ALMA Lensing Cluster Survey: Bright [CII] 158 μm Lines from a Multiply Imaged Sub-L^{\star} Galaxy at z=6.0719
Seiji Fujimoto, Masamune Oguri, Gabriel Brammer, Yuki Yoshimura, Nicolas Laporte, Jorge González-López, Gabriel B. Caminha, Kotaro Kohno, Adi Zitrin, Johan Richard, Masami Ouchi, Franz E. Bauer, Ian Smail, Bunyo Hatsukade, Yoshiaki Ono, Vasily Kokorev, Hideki Umehata, Daniel Schaerer, Kirsten Knudsen, Fengwu Sun, Georgios Magdis, Francesco Valentino, Yiping Ao, Sune Toft, Miroslava Dessauges-Zavadsky, Kazuhiro Shimasaku, Karina Caputi, Haruka Kusakabe, Kana Morokuma-Matsui, Kikuchihara Shotaro, Eiichi Egami, Minju M. Lee, Timothy Rawle, Daniel Espada
DDraft version January 7, 2021
Typeset using L A TEX twocolumn style in AASTeX63
ALMA Lensing Cluster Survey:Bright [C ii ] 158 µ m Lines from a Multiply Imaged Sub- L (cid:63) Galaxy at z = 6 . Seiji Fujimoto,
1, 2
Masamune Oguri,
3, 4, 5
Gabriel Brammer,
1, 2
Yuki Yoshimura,
6, 7
Nicolas Laporte,
8, 9
Jorge Gonz´alez-L´opez,
10, 11
Gabriel B. Caminha, Kotaro Kohno,
7, 13
Adi Zitrin, Johan Richard, Masami Ouchi,
16, 17, 5
Franz E. Bauer,
18, 19
Ian Smail, Bunyo Hatsukade, Yoshiaki Ono, Vasily Kokorev,
1, 2
Hideki Umehata,
21, 7
Daniel Schaerer,
22, 23
Kirsten Knudsen, Fengwu Sun, Georgios Magdis,
1, 2, 26
Francesco Valentino,
1, 2
Yiping Ao, Sune Toft,
1, 2
Miroslava Dessauges-Zavadsky, Kazuhiro Shimasaku,
6, 3
Karina Caputi,
28, 1
Haruka Kusakabe, Kana Morokuma-Matsui, Kikuchihara Shotaro,
6, 17
Eiichi Egami, Minju M. Lee, Timothy Rawle, and Daniel Espada Cosmic Dawn Center (DAWN), Jagtvej 128, DK2200 Copenhagen N, Denmark Niels Bohr Institute, University of Copenhagen, Lyngbyvej 2, DK2100 Copenhagen Ø, Denmark Research Center for the Early Universe, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo113-0033, Japan Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi,Chiba, 277-8583, Japan Department of Astronomy, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Institute of Astronomy, Graduate School of Science, The University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo 181-0015, Japan Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK Cavendish Laboratory, University of Cambridge, 19 JJ Thomson Avenue, Cambridge CB3 0HE, UK N´ucleo de Astronom´ıa de la Facultad de Ingenier´ıa y Ciencias, Universidad Diego Portales, Av. Ej´ercito Libertador 441, Santiago,Chile Las Campanas Observatory, Carnegie Institution of Washington, Casilla 601, La Serena, Chile Kapteyn Astronomical Institute, University of Groningen, Postbus 800, 9700 AV Groningen, The Netherlands Research Center for the Early Universe, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Physics Department, Ben-Gurion University of the Negev, P.O. Box 653, Be’er-sheva 8410501, Israel Univ Lyon, Univ Lyon1, Ens de Lyon, CNRS, Centre de Recherche Astrophysique de Lyon UMR5574, F-69230,Saint-Genis-Laval,France National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277–8582, Japan Instituto de Astrofısica, Facultad de Fısica, Pontificia Universidad Catolica de Chile Av. Vicuna Mackenna 4860, 782-0436Macul,Santiago, Chile Millennium Institute of Astrophysics (MAS), Nuncio Monse nor Santero Sanz 100, Providencia, Santiago, Chile Centre for Extragalactic Astronomy, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Observatoire de Gen`eve, Universit´e de Gen`eve, 51 Ch. des Maillettes, 1290 Versoix, Switzerland CNRS, IRAP, 14 Avenue E. Belin, 31400 Toulouse, France Department of Space, Earth and Environment, Chalmers University of Technology, Onsala Space Observatory, SE-43992 Onsala,Sweden Steward Observatory, University of Arizona, 933 N. Cherry Ave, Tucson, AZ 85721, USA DTU-Space, Technical University of Denmark, Elektrovej 327, DK2800 Kgs. Lyngby, Denmark Purple Mountain Observatory and Key Laboratory for Radio Astronomy, Chinese Academy of Sciences, Nanjing, China Kapteyn Astronomical Institute, University of Groningen, P.O. Box 800, 9700AV Groningen, The Netherlands Max-Planck-Institut f ur Extraterrestrische Physik (MPE), Giessenbachstr., D-85748, Garching, Germany. European Space Agency (ESA), ESA Office, Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA SKA Organisation, Lower Withington, Macclesfield, Cheshire SK11 9DL, UK (Received 2020 October 14; Revised 2020 December 14; Accepted 2020 December 29)
Corresponding author: Seiji [email protected] a r X i v : . [ a s t r o - ph . GA ] J a n Fujimoto et al.
ApJ in pressABSTRACTWe present bright [C ii ] 158 µ m line detections from a strongly magnified and multiply-imaged( µ ∼ L ∗ ( M UV = − . +0 . − . ) Lyman-break galaxy (LBG) at z = 6 . ± . ≥ σ exactlyat positions of two multiple images of the LBG behind the massive galaxy cluster RXCJ0600 − ∼ (cid:48)(cid:48) ) arc with a local magnification of µ ∼ ii ] line is also significantly detected. The source-plane reconstruction resolves theinterstellar medium (ISM) structure, showing that the [C ii ] line is co-spatial with the rest-frame UVcontinuum at the scale of ∼
300 pc. The [C ii ] line properties suggest that the LBG is a rotation-dominated system whose velocity gradient explains a slight difference of redshifts between the wholeLBG and its sub region. The star formation rate (SFR)– L [CII] relations from the sub to the wholeregions of the LBG are consistent with those of local galaxies. We evaluate the lower limit of the faint-end of the [C ii ] luminosity function at z = 6, and find that it is consistent with predictions from semianalytical models and from the local SFR– L [CII] relation with a SFR function at z = 6. These resultsimply that the local SFR– L [CII] relation is universal for a wide range of scales including the spatiallyresolved ISM, the whole region of galaxy, and the cosmic scale, even in the epoch of reionization. Keywords: galaxies: formation — galaxies: evolution — galaxies: high-redshift — galaxies: ISM —galaxies: kinematics and dynamics — galaxies: luminosity function INTRODUCTIONGalaxy evolution is regulated by several key mech-anisms in the interstellar medium (ISM) such as diskformation, stellar and active galactic nuclei (AGN) feed-back, mass building via star formation and galaxy merg-ers, and clump formations through disk instabilities. Re-solving the ISM structure to study local physical prop-erties in high-redshift galaxies is thus essential in orderto understand the initial phase of galaxy formation andevolution.During the past decades, hundreds of star-forminggalaxies at z > α lines (e.g., Iye et al. 2006; Vanzellaet al. 2011; Pentericci et al. 2011, 2014, 2018; Shibuyaet al. 2012, 2018; Ono et al. 2012, 2018; Finkelsteinet al. 2013; Oesch et al. 2015, 2016; Stark et al. 2017;Higuchi et al. 2019). The Atacama Large Millime-ter/submillimeter Array (ALMA) offers a rest-frame far-infrared (FIR) spectroscopic window for these z > ii ] 158 µ m and [O iii ] 88 µ m (e.g., Maiolino et al.2015; Inoue et al. 2016; Pentericci et al. 2016; Knudsenet al. 2016; Matthee et al. 2017, 2019; Carniani et al.2018; Smit et al. 2018; Bowler et al. 2018; Hashimotoet al. 2018, 2019; Tamura et al. 2019; Fujimoto et al.2019; Bakx et al. 2020). Since heavy elements producedin stars are returned into the ISM, the metal gas prop-erties traced by the fine-structure lines are good probesof the star-formation history and related physical mech- anisms (Maiolino & Mannucci 2019). In fact, recentALMA spatial and kinematic [C ii ]-line studies identifysignatures of some key mechanisms, including disk rota-tions (e.g., Jones et al. 2017; Smit et al. 2018), galaxymergers (e.g., Hashimoto et al. 2019; Le F`evre et al.2020), and outflows (e.g., Gallerani et al. 2018; Spilkeret al. 2018; Fujimoto et al. 2019, 2020b; Ginolfi et al.2020). In conjunction with other fine-structure lines of[O iii ] and [N ii ], recent ALMA observations also allowus to perform multiple line diagnostics to constrain thedominant ionization state of the ISM gas (e.g., Inoueet al. 2016; Pavesi et al. 2016; Laporte et al. 2019; No-vak et al. 2019; Harikane et al. 2020).There are several challenges related to the FIR spec-troscopy. The first is sensitivity. While ALMA isthe most sensitive mm/submm telescope and yielding alarge number of new findings about high-redshift galax-ies, the detection of FIR fine-structure lines from abun-dant, typical galaxies remains challenging. For exam-ple, to observe a [C ii ] line of ∼ × L (cid:12) from z = 6,about 2-hour observing time is required . However, sucha source typically falls in the absolute UV magnituderange of M UV ∼ − . − . Based on CASA Observing Tool calculations to detect the [C ii ]line of 1 × L (cid:12) with a line width of 200 km s − at ≥ σ in thevelocity integrated map. trongly lensed [C ii] line from a Sub- L ∗ Lyman-break galaxy at z = 6 . ∼ L ∗ in the UV luminosity function at z > (cid:38) L ∗ or sub- L ∗ luminosities. The second challenge ishigh spatial resolution observations towards these typi-cal galaxies. Recent Hubble Space Telescope ( HST ) stud-ies report that the typical effective radius ( r e ) in star-forming galaxies at z > < (cid:39) . (cid:48)(cid:48)
2) (e.g., Holwerda et al. 2015; Shibuya et al. 2015;Bouwens et al. 2017; Kawamata et al. 2018). The ISMstructure mostly comparable to the r e scale could be re-solved by ALMA high-resolution observations down tothe 0 . (cid:48)(cid:48)
02 scale. However, this requires even longer ob-serving times than (cid:38)
10 hours estimated above just forthe detection of the typical galaxies. The third challengeis the requirement of prior spectroscopic redshifts dueto the narrow frequency coverage of ALMA (7.5-GHzcoverage in a single tuning), which may cause potentialbiases. In most cases, the prior spectroscopic redshiftis obtained from Ly α lines. While high-redshift galax-ies with Ly α spectroscopic redshifts show weak [C ii ]lines at a given star-formation rate (Carniani et al. 2018;Harikane et al. 2018, 2020; cf. Schaerer et al. 2020), arecent study by Smit et al. (2018) indicates that galax-ies with no strong Ly α line may emit a strong [C ii ] line.Because the fraction of Ly α emitters (LAEs; e.g., equiv-alent width of Ly α >
25 ˚A ) is less than 30% amongstar-forming galaxies with M UV ∼ − . z > α lines will systematically miss a majority ofthe representative population at z >
6. An ALMA blindline survey is one possible solution, but novel [C ii ] lineemitters z > ii ] 158- µ m lines from strongly lensed multiple im-ages of a sub- L ∗ galaxy at z = 6 . − HST , Spitzer , and VLTand with help of gravitational lensing magnification, weresolve the ISM structures and investigate the spatiallyresolved rest-frame UV-to-FIR continuum and the [C ii ]line properties down to a (cid:39)
300 pc scale. This is the firstALMA study to resolve the ISM properties in a repre-sentative ( (cid:39) sub- L ∗ ) galaxy in the epoch of reionization. The structure of this paper is as follows. In Sec-tion 2, we overview the ALCS survey and the data setsin RXCJ0600 − ii ] line emitters at z = 6 .
