# COOL-LAMPS I. An Extraordinarily Bright Lensed Galaxy at Redshift 5.04
111This paper includes data gathered with the 6.5m Magellan Telescopes located
at Las Campanas Observatory, Chile.

Gourav Khullar Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Kavli Institute for Cosmological Physics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Katya Gozman Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Department of Astronomy, University of Michigan, 1085 South University Drive, Ann Arbor, MI 48109, USA  Jason J. Lin Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Michael N. Martinez Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Owen S. Matthews Acuña Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Elisabeth Medina  Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Kaiya Merz Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Jorge A. Sanchez Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Emily E. Sisco Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Daniel J. Kavin Stein Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Ezra O. Sukay Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Kiyan Tavangar Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Matthew B. Bayliss Department of Physics, University of Cincinnati, Cincinnati, OH 45221, USA  Lindsey E. Bleem Kavli Institute for Cosmological Physics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Argonne National Laboratory, High-Energy Physics Division, 9700 S. Cass Avenue, Argonne, IL 60439, USA  Sasha Brownsberger  Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA  HÅkon Dahle Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029, Blindern, NO-0315 Oslo, Norway  Michael K. Florian Observational Cosmology Lab Code 665, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  Michael D. Gladders Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Kavli Institute for Cosmological Physics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Guillaume Mahler Department of Astronomy, University of Michigan, 1085 South University Drive, Ann Arbor, MI 48109, USA  Jane R. Rigby Observational Cosmology Lab Code 665, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  Keren Sharon Department of Astronomy, University of Michigan, 1085 South University Drive, Ann Arbor, MI 48109, USA  Antony A. Stark Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138  Author for correspondence<EMAIL_ADDRESS>
###### Abstract

We report the discovery of COOL J1241+2219, a strongly-lensed galaxy at
redshift $z$=5.043$\pm$0.002 with observed magnitude $z_{AB}=20.47$, lensed by
a moderate-mass galaxy cluster at $z$=1.001$\pm$0.001. COOL J1241+2219 is the
brightest lensed galaxy currently known at optical and near-infrared
wavelengths at $z$ $\gtrsim$ 5; it is $\sim$5 times brighter than the prior
record-holder lensed galaxy, and several magnitudes brighter than the
brightest unlensed galaxies known at these redshifts. It was discovered as
part of COOL-LAMPS, a collaboration initiated to find strongly lensed systems
in recent public optical imaging data. We characterise the lensed galaxy, as
well as the central galaxy of the lensing cluster using ground-based $griz$JH
imaging and optical spectroscopy. We report model-based magnitudes, and derive
stellar masses, dust content, metallicity and star-formation rates via
stellar-population synthesis modeling. Our lens mass modeling, based on
ground-based imaging, implies a median source magnification of $\sim$30, which
puts the stellar mass and star formation rate (in the youngest age bin,
closest to the epoch of observation) at logM∗ = $10.11^{+0.21}_{-0.26}$ and
SFR = $27^{+13}_{-9}$ M⊙/yr, respectively. We constrain a star formation
history for COOL J1241+2219 consistent with constant star formation across
$\sim$1 Gyr of cosmic time, and that places this galaxy on the high-mass end
of the star-forming main sequence. COOL J1241+2219 is 2-4 times more luminous
than a galaxy with the characteristic UV luminosity at these redshifts. The UV
continuum slope $\beta$= -2.2$\pm$0.2 places this galaxy on the blue side of
the observed distribution of galaxies at $z$=5, although the lack of
Ly$\alpha$ emission indicates dust sufficient to suppress this emission.

Galaxies: High-redshift galaxies — galaxies: strong gravitational lensing —
galaxies: spectroscopy — galaxies: evolution

††facilities: CTIO/4m Blanco Telescope, Magellan Telescopes 6.5m (Clay/LDSS3C,
Clay/PISCO, Baade/FOURSTAR), Gemini-North Telescope (GNIRS)††software: Python
3.6 — Prospector, python-FSPS, SEDpy, pygtc, Matplotlib, Numpy, Scipy,
Astropy, LENSTOOL, Jupyter, IPython Notebooks, GALFIT, SExtractor (Bertin &
Arnouts, 1996), SAO Image DS9, IRAF, IDL

