RELICS: Strong Lensing Analysis of MACS J0417.5–1154 and Predictions for Observing the Magnified High-redshift Universe with JWST

In our view of the history of the universe, the epoch of reionization remains the least well observed. During the first billion years, the universe was largely neutral. Half the intergalactic medium (IGM) in the universe was reionized by z = 8 ± 1 (Planck Collaboration et al. 2016a) and nearly completely by z = 6. The end of reionization is evidenced by Gunn & Peterson (1965) troughs (due to absorption by neutral intergalactic hydrogen) observed in z > 6 quasar spectra, but not in spectra at z < 6 (Becker et al. 2001, 2015; Djorgovski et al. 2001; Fan et al. 2006). Observing galaxies during the epoch of reionization remains a challenge today. They are much fainter due to their great distance and smaller sizes, and any Lyα emission is often scattered or absorbed by the surrounding neutral gas.

Strong lensing magnification by clusters of galaxies offers a privileged view of the high-z universe. Several studies already highlight the high power of gravitational lenses to reveal objects that would have been inaccessible otherwise. Deep observations of Frontier Fields clusters (Lotz et al. 2017) were particularly important for probing the faint end of high-redshift luminosity functions and the galaxies most likely responsible for reionization (Atek et al. 2015, 2018; Livermore et al. 2017; Bouwens et al. 2017; Yue et al. 2018; Bhatawdekar et al. 2018; Ishigaki et al. 2018), as well as finding high-redshift candidates (e.g., a z ∼ 10 galaxy from Oesch et al. 2018). The Cluster Lensing And Supernova survey with Hubble (CLASH; Postman et al. 2012) yielded z ∼ 6–11 galaxies to be observed more brightly (Hashimoto et al. 2018; Zheng et al. 2012; Coe et al. 2013; Bradley et al. 2014). Even after these large surveys, many clusters had yet to be observed by the Hubble Space Telescope (HST) at near-infrared wavelengths (1.0–1.7 μm) to search for distant galaxies.

MACS J0417.5−1154 (hereafter, MACS J0417) was discovered by the MAssive Cluster Survey (MACS; Ebeling et al. 2001) as part of the ROSAT (Voges et al. 1999) catalog of bright sources. MACS J0417 at z = 0.443 is one of the most X-ray luminous clusters with a luminosity of 2.9 × 10⁴⁵ erg s⁻¹ between 0.1 and 2.4 keV. Based on Chandra X-ray observations, Mann & Ebeling (2012) report that the peak of the X-ray emission is centered on the primary brightest cluster galaxy (BCG) with a slight diffuse emission extended toward the second brightest galaxy in the cluster core. Dwarakanath et al. (2011), Parekh et al. (2017), and Sandhu et al. (2018) confirm this feature in the radio. Parekh et al. (2017) highlight the similarity in morphology to the clusters A2746 and 1E 0657−56 (the "Bullet cluster"), strengthening the hypothesis made by Mann & Ebeling (2012) that MACS J0417 is a recent merger, probably oriented along the line of sight, or alternatively, caught close to a turnaround. The merging state of MACS J0417 is also confirmed in the analysis of Pandge et al. (2018). Recently, Botteon et al. (2018) discovered two new cold fronts indicating that substructure dynamics are at play in MACS J0417.

MACS J0417 was also detected by the Planck Early Sunyaev–Zel'dovich (ESZ) catalog (Planck Collaboration et al. 2011), and with ${M}_{500}=(1.23\pm 0.05)\times {10}^{15}{M}_{\odot }$ had the fourth highest mass of all 1094 confirmed clusters with measured redshifts and mass estimates in the Planck PSZ2 catalog (Planck Collaboration et al. 2016b). Similarly, MACS J0417 has the third-highest mass (${M}_{1500\mathrm{kpc}}=(1.89\pm 0.25)\times {10}^{15}{M}_{\odot }$) that was measured as a part of a weak lensing analysis of 27 clusters undertaken in the "Weighing the Giants" census (Applegate et al. 2014).

Based on all of these factors, MACS J0417 was included in the Reionization Lensing Cluster Survey (RELICS). RELICS is a large HST Treasury program, GO 14096 (PI: Coe), to observe 46 fields strongly lensed by 41 massive galaxy clusters. The primary goals of the program are to identify candidates of high-redshift (6 < z < 12) galaxies magnified by the foreground clusters (Salmon et al. 2017, 2018) with photometric redshifts estimated from multiband imaging with HST and Spitzer (PI: Bradač), and to better constrain luminosity functions at the epoch of reionization. Full details of the project will be described in a forthcoming publication (D. Coe et al. 2019, in preparation). Of particular interest is the potential to identify targets to be observed with the James Webb Space Telescope (JWST). To support this goal and increase the scientific impact of this program, strong lens models are being computed by the RELICS team (Cerny et al. 2018; Acebron et al. 2018a, 2018b; Cibirka et al. 2018; Paterno-Mahler et al. 2018; Salmon et al. 2018) and released to the scientific community via the Mikulski Archive for Space Telescopes (MAST).²² The work presented here and in the companion paper, Jauzac et al. (2019), represent the first public strong lensing analyses on MACS J0417.5−1154.