07. InSection 4, we report and discuss intrinsic characteristicsof these two [C ii ] line emitters with the correction of thelensing magnification. A summary of this study is pre-sented in Section 5. Throughout this paper, we assumethe Chabrier initial mass function (Chabrier 2003) anda flat universe with Ω m = 0 .
3, Ω Λ = 0 . σ = 0 .
8, and H = 70 km s − Mpc − . We use magnitudes in the ABsystem (Oke & Gunn 1983). DATA AND REDUCTION2.1.
ALMA Lensing Cluster Survey
ALCS is a cycle-6 ALMA large program (Project ID:2018.1.00035.L; PI: K. Kohno) to map a total of 88-arcmin high-magnification regions in 33 massive galaxyclusters at 1.2-mm in Band 6. The sample is selectedfrom the best-studied clusters drawn from HST treasuryprograms, i.e., the Cluster Lensing And Supernova Sur-vey with Hubble (CLASH; Postman et al. 2012), HubbleFrontier Fields (HFF; Lotz et al. 2017), and the Reion-ization Lensing Cluster Survey (RELICS; Coe et al.2019). Observations were carried out between December2018 and December 2019 in compact array configura-tions of C43-1 and C43-2 fine tuned to recover stronglylensed (i.e., spatially elongated), low surface brightnesssources. The 1.2-mm mapping is accomplished with a15-GHz wide spectral scan in the ranges of 250.0–257.5GHz and 265.0–272.5 GHz via two frequency setupsto enlarge the survey volume for line-emitting galaxies.The spectral mode of Time Division Mode is used, whichachieves the spectral resolution of ∼
28 km s − throughthese frequency setups. A full description of the surveyand of its main objectives will be presented in a separatepaper (in preparation).2.2. RXCJ0600 − RXCJ0600 − ∼ M (cid:12) ) galaxycluster at z = 0 .
43 that is included in RELICS and wasfirstly identified in the Massive Cluster Survey (MACS;Ebeling et al. 2001). As a part of ALCS, the ALMA ob-servations for RXCJ0600 − (cid:48)(cid:48) × (cid:48)(cid:48) in 105pointings with 46–49 12-m antennae providing baselinesof 15–456 m under a precipitable water vapor (PWV)of 0.6–1.3 mm. J0522-3627 was observed as a flux cali-brator. The bandpass and phase calibrations were per-formed with J0609-1542. Fujimoto et al. : . . - : : . . : . Right ascension z6.1 z6.3 z6.1/6.2 (arc)z6.4 z6.2 z6.5 z6.3z6.4 A L C S c ov e r a g e Right ascension D ec li n a ti on : . . - : : . . : . foregroundforeground Figure 1. Left : False-color
HST image of the cluster RXCJ0600 − z = 6 .
07 estimated from our fiducial mass model. The green lines indicate the ALCSarea coverage in this cluster, within which the relative sensitivity to the deepest part of the mosaic map is greater than 30%.The five multiple image positions of RXCJ0600- z (cid:48)(cid:48) × (cid:48)(cid:48) squares. Middle : HST /F160W 6 (cid:48)(cid:48) × (cid:48)(cid:48) cutouts for the multiple images of z z z ii ] line intensity drawn at 1 σ intervals from ± σ to ± σ . We use the natural-weighted map for z z uv -tapered (1 . (cid:48)(cid:48) × . (cid:48)(cid:48)
8) map for z z galfit (see Section 3.2 and Appendix C. see also N. Laporte et al. submitted). Right : [C ii ] linespectra for z z z ii ] integration range for the velocity-integrated map whose contours are shown in the middle panel. The blue curve is thebest-fit single Gaussian. The ALMA data were reduced and calibrated with theCommon Astronomy Software Applications package ver-sion 5.4.0 ( casa ; McMullin et al. 2007) with the pipelinescript in the standard manner. With the CASA task tclean , continuum maps were produced by utilizingall spectral windows. The tclean routines were exe-cuted down to the 3 σ level. We adopted a pixel scaleof 0 . (cid:48)(cid:48)
15 and a common spectral channel bin of 30 kms − . The natural-weighted map achieved a synthesizedbeam FWHM of 1 . (cid:48)(cid:48) × . (cid:48)(cid:48)
95 with sensitivities in thecontinuum and the line in a 30-km s − width channelof 56.9 and 932 µ Jy beam − , respectively. We also pro-duced several uv -tapered maps in a parameter range of0 . (cid:48)(cid:48) × . (cid:48)(cid:48) . (cid:48)(cid:48) × . (cid:48)(cid:48) HST /ACS–WFC3 and
Spitzer /IRAC observationswere carried out as a part of RELICS (Coe et al. 2019)and
Spitzer -RELICS (Strait et al. 2020) surveys, respec- tively.
HST images were obtained in the F606W (2180s), F814W (3565 s), F105W (1411 s), F125W (711 s),F140W (736 s), and F160W (1961 s) filters. The IRACchannel 1 (3 . µ m) and channel 2 (4 . µ m) integrationsare approximately 10 hours each. We aligned all of the HST exposures to sources in the PanSTARRS (DR1)catalog (Chambers et al. 2016; Flewelling et al. 2016)—which we verified is consistent with the
GAIA
DR2(Gaia Collaboration et al. 2018) astrometric frame—and created final mosaics in a common pixel framewith 50 mas and 100 mas pixels for the ACS/WFC andWFC3/IR filters respectively. We aligned the individ-ual
Spitzer exposures to the same astrometric frame andgenerated final drizzled IRAC mosaics with a pixel scaleof 0 . (cid:48)(cid:48)
5. Further details of the
HST ( Spitzer ) image pro-cessing with the grizli ( golfir ) software will be pre-sented in Kokorev et al. (in prep). In Figure 1, wepresent the false-color HST image of RXCJ0600 − trongly lensed [C ii] line from a Sub- L ∗ Lyman-break galaxy at z = 6 . Table 1.
Observed FIR properties of bright [C ii ] line emitters identified in RXCJ0600 − z † z z z ‡ R.A. 06:00:09.13 06:00:09.55 06:00:08.58 06:00:05.55Dec. − − − − ν center [GHz] 268.682 ± ± †† –FWHM [km s − ] 169 ±
22 181 ±
34 (181) †† – z [CII] ± ± †† – S [CII] [Jy km s − ] 4.83 ± ± ± L [CII] [ × L (cid:12) ] 4.5 ± ± ± f . [mJy] 0.35 ± ± < ii ] major-axis [ (cid:48)(cid:48) ] 4.24 ± ± †† –[C ii ] minor-axis [ (cid:48)(cid:48) ] 0.63 ± ± †† –[C ii ] position angle [ ◦ ] 71 ± ±
430 – †† – Note — S/N : Signal-to-noise ratio at the peak pixel in the natural-weighted map, after velocity integration. The velocityintegration range is denoted by the yellow shaded region in the right panel of Figure 1. ν center & FWHM : [C ii ] line peakfrequency and full-width-at-half-maximum estimated from a single Gaussian fit. z [CII] : Redshift of the [C ii ] line emissionestimated from the frequency peak. S [CII] & L [CII] : The velocity integrated [C ii ] line intensity and the line luminosity withoptimized apertures. Here we adopt a velocity integration range of 1.5 × FWHM. f . : Peak 1.2-mm continuum flux densityin a uv -tapered (2 . (cid:48)(cid:48) × . (cid:48)(cid:48)
0) map. We provide a 2 σ upper limit for z [C ii ] major-/minor-axis & position angle :Deconvolved spatial size (in FWHM) and position angle of the [C ii ] line in the velocity-integrated map measured with imfit .For z uv -tapered (1 . (cid:48)(cid:48) × . (cid:48)(cid:48)
0) map to obtain the global scale property. † This source is called also as RXCJ0060-arc in N. Laporte et al. (submitted). †† We do not perform any profile fitting to the spectrum and the 2D spatial map of z z ‡ z VLT/MUSE integral field spectroscopy of theRXCJ0600 − of the cluster core. Weuse the standard MUSE reduction pipeline version 2.8.1(Weilbacher et al. 2014) to create the final data-cube. Inthis process, we used the self-calibration method basedon the MUSE Python Data Analysis Framework (Ba-con et al. 2016; Piqueras et al. 2017) and implementedin this version of the reduction pipeline. Finally, we ap-plied the Zurich Atmosphere Purge (ZAP, Soto et al.2016) to remove the sky residuals that were not com-pletely removed by the MUSE pipeline.We used the MUSE data cube to build our redshiftcatalog in two steps, similar to Caminha et al. (2017,2019). We first extracted the spectra of all sources de-tected in the HST imaging, and in a second step, weperformed a blind search for faint-line emitters. Thisprocedure allowed us to measure 76 secure redshifts, ofwhich 16 are emission from galaxies behind the clus-ter. This redshift catalogue was used to identify clustermembers and multiply imaged galaxies that were usedin strong lens mass modeling (see Section 3.3 for more details). In Appendix A, we summarize the full spectro-scopic sample from MUSE. DATA ANALYSIS3.1.