##  1 Introduction

Strong gravitational lensing can transform typically small, faint, marginally-
resolved field galaxies into highly-magnified arcs that can appear very
bright. The brightest and most magnified lensed galaxies enable exquisite
studies of internal galaxy morphologies down to scales of only tens of parsecs
even in the most distant galaxies (e.g.,Bayliss et al., 2014; Livermore et
al., 2015; Johnson et al., 2017, 2017; Cornachione et al., 2018; Rivera-
Thorsen et al., 2019; Ivison et al., 2020; Florian et al., 2020). Such lensed
sources are exceedingly rare, and are generally found by searching many
thousands of square degrees of ground-based survey imaging (e.g.,Allam et al.,
2007; Belokurov et al., 2007; Koester et al., 2010) or by dedicated imaging
programs targeting massive galaxy clusters not previously explored (Bleem et
al., 2015, 2020; Coe et al., 2019). Conversely, deep observations of known
strong lenses with large lensing cross-sections (c.f. the Hubble Frontier
Fields; Lotz et al., 2017) discover many more lensed galaxies, but these are
magnitudes fainter than the rare systems found in wide searches.

Studies of the brightest lensed galaxies are complementary to studies of faint
lensed galaxies, and unlensed field galaxies, offering both enhanced spatial
resolution in the source plane, and sufficient photons to allow exceptional
spectral resolution at useful signal-to-noise ratios. Hence, the brightest
strongly-lensed galaxies are the observational signposts with which we
navigate the more abundant but much fainter deep-field samples. To date,
searches of the Sloan Digital Sky Survey (SDSS; Ahumada et al., 2020) have
identified hundreds of bright lensed sources at $z$<3, the brightest of which
typically have integrated gAB magnitudes of $\sim$20 (e.g., Kubo et al., 2010;
Bayliss et al., 2011a; Stark et al., 2013).

This success is due to the depth and filter selection of the SDSS, sufficient
to find the bright blue arcs that are the hallmark of UV-bright lensed
galaxies at these redshifts. Many of these lensed targets have been followed
up with HST imaging that has revealed details of star-formation and structure
on spatial scales down to tens of parsecs (e.g., Johnson et al., 2017;
Cornachione et al., 2018). The brightest of these lensed galaxies — a few of
which predate the discoveries from the SDSS — have been followed up with high-
quality spectroscopy (e.g., Pettini et al., 2000; James et al., 2014; Rigby et
al., 2018a, b) that exceeds in both spectral resolution and signal-to-noise
what is available for stacks of dozens or even hundreds of field galaxies
(Shapley et al., 2003; Steidel et al., 2016).

Beyond $z\sim$3 however, bright lensed samples rapidly decline, and by
$z\sim$5, there are only a few known strongly-lensed galaxies of even modest
brightness at optical/infrared (OIR) wavelengths; the SDSS, which has been so
effective for discovery at $z\sim$2-3 has proven mostly insufficient in depths
at $z\sim$5, particularly in key redder filters as the galaxies drop out of
the bluer filters due to intervening IGM absorption. The brightest three
$z\sim$5 spectroscopically-confirmed lensed galaxies published to date have AB
magnitudes of $i$=22.2 ($z$=4.88, Gladders et al., 2002), $i$=22.6 ($z$=4.92,
Franx et al., 1997; Soifer et al., 1998), and $i$=23.3 ($z$=4.87, Frye et al.,
2002). The brightest was found through a wide-area search for arcs; the other
two were found by targeting massive galaxy clusters. In addition, the
Reionizing Lensing Cluster Survey (RELICS) program reports 5 candidate lensed
galaxies with $z_{phot}$=5.5–6 and F160W<23.6 (Salmon et al., 2020), that as
yet lack published spectroscopic redshifts. For comparison, the brightest
galaxies at $z\sim 5$ in the Hubble Ultra Deep Field (HUDF) have magnitudes
fainter than $i_{AB}=25$ (Inami et al., 2017).