The paper is organized as follows: In Section 2 we give an overview of the data. Section 3 details the strong lensing analysis, and the results are discussed in Section 4. In Section 5 we describe predictions for observing the high-redshift universe by current and future facilities. In Section 6 we summarize the main results of this work.

Throughout this paper we adopt a standard Λ-CDM cosmology with Ω_m = 0.3, Ω_Λ = 0.7 and h = 0.7. All magnitudes are given in the AB system (Oke 1974).

2.1. Imaging

2.2. Spectroscopy

2.2.1. LDSS3

We obtained multislit spectroscopy of MACS J0417 with the upgraded Low Dispersion Survey Spectrograph (LDSS3-C)²⁵ on the Magellan Clay telescope, on 2017 July 27 using the University of Michigan allocation (PI: Sharon). Two multislit masks were designed, with 10 slits placed on multiple images of lensed galaxies at the highest priority, and the rest of the mask filled with background sources and cluster-member galaxies. Due to weather conditions, only one of the masks was observed, with three exposures of 1200 s each. The seeing ranged between 05 and 07, with some clouds present during the observation. The data were obtained with the VPH-ALL grism ($4250\,\mathring{\rm A} \lt \lambda \lt 10000\,\mathring{\rm A}$) with spectral resolution R =450–1100 across the wavelength range. The spectroscopic data were reduced using the standard procedures using the COSMOS data reduction package (Dressler et al. 2011; Oemler et al. 2017). We measured a spectroscopic redshift of z_spec =0.871 for image 1.3 (α = 04:17:33.70, δ = −11:54:39.70), based on [O ii] λ 3728 and Hβ line emission. The data yielded a spectroscopic redshift for another background source (α = 4:17:35.942, δ = −11:54:59.29), at z_spec = 1.046, from [O ii] λ3728, [O iii] λ4959,5007; however, this source is not multiply imaged and was not used as a constraint in the lens model (see Section 3).

A full description of the RELICS Magellan/LDSS3 follow-up results will be presented in a future paper (R. Mainali et al. 2019, in preparation).

2.2.2. MUSE

The field was observed with the Multi Unit Spectrographic Explorer (MUSE; Bacon et al. 2010) on 2017 December 12. The MUSE exposure was 3 × 970 s, or 2910 s in total, and was taken as part of ESO project 0100.A-0792(A) (PI: Edge). The data were reduced and spectra extracted as explained in the companion paper Jauzac et al. (2019). The MUSE field of view (FOV), 1' × 1', is approximately centered on the BCG, and does not cover the full extent of the HST FOV. The MUSE spectral resolution is R = 1750–3750 across the wavelength range 4800–9300 Å.

This work makes use of the spectroscopic redshifts measured for lensed galaxies reported in the companion paper by Jauzac et al. (2019) (Table 2). The MUSE observation confirms the redshift that was obtained with LDSS3 for image 1.3, z_spec =0.871, and spectroscopically confirms images 1.1 and 1.2 as counter images of the same system. Moreover, it reveals [O ii] λ3728 emission from a fourth image at the same redshift, buried in the light of the BCG. This fourth image is likely not a complete image; therefore, we did not use it as a constraint to model the cluster. The redshifts of system 2 and system 3 are both measured at z_spec = 1.046. The two systems correspond to two different galaxies separated by ∼140 kpc in the source plane according to our modeling.