Line Identification
We conduct a blind line search in the ALMA datacubes with the channel widths of 30 km s − and 60 kms − . First, we produce three-dimensional signal-to-noiseratio (S/N) cubes by dividing each channel with its stan-dard deviation. Here we use the ALMA data cubes be-fore the primary beam correction. We then search linecandidates in the three-dimensional S/N cube by utiliz-ing a python-base software of dendrogram (Goodmanet al. 2009) whose algorithm is similar to clumpfind (Williams et al. 1994). In dendrogram , we obtainan initial candidate catalog of line sources that meetthe following criteria: at least 10 pixels and/or channelswith a pixel value of ≥ ≥ dendrogram evaluates the reliability of the initial linecandidates based on the positive and negative proper-ties of the peak S/N histograms, spatially integratedpixel values, and the channel width. This results intwo reliable, bright line emitters both at ∼ Fujimoto et al.
We note that these two lines are also robustly identi-fied with an independent blind line search method ofGonz´alez-L´opez et al. (2017). Based on morphological,redshift, and gravitational lens properties of these twoline emitters obtained in detail analyses in the followingsubsections (Section 3.2, 3.3, and 3.4), we refer to thesetwo line emitters as z z . z z z z z z z z z z ±
22 km s − .After integrating over a velocity range of 1.5 × FWHM, z z (cid:48)(cid:48) × (cid:48)(cid:48) in the velocity-integratedmaps with the CASA task of imfit yields deconvolvedspatial FWHM sizes of 4 . (cid:48)(cid:48) × . (cid:48)(cid:48)
82 and 1 . (cid:48)(cid:48) × . (cid:48)(cid:48)
29 for z z uv -tapered (1 . (cid:48)(cid:48) × . (cid:48)(cid:48)
0) map for z imfit . From line free channels, the contin-uum is also detected in the uv -tapered map (2 . (cid:48)(cid:48) × . (cid:48)(cid:48) . σ and 2 . σ level from z z imfit results and thecontinuum flux density in Table 1. Further analyses forthe continuum emission are presented in N. Laporte etal. (submitted).3.2. Optical-NIR Counterparts
The bright lines of z z ∼ ii ] (e.g., Decarli et al. 2020). To deter-mine which line corresponds to z z HST images around z z ∼ . (cid:48)(cid:48) z z ∼ µ m, and the one near z z z z +0 . − . (Kokorev et al. in prep.),presumably one of the member galaxies of RXCJ0600-2007 ( z = 0 . z eazy code (Brammer et al. 2008) . We fit the photo-metric flux densities and their uncertainties with linearcombinations of templates derived following Brammeret al. (2008) but adopting Flexible Stellar PopulationSynthesis models as the basis (Conroy et al. 2009; Con-roy & Gunn 2010). We adopt the dust attenuation lawof Kriek & Conroy (2013) with δ = 0 (i.e., a Calzettiet al. 2000 shape with an additional 2175 ˚A dust fea-ture).In Figure 2, we show probability distributions of pho-tometric redshifts for the optical-NIR counterparts of z z z z z = 6 .
0, in excellentagreement with the bright-line detection at ∼ ii ] 158 µ m line at z = 6 .
07. In this case,observed line luminosities L line (i.e., without the correc-tion of the lensing magnification) are estimated to be4.5 ± × L (cid:12) and 2.3 ± × L (cid:12) for z z z = 6 with a peak dust temperature T d = 38K (e.g., Faisst et al. 2020) and a dust emissivity index β d = 1 . L FIR to be 5.8 ± × L (cid:12) and 3.3 ± × L (cid:12) and subsequently line to rest-frame FIR luminosity ratios to be 7.8 × − and 6.8 × − , for z z ii ] line L [CII] and L FIR ratio ( L [CII] /L FIR ) among local galaxies(e.g., Brauher et al. 2008; D´ıaz-Santos et al. 2013), whichalso supports the bright lines at ∼ ii ] line. Based on the source redshift at z = 6 .
07, we http://github.com/gbrammer/eazy-py trongly lensed [C ii] line from a Sub- L ∗ Lyman-break galaxy at z = 6 . Table 2.
Observed
HST and IRAC photometry of the multiple images of RXCJ0600- z µ m 4.5 µ m( µ Jy) ( µ Jy) ( µ Jy) ( µ Jy) ( µ Jy) ( µ Jy) ( µ Jy) ( µ Jy) z < ± ± ± ± ± ± ± z ± ± ± ± ± ± ± ± z < ± ± ± ± ± < . < † z < ± ± ± ± ± ± ± Note — The photometry is performed with separate strategies for four lensed images to account for the crowded cluster fieldand varying degrees of extended source morphology (see Appendix C). For non-detection, we list the upper limit at the 2 σ level. † We obtain 0.34 ± µ Jy which we replace the 2 σ upper limit. also confirm that star-formation rate (SFR) estimatesare consistent between the SED fitting with the dustattenuation correction and the summation of the rest-frame UV ( L UV ) and L FIR following the work of Bellet al. (2005) scaled to the Chabrier IMF,SFR [ M (cid:12) yr − ] = 1 . × − ( L FIR + 2 . L UV ) . (1)Although the z z ∼
1, we also identify a 3.6- µ m excessfeature in both z z z ∼ iii ] λ β lines (e.g., Roberts-Borsani et al.2016; Harikane et al. 2018). Therefore, the high- z so-lution at z ∼ z solution mightbe CO(16-15) at z = 5 .
85 and CO(17-16) at z = 6 . L CO(16 − /L FIR and L CO(17 − /L FIR (cid:46) × − among luminous quasars at similar redshifts (Carnianiet al. 2019). This indicates that L line /L FIR of z z z z ii ] line emitters at z = 6 .
07. Note thatwe confirm that the [C ii ] line solution is further sup-ported by the lens models, intrinsic physical properties(see Section 3.4 and 3.5), and follow-up Gemini/GMOSspectroscopy (N. Laporte et al. submitted).Based on the redshift of z = 6 .
07, we also examinethe Ly α line in the MUSE data cube around z z α features neitheraround z z σ upper limits of the Ly α equiv-alent width ( EW Ly α ) at 4.4 ˚A and 3.7 ˚A for z z α line would be ascribed to dust and/or neutral hydrogenin interstellar and intergalactic media. This emphasizesthe importance of the ALMA blind line search which enable studies of galaxies irrespective of their Ly α lineproperties in particular in the epoch of reionization.3.3. Mass Model
To study intrinsic physical properties of the [C ii ]line emitters z z z = 0 . glafic (Oguri 2010), Lenstool (Jullo et al. 2007), andLight-Traces-Mass (LTM; Zitrin et al. 2015). Multipleimages are selected based on the morphology and col-ors of galaxies in the
HST images taken with RELICS,guided by y mass models. These models also exploit theMUSE spectroscopic redshift catalog (see Section 2.2)for redshift information of some multiple image systemsas well as secure identifications of cluster member galax-ies. These models adopt nearly identical sets of multi-ple image systems for constructing the mass models andprovide almost consistent predictions for multiple imagepositions and magnification factors. A brief summary ofthese mass models is also presented in N. Laporte et al.(submitted), while full details will be given in a sepa-rate paper (in preparation). In this paper, we adopt themass model of glafic as a fiducial model for our anal-yses and here describe its construction below, althoughwe also use results of
Lenstool and LTM models toevaluate uncertainties in magnification factors.We construct the mass model with glafic in the samemanner as in Kawamata et al. (2016). Our mass modelconsists of cluster-scale halos and cluster member galax-ies. We place the cluster-scale halos at the positions ofthe three brightest cluster member galaxies in the core ofthe cluster. The position of one of the three cluster-scalehalos is treated as a free parameter, whereas those ofthe other two cluster-scale halos are fixed to the galaxypositions. The cluster-scale halos are modeled by an el-liptical Navarro-Frenk-White (NFW; e.g., Navarro et al.1997) profile. The cluster member galaxies are selectedusing both photometric redshifts of galaxies measured
Fujimoto et al. mag(AB)
F606W+F814W F105W F140W+F160W ch1 ch2 F105W F140W+F160W ch1 ch2F606W+F814WF606W+F814W F105W F140W+F160W ch1 ch2 F105W F140W+F160W ch1 ch2F606W+F814W z6.1/6.2 (arc) z6.3z6.4 z6.5 λ obs [μm] z λ obs [μm] zλ obs [μm] z λ obs [μm] z f ν [ μ J y ]f ν [ μ J y ] f ν [ μ J y ]f ν [ μ J y ]
6 0.5 1.0 2.0 4.0 8.0 0 2
6 0.5 1.0 2.0 4.0 8.0 0 2
6 0.5 1.0 2.0 4.0 8.0 0 2 p ( z ) mag(AB)21222324252627mag(AB)222324252627mag(AB)242526272829 p ( z ) p ( z ) p ( z ) Figure 2.
