.11\pm 0.24$	$-0.01\pm 0.13$	$27.35\pm 0.10$	$3.17$	${5.86}_{-0.69}^{+0.67}$	$\cdots$
HFF4C-$3231$-$2579$	$177.384647$	$22.382754$	$1.23\pm 0.26$	$-0.23\pm 0.15$	$27.42\pm 0.13$	$1.68$	${6.00}_{-0.69}^{+0.69}$	$\cdots$
HFF4C-$3134$-$4050$	$177.380590$	$22.401408$	$>2.08$	$-0.03\pm 0.14$	$27.43\pm 0.11$	$2.90$	${6.53}_{-0.74}^{+0.74}$	$\cdots$
HFF4C-$3191$-$4433$	$177.382991$	$22.412040$	$>1.59$	$0.43\pm 0.18$	$27.43\pm 0.12$	$6.95$	${7.21}_{-1.34}^{+0.81}$	$\cdots$
HFF4C-$3665$-$4526$	$177.402725$	$22.414615$	$0.84\pm 0.21$	$-0.08\pm 0.15$	$27.45\pm 0.12$	$5.09$	${5.76}_{-0.66}^{+0.66}$	$\cdots$
HFF4C-$4076$-$4033$	$177.419863$	$22.400937$	$1.48\pm 0.47$	$0.26\pm 0.16$	$27.46\pm 0.12$	$2.08$	${6.09}_{-0.70}^{+0.78}$	$\cdots$
HFF4C-$3760$-$3035$	$177.406675$	$22.384327$	$>1.73$	$0.04\pm 0.17$	$27.53\pm 0.13$	$6.53$	${6.58}_{-0.74}^{+0.74}$	$\cdots$
HFF4C-$3791$-$4415$	$177.407983$	$22.411538$	$1.54\pm 0.43$	$-0.02\pm 0.16$	$27.54\pm 0.13$	$2.36$	${6.15}_{-0.70}^{+0.70}$	$\cdots$
HFF4C-$3894$-$3418$	$177.412259$	$22.394967$	$>1.55$	$0.12\pm 0.18$	$27.57\pm 0.13$	$7.09$	${6.63}_{-0.75}^{+0.75}$	$\cdots$
HFF4C-$3305$-$4210$	$177.387710$	$22.405836$	$0.89\pm 0.26$	$0.05\pm 0.17$	$27.62\pm 0.13$	$11.21$	${5.81}_{-0.67}^{+0.67}$	$\cdots$
HFF4C-$3892$-$3416$	$177.412203$	$22.394890$	$>1.40$	$0.10\pm 0.20$	$27.72\pm 0.15$	$7.26$	${6.62}_{-0.75}^{+0.75}$	$\cdots$
HFF4C-$3736$-$5005$	$177.405705$	$22.416817$	$>1.34$	$0.25\pm 0.22$	$27.76\pm 0.16$	$2.58$	${6.54}_{-1.23}^{+0.78}$	$\cdots$
HFF4C-$4205$-$3155$	$177.425223$	$22.387645$	$1.65\pm 0.52$	$-0.05\pm 0.20$	$27.77\pm 0.16$	$2.26$	${1.29}_{-0.43}^{+5.34}$	$\cdots$
HFF4C-$3991$-$3123$	$177.416321$	$22.386751$	$1.12\pm 0.41$	$0.09\pm 0.22$	$27.85\pm 0.18$	$3.56$	${5.81}_{-4.83}^{+0.71}$	$\cdots$
HFF4C-$3405$-$3155$	$177.391898$	$22.387646$	$1.22\pm 0.52$	$0.03\pm 0.22$	$27.86\pm 0.16$	$2.38$	${1.33}_{-1.15}^{+5.12}$	$\cdots$
HFF4C-$3419$-$3006$	$177.392475$	$22.383510$	$0.82\pm 0.31$	$-0.18\pm 0.20$	$27.87\pm 0.16$	$1.93$	${5.62}_{-4.57}^{+0.65}$	$\cdots$
HFF4C-$3595$-$4157$	$177.399818$	$22.404384$	$0.84\pm 0.40$	$0.09\pm 0.27$	$27.92\pm 0.20$	$684.51$	${0.31}_{-0.27}^{+3.68}$	$\cdots$
HFF4C-$3312$-$2565$	$177.388012$	$22.382380$	$>1.45$	$-0.13\pm 0.25$	$27.93\pm 0.20$	$1.73$	${6.24}_{-0.93}^{+0.72}$	$\cdots$
HFF4C-$4082$-$3192$	$177.420086$	$22.388672$	$0.89\pm 0.25$	$-0.31\pm 0.21$	$27.93\pm 0.19$	$3.01$	${5.64}_{-4.95}^{+0.65}$	$\cdots$
HFF4C-$3225$-$2532$	$177.384407$	$22.381448$	$1.23\pm 0.44$	$-0.21\pm 0.25$	$27.95\pm 0.21$	$1.63$	${1.35}_{-1.29}^{+4.93}$	$\cdots$
HFF4C-$3345$-$3553$	$177.389398$	$22.398695$	$0.93\pm 0.38$	$-0.08\pm 0.26$	$27.96\pm 0.21$	$6.34$	${0.31}_{-0.26}^{+4.63}$	$\cdots$
HFF4C-$3282$-$4046$	$177.386778$	$22.401297$	$0.85\pm 0.24$	$-0.45\pm 0.22$	$28.06\pm 0.19$	$5.23$	${5.63}_{-0.65}^{+0.65}$	$\cdots$
HFF4C-$3829$-$4199$	$177.409561$	$22.405545$	$>1.09$	$0.01\pm 0.28$	$28.17\pm 0.22$	$2.45$	${6.27}_{-1.57}^{+0.82}$	$\cdots$
MACS1149 Parallel
HFF4P-$3938$-$8196$	$177.414121$	$22.305448$	$3.02\pm 0.40$	$0.26\pm 0.02$	$25.43\pm 0.02$	$\cdots$	${6.74}_{-0.76}^{+0.76}$	$\cdots$
HFF4P-$4461$-$7461$	$177.435880$	$22.296142$	$>2.90$	$0.64\pm 0.04$	$25.82\pm 0.02$	$\cdots$	${7.54}_{-0.84}^{+0.84}$	$\cdots$
HFF4P-$4423$-$8329$	$177.434292$	$22.309154$	$2.89\pm 0.46$	$0.28\pm 0.03$	$25.87\pm 0.02$	$\cdots$	${7.13}_{-0.80}^{+0.80}$	$\cdots$
HFF4P-$3681$-$7168$	$177.403385$	$22.288000$	$1.47\pm 0.22$	$0.01\pm 0.06$	$26.46\pm 0.05$	$\cdots$	${6.15}_{-0.70}^{+0.70}$	$\cdots$
HFF4P-$4005$-$7307$	$177.416916$	$22.291875$	$>2.30$	$0.09\pm 0.06$	$26.59\pm 0.05$	$\cdots$	${6.80}_{-0.76}^{+0.76}$	$\cdots$
HFF4P-$3742$-$7453$	$177.405922$	$22.295927$	$1.31\pm 0.19$	$-0.01\pm 0.06$	$26.64\pm 0.05$	$\cdots$	${6.02}_{-0.69}^{+0.69}$	$\cdots$
HFF4P-$3815$-$7490$	$177.408969$	$22.296968$	$1.27\pm 0.23$	$0.15\pm 0.07$	$26.73\pm 0.06$	$\cdots$	${5.94}_{-0.68}^{+0.68}$	$\cdots$
HFF4P-$4208$-$8047$	$177.425354$	$22.301318$	$1.57\pm 0.27$	$-0.07\pm 0.07$	$26.79\pm 0.06$	$\cdots$	${6.20}_{-0.71}^{+0.71}$	$\cdots$
HFF4P-$3678$-$7409$	$177.403268$	$22.294703$	$>1.77$	$0.47\pm 0.10$	$26.88\pm 0.06$	$\cdots$	${7.16}_{-1.00}^{+0.80}$	$\cdots$
HFF4P-$3695$-$7381$	$177.403979$	$22.293922$	$>1.75$	$0.44\pm 0.10$	$26.93\pm 0.07$	$\cdots$	${7.15}_{-1.15}^{+0.80}$	$\cdots$
HFF4P-$3832$-$7190$	$177.409706$	$22.288622$	$1.95\pm 0.46$	$0.04\pm 0.08$	$26.94\pm 0.07$	$\cdots$	${6.36}_{-0.72}^{+0.72}$	$\cdots$
HFF4P-$4539$-$7124$	$177.439130$	$22.286794$	$1.45\pm 0.24$	$-0.08\pm 0.09$	$27.14\pm 0.08$	$\cdots$	${6.15}_{-0.70}^{+0.70}$	$\cdots$
HFF4P-$4497$-$8060$	$177.437411$	$22.301678$	$>1.94$	$0.14\pm 0.11$	$27.16\pm 0.08$	$\cdots$	${6.87}_{-0.77}^{+0.77}$	$\cdots$
HFF4P-$4269$-$8288$	$177.427882$	$22.308024$	$1.18\pm 0.28$	$-0.04\pm 0.10$	$27.17\pm 0.08$	$\cdots$	${6.00}_{-0.69}^{+0.69}$	$\cdots$
HFF4P-$4045$-$8214$	$177.418575$	$22.305965$	$1.30\pm 0.47$	$0.33\pm 0.12$	$27.24\pm 0.09$	$\cdots$	${5.81}_{-4.88}^{+1.03}$	$\cdots$
HFF4P-$4194$-$8047$	$177.424789$	$22.301318$	$1.02\pm 0.30$	$0.07\pm 0.11$	$27.27\pm 0.09$	$\cdots$	${5.86}_{-0.67}^{+0.67}$	$\cdots$
HFF4P-$4372$-$7404$	$177.432202$	$22.294557$	$>1.65$	$0.39\pm 0.13$	$27.33\pm 0.09$	$\cdots$	${7.08}_{-1.21}^{+0.79}$	$\cdots$
HFF4P-$3881$-$7423$	$177.411719$	$22.295094$	$>1.41$	$0.10\pm 0.14$	$27.48\pm 0.11$	$\cdots$	${6.75}_{-0.76}^{+0.76}$	$\cdots$
HFF4P-$4133$-$6595$	$177.422215$	$22.283195$	$1.47\pm 0.41$	$0.00\pm 0.13$	$27.48\pm 0.11$	$\cdots$	${6.11}_{-0.70}^{+0.70}$	$\cdots$
HFF4P-$3549$-$8309$	$177.397916$	$22.308605$	$>1.44$	$0.18\pm 0.18$	$27.67\pm 0.13$	$\cdots$	${6.50}_{-0.83}^{+0.74}$	$\cdots$
HFF4P-$4005$-$7321$	$177.416898$	$22.292273$	$>1.25$	$0.07\pm 0.16$	$27.67\pm 0.13$	$\cdots$	${6.62}_{-0.75}^{+0.75}$	$\cdots$
HFF4P-$4399$-$8595$	$177.433312$	$22.316552$	$>1.33$	$0.02\pm 0.16$	$27.70\pm 0.13$	$\cdots$	${5.65}_{-5.46}^{+1.13}$	$\cdots$
HFF4P-$4459$-$7323$	$177.435824$	$22.292329$	$0.94\pm 0.29$	$-0.00\pm 0.16$	$27.70\pm 0.13$	$\cdots$	${5.44}_{-5.14}^{+0.63}$	$\cdots$
HFF4P-$3860$-$7488$	$177.410866$	$22.296898$	$0.93\pm 0.45$	$0.10\pm 0.17$	$27.73\pm 0.14$	$\cdots$	${5.68}_{-5.08}^{+0.85}$	$\cdots$
HFF4P-$4250$-$7424$	$177.427107$	$22.295124$	$>1.41$	$-0.02\pm 0.18$	$27.81\pm 0.15$	$\cdots$	${6.47}_{-0.73}^{+0.73}$	$\cdots$
HFF4P-$4529$-$8297$	$177.438743$	$22.308265$	$>1.35$	$0.07\pm 0.19$	$27.81\pm 0.15$	$\cdots$	${6.53}_{-0.74}^{+0.74}$	$\cdots$
HFF4P-$4163$-$8238$	$177.423498$	$22.306622$	$1.41\pm 0.54$	$-0.22\pm 0.17$	$27.83\pm 0.14$	$\cdots$	${6.09}_{-0.70}^{+0.70}$	$\cdots$
HFF4P-$3731$-$7203$	$177.405478$	$22.288982$	$>1.29$	$-0.18\pm 0.20$	$27.84\pm 0.17$	$\cdots$	${6.08}_{-0.92}^{+0.69}$	$\cdots$
HFF4P-$3841$-$8191$	$177.410083$	$22.305310$	$1.03\pm 0.55$	$0.15\pm 0.20$	$27.84\pm 0.16$	$\cdots$	${1.32}_{-1.11}^{+4.75}$	$\cdots$
HFF4P-$4380$-$7515$	$177.432540$	$22.297653$	$0.90\pm 0.37$	$0.13\pm 0.20$	$27.87\pm 0.15$	$\cdots$	${1.17}_{-0.73}^{+4.70}$	$\cdots$
HFF4P-$3653$-$8000$	$177.402242$	$22.300011$	$>1.34$	$0.06\pm 0.20$	$27.89\pm 0.16$	$\cdots$	${6.48}_{-0.73}^{+0.73}$	$\cdots$
HFF4P-$4110$-$8223$	$177.421272$	$22.306213$	$>1.17$	$-0.04\pm 0.19$	$27.91\pm 0.15$	$\cdots$	${6.13}_{-1.38}^{+0.79}$	$\cdots$
HFF4P-$3924$-$7397$	$177.413514$	$22.294386$	$>1.16$	$-0.11\pm 0.20$	$27.94\pm 0.16$	$\cdots$	${6.39}_{-0.82}^{+0.72}$	$\cdots$
HFF4P-$4417$-$9034$	$177.434056$	$22.317617$	$>0.95$	$0.14\pm 0.21$	$27.97\pm 0.16$	$\cdots$	${1.27}_{-1.14}^{+4.75}$	$\cdots$