Table 2.  List of Lensing Constraints

ID	R.A.	Decl.	zspec	zmodel	rms ('')	zmodel	rms ('')	Classification
	J2000	J2000		silver	silver	bronze	bronze
1a.1	64.396158	−11.906760	0.8710a	⋯	0.07	⋯	0.10	gold
1a.2	64.394310	−11.907136			0.16		0.22
1a.3	64.390348	−11.910864			0.09		0.09
1b.1	64.396081	−11.907255			0.32		0.36
1b.2	64.394729	−11.907583			0.43		0.53
1b.3	64.390299	−11.911274			0.09		0.13
1 c.2	64.394371	−11.907409			0.26		0.35
1 c.1	64.396364	−11.906983			0.13		0.17
1 c.3	64.390488	−11.911052			0.10		0.12
2a.1	64.399096	−11.906369	1.0460b	⋯	0.41	⋯	0.47	gold
2a.2	64.395567	−11.911182			0.42		0.45
2a.3	64.391371	−11.912074			0.18		0.24
2b.1	64.399000	−11.906633			0.50		0.57
2b.2	64.395821	−11.911226			0.47		0.48
2b.3	64.391262	−11.912324			0.24		0.30
2 c.1	64.399004	−11.906855			0.49		0.56
2 c.2	64.395954	−11.911299			0.48		0.49
2 c.3	64.391300	−11.912493			0.24		0.30
3.1	64.393180	−11.901537	1.0460b	⋯	0.72	⋯	0.59	gold
3.2	64.390026	−11.903434			0.81		0.89
3.3	64.388304	−11.905013			0.30		0.56
4.1	64.399521	−11.907479	⋯	${2.26}_{-0.08}^{+0.08}$	0.26	${2.33}_{-0.07}^{+0.07}$	0.50	silver
4.2	64.398529	−11.909839			0.65		0.47
4.3	64.386095	−11.915359			0.60		0.34
5.1	64.379941	−11.897906	⋯	${2.27}_{-0.14}^{+0.11}$	0.24	${2.25}_{-0.07}^{+0.09}$	0.20	silver
5.2	64.382370	−11.896413			0.27		0.25
5.3	64.388438	−11.891630			0.51		0.49
6.1	64.379991	−11.897349	⋯	${2.34}_{-0.17}^{+0.11}$	0.21	${2.27}_{-0.06}^{+0.09}$	0.24	silver
6.2	64.381808	−11.896390			0.18		0.15
6.3	64.388558	−11.891170			0.46		0.42
7.1	64.394933	−11.897423	⋯	${}^{{\rm{d}}}{2.09}_{-0.05}^{+0.05}$	d0.18	${2.09}_{-0.08}^{+0.12}$	0.32	bronze
7.2	64.388688	−11.900546			d0.26		0.28
8.1	64.388372	−11.894492	⋯	${2.39}_{-0.12}^{+0.14}$	0.12	${2.35}_{-0.09}^{+0.12}$	0.06	silver
8.2	64.386885	−11.895489			0.14		0.04
9.1	64.382068	−11.899994	⋯	${5.97}_{-0.20}^{+0.01}$	0.35	${5.52}_{-0.31}^{+0.10}$	0.43	silver
9.2	64.382338	−11.899779			0.22		0.24
10.1	64.398397	−11.907143	⋯	${2.02}_{-0.10}^{+0.14}$	0.28	${2.33}_{-0.09}^{+0.07}$	0.43	silver
10.2	64.397785	−11.909114			0.37		0.76
10.3	64.385000	−11.915063		d ${2.34}_{-0.04}^{+0.05}$	d0.30		0.33	bronzec
11.1	64.401544	−11.918912	⋯	${3.47}_{-0.31}^{+0.36}$	0.18	${3.18}_{-0.11}^{+0.25}$	0.09	silver
11.2	64.399708	−11.920099			0.30		0.41
12.1	64.396902	−11.897085	⋯	${2.84}_{-0.13}^{+0.13}$	0.42	${2.81}_{-0.14}^{+0.16}$	0.34	silver
12.2	64.388640	−11.901300			0.77		0.62
12.3	64.383172	−11.906519			0.26		0.19
13.1	64.397312	−11.897068	⋯	${2.89}_{-0.13}^{+0.15}$	0.36	${2.85}_{-0.17}^{+0.14}$	0.32	silver
13.2	64.388420	−11.901684			0.73		0.58
13.3	64.383499	−11.906446			0.28		0.17
14.1	64.382335	−11.900359	⋯	d ${4.40}_{-0.21}^{+0.43}$	d0.03	${4.43}_{-0.39}^{+0.29}$	0.10	bronze
14.2	64.382972	−11.899802			d0.03		0.12
15.1	64.378193	−11.894510	⋯	${2.11}_{-0.16}^{+0.16}$	0.28	${2.09}_{-0.08}^{+0.09}$	0.15	silver
15.2	64.381890	−11.892331			0.29		0.20
15.3	64.385361	−11.890071			0.15		0.04
16.1	64.385599	−11.886984	⋯	${4.50}_{-0.96}^{+1.91}$	0.16	${4.66}_{-0.33}^{+0.58}$	0.16	silver
16.2	64.380143	−11.888425			0.31		0.26
16.3	64.376525	−11.892540			0.02		0.30
17.1	64.388212	−11.895269	⋯	${2.30}_{-0.11}^{+0.10}$	0.21	${2.16}_{-0.06}^{+0.14}$	0.10	silver
17.2	64.387833	−11.895536			0.24		0.11

Notes. R.A. and decl. refer to R.A. and decl. of the constraints position. z_spec refers to the spectroscopic constraints when available; references for the spectroscopic redshifts are given in the table footnotes. z_model indicates the best-fit redshift estimates resulting from the "silver" and "bronze" lens models with their respective statistical uncertainties. The rms is the difference between the observed position of a multiple image and the predicted position from the barycenter of our best-fit model in the image plane given in arcseconds. The classification scheme is discussed in Section 3.2.