Observed optical-NIR properties of z z z z z ∼ Top:
Cutouts of the
HST (3 (cid:48)(cid:48) × (cid:48)(cid:48) , except for z (cid:48)(cid:48) × (cid:48)(cid:48) ) and Spitzer (8 (cid:48)(cid:48) × (cid:48)(cid:48) ) images. Some of theHST images are integrated one. The filter name is presented at the top. Bottom:
HST and
Spitzer photometry (black square)and the best-fit templates, where gray triangles are the upper limits. The sum of individual eazy templates is shown in thelight blue curve. The yellow shaded region is the probability distribution of the photometric redshift p ( z ) from the SED fit.The red line indicates the spectroscopic redshift from the [C ii ] lines at ∼ µ m excess feature in z z iii ] λ β lines that are often observed in z ∼ from HST images (Coe et al. 2019) as well as galaxycolors. The position and shapes of the member galaxiesare fixed to those derived from the
HST image and treattheir velocity dispersions and truncation radii using apseudo-Jaffe ellipsoid as model parameters assuming ascaling relation (see Kawamata et al. 2016, for more de-tails). In order to achieve a good fit, a member galaxy lo-cated at (R.A., Dec.)=(06:00:10.664, − χ minimization and determine the best-fit mass modelassuming a positional error of 0 . (cid:48)(cid:48) trongly lensed [C ii] line from a Sub- L ∗ Lyman-break galaxy at z = 6 . RXCJ0600-z6.1/6.2z6.3z6.4z6.5 f ν / F W λ obs [μm] Figure 3.
Observed SEDs of the multiple images ofRXCJ0600- z HST bands normalized by the F125Wband. The green, red, brown, and blue squares present z z z z Carlo method. Our best fitting model has χ = 20 . glafic .Note that we do not include the foreground objectoverlapping z z Multiple Images
From all of our mass models, we consistently obtainthe following two predictions: i) z z ∼ z z ii ] morphology that has two closepeaks. In fact, we confirm in Appendix D that [C ii ] linespectra produced at these two peaks show line profilesconsistent with each other. In addition, almost the sameoptical-NIR SED shapes between z z z z ±
22 km s − (see Section 3.1), the offset is muchsmaller than the typical FWHM range of the [C ii ] lineamong z ∼ ∼ − ; B´ethermin et al. 2020), suggestingthat the slight velocity shift is explained by the differ- ential magnification at different regions of the galaxy.We thus interpret z z ii ] line emission at z = 6 .
07 from a Lyman-break galaxy (LBG) behind RXCJ0600-2007. Hereafterwe refer to the background LBG as RXCJ0600- z z
6, the posi-tions of which we present in Figure 1, where we identifycorresponding optical-NIR objects. We refer to thesepotential multiple images as z z z z ∼ (cid:48)(cid:48) scale. In this paper, we focus anoptical-NIR object as z z z z z z z z z z ∼
6. We further perform the optical-NIR SED fit-ting to z z z z z z z z ∼ z z ∼
6, though the
HST - Spitzer color of z z z z z ii ] line emission is detected from z z z z . (cid:48)(cid:48) z σ ) atthe consistent frequency with z z z z Fujimoto et al.
Table 3.
Observed Physical Properties of the multiple images of RXCJ0600- z z phot z spec M UV SFR M star A v µ † whole µ † local (mag) ( M (cid:12) yr − ) ( × M (cid:12) ) (mag) z +0 . − . ± − ± +45 − +0 . − . +0 . − . +4 − +27 − z +0 . − . ± − ± +11 − +1 . − . +0 . − . +14 − – z +0 . − . (6.0719) − ± +1 . − . +0 . − . +2 . − . +2 . − . – z +0 . − . – − ± +0 . − . +0 . − . +0 . − . +1 . − . – Note — Physical properties obtained from the SED fitting of the observed photometry with eazy without correcting for thelensing magnification. The intrinsic physical properties after the correction of the lensing magnification are summarized inTable 4. Based on the conversion from the UV and FIR luminosity of Bell et al. (2005) scaled to the Chabrier IMF, we obtainconsistent SFR estimates of 188 ± M (cid:12) yr − and 120 ± M (cid:12) yr − for z . / . z .
3, respectively. Because the UVluminosity dominates in both z . / . z .
3, a ±
10 K difference in the T d assumption for the L FIR calculation (Section 3.2)changes these SFR estimates by ∼ † We define µ whole and µ local as follows: µ whole = (observed luminosity of the multiple image) / (overall luminosity of the intrinsic galaxy) µ local = (observed luminosity of the multiple image) / (local luminosity of the strongly lensed, sub region near the caustic line),where the sub region corresponds to the dashed rectangle area in Figure 4. The errors are evaluated from the minimum tomaximum range among our independent mass models. the case that z z HST - Spitzer color with other multiple images, theinterpretation of z z z z z = 6 .
07 from the best-fitmass model of glafic in the left panel of Figure 1. Wesummarize the [C ii ] line properties and the SED fittingresults for all these multiple images in Table 1 and Table3, respectively.3.5. Physical Properties of RXCJ0600- z The configuration of the multiple images is helpful toobtain the precise information about the source posi-tion and its surface brightness profile in the source plane.Here we estimate the intrinsic two-dimensional (2D) sur-face brightness profile by fitting the
HST images assum-ing the fiducial mass model. Specifically, we first pro-duce a 1 . (cid:48)(cid:48) × . (cid:48)(cid:48) HST /F160W image of z r e = 1.2 +4 . − . kpc (major axis), axis ratio of 0.49 +0 . − . , position angle= 84 +2 ◦− , S´ersic index n = 2.5 +1 . − . , and central coordi- nate of (RA, Decl.)=(6:00:08.12, − χ minimization. Because we find a degener-acy between r e and n , here we restrict the S´ersic indexto the range of 1 < n < z z z z z z ∼ (cid:48)(cid:48) scale in the image plane (e.g.,Vanzella et al. 2020). This interpretation is consistentwith the slight difference in the line peak frequenciesand the line profiles between z z z z ∼
150 (163) and ∼
35 (21), respectively. The observedluminosity of z z z z trongly lensed [C ii] line from a Sub- L ∗ Lyman-break galaxy at z = 6 . . . . - : : . . . D ec li n a t i on model RXCJ0600-z6 z6.3 (whole) z6.4(whole)z6.1/6.2 (sub) z6.3 z6.4 model obs. z6.1/6.2 whole regionsub region
Right ascension D ec li n a t i o n Right ascension D ec li n a t i o n . . - : : . . - : : . . Figure 4. Left:
The best-fit 2D S´ersic profile (effective radius in major axis = 1.2 kpc, axis ratio = 0.49, S´ersic index n =2.5) and coordinate (R.A., Decl. = 6:00:08.12, − z z = 6 . χ minimization only with the 1 . (cid:48)(cid:48) × . (cid:48)(cid:48) HST /F160W cutout of z Middle:
The multipleimages of RXCJ0600- z z z z (cid:48)(cid:48) × (cid:48)(cid:48) areas around z z (cid:48)(cid:48) × (cid:48)(cid:48) area around z z Right:
The
HST /F160W image showing the multiple images of z z z we confirm that our independent mass models agree inthe ratio of magnification factors between z z L [CII] ratio of 5.7 ± z z z z M UV = − . +0 . − . , which is ∼ L ∗ of the LBG luminosity function at z = 6 ( M UV = 20 . +0 . − . ; Ono et al. 2018). In Figure5, we show the SFR and M star relation of RXCJ0600- z
6. For comparison, we also present the average relationamong z ∼ z ii ] linewidth and luminosity in RXCJ0600- z z ∼ r e , circ ≡ r e × √ axis ratio)of 0.84 kpc also falls in a typical range among z ∼ z L ∗ galaxy at this epoch. We note that these intrinsicphysical properties are consistent with independent es-timates in N. Laporte et al. (submitted) within the er-rors, even though the SED fitting strategies are differentdue to the different scopes in the paper. [C ii ] VIEWS FROM ISM TO COSMIC SCALESThe uniquely and strongly lensed galaxy near thecaustic line (Section 3.3) allows us to study ISM prop-erties from internal to whole scales of the host galaxy.For an example of the whole view of the galaxy basedon z ∼ . (cid:48)(cid:48) . (cid:48)(cid:48)
04 (corresponding to ∼
250 pcat z = 6 .
07) after the correction of the lensing magnifi-cation, providing sub-kpc scale ISM views. At the sametime, the blind aspect of the ALCS survey also allowsus to statistically evaluate the number density of the[C ii ] line emitters at z ∼ z
6. In con-junction with the rest-frame UV and FIR continuumproperties, we examine the [C ii ] line properties from theISM to cosmic scales and discuss whether there is com-2 Fujimoto et al.
Table 4.