HFF4P-$3614$-$8432$	$177.400593$	$22.312020$	$>1.13$	$0.15\pm 0.24$	$28.04\pm 0.19$	$\cdots$	${1.35}_{-1.28}^{+4.92}$	$\cdots$
HFF4P-$4579$-$7587$	$177.440827$	$22.299655$	$1.02\pm 0.40$	$-0.07\pm 0.22$	$28.04\pm 0.18$	$\cdots$	${1.26}_{-0.94}^{+4.87}$	$\cdots$
HFF4P-$4380$-$7427$	$177.432518$	$22.295209$	$>1.35$	$-0.17\pm 0.24$	$28.19\pm 0.20$	$\cdots$	${6.09}_{-0.92}^{+0.70}$	$\cdots$
AbellS1063 Cluster
HFF5C-$4581$-$2148$	$342.190894$	$-44.537462$	$1.13\pm 0.02$	$-0.05\pm 0.01$	$24.62\pm 0.01$	$5.99$	${5.97}_{-0.68}^{+0.68}$	$\cdots$
HFF5C-$4537$-$1480$	$342.189052$	$-44.530026$	$1.12\pm 0.03$	$-0.01\pm 0.01$	$24.86\pm 0.01$	$4.29$	${6.00}_{-0.69}^{+0.69}$	$\cdots$
HFF5C-$4111$-$1112$	$342.171301$	$-44.519801$	$1.03\pm 0.05$	$-0.01\pm 0.03$	$25.54\pm 0.02$	$2.47$	${5.92}_{-0.68}^{+0.68}$	$\cdots$
HFF5C-$4265$-$2489$	$342.177715$	$-44.546931$	$1.41\pm 0.16$	$-0.01\pm 0.07$	$26.69\pm 0.05$	$3.28$	${6.13}_{-0.70}^{+0.70}$	$\cdots$
HFF5C-$4159$-$1333$	$342.173329$	$-44.525929$	$1.03\pm 0.16$	$0.01\pm 0.08$	$26.76\pm 0.06$	$6.09$	${5.92}_{-0.68}^{+0.68}$	$\cdots$
HFF5C-$4227$-$2335$	$342.176131$	$-44.542664$	$1.19\pm 0.16$	$-0.04\pm 0.08$	$26.91\pm 0.06$	$10.22$	${6.02}_{-0.69}^{+0.69}$	$\cdots$
HFF5C-$4017$-$0457$	$342.167376$	$-44.512709$	$1.10\pm 0.24$	$0.18\pm 0.10$	$27.06\pm 0.07$	$1.72$	${1.15}_{-0.53}^{+4.62}$	$\cdots$
HFF5C-$3822$-$2382$	$342.159275$	$-44.543958$	$>2.14$	$0.06\pm 0.12$	$27.33\pm 0.10$	$4.40$	${6.47}_{-0.73}^{+0.73}$	$\cdots$
HFF5C-$4877$-$1209$	$342.203210$	$-44.522476$	$>1.62$	$0.31\pm 0.16$	$27.48\pm 0.11$	$8.30$	${6.16}_{-4.88}^{+1.15}$	$\cdots$
HFF5C-$3944$-$1488$	$342.164364$	$-44.530226$	$1.09\pm 0.27$	$-0.14\pm 0.15$	$27.57\pm 0.12$	$5.87$	${5.94}_{-0.68}^{+0.68}$	$\cdots$
HFF5C-$3998$-$0372$	$342.166608$	$-44.510345$	$>1.46$	$0.24\pm 0.17$	$27.57\pm 0.12$	$1.60$	${6.67}_{-0.93}^{+0.75}$	$\cdots$
HFF5C-$4213$-$1414$	$342.175551$	$-44.528186$	$1.31\pm 0.44$	$-0.04\pm 0.18$	$27.66\pm 0.15$	$58.03$	${6.03}_{-0.75}^{+0.69}$	$\cdots$
HFF5C-$4186$-$1141$	$342.174445$	$-44.520605$	$>1.23$	$0.15\pm 0.22$	$27.81\pm 0.17$	$3.02$	${6.04}_{-5.51}^{+1.05}$	$\cdots$
HFF5C-$4650$-$2338$	$342.193770$	$-44.542729$	$0.91\pm 0.29$	$-0.19\pm 0.18$	$27.82\pm 0.15$	$2.55$	${5.64}_{-5.45}^{+0.65}$	$\cdots$
HFF5C-$3930$-$1274$	$342.163789$	$-44.524303$	$0.89\pm 0.26$	$-0.21\pm 0.18$	$27.83\pm 0.15$	$2.56$	${5.65}_{-0.65}^{+0.65}$	$\cdots$
HFF5C-$4509$-$1101$	$342.187910$	$-44.519484$	$0.94\pm 0.34$	$-0.01\pm 0.20$	$27.86\pm 0.16$	$9.31$	${5.78}_{-0.82}^{+0.66}$	$\cdots$
HFF5C-$3913$-$2297$	$342.163049$	$-44.541595$	$1.57\pm 0.43$	$-0.23\pm 0.19$	$27.89\pm 0.16$	$8.72$	${6.18}_{-0.70}^{+0.70}$	$\cdots$
HFF5C-$4414$-$2071$	$342.183917$	$-44.535313$	$>1.40$	$-0.15\pm 0.27$	$27.90\pm 0.21$	$16.73$	${6.26}_{-0.75}^{+0.71}$	$\cdots$
HFF5C-$4493$-$2466$	$342.187221$	$-44.546282$	$0.83\pm 0.31$	$-0.13\pm 0.20$	$27.92\pm 0.16$	$2.50$	${5.58}_{-5.48}^{+0.64}$	$\cdots$
HFF5C-$3977$-$0487$	$342.165711$	$-44.513540$	$0.80\pm 0.31$	$-0.17\pm 0.20$	$27.96\pm 0.17$	$1.75$	${5.41}_{-5.14}^{+0.63}$	$\cdots$
HFF5C-$3960$-$0509$	$342.165033$	$-44.514157$	$0.86\pm 0.35$	$-0.09\pm 0.21$	$27.97\pm 0.17$	$1.78$	${5.66}_{-4.63}^{+0.65}$	$\cdots$
HFF5C-$4260$-$1364$	$342.177526$	$-44.526787$	$1.07\pm 0.46$	$-0.13\pm 0.25$	$28.03\pm 0.21$	$20.38$	${5.86}_{-5.14}^{+0.70}$	$\cdots$
HFF5C-$4039$-$1566$	$342.168321$	$-44.532412$	$0.82\pm 0.40$	$0.03\pm 0.25$	$28.06\pm 0.19$	$51.62$	${5.33}_{-5.11}^{+0.73}$	$\cdots$
AbellS1063 Parallel
HFF5P-$1436$-$3153$	$342.309861$	$-44.554260$	$1.91\pm 0.12$	$0.13\pm 0.03$	$25.79\pm 0.02$	$\cdots$	${6.29}_{-0.71}^{+0.71}$	$\cdots$
HFF5P-$1475$-$2258$	$342.311461$	$-44.540502$	$1.69\pm 0.11$	$0.02\pm 0.03$	$25.88\pm 0.02$	$\cdots$	${6.30}_{-0.72}^{+0.71}$	$\cdots$
HFF5P-$1436$-$3158$	$342.309845$	$-44.554390$	$1.82\pm 0.13$	$0.16\pm 0.03$	$25.94\pm 0.02$	$\cdots$	${6.22}_{-0.71}^{+0.71}$	$\cdots$
HFF5P-$1554$-$3415$	$342.314784$	$-44.561532$	$2.25\pm 0.17$	$-0.20\pm 0.04$	$26.22\pm 0.03$	$\cdots$	${6.42}_{-0.73}^{+0.73}$	$\cdots$
HFF5P-$1915$-$3110$	$342.329811$	$-44.553074$	$2.60\pm 0.35$	$-0.10\pm 0.04$	$26.34\pm 0.04$	$\cdots$	${6.50}_{-0.74}^{+0.74}$	$\cdots$
HFF5P-$2129$-$2064$	$342.338729$	$-44.535120$	$>2.62$	$0.56\pm 0.06$	$26.36\pm 0.04$	$\cdots$	${7.44}_{-0.83}^{+0.83}$	$\cdots$
HFF5P-$1929$-$2524$	$342.330388$	$-44.547896$	$>2.74$	$0.17\pm 0.05$	$26.40\pm 0.04$	$\cdots$	${6.83}_{-0.77}^{+0.77}$	$\cdots$
HFF5P-$1550$-$3408$	$342.314621$	$-44.561337$	$>3.06$	$-0.18\pm 0.06$	$26.66\pm 0.05$	$\cdots$	${6.47}_{-0.73}^{+0.73}$	$\cdots$
HFF5P-$1742$-$2148$	$342.322622$	$-44.537448$	$>2.52$	$0.12\pm 0.06$	$26.69\pm 0.05$	$\cdots$	${6.85}_{-0.77}^{+0.77}$	$\cdots$
HFF5P-$1200$-$3107$	$342.300031$	$-44.552973$	$1.89\pm 0.27$	$0.11\pm 0.07$	$26.75\pm 0.05$	$\cdots$	${6.27}_{-0.71}^{+0.71}$	$\cdots$
HFF5P-$2195$-$1585$	$342.341480$	$-44.532925$	$2.07\pm 0.24$	$-0.26\pm 0.07$	$26.92\pm 0.06$	$\cdots$	${6.38}_{-0.72}^{+0.72}$	$\cdots$
HFF5P-$1375$-$1572$	$342.307308$	$-44.532566$	$>1.90$	$0.43\pm 0.11$	$26.95\pm 0.07$	$\cdots$	${7.31}_{-1.67}^{+0.81}$	$\cdots$
HFF5P-$1545$-$2093$	$342.314400$	$-44.535944$	$2.13\pm 0.51$	$-0.12\pm 0.10$	$27.24\pm 0.08$	$\cdots$	${6.40}_{-0.73}^{+0.72}$	$\cdots$
HFF5P-$1587$-$2418$	$342.316159$	$-44.544962$	$0.95\pm 0.19$	$-0.15\pm 0.11$	$27.34\pm 0.09$	$\cdots$	${5.83}_{-0.67}^{+0.67}$	$\cdots$
HFF5P-$2100$-$3210$	$342.337526$	$-44.555841$	$1.27\pm 0.25$	$-0.12\pm 0.12$	$27.44\pm 0.10$	$\cdots$	${6.04}_{-0.69}^{+0.69}$	$\cdots$
HFF5P-$1653$-$1381$	$342.318877$	$-44.527252$	$1.21\pm 0.26$	$-0.12\pm 0.13$	$27.54\pm 0.11$	$\cdots$	${5.96}_{-0.68}^{+0.68}$	$\cdots$
HFF5P-$2357$-$2040$	$342.348226$	$-44.534471$	$1.05\pm 0.23$	$-0.02\pm 0.14$	$27.58\pm 0.11$	$\cdots$	${5.83}_{-0.67}^{+0.67}$	$\cdots$
HFF5P-$1200$-$3339$	$342.300002$	$-44.559444$	$1.68\pm 0.42$	$-0.02\pm 0.15$	$27.61\pm 0.12$	$\cdots$	${6.21}_{-0.71}^{+0.71}$	$\cdots$
HFF5P-$1512$-$3461$	$342.313006$	$-44.562829$	$>1.84$	$0.09\pm 0.15$	$27.61\pm 0.12$	$\cdots$	${6.26}_{-0.71}^{+0.75}$	$\cdots$
HFF5P-$1537$-$2327$	$342.314047$	$-44.542428$	$1.21\pm 0.46$	$0.24\pm 0.16$	$27.65\pm 0.12$	$\cdots$	${5.82}_{-5.04}^{+1.00}$	$\cdots$
HFF5P-$1372$-$3301$	$342.307199$	$-44.558381$	$>1.68$	$0.21\pm 0.17$	$27.68\pm 0.13$	$\cdots$	${6.58}_{-0.74}^{+0.74}$	$\cdots$
HFF5P-$1870$-$3096$	$342.327941$	$-44.552684$	$1.03\pm 0.43$	$0.19\pm 0.18$	$27.78\pm 0.13$	$\cdots$	${1.37}_{-1.32}^{+2.50}$	$\cdots$
HFF5P-$1423$-$3086$	$342.309306$	$-44.552397$	$1.78\pm 0.48$	$-0.20\pm 0.16$	$27.80\pm 0.13$	$\cdots$	${6.25}_{-0.71}^{+0.71}$	$\cdots$
HFF5P-$2243$-$2024$	$342.343497$	$-44.534020$	$1.03\pm 0.31$	$0.10\pm 0.18$	$27.81\pm 0.14$	$\cdots$	${5.86}_{-0.67}^{+0.67}$	$\cdots$
HFF5P-$1545$-$2521$	$342.314408$	$-44.547811$	$1.42\pm 0.47$	$-0.10\pm 0.18$	$27.91\pm 0.15$	$\cdots$	${6.11}_{-0.70}^{+0.70}$	$\cdots$
HFF5P-$1255$-$3099$	$342.302320$	$-44.552756$	$1.07\pm 0.35$	$0.01\pm 0.19$	$27.93\pm 0.15$	$\cdots$	${5.87}_{-5.07}^{+0.67}$	$\cdots$
HFF5P-$2068$-$3353$	$342.336177$	$-44.559817$	$>1.38$	$0.03\pm 0.21$	$27.95\pm 0.17$	$\cdots$	${6.41}_{-5.52}^{+0.73}$	$\cdots$
HFF5P-$1449$-$2384$	$342.310396$	$-44.544023$	$>1.48$	$-0.12\pm 0.19$	$27.97\pm 0.16$	$\cdots$	${6.12}_{-0.70}^{+0.70}$	$\cdots$
HFF5P-$2116$-$2400$	$342.338198$	$-44.544472$	$0.89\pm 0.36$	$0.13\pm 0.22$	$27.97\pm 0.17$	$\cdots$	${5.68}_{-5.49}^{+0.65}$	$\cdots$
HFF5P-$2227$-$3287$	$342.342824$	$-44.557990$	$0.91\pm 0.32$	$-0.39\pm 0.24$	$28.17\pm 0.22$	$\cdots$	${5.58}_{-0.65}^{+0.64}$	$\cdots$