^aSpectroscopic redshift from Magellan/LDSS3 (this work) and confirmed by MUSE in Jauzac et al. (2019). ^bSpectroscopic redshifts from MUSE presented in Jauzac et al. (2019). Sources 2 and 3 are at the same redshift. These galaxies are separated by ∼140 kpc in the source plane. ^cIn system 10, images 10.1 and 10.2 are classified as silver and 10.3 is classified as bronze. Image 10.3 was therefore not included in the "silver" model. ^dThese redshifts and rms values are computed using the best-fit model computed with silver constraints fixed, while only the redshifts of those systems are being optimized.

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Table 3.  Candidate Lens Models and Best-fit Parameters

Model Name	Component	Δαa	Δδa	εb	θ	σ0	rcut	rcore
(Fit statistics)	⋯	('')	('')		(deg)	(km s−1)	(kpc)	(kpc)
Silver constraints	DM	${6.2}_{-0.8}^{+1.0}$	${9.1}_{-0.9}^{+1.3}$	${0.78}_{-0.01}^{+0.01}$	${54.2}_{-0.3}^{+0.2}$	${1299.1}_{-21.4}^{+16.9}$	[1500.0]	${32.8}_{-1.2}^{+1.4}$
rms = 037	1stBCG	[0.0]	[0.1]	[0.64]	[60.5]	${587.5}_{-9.3}^{+2.7}$	${28.5}_{-3.4}^{+13.2}$	${1.2}_{-0.2}^{+0.2}$
BIC = 150	2ndBCG	[47.8]	[69.6]	[0.35]	[74.1]	${367.5}_{-18.5}^{+14.7}$	${70.6}_{-11.5}^{+18.2}$	${0.5}_{-0.3}^{+0.4}$
	3rdBCG	[46.9]	[48.4]	[0.16]	[50.6]	${256.5}_{-13.9}^{+9.9}$	${74.9}_{-24.1}^{+17.3}$	${0.2}_{-0.1}^{+0.7}$
	L* Galaxy	⋯	⋯	⋯	⋯	${119.8}_{-12.0}^{+9.7}$	⋯	⋯
⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯
Bronze constraints	DM	${6.8}_{-0.4}^{+0.4}$	${9.6}_{-0.5}^{+0.6}$	${0.77}_{-0.01}^{+0.02}$	${54.1}_{-0.3}^{+0.3}$	${1284.2}_{-35.5}^{+29.7}$	[1500.0]	${34.0}_{-1.0}^{+0.4}$
rms = 037	1stBCG	[0.0]	[0.1]	[0.64]	[60.5]	${597.0}_{-8.7}^{+3.5}$	${41.0}_{-16.3}^{+20.9}$	${1.6}_{-0.2}^{+0.2}$
BIC = 164	2ndBCG	[47.8]	[69.6]	[0.35]	[74.1]	${394.8}_{-15.1}^{+4.9}$	${55.4}_{-13.9}^{+13.9}$	${1.0}_{-0.3}^{+0.2}$
	3rdBCG	[46.9]	[48.4]	[0.16]	[50.6]	${267.0}_{-8.0}^{+17.2}$	${50.9}_{-10.6}^{+21.6}$	${0.7}_{-0.2}^{+0.7}$
	L* Galaxy	⋯	⋯	⋯	⋯	${116.0}_{-17.1}^{+9.9}$	⋯	⋯
	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯
Bridge model	DM	${4.7}_{-1.8}^{+2.2}$	${4.2}_{-1.7}^{+4.4}$	${0.78}_{-0.04}^{+0.02}$	${53.3}_{-1.0}^{+0.4}$	${1037.0}_{-136.3}^{+33.0}$	[1500.0]	${24.5}_{-6.1}^{+2.0}$
rms = 036	bridge	${14.6}_{-4.4}^{+1.8}$	${40.0}_{-1.6}^{+0.1}$	${0.8}_{-0.06}^{+0.25}$	${51.9}_{-4.9}^{+37.9}$	${692.9}_{-104.6}^{+126.7}$	[1500.0]	${45.9}_{-3.8}^{+10.1}$
BIC = 172	1stBCG	[0.0]	[0.1]	[0.64]	[60.5]	${579.0}_{-20.5}^{+14.2}$	${36.8}_{-5.0}^{+11.7}$	${0.9}_{-0.2}^{+0.3}$
	2ndBCG	[47.8]	[69.6]	[0.35]	[74.1]	${379.7}_{-8.8}^{+16.0}$	${62.1}_{-8.8}^{+16.7}$	${0.5}_{-0.1}^{+0.2}$
	3rdBCG	[46.9]	[48.4]	[0.16]	[50.6]	${298.9}_{-15.5}^{+12.7}$	${120.7}_{-21.3}^{+2.5}$	${1.5}_{-1.1}^{+0.0}$
	L* Galaxy	⋯	⋯	⋯	⋯	${94.4}_{-11.9}^{+10.8}$	⋯	⋯
⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯

Notes.