Intrinsic physical properties of strongly lensedLBG of RXCJ0600- z z z z − − z spec ± ± † EW rest Lyα [˚A] < . < . L [CII] [ × L (cid:12) ] 1.1 +0 . − . +0 . − . M UV [mag] − +0 . − . − . +0 . − . SFR [ M (cid:12) yr − ] 5.4 +4 . − . +0 . − . M star [ × M (cid:12) ] 9.6 +6 . − . +0 . − . A v [mag] 0.18 +0 . − . +0 . − . r e [kpc] 1.2 +4 . − . – n +1 . − . –axis ratio 0.49 +0 . − . –PA [ ◦ ] 84 +2 − – M dyn [ × M (cid:12) ] 3 ± M gas [ × M (cid:12) ] 2 ± f gas [%] ∼ Note — (1) The physical properties related to the whole re-gion of the galaxy that we obtain by applying µ whole (Table3) to the observed properties of z r e , n , and axis ratio) is not estimated by using µ whole ,but by optimizing the intrinsic 2D surface brightness profilein the source plane to match the 2D surface brightness pro-file of z glafic (see Section 3.5).The circularized effective radius is estimated to be 0.8 +2 . − . kpc, which is consistent within ∼ σ errors with an inde-pendent 2D surface brightness profile fit on the image planein N. Laporte et al. (submitted). We calculate M gas by sub-tracting M star from M dyn , which is consistent with anotherestimate from the empirical calibration with the [C ii ] lumi-nosity (Zanella et al. 2018) of (3 ± × M (cid:12) (see Section4.2). (2) The physical properties related to the local scale ofthe galaxy in the sub region near the caustic line, by apply-ing µ local (Table 3) to the observed properties of z † The sub region is red-shifted by 69 ±
22 km s − , whichagrees well with the velocity gradient identified in the wholescale of RXCJ0600- z mon property or a large diversity among these multiplescales.4.1. Spatial Distributions of UV, FIR, and [C ii ] downto Sub-kpc Scale Making full use of the gravitational lensing, we inves-tigate spatial distributions of the [C ii ] line, rest-frameUV and FIR continuum on the source plane and com- z6.1/6.2 RXCJ0600-z6 l e n s c o rr ec ti on (sub region)(whole region) z6.3 z ~ m a i n s e q u e n c e Figure 5.
SFR– M star relation. The red filled and opencircles indicate the relations before and after applying thecorrection of the lensing magnification to the SED fittingresults, respectively, for z z z ∼ σ uncertainty evaluated in Iyer et al. (2018). pare them. In the context of similar studies so far at z ∼ L ∗ galaxy inthe epoch of reionization.In the left panel of Figure 6, we present the rest-frame UV continuum maps for z z HST /F160Wband with the [C ii ] line (red contour) and the rest-frameFIR continuum (green contour) taken by ALMA. Theemission peaks of the [C ii ] line and rest-frame FIR con-tinuum are marked with the red and green squares (tri-angles) for z z σ error bars , re- The error is estimated by the approximate positional accuracy ofthe ALMA map ∆ p in milliarcsec, given by ∆ p = 70000/( ν ∗ B ∗ σ ),where σ is the peak SNR in the map, ν is the observing frequencyin GHz, and B is the maximum baseline length in kilometers (seeSection 10.5.2 in cycle 7 ALMA technical handbook) trongly lensed [C ii] line from a Sub- L ∗ Lyman-break galaxy at z = 6 . - : : . . . . . . . . Right ascension D ec li n a t i on . . . - : : . . . Right ascension D ec li n a t i on . . - : : . Right ascension D ec li n a t i on Image plane
Right ascension D ec li n a t i o n . - : : . . - : : . . . D ec li n a t i o n Right ascension
Source plane whole region ca u s ti c li n e a cbd z6.1/6.2sub region -7.47e-05 -7.43e-05 -7.37e-05 -7.23e-05 -6.97e-05 -6.43e-05 -5.37e-05 -3.26e-05 9.93e-06 9.41e-05 2.62e-04 . . - : : . . Right ascension D ec li n a t i on sub region ee ad c b whole regionz6.3
500 pc . Figure 6. Left: (cid:48)(cid:48) × (cid:48)(cid:48) and 6 (cid:48)(cid:48) × (cid:48)(cid:48) HST /F160W cutouts of z z a , b , and c ) and an elongated structure towards north east ( d ) in the rest-frame UVcontinuum. The dashed black cross indicates the peak position of the rest-frame UV continuum after smoothing the HST mapto match the resolution with ALMA. The red and green contours represent the [C ii ] line and the rest-frame FIR continuum fromALMA drawn at 1 σ intervals from 2 σ to 8 σ . The red and green squares (triangles) in z z ii ] line and rest-frame FIR continuum with the 1 σ error bars, respectively. The cyan contours is drawnat 2 σ for the rest-frame UV continuum. The foreground galaxies are removed with galfit for the source plane reconstruction.Here we use the natural-weighted map for the [C ii ] line, while the uv -tapered maps with 2 . (cid:48)(cid:48) × . (cid:48)(cid:48) . (cid:48)(cid:48) × . (cid:48)(cid:48) z . z . / .
2, respectively.
Right:
Source plane reconstruction of the [C ii ] line and rest-frameUV and FIR continuum of z .
3. The color and symbols follow the same assignment as the left panel, where the cyan and redcontours show 10%, 30%, 50%, and 80% of the peak. To match the spatial resolutions of ALMA and HST, the red contours aredrawn from the source plane reconstruction of the de-convolved [C ii ] spatial distribution obtained with imfit (Section 3.1) thatis smoothed with the HST PSF. The inset panel displays the source plane reconstruction of z . e which corresponds to the faint rest-frame UV clump at the western part of the whole galaxy. The white ellipsesshow the typical shape of the HST PSF reconstructed in the source plane. The error bars of the red square, triangle, and greentriangle incorporate the average lensing magnification corrections and their uncertainties. Note that two peaks (= triangles) in z spectively. Here we do not examine the rest-frame FIRcontinuum peak from z . σ level (see Section 3.1). In z a , b , and c , from brightest to faintest. The rest-frame UV continuum of z d . In z ii ] line and the rest-frame FIR continuum with the two-peak morphology. IfRXCJ0600- z z z z Fujimoto et al. two-peak morphology in the image plane due to the per-turbation by the foreground object overlapping z µ local and µ whole for z ∼ z ∼
4. Theother foreground object near z . z . ii ] morphologyat the corresponding area is not disturbed at all, sug-gesting that its lensing effect is negligible for z .
3. Wethus remove this foreground object from the mass modeland the HST map with galfit in the source plane re-construction of z . z z ii ] map fromthe de-convolved [C ii ] spatial distribution (Section 3.1),smooth it with the point spread function (PSF) of theHST F160W band, and use this PSF-matched map forthe source plane reconstruction of the [C ii ] line. Inthe right panel, the white ellipses indicate the sourceplane reconstruction of the HST PSF whose FWHMis decreased down to ∼ ×
100 pc and ∼ × z . z . / .
2, respectively. The othercolor and symbols follow the same assignment as theleft panel, where we apply the lens correction also tothe error bars. The error bar of the [C ii ] line peak po-sition in z ∼ z z z ii ] line peak shows an offsetof (cid:39)
300 pc from the brightest rest-frame UV clump ofa, but they are consistent at the 1 σ error level. Withthe axis ratio of 0.49 (Table 4), non-parametric measure-ments directly on the surface brightness distributions inthe source plane provide r e = 1.1 kpc and 2.6 kpc forthe rest-frame UV continuum and the [C ii ] line emis-sion, respectively, showing the spatially extended [C ii ]gas structure by a factor of ∼ z ∼ ii ] line is spatiallymore extended than the rest-frame UV continuum byfactors of ∼ (cid:39) a 1-kpc scale. The r e value for the rest-frame UV continuumis also consistent with the S´ersic profile fitting results of1.2 kpc in the source plane presented in Section 3.5.Secondly from the reconstruction of z ii ] line is co-spatial with the rest-frame UV continuum again, whichis separated by ∼ . ii ]line and rest-frame UV continuum from the whole re-gion of the galaxy. We mark the luminosity-weightedcenter of the sub region with the black cross labeled e .Remarkably, we find, in the independent rest-frame UVcontinuum map reconstructed from z .
3, that the faintclump exists exactly at the position of e whose peakflux density is also consistent. These agreements in theproperties of the clump e also support the robustness ofour best-fit mass models. We also find that the [C ii ]and rest-frame FIR peaks observed in the image planeare reconstructed in the source plane with a (cid:39) e . Thisindicates that the faint diffuse emission or further faintclump near the caustic line is strongly lensed and moreprominently visible in the image plane than the clump e . Given that RXCJ0600- z r e = 1 . ii ]and rest-frame FIR emitting region(s) near the causticline beyond the effective radius of the galaxy that isalmost invisible in other multiple images. Because ofthe poor significance level of the rest-frame FIR contin-uum in z .
3, we cannot conclude whether the rest-frameFIR continuum detected in z . / . trongly lensed [C ii] line from a Sub- L ∗ Lyman-break galaxy at z = 6 . ii ] line andthe rest-frame FIR continuum in z z ii ] line strength at the high signif-icance levels (8 . σ and 5 . σ ) suggests the existence ofsubstructure of the mass distribution along the line-of-sight of z flux-ratio anomaly (e.g., Mao & Schneider 1998). This is consistent withour interpretation that the central compact object in theoptical-NIR bands in z flux-ratio anomaly . How-ever, if the [C ii ] and rest-frame FIR emitting regions areidentical in the source plane, the flux ratio should be thesame between the [C ii ] and rest-frame FIR emission inthe image plane. Although the current error bars of thespatial positions are large, this independent observableof the flux ratio suggests that the faint [C ii ] and rest-frame FIR emitting regions are physically offset in thesub region of RXCJ0600- z
6. This potential separationand the detailed ISM structure in RXCJ0600- z Kinematics via [C ii ] We also examine the kinematics of RXCJ0600- z ii ] line emission. Here we focus on the[C ii ] kinematics of z . z . σ level. We find that the [C ii ]line has the velocity gradient from −
100 to +45 kms − in east south to west north with its intensity ex-tended up to a radius of ∼ . (cid:48)(cid:48)
4. Assuming the linewidth estimate of z . ∼
30 km s − for the velocity gradient due to thespectral resolution of our ALMA data cube (Section2.1), we obtain ∆ v obs / σ tot = 0 . ± .