HFF5P-$1957$-$1523$	$342.331570$	$-44.531212$	$1.10\pm 0.39$	$-0.13\pm 0.24$	$28.18\pm 0.20$	$\cdots$	${5.79}_{-0.71}^{+0.67}$	$\cdots$
HFF5P-$1908$-$3457$	$342.329506$	$-44.562705$	$0.92\pm 0.50$	$0.11\pm 0.26$	$28.19\pm 0.21$	$\cdots$	${0.27}_{-0.20}^{+5.83}$	$\cdots$
HFF5P-$1949$-$2315$	$342.331243$	$-44.542096$	$0.95\pm 0.39$	$-0.12\pm 0.24$	$28.20\pm 0.20$	$\cdots$	${5.64}_{-5.16}^{+0.69}$	$\cdots$
HFF5P-$1940$-$3315$	$342.330870$	$-44.558773$	$0.94\pm 0.54$	$0.16\pm 0.27$	$28.21\pm 0.21$	$\cdots$	${5.66}_{-5.11}^{+1.16}$	$\cdots$
HFF5P-$1716$-$2450$	$342.321503$	$-44.545838$	$0.96\pm 0.48$	$0.05\pm 0.25$	$28.22\pm 0.20$	$\cdots$	${5.66}_{-5.37}^{+0.80}$	$\cdots$
HFF5P-$2055$-$2411$	$342.335663$	$-44.544752$	$>1.16$	$0.03\pm 0.27$	$28.25\pm 0.21$	$\cdots$	${1.36}_{-1.31}^{+3.06}$	$\cdots$
HFF5P-$1992$-$3212$	$342.333018$	$-44.555916$	$>1.07$	$-0.02\pm 0.26$	$28.26\pm 0.21$	$\cdots$	${6.45}_{-1.04}^{+0.73}$	$\cdots$
HFF5P-$1226$-$3152$	$342.301115$	$-44.554238$	$1.05\pm 0.44$	$-0.09\pm 0.25$	$28.27\pm 0.21$	$\cdots$	${5.87}_{-1.29}^{+0.67}$	$\cdots$
HFF5P-$1542$-$1441$	$342.314282$	$-44.528924$	$>1.10$	$0.07\pm 0.27$	$28.29\pm 0.22$	$\cdots$	${5.93}_{-5.29}^{+0.93}$	$\cdots$
Abell370 Cluster
HFF6C-$5526$-$4003$	$39.980271$	$-1.566761$	$0.92\pm 0.07$	$-0.12\pm 0.07$	$26.11\pm 0.06$	$13.34$	${5.85}_{-0.67}^{+0.67}$	$\cdots$
HFF6C-$5522$-$4002$	$39.980113$	$-1.566731$	$0.85\pm 0.08$	$-0.26\pm 0.09$	$26.48\pm 0.08$	$12.40$	${5.75}_{-0.66}^{+0.66}$	$\cdots$
HFF6C-$5715$-$4130$	$39.988155$	$-1.570302$	$0.81\pm 0.15$	$0.05\pm 0.14$	$26.72\pm 0.11$	$3.36$	${5.42}_{-1.08}^{+0.63}$	$\cdots$
HFF6C-$5659$-$4166$	$39.985811$	$-1.571303$	$1.50\pm 0.24$	$-0.01\pm 0.14$	$26.76\pm 0.11$	$4.35$	${6.16}_{-0.70}^{+0.70}$	$\cdots$
HFF6C-$4926$-$4158$	$39.955258$	$-1.571082$	$0.88\pm 0.14$	$0.06\pm 0.11$	$26.77\pm 0.10$	$3.62$	${5.83}_{-0.67}^{+0.67}$	$\cdots$
HFF6C-$5262$-$3591$	$39.969255$	$-1.566441$	$1.39\pm 0.27$	$-0.28\pm 0.17$	$27.09\pm 0.15$	$4.21$	${6.09}_{-0.70}^{+0.70}$	$\cdots$
HFF6C-$5001$-$4358$	$39.958395$	$-1.576620$	$1.69\pm 0.43$	$-0.27\pm 0.23$	$27.60\pm 0.21$	$4.26$	${6.19}_{-0.70}^{+0.70}$	$\cdots$
Abell370 Parallel
HFF6P-$1557$-$6475$	$40.064896$	$-1.613212$	$1.47\pm 0.02$	$0.11\pm 0.01$	$24.41\pm 0.01$	$\cdots$	${6.05}_{-0.69}^{+0.69}$	$\cdots$
HFF6P-$1405$-$7142$	$40.058557$	$-1.620629$	$3.55\pm 0.44$	$0.28\pm 0.02$	$25.23\pm 0.01$	$\cdots$	${7.14}_{-0.80}^{+0.80}$	$\cdots$
HFF6P-$1422$-$8041$	$40.059266$	$-1.634499$	$1.83\pm 0.13$	$0.04\pm 0.03$	$25.84\pm 0.02$	$\cdots$	${6.27}_{-0.71}^{+0.71}$	$\cdots$
HFF6P-$1512$-$7449$	$40.063019$	$-1.629157$	$2.07\pm 0.18$	$0.05\pm 0.03$	$25.96\pm 0.03$	$\cdots$	${6.41}_{-0.73}^{+0.73}$	$\cdots$
HFF6P-$1066$-$7101$	$40.044450$	$-1.619499$	$1.31\pm 0.10$	$0.02\pm 0.04$	$26.26\pm 0.04$	$\cdots$	${6.01}_{-0.69}^{+0.69}$	$\cdots$
HFF6P-$1553$-$6472$	$40.064711$	$-1.613127$	$1.88\pm 0.23$	$0.21\pm 0.05$	$26.37\pm 0.04$	$\cdots$	${6.32}_{-0.72}^{+0.72}$	$\cdots$
HFF6P-$0962$-$7254$	$40.040085$	$-1.623733$	$1.43\pm 0.12$	$-0.10\pm 0.05$	$26.47\pm 0.04$	$\cdots$	${6.15}_{-0.70}^{+0.70}$	$\cdots$
HFF6P-$1112$-$8152$	$40.046339$	$-1.637564$	$1.10\pm 0.13$	$0.16\pm 0.06$	$26.60\pm 0.05$	$\cdots$	${5.19}_{-0.61}^{+0.67}$	$\cdots$
HFF6P-$1365$-$7298$	$40.056894$	$-1.624969$	$1.03\pm 0.17$	$0.09\pm 0.07$	$26.84\pm 0.06$	$\cdots$	${1.06}_{-0.61}^{+0.31}$	$\cdots$
HFF6P-$1338$-$7507$	$40.055776$	$-1.630760$	$2.21\pm 0.44$	$0.05\pm 0.08$	$26.90\pm 0.06$	$\cdots$	${6.45}_{-0.73}^{+0.73}$	$\cdots$
HFF6P-$1443$-$8334$	$40.060155$	$-1.642617$	$1.03\pm 0.16$	$-0.14\pm 0.09$	$27.04\pm 0.07$	$\cdots$	${5.89}_{-0.68}^{+0.68}$	$\cdots$
HFF6P-$1496$-$6574$	$40.062337$	$-1.615954$	$>1.95$	$0.29\pm 0.10$	$27.07\pm 0.08$	$\cdots$	${7.11}_{-0.79}^{+0.80}$	$\cdots$
HFF6P-$1135$-$6350$	$40.047325$	$-1.609738$	$>1.87$	$0.34\pm 0.11$	$27.11\pm 0.08$	$\cdots$	${6.30}_{-0.72}^{+0.84}$	$\cdots$
HFF6P-$1233$-$7093$	$40.051408$	$-1.619257$	$>2.18$	$0.04\pm 0.10$	$27.12\pm 0.08$	$\cdots$	${6.51}_{-0.74}^{+0.74}$	$\cdots$
HFF6P-$1242$-$7083$	$40.051751$	$-1.618991$	$1.74\pm 0.36$	$-0.04\pm 0.10$	$27.17\pm 0.08$	$\cdots$	${6.30}_{-0.72}^{+0.71}$	$\cdots$
HFF6P-$1203$-$7168$	$40.050146$	$-1.621357$	$>1.94$	$0.21\pm 0.11$	$27.18\pm 0.08$	$\cdots$	${6.50}_{-1.08}^{+0.74}$	$\cdots$
HFF6P-$0954$-$7261$	$40.039781$	$-1.623927$	$1.39\pm 0.25$	$-0.09\pm 0.11$	$27.29\pm 0.09$	$\cdots$	${6.11}_{-0.70}^{+0.70}$	$\cdots$
HFF6P-$1339$-$7197$	$40.055809$	$-1.622150$	$1.74\pm 0.46$	$0.01\pm 0.12$	$27.39\pm 0.10$	$\cdots$	${6.29}_{-0.71}^{+0.71}$	$\cdots$
HFF6P-$1619$-$8043$	$40.067498$	$-1.634549$	$1.61\pm 0.49$	$0.20\pm 0.13$	$27.42\pm 0.10$	$\cdots$	${6.20}_{-0.71}^{+0.71}$	$\cdots$
HFF6P-$1406$-$8067$	$40.058588$	$-1.635205$	$>1.95$	$-0.10\pm 0.12$	$27.43\pm 0.10$	$\cdots$	${6.43}_{-0.73}^{+0.73}$	$\cdots$
HFF6P-$1120$-$6563$	$40.046698$	$-1.615649$	$>1.69$	$0.19\pm 0.14$	$27.47\pm 0.11$	$\cdots$	${6.28}_{-0.71}^{+0.76}$	$\cdots$
HFF6P-$1404$-$6507$	$40.058514$	$-1.614092$	$1.12\pm 0.25$	$-0.09\pm 0.14$	$27.52\pm 0.12$	$\cdots$	${5.94}_{-0.68}^{+0.68}$	$\cdots$
HFF6P-$1111$-$8294$	$40.046301$	$-1.641520$	$1.34\pm 0.29$	$-0.14\pm 0.14$	$27.53\pm 0.12$	$\cdots$	${6.05}_{-0.69}^{+0.69}$	$\cdots$
HFF6P-$1650$-$7475$	$40.068770$	$-1.629867$	$1.36\pm 0.38$	$-0.16\pm 0.16$	$27.75\pm 0.14$	$\cdots$	${6.09}_{-0.70}^{+0.70}$	$\cdots$
HFF6P-$0940$-$7273$	$40.039181$	$-1.624272$	$1.52\pm 0.35$	$-0.33\pm 0.16$	$27.76\pm 0.14$	$\cdots$	${6.14}_{-0.70}^{+0.70}$	$\cdots$
HFF6P-$1631$-$7409$	$40.067987$	$-1.628035$	$1.55\pm 0.48$	$-0.12\pm 0.17$	$27.77\pm 0.14$	$\cdots$	${6.16}_{-0.70}^{+0.70}$	$\cdots$
HFF6P-$1513$-$6504$	$40.063047$	$-1.614000$	$1.15\pm 0.33$	$-0.09\pm 0.17$	$27.78\pm 0.15$	$\cdots$	${5.89}_{-0.68}^{+0.68}$	$\cdots$
HFF6P-$1282$-$8053$	$40.053420$	$-1.634833$	$0.88\pm 0.29$	$-0.10\pm 0.18$	$27.87\pm 0.15$	$\cdots$	${5.79}_{-0.67}^{+0.67}$	$\cdots$
HFF6P-$0963$-$7467$	$40.040146$	$-1.629650$	$>1.51$	$0.12\pm 0.20$	$27.89\pm 0.16$	$\cdots$	${6.48}_{-0.97}^{+0.73}$	$\cdots$
HFF6P-$1352$-$6549$	$40.056353$	$-1.615251$	$>1.13$	$0.22\pm 0.22$	$27.95\pm 0.17$	$\cdots$	${6.00}_{-5.53}^{+0.86}$	$\cdots$
HFF6P-$1352$-$8104$	$40.056373$	$-1.636246$	$1.05\pm 0.36$	$-0.21\pm 0.20$	$28.00\pm 0.18$	$\cdots$	${5.68}_{-4.80}^{+0.65}$	$\cdots$
HFF6P-$1636$-$7324$	$40.068190$	$-1.625671$	$>1.36$	$-0.00\pm 0.21$	$28.00\pm 0.17$	$\cdots$	${6.45}_{-0.76}^{+0.73}$	$\cdots$
HFF6P-$1197$-$8268$	$40.049891$	$-1.640781$	$>1.65$	$-0.22\pm 0.21$	$28.02\pm 0.19$	$\cdots$	${6.41}_{-0.73}^{+0.73}$	$\cdots$
HFF6P-$1485$-$8415$	$40.061875$	$-1.644873$	$0.88\pm 0.38$	$-0.04\pm 0.22$	$28.03\pm 0.18$	$\cdots$	${5.67}_{-1.66}^{+0.65}$	$\cdots$
HFF6P-$1346$-$7336$	$40.056107$	$-1.626010$	$>1.06$	$0.18\pm 0.23$	$28.04\pm 0.18$	$\cdots$	${6.07}_{-0.81}^{+0.82}$	$\cdots$
HFF6P-$1534$-$8390$	$40.063919$	$-1.644193$	$1.09\pm 0.46$	$-0.05\pm 0.22$	$28.04\pm 0.18$	$\cdots$	${5.74}_{-5.48}^{+0.70}$	$\cdots$
HFF6P-$1105$-$8129$	$40.046060$	$-1.636943$	$0.98\pm 0.40$	$-0.01\pm 0.24$	$28.08\pm 0.20$	$\cdots$	${5.67}_{-4.66}^{+0.65}$	$\cdots$
HFF6P-$1437$-$6560$	$40.059896$	$-1.615568$	$0.91\pm 0.41$	$-0.08\pm 0.24$	$28.12\pm 0.20$	$\cdots$	${5.76}_{-4.85}^{+0.66}$	$\cdots$
HFF6P-$1197$-$8275$	$40.049900$	$-1.640994$	$>1.42$	$-0.13\pm 0.25$	$28.16\pm 0.22$	$\cdots$	${6.21}_{-0.71}^{+0.71}$	$\cdots$
HFF6P-$1554$-$7558$	$40.064752$	$-1.632167$	$0.81\pm 0.39$	$-0.14\pm 0.24$	$28.20\pm 0.21$	$\cdots$	${1.17}_{-1.06}^{+3.86}$	$\cdots$