Strong-lensing searches in the latest generation of imaging surveys,
particularly the Dark Energy Camera Legacy Survey (DECaLS; Huang et al.,
2020), the Dark Energy Survey (DES; Diehl et al., 2017; Jacobs et al., 2019),
the Kilo-Degree Survey (KiDS; Petrillo et al., 2019), the Hyper Suprime-Cam
Subaru Strategic Program (HSC-SSP) Survey (Jaelani et al., 2020), should
significantly increase the number of known bright $z>3$ lensed galaxies, as
these data are deeper, particularly in redder filters, than the SDSS. Here, we
report and characterize one such object, a spectroscopically confirmed
$z$=5.043 strongly-lensed galaxy, with an extraordinarily bright $z_{AB}$
apparent magnitude of 20.47. As such, this is the brightest $z\gtrsim$5 UV-
bright galaxy found so far.

Figure 1: (Top) RGB image of the lens and COOLJ1241+2219. This was constructed
using the Magellan/PISCO $g,r$ and $i+z$ images in each channel. The arc
radius about the central lens galaxy is $\sim$6”, indicating that the lens has
the mass of a large group or small cluster, consistent with the presence of
other red sequence galaxies. The faint red source immediately NW of the main
lens galaxy has colors and surface brightness suggestive of a lensed
counterimage, marked with solid white lines. (Inset images) $griz$JH images
from a 16"x16" field-of-view centered at the lens. (Inset image: far left) The
central portion over the same area of the 45"x45" DECaLS $grz$ discovery
image.

This paper is structured as follows. Section 2 lays out the details of the
public data search that led to the discovery of COOL-J1241+2219. Section 3
describes follow-up imaging and spectroscopy of COOL-J1241+2219, while Section
4 describes the analyses of these data and the results from stellar population
synthesis and strong lens modeling. Section 5 places these results in the
context of other objects known in the $z>5$ Universe.

All reported magnitudes are calibrated to the AB system. The fiducial
cosmology model used assumes a standard flat cold dark matter universe with a
cosmological constant $(\Lambda$CDM), corresponding to WMAP9 observations
(Hinshaw et al., 2013). For inferred parameters with uncertainties, we report
16th, 50th and 84th percentile values, unless otherwise specified.

##  2 Discovery

The COOL-LAMPS project — ChicagO Optically-selected strong Lenses - Located At
the Margins of Public Surveys — initiated as the central focus of an
undergraduate research class, is an effort to find strong gravitational lenses
in recent public imaging data. Though the lensing search is designed to find a
wide variety of lenses and lensed sources, the particular focus of our follow-
up is sources that are photometrically at the margins of the distributions of
source color and brightness. The details and results of this search will be
presented in an upcoming publication , and we provide only a brief description
here.

COOL J1241+2219 was found in the DECaLS $grz$ Data Release 8 (DR8, Dey et al.,
2019) imaging data, as part of a comprehensive visual search of the northern
galactic cap portion of the DECaLS dataset. The complete search comprised two
separate efforts, one targeting potential lenses at low redshift ($z<0.7$) and
the other extending to higher redshift potential lenses. COOL-J1241+2219 was
found in the latter.

Figure 2: The extracted optical/near-IR Magellan/LDSS3 spectra of the central
lens galaxy (top), brightest knot in the arc (middle top), the noise spectrum
(middle bottom) and telluric correction applied (bottom). The noise and
transmission spectra are shown covering the same observed wavelength range,
corresponding to the indicated restframe wavelength range for redshifts of
1.001$\pm$0.001 and 5.043$\pm$0.002 for the top and middle top panels
respectively. The raw spectra are plotted in pale blue, and versions of those
data filtered (via a median and tophat filter kernel) to visually emphasize
features relevant for redshift determinations, are over plotted in orange. The
inset top-left shows the slit positioning for these observations. In the top
panel, vertical dotted lines indicate significant spectral features used to
infer the redshifts for the lens galaxy; black lines (from left to right) mark
the CaII H&K lines, and the G-band. For the lensed source spectrum, we mark
for reference Ly$\alpha$ in absorption at 1215Å, though note that the redshift
is determined from an uncertainty-weighted cross correlation with the
reference spectrum (from Rigby et al., 2018b) overplotted in green. To ease
visual comparison, we have scaled the reference spectrum using a low-order
polynomial computed redward of Ly$\alpha$ to match its amplitude to the lensed
source spectrum. To visually confirm the redshift, we mark UV stellar and
nebular absorption features with red lines — (from left to right, in rest-
frame Å units) SiII 1260, OI/SiII 1302/1304, CII 1334, SiIV 1393, SiII 1526,
CIV 1548/1550.