26, where ∆ v obs and σ tot are the full observed velocity gradient (uncor-rected for inclination) and the spatially-integrated ve-locity dispersion, respectively. With an approximatediagnostic for the classification of rotation-dominatedand dispersion-dominated systems, ∆ v obs / σ tot = 0 . z . z . v obs / σ tot value without the beamsmearing effect.To study the rotation kinematics, we analyze our datain the image plane with softwares of barolo (DiTeodoro & Fraternali 2015) and galpak3d (Bouch´eet al. 2015) that are tools for fitting 3D models toemission-line data cubes. In the left panel of Figure7, we also show the best-fit 3D model and residual mapswith barolo by assuming three annuli for its tiltedring fitting algorithm. We find an excellent agreementon the intensity map and that the residual velocities invelocity-weighted and velocity-dispersion maps are gen-erally less than the spectral resolution of our ALMAdata cube ( ∼
28 km s − ; Section 2.1). Although theresidual in the velocity dispersion is relatively large nearthe edge of the mask, this is likely because the faint out-skirt emission near the edge is masked in some velocitychannels and the observed velocity dispersion is underes-timated. These results suggest that the [C ii ] kinematicsof z . galpak3d also provides the best-fitvalues of the rotation velocity, the velocity dispersion,and the inclination fully consistent within errors withthe barolo results. We summarize the details forthe 3D modeling and the results in Appendix E.In the middle panel, we present the velocity-weightedmap of z . galpak3d for the reconstruction. In theright panel, we also show the [C ii ] radial velocity ex-tracted from the three annuli with barolo (black cir-cle) as well as the best-fit (black line) and the 1 σ error(gray shade) of the rotation curve in the tanh formal-ization obtained from galpak3d . The correction thelensing magnification is applied to the radius scale. Forcomparison, the spatial and velocity offsets of z . / . z z z z
6. This suggests that the clump e in thesub region of the galaxy (Section 4.1) is likely a smallstar-forming region within the rotation disk of the hostgalaxy.6 Fujimoto et al. . . - : : . . Right ascension D ec li n a ti on RXCJ0600-z6
Data Model Residual D i s p e r s i on V e l o c it y I n t e n s it y [ k m / s ] [ k m / s ][ m J y k m / s ] Radius [kpc] V e l o c it y [ k m / s ] (sub region) z . ( w ho l e r e g i on ) z6.1/6.2 Figure 7.
Kinematic properties of RXCJ0600- z Left:
Velocity-integrated (i.e., intensity; top), velocity-weighted (middle),and velocity-dispersion (bottom) maps of z . barolo and theresidual maps are presented in the middle and right columns, respectively. The image size is 3 (cid:48)(cid:48) × (cid:48)(cid:48) . Middle:
Source-planereconstruction of the intrinsic velocity-weighted map of z galpak3D . We limit the reconstruction upto the radius of 1 . (cid:48)(cid:48) ii ] intensity peak in the image plane. The grey dashed line is the caustic line. The red triangleshows the luminosity-weighted center of the sub region of the galaxy. Right:
Observed radial velocity profile of z . barolo analysis (black circles) and the spatial and velocity offsets of the sub regionof the galaxy observed in z . / . σ error (greyshade), of the radial velocity profile of z . galpak3d . For the rotation-dominated system, we obtain the dy-namical mass M dyn of (3 ± × M (cid:12) based on anassumption of the disk-like gas potential distribution,following the equation (4) in Dessauges-Zavadsky et al.(2020) (cid:18) M dyn M (cid:12) (cid:19) = 1 . × (cid:16) v rot km s − (cid:17) (cid:18) r e kpc (cid:19) , (2)where v rot is the rotation velocity of the gaseous disk af-ter the inclination correction. We calculate the inclina-tion from the axis ratio of the best-fit surface brightnessprofile results for the rest-frame UV continuum (Section3.5), assuming that the higher-resolution map providesa better constrain for the inclination. We adopt r e and v rot from the source plane reconstruction of the [C ii ] line(Section 4.1) and the galpak3d results, respectively.We caution that the uncertainty of the inclination couldremain by ∼
30% even in the spatially resolved analy-sis (e.g., Rizzo et al. 2020), and thus the uncertainty inthe above M dyn estimate could be even larger. Giventhe negligible contribution of the dark matter halo inthe galactic scale, we estimate the molecular gas mass M gas to be ∼ × M (cid:12) by subtracting M star (Sec-tion 3.5) from M dyn . . It is worth noting that this M gas range agrees with another estimate based on an empir-ically calibrated method in Zanella et al. (2018), givenby (cid:18) L [CII] L (cid:12) (cid:19) = 10 − .
28 ( ± . × (cid:18) M gas M (cid:12) (cid:19) .
98 ( ± . , (3) which suggests M gas = 3 +2 − × M (cid:12) , despite the poten-tially large uncertainty of the inclination. These resultsindicate that RXCJ0600- z f gas ( ≡ M gas / ( M star + M gas )) ∼ ii ]-detected ALPINE galaxies with M star ∼ × M (cid:12) have f gas ∼ M dyn , M gas ,and f gas estimates are also listed in Table 4.Note that we cannot rule out the possibility that thevelocity gradient is originally caused by complex dynam-ics with interacting, merging galaxies. Future higher res-olution observations will confirm the smooth rotation ofthe disk or break the complex dynamics into the multi-ple components.4.3. SFR and L [CII] Relation
In the left panel of Figure 8, we show the relationbetween SFR and L [CII] for z z L [CII] –SFRrelation obtained from local star-forming galaxies in DeLooze et al. (2014). The observed L [CII] of both z z L [CII] regime amongtypical (e.g., SFR (cid:46) M (cid:12) yr − ) high- z star-forminggalaxies, demonstrating the power of the gravitational trongly lensed [C ii] line from a Sub- L ∗ Lyman-break galaxy at z = 6 . Recent ALMA(z > 5)ALPINE(z ~ 4-6)SMG(z ~ 2-6) z6.1/6.2
RXCJ0600-z6 (sub region)(whole region) local galaxies z6.3 (spatially resolved) z6.1/6.2 (sub region)z6.3 (whole region)
Figure 8. Left: L [CII] –SFR relation. The red filled and open circles indicate z z z star-forming galaxiesare shown with black circles (local LIRGs; D´ıaz-Santos et al. 2013), black squares (local dwarfs; De Looze et al. 2014), blacktriangles (local spirals; Malhotra et al. 2001), black inverse triangles ( z ∼ . z ∼ z ∼ z ∼ z > z H ii -galaxy/starburst sample from De Looze et al. (2014), which is adjusted to the Chabrier IMF by reducing the SFR bya factor of 1.06 in the same manner as Schaerer et al. (2020). The arrow indicates the 3 σ upper limit. The L FIR value in theliterature is firstly converted into a total IR luminosity L TIR (8–1000 µ m), and then we calculate SFR by using the calibration ofMurphy et al. (2011). The spatially resolved results (ΣSFR and Σ L [CII] ) for local galaxies are also presented with open triangles(Herrera-Camus et al. 2015) by assuming the area of 1 kpc . The dashed line and gray shade denote the L [CII] –SFR relationobtained from local star-forming galaxies (De Looze et al. 2014) and its dispersion, respectively. Right: L [CII] /SFR–ΣSFRrelation. The color assignments on the symbols are the same as the left panel. We define the star-forming area by a circulararea of the rest-frame UV emission with a radius of √ × r e , circ for the Σ SFR estimate. We use the factor of √ z z ii ] size measurements with imfit (Table 1) by a factor of 2 (Section 4.1). For the ALPINE sources, we use the rest-frame UV size measurement results inFujimoto et al. (2020b). For local LIRGs and lensed SMGs, we use the rest-frame FIR size measurement results in Spilker et al.(2016) by assuming that the star-forming activity is dominated in the rest-frame FIR emitting regions in these objects. lensing. After the correction of the lensing magnifica-tion, we find that both z z L [CII] relation ofthe local galaxies within the dispersion. This is consis-tent with recent ALMA results that the average SFR– L [CII] relation among high-redshift star-forming galaxiesat z ∼ z L ∗ galaxy at z = 6 (see Section3.5), these results may suggest that the SFR– L [CII] rela-tion, defined by local galaxies, holds from the spatially resolved sub-kpc ISM to the whole scales in abundantgalaxies even up to the epoch of reionization.To further study the L [CII] –SFR relation, the rightpanel of Figure 8 presents L [CII] /SFR and SFR surfacedensity (ΣSFR). This relation or another relation be-tween L [CII] /L FIR and L FIR surface density (Σ L FIR ) areknown to have tight anti-correlations where the deficit ofthe [C ii ] line is explained by the high ionization state inthe ISM around regions with high ΣSFR or Σ L FIR (e.g.,D´ıaz-Santos et al. 2013; Spilker et al. 2016; Gullberget al. 2018; Ferrara et al. 2019). Importantly, these rela-tions are not affected by the lensing magnification, be-8
Fujimoto et al. cause the same magnification factor applies to all thesevalues. We find that z L [CII] /SFRratio, while both z z ii ] lineluminosity at a given SFR between z z ii ]-emittingregion of z ∼ ii ] line from similarly star-forming galaxies at z ∼ L [CII] –SFR relations are different fromthose of the local galaxies. Given the requirement ofprior spectroscopic redshift with the Ly α line in mostcases (Section 3.2), those non-detections might be re-lated to recent reports of the potential anti-correlationbetween L [CII] /SFR and EW Ly α (Harikane et al. 2018,2020; Carniani et al. 2018). In contrast to the mostcases, RXCJ0600- z Ly α < z = 6 .