Table 5. Table 5 Dropout candidates at z ∼ 8 similar-to 𝑧 8 z\sim 8

ID	R.A. (J2000)	Dec (J2000)	$Y_{105}-J_{125}$	$J_{125}-J{H}_{140}$	$J{H}_{140}$aaTotal magnitudes $m_{\mathrm{tot}}$ estimated with the aperture correction $m_{\mathrm{tot}}=m_{\mathrm{AP}}-0.82$.	$\mu$bbMagnifications calculated with mass models in Kawamata et al. (2017).	Photo-$z$	ReferenceccReferences. (1)Atek et al. (2014), (2)Atek et al. (2015a), (3)Coe et al. (2015), (4)Laporte et al. (2014), (5)Laporte et al. (2015), (6)Laporte et al. (2016), (7)Livermore et al. (2017), (8)McLeod et al. (2016), (9)Oesch et al. (2015) (10)Zheng et al. (2014), (11)Zitrin et al. (2014)
Abell2744 Cluster
HFF1C-$2508$-$2496$	$3.604518$	$-30.380467$	$1.17\pm 0.07$	$0.04\pm 0.04$	$25.92\pm 0.03$	$1.31$	${8.00}_{-0.88}^{+0.88}$	(1), (2), (3), (4), (10)
HFF1C-$2481$-$2561$	$3.603378$	$-30.382254$	$1.27\pm 0.15$	$0.14\pm 0.08$	$26.64\pm 0.05$	$1.40$	${8.20}_{-0.90}^{+0.90}$	(2), (3), (7), (10)
HFF1C-$2306$-$3089$	$3.596091$	$-30.385833$	$1.30\pm 0.16$	$0.06\pm 0.08$	$26.68\pm 0.06$	$2.04$	${8.18}_{-0.90}^{+0.90}$	(2), (3), (7), (10)
HFF1C-$2555$-$2515$	$3.606461$	$-30.380996$	$1.12\pm 0.14$	$-0.18\pm 0.09$	$26.95\pm 0.07$	$1.33$	${7.96}_{-0.88}^{+0.88}$	(2), (3), (7), (10)
HFF1C-$2492$-$2561$	$3.603859$	$-30.382263$	$1.92\pm 0.37$	$0.16\pm 0.11$	$26.99\pm 0.07$	$1.40$	${8.40}_{-0.92}^{+0.92}$	(2), (3), (7), (8), (10)
HFF1C-$2557$-$2513$	$3.606577$	$-30.380924$	$1.10\pm 0.24$	$0.22\pm 0.13$	$27.17\pm 0.08$	$1.32$	${7.88}_{-6.13}^{+0.87}$	(2), (10)
HFF1C-$2135$-$2432$	$3.588980$	$-30.378668$	$1.13\pm 0.19$	$-0.19\pm 0.13$	$27.30\pm 0.10$	$1.69$	${7.94}_{-0.88}^{+0.88}$	(2), (3), (10)
HFF1C-$2495$-$2562$	$3.603997$	$-30.382304$	$1.05\pm 0.32$	$0.13\pm 0.19$	$27.61\pm 0.12$	$1.40$	${7.90}_{-6.08}^{+0.87}$	(10)
HFF1C-$2216$-$4356$	$3.592349$	$-30.409892$	$0.60\pm 0.28$	$-0.30\pm 0.25$	$28.01\pm 0.20$	$8.56$	${7.22}_{-2.02}^{+0.81}$	(2), (7), (10)
HFF1C-$2521$-$2532$	$3.605062$	$-30.381463$	$0.84\pm 0.32$	$-0.16\pm 0.25$	$28.07\pm 0.18$	$1.35$	${7.67}_{-6.39}^{+0.85}$	(2), (7)
Abell2744 Parallel
HFF1P-$5398$-$1451$	$3.474918$	$-30.362542$	$0.60\pm 0.12$	$-0.05\pm 0.11$	$27.03\pm 0.08$	$\cdots$	${7.50}_{-1.52}^{+0.83}$	$\cdots$
HFF1P-$5021$-$2024$	$3.459245$	$-30.367360$	$0.70\pm 0.20$	$-0.06\pm 0.17$	$27.53\pm 0.12$	$\cdots$	${7.56}_{-1.80}^{+0.84}$	$\cdots$
HFF1P-$5512$-$1588$	$3.479684$	$-30.366359$	$0.86\pm 0.36$	$0.21\pm 0.25$	$27.81\pm 0.15$	$\cdots$	${7.76}_{-6.38}^{+0.86}$	$\cdots$
HFF1P-$5530$-$3153$	$3.480419$	$-30.387608$	$0.55\pm 0.25$	$0.08\pm 0.22$	$27.84\pm 0.15$	$\cdots$	${7.28}_{-6.27}^{+0.81}$	$\cdots$
MACS0416 Cluster
HFF2C-$1151$-$4540$	$64.047984$	$-24.081670$	$1.92\pm 0.20$	$0.01\pm 0.06$	$26.50\pm 0.04$	$1.44$	${8.39}_{-0.92}^{+0.92}$	(3), (5), (8)
HFF2C-$0939$-$5354$	$64.039164$	$-24.093183$	$2.19\pm 0.34$	$0.18\pm 0.08$	$26.61\pm 0.05$	$1.38$	${8.50}_{-0.93}^{+0.93}$	(5), (8)
HFF2C-$1153$-$4531$	$64.048057$	$-24.081431$	$2.28\pm 0.56$	$0.49\pm 0.11$	$26.80\pm 0.06$	$1.44$	${8.67}_{-0.95}^{+0.95}$	(3), (5)
HFF2C-$0901$-$5171$	$64.037567$	$-24.088109$	$1.94\pm 0.63$	$0.12\pm 0.18$	$27.56\pm 0.12$	$1.70$	${8.36}_{-0.92}^{+0.92}$	(5), (7), (8)
HFF2C-$1447$-$3538$	$64.060329$	$-24.064958$	$0.86\pm 0.19$	$-0.31\pm 0.16$	$27.71\pm 0.12$	$1.79$	${7.70}_{-0.85}^{+0.85}$	(7)
MACS0416 Parallel
HFF2P-$2912$-$7330$	$64.121367$	$-24.125856$	$0.69\pm 0.11$	$-0.14\pm 0.09$	$27.07\pm 0.06$	$\cdots$	${7.62}_{-0.84}^{+0.84}$	$\cdots$
HFF2P-$3286$-$6419$	$64.136930$	$-24.111643$	$0.98\pm 0.18$	$0.13\pm 0.10$	$27.21\pm 0.06$	$\cdots$	${7.81}_{-0.86}^{+0.86}$	$\cdots$
HFF2P-$3596$-$6480$	$64.149865$	$-24.113353$	$1.74\pm 0.58$	$0.39\pm 0.17$	$27.56\pm 0.09$	$\cdots$	${8.52}_{-0.93}^{+0.93}$	(3), (8)
HFF2P-$3044$-$6002$	$64.126862$	$-24.100067$	$1.20\pm 0.27$	$-0.21\pm 0.16$	$27.80\pm 0.12$	$\cdots$	${1.76}_{-0.27}^{+6.42}$	(8)
HFF2P-$3042$-$6011$	$64.126779$	$-24.100323$	$1.33\pm 0.43$	$0.18\pm 0.19$	$27.81\pm 0.12$	$\cdots$	${8.19}_{-0.94}^{+0.90}$	(3), (8)
HFF2P-$3549$-$6422$	$64.147904$	$-24.111729$	$2.26\pm 0.97$	$-0.02\pm 0.21$	$28.02\pm 0.14$	$\cdots$	${8.35}_{-0.92}^{+0.92}$	$\cdots$
HFF2P-$2862$-$7348$	$64.119271$	$-24.126357$	$0.78\pm 0.31$	$-0.09\pm 0.23$	$28.07\pm 0.16$	$\cdots$	${5.74}_{-5.18}^{+2.19}$	$\cdots$
HFF2P-$3642$-$6304$	$64.151758$	$-24.108450$	$>2.04$	$0.15\pm 0.27$	$28.13\pm 0.17$	$\cdots$	${8.61}_{-6.48}^{+0.94}$	(3), (8)
HFF2P-$2871$-$7010$	$64.119662$	$-24.116955$	$0.86\pm 0.31$	$-0.12\pm 0.22$	$28.14\pm 0.16$	$\cdots$	${7.69}_{-6.20}^{+0.85}$	$\cdots$
MACS0717 Parallel
HFF3P-$2251$-$9452$	$109.343797$	$37.829234$	$1.35\pm 0.33$	$0.21\pm 0.15$	$27.26\pm 0.10$	$\cdots$	${8.25}_{-0.91}^{+0.91}$	(6)
HFF3P-$1788$-$9254$	$109.324524$	$37.823744$	$1.26\pm 0.27$	$-0.05\pm 0.15$	$27.37\pm 0.10$	$\cdots$	${8.06}_{-0.89}^{+0.89}$	(6)
HFF3P-$1891$-$8538$	$109.328823$	$37.814951$	$0.61\pm 0.19$	$-0.19\pm 0.17$	$27.62\pm 0.13$	$\cdots$	${5.51}_{-4.87}^{+1.66}$	(6)
HFF3P-$1672$-$0089$	$109.319676$	$37.835808$	$0.54\pm 0.24$	$-0.01\pm 0.20$	$27.67\pm 0.14$	$\cdots$	${7.29}_{-2.23}^{+0.81}$	$\cdots$
HFF3P-$1854$-$0446$	$109.327261$	$37.845741$	$0.92\pm 0.33$	$-0.09\pm 0.24$	$27.93\pm 0.18$	$\cdots$	${7.76}_{-2.74}^{+0.86}$	$\cdots$
HFF3P-$2153$-$9369$	$109.339742$	$37.826923$	$0.95\pm 0.34$	$-0.11\pm 0.25$	$27.95\pm 0.18$	$\cdots$	${7.76}_{-6.00}^{+0.86}$	(6)
MACS1149 Cluster
HFF4C-$4025$-$5027$	$177.417749$	$22.417435$	$0.57\pm 0.03$	$0.02\pm 0.02$	$25.19\pm 0.02$	$1.57$	${7.50}_{-0.83}^{+0.83}$	$\cdots$
HFF4C-$4024$-$4492$	$177.417702$	$22.413687$	$1.61\pm 0.50$	$0.35\pm 0.19$	$27.26\pm 0.12$	$1.63$	${8.42}_{-0.92}^{+0.92}$	$\cdots$
MACS1149 Parallel
HFF4P-$3745$-$6484$	$177.406060$	$22.280113$	$1.71\pm 0.29$	$0.36\pm 0.10$	$26.66\pm 0.06$	$\cdots$	${8.37}_{-0.92}^{+0.92}$	$\cdots$
HFF4P-$3998$-$8560$	$177.416587$	$22.315557$	$1.16\pm 0.15$	$0.07\pm 0.09$	$26.85\pm 0.06$	$\cdots$	${7.96}_{-0.88}^{+0.88}$	$\cdots$
HFF4P-$3959$-$8115$	$177.414974$	$22.303195$	$0.63\pm 0.16$	$-0.00\pm 0.14$	$27.36\pm 0.09$	$\cdots$	${7.53}_{-2.07}^{+0.84}$	$\cdots$
HFF4P-$3612$-$8473$	$177.400509$	$22.313149$	$0.68\pm 0.19$	$-0.03\pm 0.16$	$27.55\pm 0.11$	$\cdots$	${7.57}_{-6.25}^{+0.84}$	$\cdots$
HFF4P-$4149$-$8180$	$177.422903$	$22.305006$	$0.83\pm 0.23$	$0.02\pm 0.18$	$27.67\pm 0.12$	$\cdots$	${7.73}_{-6.66}^{+0.86}$	$\cdots$
HFF4P-$3769$-$8456$	$177.407054$	$22.312680$	$0.60\pm 0.20$	$-0.17\pm 0.19$	$27.78\pm 0.14$	$\cdots$	${7.38}_{-1.50}^{+0.82}$	$\cdots$
HFF4P-$4419$-$8349$	$177.434162$	$22.309708$	$0.76\pm 0.23$	$-0.28\pm 0.21$	$27.98\pm 0.17$	$\cdots$	${1.71}_{-1.19}^{+6.08}$	$\cdots$
HFF4P-$3878$-$7079$	$177.411594$	$22.285550$	$1.02\pm 0.40$	$0.04\pm 0.25$	$28.01\pm 0.17$	$\cdots$	${7.86}_{-6.63}^{+0.87}$	$\cdots$
HFF4P-$4553$-$7304$	$177.439740$	$22.291792$	$0.78\pm 0.32$	$0.02\pm 0.24$	$28.01\pm 0.17$	$\cdots$	${7.54}_{-6.48}^{+0.84}$	$\cdots$
HFF4P-$3593$-$8440$	$177.399737$	$22.312238$	$0.79\pm 0.28$	$-0.31\pm 0.25$	$28.15\pm 0.19$	$\cdots$	${7.45}_{-6.68}^{+0.83}$	$\cdots$
AbellS1063 Cluster
HFF5C-$4316$-$1323$	$342.179848$	$-44.525661$	$1.48\pm 0.26$	$0.08\pm 0.11$	$26.97\pm 0.08$	$27.72$	${8.21}_{-0.90}^{+0.90}$	$\cdots$
HFF5C-$4374$-$1338$	$342.182266$	$-44.526074$	$1.88\pm 0.57$	$0.35\pm 0.16$	$27.21\pm 0.09$	$24.75$	${8.52}_{-0.93}^{+0.93}$	$\cdots$
HFF5C-$4111$-$2125$	$342.171304$	$-44.536810$	$0.54\pm 0.23$	$-0.22\pm 0.22$	$27.60\pm 0.17$	$4.10$	${1.64}_{-1.53}^{+0.47}$	$\cdots$
HFF5C-$3935$-$1469$	$342.163986$	$-44.529704$	$1.06\pm 0.41$	$0.15\pm 0.25$	$27.89\pm 0.16$	$5.13$	${7.92}_{-6.93}^{+0.87}$	$\cdots$
AbellS1063 Parallel
HFF5P-$2129$-$2064$	$342.338729$	$-44.535120$	$0.56\pm 0.06$	$0.03\pm 0.05$	$26.33\pm 0.03$	$\cdots$	${7.44}_{-0.83}^{+0.83}$	$\cdots$
HFF5P-$1912$-$1491$	$342.329688$	$-44.530307$	$0.96\pm 0.10$	$-0.04\pm 0.07$	$26.75\pm 0.05$	$\cdots$	${7.88}_{-0.87}^{+0.87}$	$\cdots$
HFF5P-$1278$-$2047$	$342.303254$	$-44.534661$	$1.17\pm 0.45$	$0.16\pm 0.24$	$27.85\pm 0.15$	$\cdots$	${7.98}_{-6.34}^{+0.88}$	$\cdots$
HFF5P-$2027$-$2472$	$342.334489$	$-44.546470$	$0.55\pm 0.21$	$-0.27\pm 0.21$	$28.07\pm 0.15$	$\cdots$	${7.21}_{-6.07}^{+0.81}$	$\cdots$
HFF5P-$1617$-$1544$	$342.317413$	$-44.531796$	$0.80\pm 0.34$	$-0.08\pm 0.25$	$28.19\pm 0.18$	$\cdots$	${1.75}_{-1.46}^{+5.27}$	$\cdots$
HFF5P-$1222$-$3093$	$342.300944$	$-44.552588$	$1.09\pm 0.41$	$-0.08\pm 0.25$	$28.20\pm 0.17$	$\cdots$	${7.88}_{-6.46}^{+0.87}$	$\cdots$
Abell370 Cluster
HFF6C-$5058$-$4269$	$39.960762$	$-1.574159$	$0.83\pm 0.05$	$-0.06\pm 0.04$	$25.62\pm 0.03$	$8.65$	${7.78}_{-0.86}^{+0.86}$	$\cdots$
HFF6C-$5131$-$4097$	$39.963821$	$-1.569362$	$0.96\pm 0.09$	$-0.07\pm 0.07$	$25.99\pm 0.05$	$8.93$	${7.88}_{-0.87}^{+0.87}$	$\cdots$
HFF6C-$5578$-$4519$	$39.982425$	$-1.581097$	$1.63\pm 0.22$	$-0.04\pm 0.10$	$26.49\pm 0.07$	$8.05$	${8.23}_{-0.90}^{+0.90}$	$\cdots$
HFF6C-$5420$-$5141$	$39.975874$	$-1.587261$	$1.78\pm 0.35$	$-0.08\pm 0.15$	$26.93\pm 0.11$	$4.66$	${8.22}_{-0.90}^{+0.90}$	$\cdots$
HFF6C-$4926$-$4404$	$39.955279$	$-1.577912$	$2.03\pm 0.47$	$0.02\pm 0.16$	$26.98\pm 0.11$	$3.16$	${8.34}_{-0.92}^{+0.92}$	$\cdots$
HFF6C-$5187$-$5411$	$39.966133$	$-1.594771$	$0.61\pm 0.27$	$0.07\pm 0.24$	$27.34\pm 0.16$	$17.57$	${7.38}_{-5.89}^{+0.82}$	$\cdots$
Abell370 Parallel
HFF6P-$1733$-$6559$	$40.072227$	$-1.615552$	$0.78\pm 0.23$	$0.19\pm 0.17$	$27.49\pm 0.11$	$\cdots$	${7.58}_{-2.15}^{+0.84}$	$\cdots$
HFF6P-$1374$-$7002$	$40.057265$	$-1.616732$	$0.69\pm 0.27$	$-0.04\pm 0.24$	$27.97\pm 0.17$	$\cdots$	${1.64}_{-0.54}^{+6.17}$	$\cdots$
HFF6P-$1167$-$6515$	$40.048638$	$-1.614306$	$0.66\pm 0.33$	$-0.08\pm 0.30$	$28.25\pm 0.22$	$\cdots$	${1.77}_{-1.56}^{+1.36}$	$\cdots$