^a ${\rm{\Delta }}\alpha$ and Δδ are measured relative to the reference coordinate point: (α = 04:17:34.6925 , δ = −11:54:31.9356). ^bEllipticity (ε) is defined to be $({a}^{2}-{b}^{2})/({a}^{2}+{b}^{2})$, where a and b are the semimajor and semiminor axes of the ellipse. ^cQuantities in brackets are fixed parameters.

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For images 4.2 and 4.1, the MUSE data are consistent with a low-confidence redshift of z = 3.10. Due to the low confidence of this measurement, we do not use it as a constraint. A full description of the data and results related to other objects in the field are given in our companion paper by Jauzac et al. (2019).

3.1. Methodology

3.2. Lensing Constraints

We identify 57 images of 17 systems that are used as constraints and seven candidates of strongly lensed images. Following the Hubble Frontier Fields ranking process, we classify the observed lensed images into three categories: gold, silver, and bronze. The gold category includes robustly identified multiply imaged systems with a measured spectroscopic redshift; three systems fall into this category. The silver classification is given to multiply imaged systems that are reliably identified as such by morphology, surface brightness, and lensing symmetry; 12 systems fall into this category. Images that have less robust identification, or would not be identified as counter images without an accurate lens model, were put in the bronze category and not used as constraints in our fiducial (silver) model. All systems are shown in Figure 1, and their coordinates, redshifts, and ranking, are tabulated in Table 2. We note that system 4 has a possible redshift of 3.1 from MUSE; however, it is based on low-confidence features. We choose to not include the redshift as a constraint in the model, as if it is incorrect the redshift might bias the model as was shown by, e.g., Jauzac et al. (2015), Johnson & Sharon (2016), Cerny et al. (2018), and Remolina González et al. (2018).

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We identify several other strong lensing features in the field, which, at the depth of the data in hand, are not deemed reliable enough to be used as constraints. We list these candidates in this paper for completeness. All the candidates are presented in Figure 1, and their coordinates are tabulated in Table 4 in the Appendix A.

Table 4.  List of Candidate Lensed Galaxies

ID	R.A.	Decl.
	J2000	J2000
c18.1	64.40084583	−11.91028778
c18.2	64.40074167	−11.91053000
c19.1	64.38539166	−11.90097528
c19.2	64.38445834	−11.90156944
c20.1	64.39867042	−11.91895096
c21.1	64.40059584	−11.91285222
c21.2	64.39874584	−11.91455333
c22.1	64.39631667	−11.91718722
c22.2	64.39631667	−11.91718722
c23.1	64.38672916	−11.90686278
c23.2	64.38670763	−11.90698944
c24.1	64.39396249	−11.91067667
c24.2	64.39380000	−11.91072361

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3.3. Mass Model Components

As described in Section 3.1, and as is typical for parametric lens modeling algorithms, the lens plane is described by a combination of several DM halos whose parameters are allowed to vary, with contribution from galaxy-scale halos that follow scaling relations. The lens model of MACS J0417 includes four "free" DM halos, all parameterized as PIEMDs. The dominant component is a cluster-scale halo, whose parameters are all allowed to vary, with the exception of the truncation radius r_cut that extends beyond the strong lensing regime and cannot be constrained by the strong lensing evidence. Three other halos are placed on the three BCGs, with positional parameters (x, y, ε, and θ) following their light distribution, and the other parameters set free. We emphasize that the halos placed on these galaxies are not to be considered strictly galaxy halos. The model cannot disentangle the DM halo in which the galaxy is embedded from the underlying DM halo of the cluster or group.

Table 3 lists the best-fit parameters of each halo, for several lens models. The "Silver" model uses as constraints the gold and silver arcs. The "Bronze" model uses gold, silver, and bronze constraints. We describe the third test model, labeled "Bridge," below.

As can be visually gleaned from the distribution of galaxies (Figure 1), the cluster core is fairly elongated, with the second and third brightest galaxies significantly separated in projection from the BCG. In the X-ray, Mann & Ebeling (2012) and Parekh et al. (2017) report extended emission elongated in the SE–NW direction. We, therefore, compute an additional lens model that includes a fifth PIEMD DM halo, forming a mass "bridge" between the central and NW components. We test this hypothesis using the gold+silver list of constraints. The fifth halo is free to vary between the BCG and the NW component. The core radius of the potential is intentionally free to vary up to a high value (300 kpc) to allow a possible flat profile. The cut radius is fixed to a 1.5 Mpc as the main DM halo potential

We quantitatively compare the quality of the three lens models using two criteria. The first one is the rms, which describes how well the model reproduces the image-plane positions of the constraints. The second one is the Bayesian Information Criterion (BIC; introduced by Schwarz 1978), which is a statistical measurement based on the model likelihood ${ \mathcal L }$, penalized by the number of free parameters k and the number of constraints n:

$$\begin{eqnarray}&&\mathrm{BIC}=-2\times \mathrm{log}({ \mathcal L })+k\times \mathrm{log}(n).\end{eqnarray} \tag{ 1 }$$