We selected luminous red galaxies, classified as having de Vaucouleurs
profiles (de Vaucouleurs, 1948), and appropriate colors and magnitudes, as
potential lenses. Color and magnitude cuts were informed by prior experience
with strong lens selection in the SDSS (Bayliss et al., 2011a; Sharon et al.,
2020; to first-order, the selected galaxies are objects brighter and redder
than a color-magnitude model corresponding to a passively evolving galaxy
formed at $z$=3, with an absolute magnitude tuned to capture a reasonable
number of target objects. In practice, this magnitude limit is approximately
M∗. Specifically, COOL J1241+2219 ’s measured photometry puts it at $\sim$ 0.2
magnitudes redder and brighter than the selection cut, and further away from
the selection cut than the median potential lens selected by that cut.

We followed a visual examination strategy employed by the Sloan Giant Arcs
Survey (SGAS; e.g., Bayliss et al., 2011b; Sharon et al., 2020). In the high-
redshift portion of our search, a total of 271,460 lines of sight were
examined by at least 3 of the co-authors, primarily via a custom Python-based
image viewer and lens-ranker. We examined lines of sight four-at-a-time in a
2$\times$2 grid, with each individual cutout covering $45"\times 45"$ centered
on each potential lens. We constructed custom color images from the DECaLS
$grz$ imaging data, tuned to emphasize faint extended features. Each
2$\times$2 composite image was given an integer score from 0 to 3 by each
examiner, with a score of 3 indicating a definite strong lens, a score of 0
indicating no evidence for strong lensing, and the remainder shading between
those extremes. The initial average score for COOL-J1241+2219 was 2. The
central portion of the image in which COOL-J1241+2219 was found is shown in
the first inset panel of Figure 1.

The lensed arc is detected in the DECaLS catalogs at RA, Dec (J2000) =
$(190.3743,22.3282)$ with reported AB magnitudes of $g$=25.10, $r$=23.82,
$z$=21.13; the model-based photometry of these catalogs assumes elliptical
sources, and must therefore miss a significant fraction of the source light in
this case. However, this initial photometry and the observed red color and
morphology of this apparent arc motivated follow-up observations.

##  3 Follow-up Observations and Redshifts

###  3.1 Photometry

Near-infrared imaging of COOL J1241+2219 in the J- and H-bands was obtained
using the FourStar Infrared Camera (FOURSTAR; Persson et al., 2008) on the
Magellan/Baade telescope, Chile, on 2020 February 22. The total integration
times were 335s and 3578s in the J- and H-bands respectively. Data were
reduced to final astrometrically- and photometrically-calibrated stacked
images using a custom pipeline built via IRAF and PHOTPIPE (Rest et al., 2005;
Garg et al., 2007; Miknaitis et al., 2007).

We then obtained deep simultaneous optical imaging — $griz$ — using the
Parallel Imager for Southern Cosmology Observations (PISCO; Stalder et al.,
2014) on the Magellan/Clay telescope, on 2020 February 29. The total
integration time for the imaging with a field-of-view of 5.5’ x 7.5’ was
3060s. Data were processed and stacked to final astrometrically-calibrated
images using a custom pipeline that makes standard corrections, as well as
removing effects of non-linearity and bright stars peculiar to the PISCO
detectors. Figure 1 shows a color image for COOL J1241+2219 constructed from
the PISCO images, as well as smaller greyscale cutouts for all of the follow-
up imaging focused on the arc and central lens galaxy.

As can be seen in Figure 1, these data show that COOL J1241+2219 is blue in
the z—J and z—H colors. In combination with the observed red optical colors
this indicates that this arc is the strongly-lensed image of a high-redshift
galaxy.

###  3.2 Spectroscopy

Spectroscopic observations for COOL J1241+2219 were obtained on 2020 March 2,
using the Low Dispersion Survey Spectrograph - 3C
(LDSS-3C222http://www.lco.cl/Members/gblanc/ldss-3/ldss-3-user-manual-tmp),
with the VPH-Red grism and a 1″.0 longslit placed to cover a wavelength range
of 6700Å and redward, to the limits of the instrument response at $\sim$10500Å
. The slit was oriented to include the brightest clump in the lensed arc, the
fiducial counter-image, and the apparent lens galaxy (with a slight offset).
The precise slit placement is shown in the top inset portion of Figure 2.