15 (Calura et al. 2021) also follows the similartrend with relatively large rest-frame EW Ly α (60 ± L [CII] /SFR ( ∼ × ). A caution stillremains that Schaerer et al. (2020) report a weak de-pendence of L [CII] /SFR of EW Ly α . Since the [C ii ] lineemissivity depends on the ISM properties such as theionization state, metallicity, and gas density (e.g., Valliniet al. 2015), the different L [CII] –SFR relations could bealternatively explained by a larger dispersion of the ISMproperties in high- z galaxies than in local galaxies. Theuncertainties of the SFR estimates might contribute tothe large dispersion in high- z galaxies due to assump-tions of the star-formation history, the dust-attenuationcurve, and the stellar population age as discussed in Car-niani et al. (2020) and Schaerer et al. (2020). Anotherrecent reports of the extended [C ii ] line morphology upto a radius of ∼
10 kpc (e.g., Fujimoto et al. 2019, 2020b;Ginolfi et al. 2020; Novak et al. 2020) might be also re-lated to some of those non-detections, because the sur-face brightness of the extended emission is significantlydecreased in relatively high-resolution maps (Carnianiet al. 2020). Based on the visibility-based stacking, thesecondary extended component up to the 10-kpc scale isestimated to have the average contribution to the totalline luminosity of ∼
50 % around star-forming galax- ies (Fujimoto et al. 2019) and ∼
20% around quasars(Novak et al. 2020) at z ∼
6. These non-negligible con-tributions could matter if the request sensitivity is closeto the detection limit around the 5 σ level. However, thisis not the case if the carbon in the extended [C ii ] gas isionized by such as the gravitational energy in the coldstream, the shock heating in the outflow and/or inflowgas, and the AGN feedback, instead of the photoion-ization powered from the star-forming regions (see e.g.,Section 5 of Fujimoto et al. 2019).4.4. [C ii ] Luminosity Function A key goal of ALCS is to constrain the number densityof the line emitters. Although the complete blind linesurvey results with all 33 fields will be presented in aseparate paper (in preparation), we can evaluate a lowerlimit of the [C ii ] luminosity function at z ∼ ii ] line detection from the strongly lensed LBG at z = 6 . z ∼ ∼
49 (2) arcmin at L [CII] = 1 . × (10 ) L (cid:12) , assuming the line widthof FWHM=200 km s − with the 5 σ detection limit. Wethen convert the effective survey area to the survey vol-ume, based on the frequency setup in the ALCS observa-tions covering the [C ii ] line emission at z = 5 . ii ]luminosity function at z = 6.In Figure 9, we present the number density of [C ii ]line emitters at z = 6, including recent [C ii ] line studiesat z > ii ] luminosity functions fromsemi-analytical models (Popping et al. 2016; Lagacheet al. 2018) and from the observed SFR function (SFRF;Smit et al. 2016) of optically-selected galaxies. For theconversion from SFRF to [C ii ] luminosity function, weadopt the [C ii ]–SFR relation of the local star-forminggalaxies estimated in De Looze et al. (2014). We findthat our lower limit estimate is consistent with both thesemi-analytical results and SFRF. Note that we do notapply any completeness corrections to our lower limit es-timate. The incompleteness for strongly lensed sourceswith large spatial sizes is generally significant due to itslow surface brightness (e.g., Bouwens et al. 2017; Kawa-mata et al. 2018; Fujimoto et al. 2017). Although the in-completeness largely depends on the assumption of theintrinsic source size, this may indicate that the lower trongly lensed [C ii] line from a Sub- L ∗ Lyman-break galaxy at z = 6 . ALPINE (z~5)
SMGs (z~5)
Recent ALMA (z~6)
This work
Popping+16 (z=6) L a g ac h e + ( z = ) SF R F ( z = ) × SF R -[ C II]
Figure 9.
Cumulative [C ii ] luminosity function at z = 6with recent [C ii ] line studies at z > ii ] line emitter based on oursuccessful detection from the strongly lensed LBG with theeffective survey volume of the full ALCS data cubes com-posed of 33 galaxy clusters. The lower limit is estimatedfrom the Poisson uncertainty at the single-sided confidencelevel of 84.13% presented in Gehrels (1986). Recent ALMAblind line survey results are presented with blue triangle (243archival data cubes; Matsuda et al. 2015), blue inverse tri-angle (four massive galaxy clusters; Yamaguchi et al. 2017),blue square (ASPECS; Decarli et al. 2020), and blue cross(SSA22; Hayatsu et al. 2017, 2019). The green circle presentsthe ALPINE results (Loiacono et al. 2020; Yan et al. 2020).Here we show only the estimate from the serendipitous [C ii ]line detection at z ∼ ii ] line detection from bright SMGs at z ∼ L [CII] withthe local [C ii ]–SFR relation (De Looze et al. 2014). limit could be placed still higher and that the faint-end of the [C ii ] luminosity function might be close toSFRF. Indeed, other constraints from the recent [C ii ]line studies are also consistent with SFRF at the brightregime ( L [CII] (cid:38) . L (cid:12) ). Although the brightest-end( L [CII] (cid:38) . L (cid:12) ) of SFRF is smaller than the con-straints obtained from the SMG studies (Cooke et al.2018), this is explained by the absence of such dusty- obscured galaxies in the SFRF based on the optically-selected galaxies. Therefore, the constraints of the [C ii ]luminosity function so far obtained are likely consistentwith the prediction from the local SFR– L [CII] relationand the SFRF at z = 6.4.5. From ISM to Cosmic Scales
The source plane reconstruction in Section 4.1 unveilsthe ISM structure down to a few hundred parsec scales,where we find that [C ii ] line is not displaced beyond a ∼ L [CII] relations from the spatiallyresolved ISM to the whole galaxy are consistent withthose of local galaxies. In Section 4.4, we obtain thelower limit at the faintest regime of the z = 6 [C ii ]luminosity function. We find that the prediction fromthe z = 6 SFR function and the SFR– L [CII] relationof the local galaxies is consistent with our and previ-ous constraints on the z = 6 [C ii ] luminosity functionin the wide L [CII] range. Given the unbiased aspect ofthe ALCS survey and indeed the representative physicalproperties of RXCJ0600- z z ∼ L [CII] relation of local star-forming galaxies is uni-versal for a wide range of scales including the spatiallyresolved ISM, the whole region of the galaxy, and thecosmic scale. SUMMARYIn this paper, we present the blind detection ofa multiply-imaged line emitter behind the massivegalaxy cluster RXCJ0600 − ii ] 158 µ m line froma Lyman-break galaxy (LBG) at z = 6 . ± . ii ] line luminosity( L [CII] ), the morphology, and the kinematics in the spa-tially resolved interstellar medium (ISM) as well as thewhole scale of the LBG, and provide a lower limit atthe faint-end of the [C ii ] luminosity function at z ∼ ≥ σ levels at 268.682 ± ± Fujimoto et al. at ∼ ii ] 158 µ m at z = 6 .
07. The optical–NIR spectral energy distribution (SED) analysisshows that probability distributions of their pho-tometric redshifts are in excellent agreement withthe [C ii ] line redshift, while other possible FIRlines at z ∼ ii ] lines.2. Our lens models, updated with the latest spectro-scopic follow-up results with VLT/MUSE, suggestthat these lines arise from a strongly magnifiedand multiply imaged ( µ (cid:39) − z = 6 . ∼ ∼ M UV = − . +0 . − . ) than the characteristic lumi-nosity at this epoch. A sub region of the LBGcrosses the caustic line in the source plane andthus stretched into an arc over ∼ (cid:48)(cid:48) in the imageplane, for which the [C ii ] line is also significantlydetected. Our lens models also predict anothertwo multiple images in this field. We identify thesources at the predicted positions and find thattheir optical–NIR colors agree with the other mul-tiple images of the LBGs. One of them falls in theALCS area coverage, where we detect a tentative[C ii ] line (3 . σ ) at the same frequency as the othermultiple images.3. After the correction of the lensing magnification,the whole of the LBG and its sub region are char-acterized with L [CII] of 1.1 +0 . − . × and 0.3 +0 . − . × L (cid:12) , SFR of 5.4 +4 . − . and 0.8 +0 . − . M (cid:12) yr − , andstellar mass ( M star ) of 9.6 +6 . − . × and 2.6 +0 . − . × M (cid:12) , respectively. From the whole to sub re-gions of the LBG, the SFR and M star values fallson the average relation among z ∼ ∼ ii ] line from thewhole region of the LBG is co-spatial with therest-frame UV continuum, while the sub region ofthe LBG is placed ∼ ii ] lineand rest-frame FIR continuum in the arc show a ∼ ii ] line and the rest-frameFIR continuum exhibit the flux ratio anomaly dif-ferently, which suggests that the faint [C ii ]- andFIR-emitting regions are displaced near the caus-tic.5. We find that our results in both whole and subregions of the LBG fall on the SFR– L [CII] and sur-face density of SFR (ΣSFR)– L [CII] /SFR relationsobtained in local star-forming galaxies. The subregion of the galaxy has a lower ΣSFR and a higher L [CII] /SFR value. This is consistent with the ab-sence of the bright rest-frame UV clumps aroundthe sub region of the LBG that is placed ∼ ii ] line emission. The 3Dmodeling with Barolo and galpak3D provideconsistent results for the rotation kinematics thatexplains the spatial and velocity offsets of the subregion of the LBG. We estimate the dynamicalmass of M dyn = (3 ± × M (cid:12) and obtain thegas fraction of ∼ ii ] luminosityfunction at z = 6. We find that it is consistentwith current semi-analytical model predictions. Inconjunction with previous ALMA results, we alsofind that constraints on the [C ii ] luminosity func-tion at z = 6 so far obtained agree with the pre-diction from the SFR– L [CII] relation of local star-forming galaxies and the SFR function at z = 6.8. With the blind aspect of the ALCS survey and theSFR– L [CII] relations from the sub to whole regionsof the LBG, our results may imply that the localSFR– L [CII] relation is universal for a wide rangeof scales including the spatially resolved ISM, thewhole region of the galaxy, and the cosmic scaleeven up to z = 6, which we derive in an unbiasedmanner.We thank the anonymous referee for the careful reviewand valuable comments that improved the clarity of thepaper. We thank Justin Spilker and Tanio D´ıaz-Santosfor sharing their measurements. We also thank John R.Weaver and Yuchi Harikane for useful comments on thepaper and Francesca Rizzo for helpful comments for thekinematic analysis. This paper makes use of the ALMA trongly lensed [C ii] line from a Sub- L ∗ Lyman-break galaxy at z = 6 . SpitzerSpace Telescope , which is operated by the Jet Propul-sion Laboratory, California Institute of Technology, un-der a contract with NASA along with archival datafrom the NASA/ESA
Hubble Space Telescope . Thisresearch made also use of the NASA/IPAC InfraredScience Archive (IRSA), which is operated by the JetPropulsion Laboratory, California Institute of Technol-ogy, under contract with the National Aeronautics andSpace Administration. This work was supported in partby World Premier International Research Center Initia-tive (WPI Initiative), MEXT, Japan, and JSPS KAK-ENHI Grant Number JP18K03693. S.F. acknowledgessupport from the European Research Council (ERC)Consolidator Grant funding scheme (project ConTExt,grant No. 648179) and Independent Research Fund Den-mark grant DFF–7014-00017. The Cosmic Dawn Cen-ter is funded by the Danish National Research Foun-dation under grant No. 140. NL acknowledges theKavli Fundation. GBC and KIC acknowledge fundingfrom the European Research Council through the Con-solidator Grant ID 681627-BUILDUP. F.E.B acknowl-edges supports from ANID grants CATA-Basal AFB-170002, FONDECYT Regular 1190818, and 1200495,and Millennium Science Initiative ICN12 009. IRS ac-knowledges support from STFC (ST/T000244/1). KKacknowledges support from the Swedish Research Coun-cil and the Knut and Alice Wallenberg Foundation.