The rms gives a good indication of the global distance between the predicted image positions compared to the observed ones; thus for a fixed number of constraints a low rms generally implies a better model. The BIC quantifies an improvement in the model likelihood while taking into account a possible difference in the number of parameters and/or constraints between models. Thus a favorable model will be one with the best likelihood while keeping the lowest BIC value possible. Such criteria were used in previous analyses (Lagattuta et al. 2017; Jauzac et al. 2018; Mahler et al. 2018) to compare different variation models for a single cluster. The rms of the "Bridge" model is slightly better (036) compared to the fiducial model (037). However, the BIC shows an opposite trend when comparing the two models. We interpret a higher BIC value for the "Bridge" model as an over-fit of the model compared to a model without the bridge. In other words, the model does not improve enough to justify the addition of new parameters. Similar statistical analyses were made in other studies, e.g., using a discrimination by the evidence (Limousin et al. 2010), other likelihood penalization: Akaike Information Criterion (Acebron et al. 2017) or a combination of a large number of indicators (Jauzac et al. 2018).

We compare the mass distribution between the models and plot their mass contours in Figure 2. The difference between the two models is most notably the southeast region of the cluster. While the BCG area is well-constrained by systems surrounding the BCG, there is only one system with two images farther out. A confirmation of some of the lensed galaxy candidates with deeper observations would better constrain this region.

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The spectroscopic capabilities of MUSE allow us to detect a central image for system 1 buried in the light of the BCG. Our model predicts a radial pair at this location; however, only a single peak of emission is visible. We interpret that as the likely result of the source-plane caustic bisecting the galaxy in the source plane, resulting in a merging pair configuration where only a small fraction of the source galaxy is lensed into these positions. A more detailed analysis of the lensing configuration of this galaxy is presented in the companion paper by Jauzac et al. (2019).

We report an effective Einstein radius of ${\theta }_{E}\simeq 36^{\prime\prime}$ for a source at z = 9. The effective Einstein radius is the radius of a circle with the same area as an ellipse fitted to the critical curve. We measure a total projected mass of ${M}_{(200\mathrm{kpc})}={1.78}_{-0.03}^{+0.01}\,\times {10}^{14}$M${}_{\odot }$ within 200 kpc. Figure 3 shows the radial mass profile centered on the BCG. Using the capability of our parametric approach we compute the mass profile of five different components of our cluster model: the main cluster-scale DM halo, the halos centered on the three BCGs, and the mass distribution of all the other galaxies, which follow a mass-to-light relation.

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We qualitatively report a mass ratio of order 100:1 between the main cluster halo and the mass associated with the light of cluster elliptical galaxies, excluding the three brightest galaxies (dark green and magenta lines in Figure 3). This is consistent with the relative mass to light ratio of rich clusters of about 10¹⁴M${}_{\odot }$ as reported in Girardi et al. (2002). One will see that this qualitative result has no uncertainties attached, since the statistical uncertainties of the mass profile in Section 4 are likely underestimating the true uncertainty due to modeling assumptions (e.g., Meneghetti et al. 2017 and structure along the line of sight; Chirivì et al. 2018).

4.1. Photometric Redshifts

During the first year of JWST science operations, at least 13 galaxy clusters will be observed in the context of the Guaranteed Time Observations (GTO) and Director's Discretionary Early Release Science (DD-ERS) programs (PIs: Windhorst, Willott, Stiavelli, Rigby, and Treu) using all four JWST instruments: the Near-Infrared Camera (NIRCam), the Near-Infrared Imager and Slitless Spectrograph (NIRISS), Near-Infrared Spectrograph (NIRSpec), and the Mid-Infrared Instrument (MIRI). These observations will include NIRCam imaging to various depths for all 13 clusters. MACS J0417.5−1154 is included in this list of 13 clusters and will be observed thanks to the Canadian NIRISS Unbiased Cluster Survey GTO program (CANUCS; PI: Willott).

We use our lens model and UV luminosity functions from Mason et al. (2015) to predict numbers of objects observable by JWST at 8 < z < 16, before and during the epoch of reionization. We also explore and discuss the expectations from the HST RELICS observations that yielded 321 candidates with photometric redshifts z_phot ∼ 6–8 in 46 cluster fields, but none from this cluster (Salmon et al. 2017).

Observing the high-redshift universe behind a cluster offers a boost in sensitivity to lower luminosities, but diminishes the FOV. In Figure 5, we demonstrate how the effective observed FOV of 22 × 22 (4.8 arcmin², or one of the two modules observed by the JWST/ NIRCam), is affected by gravitational lensing. The magnification map for a source at z = 16 is ray-traced through the best-fit model to the source plane. This transformation reveals the spatial extent of the background area covered by such an observation, resulting in an unlensed observed high-z area of 1.3 arcmin².