Table 6. Table 6 Dropout candidates at z ∼ 9 similar-to 𝑧 9 z\sim 9

ID	R.A. (J2000)	Dec (J2000)	$YJ-J{H}_{140}$	$J{H}_{140}-H_{160}$	$H_{160}$aaTotal magnitudes $m_{\mathrm{tot}}$ estimated with the aperture correction $m_{\mathrm{tot}}=m_{\mathrm{AP}}-0.82$.	$\mu$bbMagnifications calculated with mass models in Kawamata et al. (2017).	Photo-$z$	ReferenceccReferences. (1)Atek et al. (2014), (2)Atek et al. (2015a), (3)Coe et al. (2015), (4)Laporte et al. (2014), (5)Laporte et al. (2015), (6)Laporte et al. (2016), (7)Livermore et al. (2017), (8)McLeod et al. (2016), (9)Oesch et al. (2015) (10)Zheng et al. (2014), (11)Zitrin et al. (2014)
Abell2744 Cluster
HFF1C-$2481$-$2561$	$3.603380$	$-30.382255$	$0.78\pm 0.08$	$-0.05\pm 0.07$	$26.69\pm 0.05$	$1.40$	${8.19}_{-0.90}^{+0.90}$	(2), (3), (7), (10)
HFF1C-$2492$-$2561$	$3.603859$	$-30.382262$	$1.12\pm 0.11$	$0.19\pm 0.09$	$26.79\pm 0.06$	$1.40$	${8.40}_{-0.92}^{+0.92}$	(1), (2), (3), (7), (10)
HFF1C-$2220$-$4053$	$3.592512$	$-30.401486$	$>1.21$	$0.55\pm 0.30$	$27.38\pm 0.17$	$14.13$	${9.54}_{-7.31}^{+1.03}$	(9), (11)
Abell2744 Parallel
HFF1P-$5363$-$4016$	$3.473469$	$-30.400460$	$0.96\pm 0.18$	$0.08\pm 0.15$	$27.44\pm 0.10$	$\cdots$	${8.30}_{-6.63}^{+0.91}$	$\cdots$
HFF1P-$5364$-$3024$	$3.473522$	$-30.384024$	$>1.34$	$0.26\pm 0.22$	$27.77\pm 0.13$	$\cdots$	${8.73}_{-6.34}^{+0.95}$	(8)
HFF1P-$5733$-$3462$	$3.488893$	$-30.396183$	$1.65\pm 0.26$	$-0.23\pm 0.18$	$27.77\pm 0.14$	$\cdots$	${8.72}_{-0.95}^{+0.95}$	(8)
HFF1P-$5386$-$2074$	$3.474445$	$-30.368728$	$>1.80$	$-0.26\pm 0.27$	$28.17\pm 0.21$	$\cdots$	${8.89}_{-6.87}^{+0.97}$	$\cdots$
MACS0416 Cluster
HFF2C-$1151$-$4540$	$64.047984$	$-24.081671$	$0.97\pm 0.06$	$0.00\pm 0.06$	$26.50\pm 0.04$	$1.44$	${8.39}_{-0.92}^{+0.92}$	(3), (5), (8)
HFF2C-$0939$-$5354$	$64.039161$	$-24.093184$	$1.27\pm 0.08$	$0.06\pm 0.07$	$26.55\pm 0.05$	$1.39$	${8.51}_{-0.93}^{+0.93}$	(5), (8)
HFF2C-$0901$-$5172$	$64.037566$	$-24.088113$	$1.06\pm 0.18$	$-0.25\pm 0.20$	$27.82\pm 0.15$	$1.70$	${8.34}_{-0.92}^{+0.92}$	(5), (7), (8)
MACS0416 Parallel
HFF2P-$3441$-$6014$	$64.143391$	$-24.100397$	$1.00\pm 0.22$	$0.15\pm 0.13$	$27.43\pm 0.09$	$\cdots$	${2.12}_{-0.54}^{+6.06}$	$\cdots$
HFF2P-$3596$-$6480$	$64.149865$	$-24.113352$	$1.26\pm 0.17$	$0.03\pm 0.13$	$27.53\pm 0.09$	$\cdots$	${8.51}_{-0.93}^{+0.93}$	(3), (8)
HFF2P-$3549$-$6422$	$64.147905$	$-24.111729$	$1.11\pm 0.21$	$0.18\pm 0.19$	$27.84\pm 0.13$	$\cdots$	${8.35}_{-0.92}^{+0.92}$	$\cdots$
HFF2P-$3042$-$6011$	$64.126779$	$-24.100325$	$0.84\pm 0.19$	$-0.16\pm 0.19$	$27.97\pm 0.14$	$\cdots$	${8.19}_{-0.92}^{+0.90}$	(3), (8)
HFF2P-$3172$-$6467$	$64.132190$	$-24.112994$	$>1.45$	$0.04\pm 0.22$	$28.08\pm 0.15$	$\cdots$	${8.84}_{-2.06}^{+0.96}$	(8)
HFF2P-$3736$-$6107$	$64.155668$	$-24.102997$	$1.29\pm 0.35$	$-0.27\pm 0.22$	$28.15\pm 0.18$	$\cdots$	${8.55}_{-6.81}^{+0.94}$	$\cdots$
MACS0717 Parallel
HFF3P-$2251$-$9452$	$109.343799$	$37.829235$	$0.89\pm 0.15$	$-0.27\pm 0.16$	$27.53\pm 0.13$	$\cdots$	${8.25}_{-0.91}^{+0.91}$	(6)
HFF3P-$1821$-$9546$	$109.325904$	$37.831848$	$1.03\pm 0.33$	$0.14\pm 0.18$	$27.54\pm 0.12$	$\cdots$	${2.17}_{-0.64}^{+6.27}$	$\cdots$
HFF3P-$1762$-$9402$	$109.323423$	$37.827843$	$1.00\pm 0.29$	$-0.26\pm 0.23$	$27.94\pm 0.18$	$\cdots$	${7.57}_{-6.11}^{+1.11}$	(6)
MACS1149 Cluster
HFF4C-$3358$-$4457$	$177.389950$	$22.412710$	$>2.39$	$0.19\pm 0.05$	$25.80\pm 0.03$	$17.53$	${9.21}_{-1.00}^{+1.00}$	(8)
HFF4C-$4024$-$4492$	$177.417700$	$22.413691$	$1.11\pm 0.19$	$-0.15\pm 0.17$	$27.44\pm 0.12$	$1.63$	${8.40}_{-0.92}^{+0.92}$	$\cdots$
HFF4C-$3373$-$4483$	$177.390553$	$22.413417$	$>1.30$	$0.15\pm 0.29$	$27.75\pm 0.17$	$63.86$	${8.65}_{-6.85}^{+0.95}$	(8)
HFF4C-$3617$-$3327$	$177.400727$	$22.392425$	$>1.28$	$-0.17\pm 0.30$	$27.89\pm 0.22$	$35.36$	${8.45}_{-6.17}^{+0.93}$	$\cdots$
MACS1149 Parallel
HFF4P-$3745$-$6484$	$177.406057$	$22.280112$	$1.22\pm 0.10$	$0.21\pm 0.07$	$26.44\pm 0.05$	$\cdots$	${8.36}_{-0.92}^{+0.92}$	$\cdots$
HFF4P-$3994$-$7367$	$177.416441$	$22.293541$	$>1.98$	$0.02\pm 0.14$	$27.33\pm 0.09$	$\cdots$	${9.20}_{-1.00}^{+1.00}$	(8)
HFF4P-$4205$-$8351$	$177.425216$	$22.309763$	$1.19\pm 0.39$	$-0.00\pm 0.31$	$28.28\pm 0.22$	$\cdots$	${2.13}_{-0.81}^{+7.20}$	$\cdots$
AbellS1063 Cluster
HFF5C-$4316$-$1323$	$342.179874$	$-44.525660$	$0.78\pm 0.12$	$-0.03\pm 0.12$	$27.07\pm 0.08$	$29.58$	${8.15}_{-0.90}^{+0.90}$	$\cdots$
HFF5C-$4374$-$1338$	$342.182264$	$-44.526074$	$1.29\pm 0.16$	$-0.13\pm 0.14$	$27.34\pm 0.11$	$24.15$	${8.52}_{-0.93}^{+0.93}$	$\cdots$
AbellS1063 Parallel
HFF5P-$1975$-$2112$	$342.332299$	$-44.536446$	$1.05\pm 0.23$	$0.21\pm 0.16$	$27.47\pm 0.10$	$\cdots$	${2.13}_{-0.45}^{+6.51}$	$\cdots$
HFF5P-$2042$-$2369$	$342.335117$	$-44.543602$	$0.94\pm 0.36$	$0.17\pm 0.30$	$28.20\pm 0.20$	$\cdots$	${8.29}_{-6.63}^{+1.01}$	$\cdots$
HFF5P-$2092$-$3100$	$342.337186$	$-44.552795$	$>0.94$	$0.00\pm 0.32$	$28.42\pm 0.24$	$\cdots$	${8.19}_{-2.43}^{+0.90}$	$\cdots$
Abell370 Cluster
HFF6C-$5578$-$4519$	$39.982427$	$-1.581097$	$0.78\pm 0.10$	$0.04\pm 0.10$	$26.45\pm 0.06$	$8.26$	${8.23}_{-0.90}^{+0.90}$	$\cdots$
HFF6C-$5421$-$5141$	$39.975875$	$-1.587260$	$0.81\pm 0.15$	$-0.07\pm 0.15$	$27.01\pm 0.10$	$4.55$	${8.23}_{-0.90}^{+0.90}$	$\cdots$
Abell370 Parallel
HFF6P-$1732$-$6562$	$40.072207$	$-1.615618$	$0.85\pm 0.17$	$0.03\pm 0.15$	$27.43\pm 0.10$	$\cdots$	${8.14}_{-1.41}^{+0.90}$	$\cdots$
HFF6P-$1247$-$6578$	$40.051970$	$-1.616066$	$0.82\pm 0.25$	$0.08\pm 0.17$	$27.60\pm 0.11$	$\cdots$	${2.05}_{-0.73}^{+5.75}$	$\cdots$
HFF6P-$1350$-$7372$	$40.056259$	$-1.627015$	$1.14\pm 0.36$	$0.22\pm 0.21$	$27.69\pm 0.12$	$\cdots$	${8.33}_{-6.56}^{+1.18}$	$\cdots$
HFF6P-$1194$-$8213$	$40.049783$	$-1.639252$	$>1.83$	$-0.17\pm 0.19$	$27.81\pm 0.13$	$\cdots$	${8.89}_{-0.97}^{+0.97}$	$\cdots$
HFF6P-$1311$-$7372$	$40.054627$	$-1.627015$	$1.24\pm 0.30$	$-0.05\pm 0.24$	$28.02\pm 0.17$	$\cdots$	${8.49}_{-6.68}^{+0.93}$	$\cdots$
HFF6P-$1293$-$6262$	$40.053900$	$-1.607296$	$>1.83$	$-0.19\pm 0.22$	$28.03\pm 0.16$	$\cdots$	${8.90}_{-6.47}^{+0.97}$	$\cdots$
HFF6P-$1514$-$7171$	$40.063097$	$-1.621433$	$1.46\pm 0.67$	$-0.15\pm 0.28$	$28.29\pm 0.20$	$\cdots$	${8.61}_{-7.00}^{+1.10}$	$\cdots$