Software: casa (v5.4.0; McMullin et al. 2007), gri-zli (Brammer et al. 2008), dendrogram (Goodmanet al. 2009), galfit (Peng et al. 2010), eazy (Brammeret al. 2008), scarlet (Melchior et al. 2018), Barolo(DiTeodoro & Fraternali 2015), galpak3d (Bouch´e et al.2015) , glafic (Oguri 2010), lenstool (Jullo et al.2007), ltm (Zitrin et al. 2015)2
Fujimoto et al.
APPENDIX A. MUSE SPECTROSCOPIC CATALOGIn Table 5, we summarize the spectroscopic samplefrom VLT/MUSE (ESO program ID 0100.A-0792, PI:A. Edge) which we use for constraining our lens massmodels.
Table 5 . MUSE Spectroscopic CatalogRELICS ID R.A. Dec. z spec flagdeg deg(1) (2) (3) (4) (5)467 90.0386151 − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . (1) ID from the RELICS public catalogue ofhlsp relics hst wfc3ir rxc0600-20 multi v1 cat.txt . IDs start- https://relics.stsci.edu/ trongly lensed [C ii] line from a Sub- L ∗ Lyman-break galaxy at z = 6 . ing with 900 are MUSE detections with no counterpart in thementioned catalogue. (2) Observed right ascension in degrees.(3) Observed declination in degrees. (4) MUSE spectroscopic red-shift. (5) Redshift quality flag. 2: likely, 3: secure measurement,9: single line measurement, and 4: field stars. B. TWO-PEAK MORPHOLOGY IN Z ii ] line in z simobserve towards z ii ] line surfacebrightness distribution of z imfit results in the uv -tapered map (Section 3.1). We thenobtain the visibility data set through simobserve andproduce the natural-weighted velocity-integrated map ofthe [C ii ] line. We repeat the mock observation to pro-ducing the map 1,000 times. Given that the spatial off-set of ∼ . (cid:48)(cid:48) σ and 5.4 σ between the two peaks in z . (cid:48)(cid:48) ≥ . σ levels, utilizingSExtractor version 2.5.0 (Bertin & Arnouts 1996). Weidentify 7 out of 1,000 maps have the multiple peaks thatmeet the above criteria. These results indicate that thetwo-peak morphology of the [C ii ] line in z ∼ z ∼ z z . (cid:48)(cid:48)
7. Therefore,we conclude that the possibility of the noise fluctuationis negligible in the two-peak [C ii ] line morphology of z C. OPTICAL–NIR PHOTOMETRYWe adopt separate strategies for extracting robustphotometry for the four lensed images as described be-low to account for the crowded cluster field and varyingdegrees of extended source morphology. In general, wemodel the full IRAC mosaics using a strategy similar tothat of Merlin et al. (2015), where we use image thumb-nails of each source and neighbors taken from the high-resolution
HST /WFC3 F160W image and knowledge ofthe WFC3 and IRAC point spread functions (PSFs) tomodel the low-resolution IRAC image. C.1.
Images z z The sources of interest in these images are relativelybright and fairly well separated from their nearest bright(projected) neighbors (Figure 1). We measure aper-ture flux densities in each of the
HST filters using fixed D = 0 . (cid:48)(cid:48) Scarlet (Melchior et al.2018). All of the WFC3/IR images (and their PSFs) areused to constrain the
Scarlet morphological model.We scale all of the
HST aperture measurements F ap, i by the aperture correction F S, F160W /F ap, F160W , where F S, F160W is the integral of the
Scarlet model evalu-ated in the F160W filter and F S, F160W is the aperturemeasurement in that filter. The photometric uncertain-ties are measured in the same apertures on the inversevariance image in each filter. For the IRAC flux densitiesof these images, we subtract all modeled sources otherthan the source of interest and perform aperture pho-tometry on this cleaned image using D = 3 . (cid:48)(cid:48) HST using aperture corrections of 1.6 and 1.7 for channels 1and 2, respectively, that were derived from a separatebright, isolated source in the field.C.2.
Extended arc image z This image is a highly elongated arc extending over ≈ galfit software (Peng et al. 2010).For the photometry of the lensed arc and foregroundimage in the WFC3/IR filters, we fit for the relativenormalizations of the two Sersic components convolvedwith the appropriate PSFs. For IRAC, we convolvethe model Sersic profiles with the IRAC PSF and fitfor the normalization of the source of interest and allneighboring sources in the least-squares optimization.As for HST, the normalization of the scaled morpho-logical components is adopted as the photometric mea-surement without additional aperture corrections. Forthe optical images where the arc is not readily visible,we measure an aperture flux density and its associateduncertainty within a large rectangle aperture approxi-mately 1 . (cid:48)(cid:48) × . (cid:48)(cid:48) . +0 . − . which is close to the cluster redshift at z = 0 .
43 (see alsoLaporte et al. submitted). Although this suggests the4
Fujimoto et al. z6.1 z6.2
Figure 10.
Zoom-in [C ii ] line spectra of z . z z z . ii ]spectra for z . z .
2, respectively. The black line andthe grey shade indicate the integrated [C ii ] line spectrum of z . ii ]-detected channels, respectively. Thered and blue lines present the [C ii ] spectra for z . z . foreground to be one of the cluster members, we do notinclude it in our fiducial mass model due to potentialsystematics in the de-blending process. The detail con-tribution of the foreground object to morphology andmagnification factors of z Faint image z The final faint image of z D = 0 . (cid:48)(cid:48) D = 3 . (cid:48)(cid:48) HST and IRAC filter mosaics, respectively, and scale thesemeasurements by aperture corrections derived for pointsources. D. [C ii ] SPECTRA OF z . z . ii ] line emitters consists of a pair of multiple imagesof z . z .
2, we compare [C ii ] spectra between z . z .
2. In Figure 10, we show the [C ii ] spectra of z . z . z z . z . ii ] line profiles consistent with each other withinthe errors, which agrees with our interpretation of z . z . E. [C ii ] ROTATION MODELINGIn Section 4.2, we find that z . ii ] line around z . barolo (Di Teodoro & Fraternali 2015) and gal-pak3d (Bouch´e et al. 2015). For barolo , becausethe ALMA beam has a half-width-at-half-maximum(HWHM) of ∼ . (cid:48)(cid:48)
45 at the [C ii ] line frequency alongthe orientation of the velocity gradient, we adopt three( ∼ . (cid:48)(cid:48)
45 for the tiltedring fitting algorithm. We use the THRESHOLD maskwith the 2 σ limit for the data cube, and the spatial cen-ter, systemic velocity, rotation velocity ( v rot ), velocitydispersion ( σ vel ), position angle (PA), and inclination(incl.) are used as free parameters in the fitting. The er-rors are estimated based on the minimization algorithmin a Monte Carlo approach. For galpak3d , we adoptthe exponential-disk for the flux profile, the Gaussianfor the thickness profile, and the tanh formalization of V max × tanh( r/r V ) for the rotation curve, where V max and r V are the maximum velocity and the turnover ra-dius, respectively. In place of the mask, we use a cutoutdata cube by 3 . (cid:48)(cid:48) × . (cid:48)(cid:48) − − forthe fitting. We set the maximum iteration number of20,000. The spatial center, systemic velocity, flux, r e ,PA, incl., r V , V max , and σ vel are used as free parame-ters. The errors are evaluated based on a Markov chainMonte Carlo approach.REFERENCES Aravena, M., Decarli, R., Walter, F., et al. 2016, ApJ, 833,71 Bacon, R., Piqueras, L., Conseil, S., Richard, J., &Shepherd, M. 2016, MPDAF: MUSE Python DataAnalysis Framework, ascl:1611.003 trongly lensed [C ii] line from a Sub- L ∗ Lyman-break galaxy at z = 6 . Table 6.
3D Modeling Results barolo galpak3d Ring1 Ring2 Ring3 Exponential diskradius a [ (cid:48)(cid:48) ] 0–0.45 0.45–0.9 0.9–1.35 0.55 ± v LOS b [km s − ] 22 +5 − +22 − +4 − ± σ vel [km s − ] 46 +9 − +11 − +7 − ± ± c [ ◦ ] 36 32 27 21 ± a Inner and outer radii of the tilted rings for barolo andeffective radius for galpak3d . The turnover radius is esti-mated to be 0 . (cid:48)(cid:48) ± . (cid:48)(cid:48)
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