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Figure 6 shows the expected cumulative number counts (not accounting for incompleteness) for MACS J0417, or a galaxy cluster with similar lensing strength, as a function of magnitude, for galaxies at z = 6, 8, 10, 12, 14, and 16 within the FOV of a single NIRCam module (roughly aligned with the WFC3/IR FOV). We adopt blank field luminosity functions from Mason et al. (2015) due to its ability to predict density at any redshift. The faint-end slope of this luminosity function increases from α = −2.1 at z = 8 to α = −3.5 at z = 16. Such steep faint-end slopes would imply that many small, faint galaxies are magnified into view by lensing and that there is a significant efficiency gain from strong lensing to discover the first galaxies with JWST.

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Cluster observations scheduled for the first year of JWST will typically reach magnitudes of ∼29 AB and fainter. From Figure 6, we expect that at this magnitude limits this field hosts three lensed galaxies at z = 10, and less than one galaxy in each of the higher redshift bins, not accounting for detection efficiency and incompleteness. Observing an order of a dozen clusters should yield galaxies as distant as z = 12 and a substantial sample of high-z galaxies at the epoch of reionization.

In Figure 7, we compare the lensing strength of MACS J0417 to other clusters from the RELICS program for which lens models are publicly available on the MAST, including those published by Cerny et al. (2018); Acebron et al. (2018a, 2018b); Cibirka et al. (2018), and Paterno-Mahler et al. (2018). The previous version of MACS J0417 lens model, V1, available on the MAST, predicts ∼20% higher number counts for relatively bright sources (AB mag 25), and similar number counts for faint sources, giving an indication of the systematic uncertainties due to spectroscopic redshift availability, and different modeling assumptions.

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With the updated model (V2), we find that MACS J0417 is ranked in the lower 25th percentile of these clusters when it comes to the lensing strength. However, as other RELICS clusters, MACS0417 is among the most powerful lenses known to date.

In a photometric search for z ∼ 6–8 galaxies in the entire RELICS survey, Salmon et al. (2017) report 321 candidates, with a median of six candidates per field and an average of seven, none of which are in the field of MACS J0417. From Poisson statistics alone, there is a 4% chance that at least 1 of the 46 RELICS fields would yield no z ∼ 6–8 candidates, given the average of seven per field. Cosmic variance would increase this likelihood somewhat (Trenti & Stiavelli 2008), especially in a lensed field (Robertson et al. 2014). However, our lensing analysis indicates that the lensing strength of MACS J0417 is not extraordinarily low compared to other RELICS clusters for which models are available. It is therefore odd that Salmon et al. (2017) detected no z_phot ∼ 6–8 candidates in this field.

Quantitatively, the prediction for MACS J0417, shown in Figure 7, indicates that this field should host about 5.34 z ∼ 6 magnified galaxies at, or brighter than, 27 mag. The actual expected number would be lower, due to incompleteness. A thorough investigation, including completeness estimates, is required (e.g., Livermore et al. 2017). However, we can get a rough estimate of the detection efficiency of Salmon et al. (2017) for the discovery of z ∼ 6 galaxies from their actual detection histograms. Salmon et al. (2017) discovered 211 candidates with F160W AB mag ≤27 in the z_phot = 6 bin in all of the RELICS fields. From Figure 7, we expect there to be at most 300 galaxies at z = 6 with observed AB magnitude below 27 within the same observed area. A comparison of the number of candidates observed with the predicted number implies an estimated average efficiency of at least 70%. Assuming this efficiency, we would have expected Salmon et al. (2017) to find at least 5.34 × 70% = 3.74 galaxies in this range behind MACS J0417. Assuming small number statistics, the zero detection is discrepant with this estimated expectation (for example, Poisson statistics would give a range of 1–8 at 95% confidence level). The low number of candidates in this field could be a result of lower-than-average density of galaxies at this location due to cosmic variance. However, such discrepancy suggests a reanalysis of this particular field is needed.

As can be seen in Figures 3 and 8, some of the eazy photo-z PDFs favor z > 5.5 solutions for some of the multiple images. A preliminary bpz reanalysis of this field puts source 9 slightly above z_phot = 5.5, which would increase the number of candidates in this field to two z ∼ 6 candidates. Therefore, reducing the disagreement between predictions and detections.

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An analysis of this field and all RELICS fields based on the combined HST+Spitzer photometry is in progress (V. Strait et al. 2019, in preparation). Adding the Spitzer photometry could remove some of the degeneracies and improve the photometric redshift estimates.

We present a strong lens model of MACS J0417.5−1154, updating the model previously released by the RELICS collaboration. This cluster was selected by the RELICS program for its promising lensing capabilities. We identified 57 multiple images belonging to 17 lensed background sources. We also report lensing candidates that were not reliable enough to be used as constraints but are nevertheless of potential interest for further study by current or upcoming facilities such as JWST. This study and the companion paper by Jauzac et al. (2019) represent the first published strong lensing analyses of this cluster.