Equations

$$i_{814}-Y_{105}>0.8,$$

$$Y_{105}-J_{125}<0.8,$$

$$i_{814}-Y_{105}>2(Y_{105}-J_{125})+0.6,$$

$$Y_{105}-J_{125}>0.5,$$

$$J_{125}-J{H}_{140}<0.5,$$

$$Y_{105}-J_{125}>1.6(J_{125}-J{H}_{140})+\mathrm{0.4.}$$

$$(Y_{105}+J_{125})/2-J{H}_{140}>0.75,$$

$$\begin{array}{r}(Y_{105}+J_{125})/2-J{H}_{140}>\\ 0.8(J{H}_{140}-H_{160})+0.75,\end{array}$$

$$J_{125}-H_{160}<1.15,$$

$$J{H}_{140}-H_{160}<\mathrm{0.6.}$$

$$J_{125}-H_{160}>1.2,$$

$$S/N(B_{435}\mathrm{to}{Y}_{105})<2.$$

$$\begin{array}{r}\Phi (M_{\mathrm{UV}},{\varphi }_{\ast },M_{\ast },\alpha )d{M}_{\mathrm{UV}}=0.4{\varphi }_{\ast }\ln (10)\\ \times \exp \left[10^{-0.4(M_{\mathrm{UV}}-M_{\ast })}\right]10^{-0.4(\alpha +1)(M_{\mathrm{UV}}-M_{\ast })}d{M}_{\mathrm{UV}}.\end{array}$$

$$\mathcal{L}\propto \prod _{\mathrm{field}}\prod _i{n}_{\mathrm{sim},i}^{n_{\mathrm{obs},i}}{e}^{-n_{\mathrm{sim},i}},$$

$${\rho }_{\mathrm{UV}}(z)={\int }_{-\infty }^{M_{\mathrm{trunc}}}\Phi (M)L(M)dM,$$

$${\dot{Q}}_{{\mathrm{H}}_{\mathrm{II}}}=\frac{{\dot{n}}_{\mathrm{ion}}}{⟨n_{\mathrm{H}}⟩}-\frac{Q_{{\mathrm{H}}_{\mathrm{II}}}}{t_{\mathrm{rec}}}.$$

$${\dot{n}}_{\mathrm{ion}}$$

$$⟨n_{\mathrm{H}}⟩$$

$$t_{\mathrm{rec}}=\frac{1}{C_{{\mathrm{H}}_{\mathrm{II}}}{\alpha }_{\mathrm{B}}(T)(1+Y_{\mathrm{p}}/4X_{\mathrm{p}})⟨n_{\mathrm{H}}⟩(1+z{)}^3},$$

$$C_{{\mathrm{H}}_{\mathrm{II}}}=2.9\times {\left[\frac{(1+z)}{6}\right]}^{-1.1},$$

$$\begin{array}{r}{\tau }_e(z)={\int }_0^z\frac{c(1+z^{\prime }{)}^2}{H(z^{\prime })}{Q}_{{\mathrm{H}}_{\mathrm{II}}}{\sigma }_{\mathrm{T}}⟨n_{\mathrm{H}}⟩\\ \times (1+\eta Y_{\mathrm{p}}/4X_{\mathrm{p}})d{z}^{\prime },\end{array}$$

$${\rho }_{\mathrm{UV}}(z)=a_p\frac{(1+z{)}_p^b}{1+{\left[(1+z)/c_p\right]}_p^d},$$

$${\rho }_{\mathrm{UV}}(z)=\frac{2{\rho }_{\mathrm{UV}}^{\ast }}{10^{a(z-z_{\ast })}+10^{b(z-z_{\ast })}},$$

Full text

††slugcomment: Accepted for publication in ApJ

1. Introduction

Understanding the sources of cosmic reionization is one of the goals of modern astronomy. Observational studies show that the reionization occurred at $z\gtrsim 6$ (Fan et al. 2006; Pentericci et al. 2011, 2014; Ono et al. 2012; Totani et al. 2006, 2014; Kashikawa et al. 2011; Ouchi et al. 2010; Konno et al. 2014; Treu et al. 2013). Major sources of the cosmic reionization are thought to be star-forming galaxies. Recent studies indicate that UV luminosity functions of the star-forming galaxies have steep faint-end slopes at $z\gtrsim 6$ (Bouwens et al. 2015; Schenker et al. 2013; McLure et al. 2013), which suggests that the ionizing photons are mainly supplied by faint galaxies. However, high-$z$ galaxy observations, such as Hubble Ultra Deep Field, can reach the limiting absolute magnitudes down to $\lesssim-16$ mag at $z\gtrsim 6$. The abundance of galaxies is not well known at the magnitude fainter than $\sim-16$ where contributions to ionizing photon budget may be dominated. Moreover, there exist large uncertainties of various parameters to estimate an ionizing photon emission rate from the galaxy abundance obtained by observations. One of the important parameters is the numerical factor $\xi_{\mathrm{ion}}$ that converts a UV luminosity density to the ionizing photon emission rate of a star-forming galaxy. Bouwens et al. (2016a) estimated that $\log\xi_{\mathrm{ion}}/[\mathrm{erg}^{-1}\ \mathrm{Hz}]$ has a mean value of $25.34\pm 0.02$, albeit at $z\sim 4-5$, the post-reionization epoch. (see also Nakajima et al. (2016) for the recent studies of $\xi_{\mathrm{ion}}$). Another important parameter is the escape fraction of ionizing photons $f_{\mathrm{esc}}$, which is the fraction of the number of escaping ionizing photons to that of ionizing photons produced in a galaxy. Steidel et al. (2001) estimated that the average value of $f_{\mathrm{esc}}$ is $\sim 0.1$ at $z\sim 3$ (see also Shapley et al. 2006; Iwata et al. 2009; Nestor et al. 2011; Japelj et al. 2017). Ono et al. (2010) investigated the stellar populations of Ly$\alpha$ emitters at $z\sim 6$, and obtained weak upper limits of $f_{\mathrm{esc}}\sim 0.6$ at $z=5.7$ and $f_{\mathrm{esc}}\sim 0.9$ at $z=6.6$, based on the constraints on the nebular emission line fluxes. Although many constraints are given by these studies, reasonable constraints on $\xi_{\mathrm{ion}}$ and $f_{\mathrm{esc}}$ at the epoch of reionization have not been obtained so far.

Gravitational lensing is an effective tool for studying high-redshift galaxies. Cluster Lensing And Supernova survey with Hubble (CLASH; Postman et al. 2012) has discovered many candidates of faint galaxies at $z\gtrsim 6$ strongly lensed by galaxy clusters. In October 2013, Hubble Frontier Fields (HFF; PI: Lotz) program has started observing six massive clusters: Abell 2744, MACSJ0416, MACSJ0717, MACSJ1149, AbellS1063, and Abell370 (Lotz et al. 2017). The HFF program achieves the limiting magnitudes $\sim 29$ AB mag at the $5\sigma$ level, which are $\sim 1$ mag deeper than those of CLASH. Many groups study the properties of high-redshift galaxies using a part of the HFF data (Atek et al. 2015a, b; Zheng et al. 2014; Coe et al. 2015; Oesch et al. 2015; Ishigaki et al. 2015, 2016; Kawamata et al. 2015, 2016; Livermore et al. 2017; Bouwens et al. 2017a, b; McLeod et al. 2015, 2016). In September 2016, the observations for all of the six HFF clusters are completed. Here we exploit the full six cluster HFF data to investigate the galaxies at the reionization epoch.

In this paper, we first present details of the HFF data in Section 2. In Section 3, we select high-redshift galaxies with the dropout selection technique. We obtain UV luminosity functions in Section 4, and discuss the properties of the faint galaxies in Section 5. Finally, we summarize our results in Section 6. Throughout this paper, we use a cosmology with $\Omega_{\mathrm{m}}=0.3$, $\Omega_{\mathrm{\Lambda}}=0.7$, $\Omega_{\mathrm{b}}=0.04$, and $H_{0}=70$ km s*-1* Mpc*-1*.

2. Data

For determination of UV luminosity functions, we use the complete samples of the HFF fields; Abell 2744, MACSJ0416, MACSJ0717, MACSJ1149, AbellS1063, and Abell370. Cluster and parallel fields of the six massive clusters have been observed with Advanced Camera for Surveys (ACS) and Wide Field Camera 3 (WFC3) of Hubble Space Telescope (HST) through 2013 October to 2016 September. The total survey area covers $\sim 56$ arcmin2. Drizzled and weight images are produced and released by the Space Telescope Science Institute (STScI) at the HFF Web site.111http://www.stsci.edu/hst/campaigns/frontier-fields/ The images consist of three ACS bands and four WFC3-IR bands; F435W ($B_{435}$), F606W ($V_{606}$), F814W ($i_{814}$), F105W ($Y_{105}$), F125W ($J_{125}$), F140W ($JH_{140}$), and F160W ($H_{160}$).

First, we homogenize the Point Spread Function (PSF) of the WFC3 images. The PSF FWHM of homoginized images is $\sim 0.18$ arcsec. We then measure the limiting magnitudes. We divide each image into $4\times 4$ grid cells and define the limiting magnitude in each cell. This is because limiting magnitudes are not homogeneous due to the intra cluster light. The $5\sigma$ limiting magnitudes in the $H_{160}$ band images are $\sim 28.5-29$ mag in a $0\farcs 35$-diameter circular aperture. Details of the PSF homogenization procedure and the limiting magnitude measurements are described in Kawamata et al. (2016) (see also Ishigaki et al. 2015). A summary of the observational properties is provided in Tables 1 and 2.

3. Samples

In this study, we select $i$-dropout ($z\sim 6-7$), $Y$-dropout ($z\sim 8$), $YJ$-dropout ($z\sim 9$), and $J$-dropout ($z\sim 10$) galaxy candidates. A detailed description of the dropout selections is given by Kawamata et al. (2016). In this section, we give a brief description about dropout selections. First, we create detection images using SWarp (Bertin et al. 2002). The dection images are combination of $J_{125}$, $JH_{140}$, and $H_{160}$ bands for the $i$- and $Y$-dropout selections, $JH_{140}$ and $H_{160}$ bands for the $YJ$-dropout selection, and $H_{160}$ band for the $J$-dropout selection, respectively. We run SExtractor (version 2.8.6; Bertin & Arnouts 1996) in dual-image mode using the detection images, and create photometric catalogs. The colors of galaxies are measured with MAG_APER $m_{\mathrm{AP}}$. The total magnitudes of galaxies $m_{\mathrm{tot}}$ are defined with the equation $m_{\mathrm{tot}}=m_{\mathrm{AP}}-0.82$, where the offset $0.82$ corresponds to the aperture correction and was derived in Ishigaki et al. (2015). Selection criteria of $i$-dropout galaxies are

[TABLE]

which are used in Atek et al. (2015b). We require the detection significance levels beyond $5\sigma$ level in the $Y_{105}$ band and $J_{125}$ band. We exclude the objects that are detected at the $2\sigma$ level in both the $B_{435}$ and $V_{606}$ bands or in the $B_{435}+V_{606}$ stacked images.

For $Y$-dropouts, we adopt the selection criteria given by Atek et al. (2014):

[TABLE]

Similarly, we apply the source detection thresholds of the $>5\sigma$ significance levels in the $J_{125}$, $JH_{140}$, and $H_{160}$ bands. We remove the objects that are detected at the $2\sigma$ level in at least one of the $B_{435}$, $V_{606}$, or $i_{814}$ bands.

For $YJ$-dropouts, we use criteria presented in Oesch et al. (2013) and Ishigaki et al. (2015):

[TABLE]

We require the detection significance levels beyond $3\sigma$ level in both the $JH_{140}$ and $H_{160}$ bands and $3.5\sigma$ level in one of the $JH_{140}$ or $H_{160}$ bands. Again, we remove the objects that are detected at the $2\sigma$ level in the $B_{435}$, $V_{606}$, or $i_{814}$ bands.

For $J$-dropouts, we apply the criteria used in Oesch et al. (2015):

[TABLE]

We also require $\chi^{2}_{opt+Y}<2.5$, where $\chi^{2}_{opt+Y}$ is defined by $\chi^{2}_{opt+Y}\equiv\sum_{n}\mathrm{SGN}(f_{n})S/N(n)^{2}$. $f_{n}$ is the $n$th band flux in $B_{435}$, $V_{606}$, $i_{814}$, and $Y_{105}$. $\mathrm{SGN}(f_{n})$ is a sign function. $S/N$s in the $JH_{140}$ and $H_{160}$ bands are required to be $>3.5\sigma$ in both bands and $>5\sigma$ in one of the two bands. Finally, spurious sources are removed from the dropout galaxy candidates by visual inspection.

In this study, we find no $J$-dropout candidates in the all cluster and parallel fields. Our dropout samples consist of 350 $i$-dropouts, 66 $Y$-dropouts, and 40 $YJ$-dropouts in total. The number of the dropout candidates in each field is listed in Table 1. We list these dropout candidates in Tables 4, 5, and 6. The values of magnitudes are slightly different from those in Kawamata et al. (2016) because Kawamata et al. (2016) used an older version of SExtractor.

4. UV Luminosity Functions

In this section, we calculate UV luminosity functions at $z\sim 6-7$, $8$, $9$, and $10$. UV luminosity functions are represented by the Schechter function with three parameters; $\phi_{\ast}$, $M_{\ast}$, and $\alpha$:

[TABLE]

We derive the luminosity functions basically in the same manner as that described in Section 5 of Ishigaki et al. (2015), that adopt the luminosity function fitting on the image plane. We refer to the method as the image plane method in the remainder of this paper. The image plane method deals with not only the lensing magnification effects, but also the distortion and multiplication of lensed images in a self-consistent way. Oesch et al. (2015) showed that the detection completeness of galaxies strongly depends on the galaxy size and the image distortion, especially at areas with high magnifications. It is critical to properly evaluate the lensing effects and the properties of high-redshift galaxies to derive the luminosity functions, as done in this paper. In this study, we define $M_{\mathrm{UV}}$ as the magnitude in the rest-frame wavelength of $1500$Å. This wavelength roughly corresponds to $J_{125}$, $JH_{140}$, $H_{160}$, and $H_{160}$ bands at $z\sim 6-7$, $8$, $9$, and $10$, respectively.