Our strong lensing analysis compares models based on constraints with different levels of reliability (silver and bronze) as well as different levels of complexity of the lens plane, for example when including a bridge of matter between the two main substructures of the cluster. Our analysis reveals that the addition of a bridge potential, while giving a lower rms does not satisfy our BIC criteria. Therefore, we keep a fiducial model constrained by our silver sample with no potential acting as a bridge of matter between substructures of the cluster.

From our strong lensing mass modeling, we measure a total projected mass within 200 kpc of ${M}_{(200\mathrm{kpc})}={1.78}_{-0.03}^{+0.01}\,\times {10}^{14}$M${}_{\odot }$. Using the parametric capability of our modeling we estimate the mass ratio between the large-scale halo and the galaxy halos to be of order 100:1. Extrapolating the mass model to a large projected radius, we find a mass at 1.5 Mpc of ${M}_{(1.5\mathrm{Mpc})}={12.88}_{-0.51}^{+0.16}\times {10}^{14}$M${}_{\odot }$. Despite the limited ability of strong lens models to measure the mass beyond the multiple image region, this value is within 3σ of the mass ${M}_{1.5\mathrm{Mpc}}\,=(18.9\pm 0.25)\times {10}^{14}{M}_{\odot }$ measured by weak lensing analysis (Applegate et al. 2014). We report for this cluster an Einstein radius of ${\theta }_{E}\simeq 36^{\prime\prime}$ at z = 9. Using the parameters of the spherical Navarro–Frenk–White (NFW; Navarro et al. 1997) profile fitted in Applegate et al. (2014), we derived an Einstein radius at z = 9 of ${\theta }_{{E}_{\mathrm{NFW}}}\simeq 26^{\prime\prime}$. The large mass reported by Applegate et al. (2014) still provides a reasonably close Einstein radius compare to our analysis. In addition, strong lensing analysis of CLASH clusters (Zitrin et al. 2015) report, for comparable clusters, similar values.

We examine the agreement between photo-z and model-z for the sample of multiple images selected in our study. There is a general agreement when the low-z solutions for the photo-z are excluded. System 7 might be a misidentification. The agreements for systems 12 and 13 benefit from the reduced redshift range during the optimization of system 9 induced by the initial disagreement with photo-z. A detailed study of the influence of the photometric redshift algorithm or the data set is beyond the scope of this paper as this would need more spectroscopic redshifts to be used as a benchmark to remove biases in the comparison.

Our previous model of MACS J0417 suggested its lensing strength was about average among all RELICS clusters modeled to date (all of which are powerful lenses). The new lens model presented here suggests MACS J0417 is in the lower 25th percentile of the RELICS clusters. Still the lack of any z_phot ∼ 6–8 candidates in this field is at odds with the expected number, estimated from the lensing magnification of this field, assumptions on the high-z luminosity functions, and our estimate of the average detection efficiency of Salmon et al. (2017). We primarily attribute this to cosmic variance, but we will reanalyze this field and perform completeness simulations to determine if there are some other reasons besides cosmic variance for the low yield of high-z candidates. MACS J0417 is still expected to be an efficient lens for upcoming JWST GTO observations to discover fainter and higher redshift candidates. Strong lensing clusters will continue to deliver significant efficiency gains toward discovering high-redshift galaxies and the first galaxies with JWST.

Support for program GO-14096 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. This paper is based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with program GO-14096. Archival data are associated with program GO-12009. This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile. M.J. was supported by the Science and Technology Facilities Council (grant No. ST/L00075X/1) and used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/H008519/1, and STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure. A.C.E. acknowledges support from STFC grant ST/P00541/1. I.U.R. acknowledges support from NSF grants AST-1613536 and AST-1815403. Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the U.S. Department of Energy, National Nuclear Security Administration under Contract DE-AC52-07NA27344

Facilities: HST(WFC3 - , ACS) Magellan(LDSS3) - , VLT(MUSE) - .

We provide a list of candidate multiple images that were discovered in this work. These galaxies were not deemed reliable enough to be used as constraints. If confirmed with deeper observations, they could become useful lensing evidence to constrain areas in the field that are currently under-constrained. Table 4 lists the candidate IDs and coordinates. They are plotted in Figure 1.

The photo-z estimates that were used in this analysis are computed with two different algorithms, the HST-only analysis was done with BPZ and matches the catalogs that are publicly available on MAST. The HST+Spitzer analysis uses EAZY. In this appendix, we repeat the comparison between model-predicted redshift PDFs and those of the photo-z estimates, using EASY for both sets of photo-z measurements (see Figure 8). The same HST photometric catalogs, also available on MAST, were used in all cases. We find that the choice of photo-z algorithm does not significantly change our conclusion that the photometric redshifts and model redshifts are generally in good agreement.