In section 4.1, we create mock catalogs of high-redshift galaxies and obtain number densities on the image plane. In section 4.2, we compare number densities of the mock catalogs with those of the observation, and determine the best fit Schechter parameters.

4.1. Creation of Mock Catalogs

We create mock catalogs of simulated high-redshift galaxies at $z\sim 5.0-12$. The number densities of the galaxies follow the Schechter functions. The half-light radius of the galaxies are $\sim 0.45$, $\sim 0.22$, and $\sim 0.11$ kpc for galaxies with magnitudes of $M_{\mathrm{UV}}<-20$, $-20<M_{\mathrm{UV}}<-16$, and $M_{\mathrm{UV}}>-16$, respectively. This assumption is consistent with the size–luminosity relations adopted in previous studies. The Sérsic index is assumed to be $1$. The ellipticities are randomly chosen from the range of $0.0$–$0.9$, because high-redshift galaxy studies show roughly uniform distributions of the ellipticities (e.g. Ravindranath et al. 2006). The UV spectral slope $\beta$ is assumed to be $\beta=-2$, which is consistent with the result of Bouwens et al. (2014). The UV spectra are attenuated with the IGM absorption model of Madau et al. (1996). The mock galaxies are distributed in random positions of the source plane. We create images of the mock galaxies with writeimage function in the lens model software glafic (Oguri 2010). The writeimage function calculates the gravitational lensing effects including magnification, distortion, and multiplication, for an object and produce the image(s) in the image plane. Here we use the mass models of the six clusters described in Kawamata et al. (2016) and Kawamata et al. (2017). Three out of the six models are released in the HFF Web site222https://archive.stsci.edu/prepds/frontier/lensmodels/ as version 3 for Abell 2744, MACS0717, and MACS1149. We use an updated version of the mass model for MACS0416 (Kawamata et al. 2017). In the parallel fields, we use writeimage_ori function, which creates unlensed images. We add the simulated images in the real HFF data. Then we detect the mock galaxies with SExtractor and select dropouts in the mock catalogs with the color criteria same as the observations described in Section 3. We obtain number densities of dropouts in the mock catalogs.

Low-redshift galaxies are potentially contaminate the dropout catalogs of the observational data. We estimate the contamination rate by the following procedure. First, we create the catalogs of bright ($22<H_{160}<25$) objects in the HFF images. In this magnitude range, all objects do not meet the color criteria of the dropouts, which are probably low-redshift interlopers. Then we create interloper catalogs of faint objects ($25<H_{160}<29$). We fit the number densities of the bright interlopers with a power-law function, and match the number densities of the faint interlopers to those extrapolated from the bright magnitudes. We assume that the physical properties of faint interlopers such as the color and size are the same as those of the bright objects. We create images of artificial objects from these catalogs with the mkobjects package of iraf, and randomly place them on the HFF images. We detect the artificial objects with SExtractor, and select the artificial objects that meet the dropout selection criteria. We regard these selected objects as contaminants. We thus obtain the contamination rate of dropouts as a function of magnitude. The contamination rate is $\sim 9\%$ ($\sim 32\%$) in the magnitude range of $M_{\mathrm{UV}}<27.25$ ($M_{\mathrm{UV}}>27.25$) on average. We add the number densities of the contaminants to the total number densities of the dropouts in the mock catalogs.

4.2. Luminosity Function Fitting

We compare the observed number densities of dropouts with the number density obtained in the simulations, which is described in the Section 4.1. We obtain the best-fit luminosity function by fitting these number densities with a maximum likelihood method. We calculate the likelihood with the following equation, assuming the Poisson errors:

[TABLE]

where $n_{{\rm sim},i}$ is the simulated number counts in an $i$th magnitude bin, and $n_{{\rm obs},i}$ is the observed number counts in the HFF in the magnitude bin. We treat the three Schechter parameters, $\phi_{\ast}$, $M_{\ast}$, and $\alpha$, as free parameters in the fitting of luminosity functions at $z\sim 6-7$ and $8$. The number counts at $z\sim 9$ and $z\sim 10$ have too poor statistcis to constrain the three Schechter parameters. Therefore, we also provide results where we treat $\phi_{\ast}$ as the only free parameter at $z\sim 9$ and $10$, and fix $M_{\ast}$ and $\alpha$ to the values at $z\sim 8$, $-20.35$ and $-1.96$, respectively. In order to improve the statistics, we simultaneously fit our number counts data and UV luminosity function data points from previous studies. We use recent results of blank field surveys; Bouwens et al. (2015); Bowler et al. (2014); Ouchi et al. (2009); Bradley et al. (2012); Oesch et al. (2013); Calvi et al. (2016). Although Schmidt et al. (2014) presented an updated result of the BoRG survey (Bradley et al. 2012), we do not incorporate their result because they do not provide number densities at individual magnitudes. We iterate the luminosity function fitting with various Schechter parameter sets, and obtain the best-fit parameters.

One of the advantages of the image plane method is that the result is not affected by uncertainties of magnification factors of dropout candidates. If a galaxy has magnification factor larger than $\sim 100$, the $1\sigma$ error of the magnification is as large as itself (Tables 10 to 12 in Kawamata et al. 2016). Luminosity function fitting on the source plane has large uncertainty in the faint end, because the galaxy samples in the faint magnitude bins consists of galaxies with high magnification factors. The disadvantage of the image plane method is that there is a degeneracy between number densities of intrinsically bright and faint galaxies with the same apparent magnitude. The constraints on the faint end of luminosity functions are weaker than those with fitting on the source plane. In order to strengthen the constraints on the faint end, we divide the dropout samples into subsamples with magnification factor binning of $\mu<2$, $2<\mu<6$, $6<\mu<18$, and $\mu>18$ at $z\sim 6-7$. We use the surface number density in each magnitude bin and in each magnification factor bin for fitting. Note that the number densities divided with magnification factor bins depend on mass models, although the uncertainty is not larger than the one in fitting on the source plane. We estimate the uncertainty of mass models in the end of this section. At $z\gtrsim 8$, we do not divide the samples, because the number of $z\gtrsim 8$ galaxy candidates is not large enough for making subsamples.

The best-fit parameters are shown in Table 3. We find that the uncertainties in $M_{*}$ and $\phi_{*}$ are considerably large due to a degeneracy between the two parameters when all parameters are variable. Plotted in Figure 1 is the faint-end slope $\alpha$ as a function of redshift. Our results indicate that the best-fit values of $\alpha$ are about $-2$ at $z\sim 6-7$ to $10$, which are steeper than those at lower redshift (e.g. $\alpha\sim-1.6$ at $z\sim 4$ in Bouwens et al. 2015). We show the fitting results at $z\sim 6-7$, $8$, $9$, and $10$ in Figures 2, 3, 4, and 5, respectively. The top and bottom panel present the observed number densities and the best-fit luminosity functions in the image plane and the source plane, respectively. We also plot the results of previous blank-field surveys (Bouwens et al. 2015; Bowler et al. 2014; Ouchi et al. 2009; Schenker et al. 2013; Bradley et al. 2012; Finkelstein et al. 2015; McLure et al. 2013; Oesch et al. 2013; Calvi et al. 2016) and recent HFF results in other studies (Laporte et al. 2016; Atek et al. 2015a; McLeod et al. 2016). The best-fit parameters are consistent with those in previous studies. In the top panel of Figure 2, there may be an excess in the observed surface number density at $J_{125}=28.5$. The reason for this excess is not clear, although using a size–luminosity relation which gives smaller sizes at faint magnitudes may reduce this excess. At $z\sim 8$, the observed number densities at the bright end are slightly larger than the number densities in the simulation. It is probably due to the existence of an overdense region of $z\sim 8$ dropouts in the Abell 2744 cluster field. We discussed the properties of the overdensity in Ishigaki et al. (2016) (see also Atek et al. 2015b and Zheng et al. 2014). At $z\sim 10$, although we detect no galaxies, we can place a constraint on the luminosity function from the non-detection. Based on the best-fit parameters where only $\phi_{*}$ is variable, $\sim 1.4$ galaxies are expected to be detected in the HFF fields. The middle panels of Figures 2–5 show histograms of the number of the dropouts. It is seen that our samples push the magnitude limits of the luminosity functions significantly by up to $\sim 3$ magnitude.

Bouwens et al. (2017b) claim that the accuracy of UV luminosity functions is limited due to the uncertainty of mass models. In order to estimate the uncertainty of mass models with the method we use for the luminosity function at $z\sim 6-7$, we check the magnification factors of the dropout candidates with five different mass models from Bradac (v2 for Abell 2744, v3 for MACS0416, and v1 for MACS0717, MACS1149, AbellS1063, and Abell370; Wang et al. 2015, Hoag et al. 2016, see also Bradač et al. 2009), CATS (v3.1 for Abell 2744, v3.1 for MACS0416, v1 for MACS0717, MACS1149, AbellS1063, and Abell370; Jauzac et al. 2015), Sharon (v3 for Abell 2744 and MACS0416, v2 for MACS0717, v2.1 for MACS1149, v1 for Abell370 and AbellS1063; Johnson et al. 2014), Williams (v3 for Abell 2744, v3.1 for MACS0416, v1 for MACS0717, MACS1149, AbellS1063, and Abell370), and Zitrin (LTM v1 for all the six clusters; Zitrin et al. 2009, Zitrin et al. 2013). We obtain the UV luminosity functions at $z\sim 6-7$ with these five different mass models. Figure 7 shows the best-fit Schechter parameters and the 68% and 95% confidence levels. We confirm that the difference of the best-fit parameters are $\Delta\phi_{\ast}\sim 0.2$, $\Delta M_{\ast}\sim 0.2$, and $\Delta\alpha\sim 0.1$, which are comparable to the statistical errors of these parameters (Table 3). Magnification factor of each dropout could be different from others in different mass model (see also Figure 11 of Ishigaki et al. 2015), but the values of the best-fit Schechter parameters are almost the same in all the mass models.

5. Discussion

In the previous section, we derive the UV luminosity functions at $z\sim 6-10$ from the HFF data and the previous blank field data. In this section, we estimate the UV luminosity densities $\rho_{\mathrm{UV}}$ from the luminosity functions which constrain the physical properties of ionizing sources and reionization.

5.1. Evolution of the UV Luminosity Density

The value of $\rho_{\mathrm{UV}}$ is calculated with the following equation:

[TABLE]

where $L(M)$ is the UV luminosity corresponding to the UV magnitude $M$. The value of $M_{\mathrm{trunc}}$ is the truncation magnitude of the UV luminosity function, i.e., there are no galaxies with the magnitudes fainter than $M_{\mathrm{trunc}}$. We calculate $\rho_{\mathrm{UV}}$ at $z\sim 6-7$, $8$, $9$, and $10$ using the best-fit Schechter functions obtained in Section 4.2. Figure 8 shows $\rho_{\mathrm{UV}}$ calculated from Equation (15) with $M_{\mathrm{trunc}}=-15.0$ and $M_{\mathrm{trunc}}=-17.0$. The right axis in Figure 8 presents cosmic star formation rate densities (SFRDs) from a given luminosity density that are estimated from $\rho_{\mathrm{UV}}$ based on Equation (2) of Madau et al. (1998).

For comparisons, we also show the data plots of $\rho_{\mathrm{UV}}$ with $M_{\mathrm{trunc}}=-15.0$ and $M_{\mathrm{trunc}}=-17.0$ at $z\sim 4-12$ that are taken from previous studies (Bouwens et al. 2015; McLeod et al. 2016; Coe et al. 2013; Ellis et al. 2013). In Figure 8, we include total $\rho_{\mathrm{UV}}$ at $z\sim 0-3$ (Steidel et al. 1999; Wyder et al. 2005; Schiminovich et al. 2005; Reddy & Steidel 2009), and cosmic SFRDs at $z\sim 1-4$ based on $\rho_{\mathrm{UV}}$ ($M_{\mathrm{trunc}}=-15.0$) and IR luminosity densities (the sensitivity corresponding to $\simeq 30$ $\mu$Jy) (Dunlop et al. 2017). Our results are consistent with these previous studies at $z\sim 6-10$.

Our results support a non-accelerated decline of $\rho_{\mathrm{UV}}$ toward high redshifts in the case of $M_{\mathrm{trunc}}=-15.0$ (see also McLeod et al. 2016). We check whether we can approximate the evolution of $\log\rho_{\mathrm{UV}}$ from $z=4$ to $10$ as a linear function. We fit the $\log\rho_{\mathrm{UV}}$ from this work and Bouwens et al. (2015) with linear and quadratic functions. The Akaike Information Criterion corrected for small data sets (AICc; Sugiura 1978) for the linear function is smaller by $\Delta\mathrm{AIC}c=3.69$ than that for the quadratic function, suggesting a non-accelerated $\rho_{\mathrm{UV}}$ evolution.

However, we find an accelerated decline when a brighter truncation magnitude of $M_{\mathrm{trunc}}=-17.0$ is adopted, which is closer to $M_{\mathrm{trunc}}=-17.7$ adopted in Oesch et al. (2013), who support an accelerated decline. In Figure 8, we present fitting results to $\rho_{\mathrm{UV}}$ in this work and Bouwens et al. (2015) with a linear function at $z\sim 4-8$ and its extrapolation toward $z\sim 10$. This indicates the trends of non-accelerated and accelerated declines in the cases of $M_{\mathrm{trunc}}=-15.0$ and $-17.0$, respectively. One possible explanation for this dependence on $M_{\mathrm{trunc}}$ is the evolution of the faint-end slope toward steeper value at higher redshifts (see Figure 1). The faint-end slope steepening makes the $\rho_{\mathrm{UV}}$ difference (between the cases of $M_{\mathrm{trunc}}=-15.0$ and $-17.0$) larger at $z\sim 10$ than at $z\sim 8$. The redshift evolution of $M_{\ast}$ toward fainter magnitudes (see Figure 6) would also contribute to this larger increases of $\rho_{\mathrm{UV}}$ at higher redshifts.

On the other hand, our previous study in Ishigaki et al. (2015) has claimed that $\rho_{\mathrm{UV}}$ shows an accelerated decrease beyond $z\sim 8$. This can be because they adopt a brighter truncation magnitude of $M_{\mathrm{trunc}}=-17.0$. Another possible explanation for the difference is cosmic variance. Ishigaki et al. (2015) only use the data of Abell 2744 cluster and parallel fields. In these fields, the galaxy density at $z\sim 8$ is $\sim 0.1$ dex higher than the average of total fields (Ishigaki et al. 2016), and the one at $z\sim 9$ is $\sim 0.1$ dex lower than the average.

5.2. Preperties of the Ionizing Sources

In this section, we calculate the ionized hydrogen fraction $Q_{\mathrm{HII}}$ and the Thomson scattering optical depth $\tau_{\mathrm{e}}$, basically in the same manner as that described in Section 5 of Ishigaki et al. (2015).

The value of $Q_{\mathrm{HII}}$ is calculated with the following equation (e.g. Robertson et al. 2013):

[TABLE]

In the first term of Equation (16), $\dot{n}_{\mathrm{ion}}$ and $\langle n_{\mathrm{H}}\rangle$ denote the production rate of ionizing photons and the mean hydrogen number density, respectively. $\dot{n}_{\mathrm{ion}}$ and $\langle n_{\mathrm{H}}\rangle$ are defined by the following equations:

[TABLE]

where $X_{\mathrm{p}}$ is the primordial mass fraction of hydrogen, $\rho_{\mathrm{c}}$ is the critical density, and $m_{\mathrm{H}}$ is the mass of the hydrogen atom. $f_{\mathrm{esc}}$ is the fraction of the number of escaping ionizing photons to those produced in a galaxy. $\xi_{\mathrm{ion}}$ is the numerical factor that converts a UV luminosity density to the ionizing photon emission rate of a star-forming galaxy. Note that $f_{\mathrm{esc}}$ and $\xi_{\mathrm{ion}}$ appear in the product form in Equation (17). Here we assume that $f_{\mathrm{esc}}$ and $\xi_{\mathrm{ion}}$ do not depend on $M_{\mathrm{UV}}$. We present the magnitude-averaged value of the product of $f_{\mathrm{esc}}$ and $\xi_{\mathrm{ion}}$ as $\left<f_{\rm esc}\xi_{\rm ion}\right>$. In the second term of Equation (16), $t_{\mathrm{rec}}$ represents the averaged gas recombination time:

[TABLE]

where $\alpha_{\mathrm{B}}$ is the case-B hydrogen recombination coefficient, $T$ is the IGM temperature, and $Y_{\mathrm{p}}$ is the primordial helium mass fraction. $C_{\mathrm{H_{II}}}\equiv\left<n_{\mathrm{H_{II}}}^{2}\right>/\left<n_{\mathrm{H_{II}}}\right>^{2}$ is a clumping factor, where $n_{\mathrm{H_{II}}}$ is the local number density of ionized hydrogen. In this work, we use the following equation:

[TABLE]

which was obtained from the hydrodynamical $+$ $N$-body simualtions in Shull et al. (2012). The value of the clumping factor is not accurately known observationally, although many theoretical studies suggest similar values of clumping factor, $C_{\mathrm{H_{II}}}\sim 1-6$, in the epoch of reionization (Sokasian et al. 2003; Iliev et al. 2006; Finlator et al. 2012).

The value of $\tau_{\mathrm{e}}$ is calculated with the following equation (Kuhlen & Faucher-Giguère 2012):

[TABLE]

where $H(z)$ is the Hubble parameter, $\sigma_{\mathrm{T}}$ is the Thomson scattering cross section, and $c$ is the speed of light. We assume that helium is singly ionized (corresponding to $\eta=1$) at $z>4$ and doubly ionized (corresponding to $\eta=2$) at $z\leq 4$, following Kuhlen & Faucher-Giguère (2012). Recently, Planck Collaboration et al. (2016) have obtained $\tau_{\mathrm{e}}=0.058\pm 0.012$ from the measurement of $TT$ power spectrum and $EE$ polarization of CMB. The value of $\tau_{\mathrm{e}}$ from Planck Collaboration et al. (2016) is smaller than the one obtained in previous observations by nine-year WMAP ($\tau_{\mathrm{e}}=0.088\pm 0.013$, Bennett et al. 2013; Hinshaw et al. 2013) and Planck 2014 ($\tau_{\mathrm{e}}=0.092\pm 0.013$, Planck Collaboration et al. 2014).

We assume the following two functional form of $\rho_{\mathrm{UV}}$. One is the four-parameter function from Madau & Dickinson (2014) (see also Robertson et al. 2015):

[TABLE]

which has free parameters of $a_{p}$, $b_{p}$, $c_{p}$, and $d_{p}$. The other is a logarithmic double power law function used in Ishigaki et al. (2015):

[TABLE]

which also has four free parameters; $\rho_{\mathrm{UV}}^{\ast}$, $z_{\ast}$, $a$, and $b$. We perform $\chi^{2}$ fitting to the observational data of $\rho_{\mathrm{UV}}$, $Q_{\mathrm{HII}}$, and $\tau_{\mathrm{e}}$. In each parameter space, we adopt one of the two functional forms of $\rho_{\mathrm{UV}}(z)$ whose minimum $\chi^{2}$ is smaller than the one of the other. We use the $\rho_{\mathrm{UV}}$ data points at $z\sim 6-7$, $8$, $9$, and $10$ (this work) and $z\sim 4$, $5$, and $6$ (Bouwens et al. 2015) that are presented in the left panel of Figure 9. Although $\rho_{\mathrm{UV}}$ at $z\sim 10$ scatters upward due to the large uncertainty in $\alpha$, this does not significantly affect the fitting result because of its large uncertainty. We also use the $Q_{\mathrm{HII}}$ data plotted in the right panel of Figure 9 from Bolton et al. (2011); Carilli et al. (2010); Chornock et al. (2013, 2014); Dijkstra et al. (2011); Konno et al. (2014); McGreer et al. (2011); McQuinn et al. (2007, 2008); Mesinger & Furlanetto (2008); Mesinger (2010); Ouchi et al. (2010); Ota et al. (2008); Patel et al. (2010); Totani et al. (2006, 2014). In addition to these observational constraints, we compare $\tau_{\mathrm{e}}=0.058\pm 0.012$ (Planck Collaboration et al. 2016) with the value of $\tau_{\mathrm{e}}$ at $z=30$ calculted from Equation (21). There are six free parameters in the $\chi^{2}$ fit, $\left<f_{\rm esc}\xi_{\rm ion}\right>$, $M_{\mathrm{trunc}}$, and the four parameters in the function of $\rho_{\mathrm{UV}}(z)$. The parameter range of $\left<f_{\rm esc}\xi_{\rm ion}\right>$ is [math] to $10^{25.34}$ [erg*-1* Hz], where we assume that $0<f_{\mathrm{esc}}<1$ and $\log\xi_{\mathrm{ion}}/[\mathrm{erg}^{-1}\ \mathrm{Hz}]=25.34$ (Bouwens et al. 2016a). The parameter range of $M_{\mathrm{trunc}}$ is $-16$ to $-10$; $M_{\mathrm{trunc}}=-16$ mag corresponds to the detection limit of current observations, and $M_{\mathrm{trunc}}=-10$ mag is the magnitude of minimium halos which have star forming galaxies predicted by Faucher-Giguère et al. (2011).

We calculate the total $\chi^{2}$ value by summing up the $\chi^{2}$ of the data points of $\rho_{\mathrm{UV}}$, $Q_{\mathrm{HII}}$, and $\tau_{\mathrm{e}}$, and derive the best-fit parameters. The best-fit parameters are $\log a_{p}=25.9$, $b_{p}=3.7$, $c_{p}=2.3$, $d_{p}=5.5$, $\left<\log f_{\rm esc}\xi_{\rm ion}\right>=24.57$ and $M_{\mathrm{trunc}}=-11.0$, and the $\chi^{2}$ is $9.28$ for $12$ degrees of freedom. Figure 9 shows the best-fit functions of $\rho_{\mathrm{UV}}$, $\tau_{\mathrm{e}}$, and $Q_{\mathrm{HII}}$. These best-fit functions agree well with the data points of the observations. This result is in contrast with the conclusion of our previous study of Ishigaki et al. (2015), which claim that no parameter set can reproduce both the $\rho_{\mathrm{UV}}$ evolution and the value of $\tau_{\mathrm{e}}$. The main reason for this difference is that Ishigaki et al. (2015) use the value $\tau_{\mathrm{e}}=0.091^{+0.013}_{-0.014}$ from Planck Collaboration et al. (2014), which is significantly larger than the latest result used in our study ($\tau_{\mathrm{e}}=0.058\pm 0.012$; Planck Collaboration et al. 2016). Another reason is that this study supports a non-accelerated decline of $\rho_{\mathrm{UV}}$ toward high redshift as explained in Section 5.1. In this study, the small value of $\tau_{\mathrm{e}}$ and a non-accelerated decline of $\rho_{\mathrm{UV}}$ alleviate the tension between $\tau_{\mathrm{e}}$ and $\rho_{\mathrm{UV}}$ claimed by Ishigaki et al. (2015).

Figure 10 presents the $68\%$ and $95\%$ confidence intervals on the $\left<f_{\rm esc}\xi_{\rm ion}\right>$–$M_{\mathrm{trunc}}$ plane with megenta contours. The best-fit value and the 68% interval are $\left<\log f_{\rm esc}\xi_{\rm ion}\right>=24.57^{+0.15}_{-0.08}$ and $M_{\mathrm{trunc}}>-14.0$. If we assume $\log\xi_{\mathrm{ion}}/[\mathrm{erg}^{-1}\ \mathrm{Hz}]=25.34$ obtained in Bouwens et al. (2016a), we place upper and lower limits on the escape fraction, $f_{\mathrm{esc}}<0.24$ and $f_{\mathrm{esc}}>0.14$, respectively. These constraints of $f_{\mathrm{esc}}$ and $M_{\mathrm{trunc}}$ are mainly driven by the observational constraints of $Q_{\mathrm{HII}}$. We also derive the length of the reionization period $\Delta z$ that is defined by the period bracketed by two redshifts whose $Q_{\mathrm{HII}}$ values are $0.1$ and $0.99$. Figure 10 shows the contours of $\Delta z$ predicted by our $\chi^{2}$ fitting results. The contours suggest $\Delta z=3.9^{+2.0}_{-1.6}$ in the $68\%$ confidence interval on the $\left<f_{\rm esc}\xi_{\rm ion}\right>$–$M_{\mathrm{trunc}}$ plane. Planck Collaboration et al. (2016) obtain $\Delta z<2.8$ from kSZ constraints and a reionization model, which is indicative of the relatively sharp reionization history. The blue shade in Figure 10 presents the $68\%$ confidence interval constrained from the result of Planck Collaboration et al. (2016) on the $\left<f_{\rm esc}\xi_{\rm ion}\right>$–$M_{\mathrm{trunc}}$ plane. Our constraints on $\Delta z$ are complimentary to those of Planck Collaboration et al. (2016), giving both the upper and lower limit of $\Delta z$. The combination of the constraints from our and Planck Collaboration et al. (2016) studies suggest $\Delta z\sim 2-3$, which suggests the moderately sharp reionization history.

6. Summary

In this study, we have produced catalogs of dropout galaxies at $z\sim 6-10$ using the all cluster and parallel fields data taken by the HFF program. Using our new mass models, we have conducted Monte-Carlo simulations, and estimated the number densities of dropout galaxies at $z\sim 6-10$. We then derive the UV luminosity densities and discuss the properties of ionizing sources and reionization. The results in this study are summarized below:

With the dropout selection technique, we identify $\sim 400$ star-forming galaxies over the redshift range $z\sim 6-10$, which include 350 $i$-dropout, 66 $Y$-dropout, and 40 $YJ$-dropout candidates. We do not find $J$-dropout candiates in the HFF data. The number of dropout candidates in our catalogs is six times larger than the one obtained in our previous study (Ishigaki et al. 2015) that use one set of the cluster and parallel field data. 2. 2.

The faint end slope of UV luminosity functions has a very steep value $\alpha\sim-2$. The UV luminosity densities calculated from the UV luminosity functions are consistent with those in previous studies. Our results support the evolutionary trend of a non-accelerated decline in the UV luminosity densities beyond $z\sim 8$ in the case of $M_{\mathrm{trunc}}=-15$, consistent with the conclusions of McLeod et al. (2016), while an accelerated decline in the case of a brighter truncation magnitude of $M_{\mathrm{trunc}}=-17$, consistent with the conclusions of Oesch et al. (2013); Bouwens et al. (2015); Ishigaki et al. (2015); Oesch et al. (2015). 3. 3.

Using the standard analytical reionization model, we calculate the physical parameters related to reionization, such as the Thomson scattering optical depth $\tau_{\mathrm{e}}$ and the ionized hydrogen fraction $Q_{\mathrm{HII}}$. The values of $\tau_{\mathrm{e}}$ and $Q_{\mathrm{HII}}$ are consistent with the latest result of Planck Collaboration et al. (2016) ($\tau_{\mathrm{e}}=0.0058\pm 0.0012$) and previous studies of $Q_{\mathrm{HII}}$ obtained with Ly$\alpha$ absorptions found in QSOs, GRBs, and galaxies. We obtain the constraints on the parameters of ionizing sources. The best-fit value and the $68\%$ confidence intervals of the averaged value of the escape fraction and truncation magnitude are $f_{\rm esc}=0.17^{+0.07}_{-0.03}$ and $M_{\mathrm{trunc}}>-14.0$, respectively, under the assumption of $\log\xi_{\mathrm{ion}}/[\mathrm{erg}^{-1}\ \mathrm{Hz}]=25.34$. The results suggest that the length of the reionization period is $\Delta z=3.9^{+2.0}_{-1.6}$ which is consistent with the $\Delta z$ estimate from the kinetic Sunyaev-Zel’dovich effect in Planck Collaboration et al. (2016).

We are grateful to Akio Inoue, Masayuki Umemura, Masanori Iye, Kentaro Nagamine, Takatoshi Shibuya for useful comments and discussions. This research was supported by the Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG cluster of excellence ”Origin and Structure of the Universe”. This work is supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, and KAKENHI (JP15H02064, JP26800093, and JP15H05892) Grant-in-Aid for Scientific Research (A) through Japan Society for the Promotion of Science (JSPS). M.I. acknowledges support by Grant-in-Aid for JSPS Research Fellow (JP16J03727) and an Advanced Leading Graduate Course for Photon Science grant. R.K. acknowledges support by Grant-in-Aid for JSPS Research Fellow (JP16J01302). Facilities: HST (WFC3, ACS)

Appendix A Lists of Dropout Candidates at $z\sim 6-7$, $8$, and $9$