We acquired six 900s integrations, dithered between two slit positions along
the slit diection, in non-photometric conditions at airmasses of 1.6-1.8, with
a typical on-instrument seeing of 1$\farcs$1, as well as observations of a
spectrophotometric standard for both flux calibration and the removal of
telluric features in the spectra. Reduction to wavelength- and flux-calibrated
1D spectra was accomplished using a combination of standard routines and
custom software, implemented in IRAF and IDL. The spectra for the apparent
central lens galaxy and COOL J1241+2219 are shown in Figure 2, along with an
estimate of the noise spectrum, and the applied telluric correction. We
measure the lens redshift from the marked features in Figure 2 as $z=1.001\pm
0.001$, and the lensed source redshift from cross-correlation with the stacked
rest-UV galaxy spectrum from Rigby et al. (2018b) as $z=5.043\pm 0.002$.

The high-airmass and non-parallactic slit positioning of these observations in
sub-optimal conditions makes the fluxing and telluric calibrations
irretrievably uncertain. However, as is obvious from Figure 2, both spectra
are sufficient to establish redshifts robustly.

At the measured redshift, the entire restframe optical band for the lensed
galaxies is shifted to wavelengths not readily accessed from ground-based
observatories. The only observable standard emission line used in studies of
galaxies at lower redshifts is the [O II] 3727,3729Å doublet. We observed COOL
J1241+2219 using the Gemini-North Near-infrared Spectrograph (GNIRS)
spectrograph (Elias et al., 2006) at NOIRLAB/Gemini, Mauna Kea, in Director’s
Discretionary Time on July 4th, 2020 in an attempt to measure this feature. We
acquired eight 257s integrations using GNIRS with a 0″.675 slit in cross-
dispersed mode and with the short camera, at an airmass$\sim$1.5, with a
typical on-instrument seeing of 0″.6. These observations targeted the same
bright peak along the arc observed with LDSS-3C. The data were reduced
primarily using the Gemini/GNIRS
pipeline333https://www.gemini.edu/instrumentation/gnirs/data-reduction. The
resulting spectrum was calibrated against a telluric standard star observed
immediately after. Analysis of these data is detailed in Section 4.

##  4 Analysis and Results

###  4.1 Zeropoint Calibration

The J- and H-band images are calibrated to 2MASS stars (Jarrett et al., 2000)
within the field of view, with the calibration derived automatically by
PHOTPIPE routines. Uncertainties on these zeropoints relative to 2MASS are
$\sim$ 0.03 magnitudes.

The PISCO data are calibrated to existing DECaLS ($grz$-bands) and Pan-STARRS
(DR2,Chambers et al., 2016) ($i$-band) data. We used SExtractor (Bertin &
Arnouts, 1996) MAG_AUTO magnitudes for detected objects in all bands to
establish image zeropoints. The PISCO data are much deeper than the reference
data, and so object-by-object uncertainties in the comparison are dominated by
uncertainties in the reference measurements. Limiting the comparison to
objects with a measured DECaLS SNR of $>$20 yields a matched catalog
sufficient to established zeropoints, and linear color terms, accurate to
better than 0.02 magnitudes, and we derive a similar result in comparison to
the Pan-STARRS data.

Figure 3: 12"x12" cutouts, all at the same intensity scaling, of the (left)
PISCO i band image, (center) GALFIT model of the central lens galaxy, the arc,
and other galaxies, and (right) the residual image (with inverted colors to
highlight the lack of residual structures). Table 1: Model photometry-based
magnitudes for COOL J1241+2219

| $g$ | $r$ | $i$ | $z$ | J | H
---|---|---|---|---|---|---
Central Lens Galaxy | 23.86 ${}_{-0.20}^{+0.24}$ | 21.960$\pm 0.046$ | 20.76$\pm 0.05$ | 19.630$\pm 0.048$ | 18.955$\pm 0.059$ | 18.564$\pm 0.054$
Arc | >25.11 | 23.197 ${}_{-0.358}^{+0.353}$ | 21.616 ${}_{-0.050}^{+0.049}$ | 20.472 ${}_{-0.048}^{+0.047}$ | 20.53 ${}_{-0.285}^{+0.273}$ | 20.556 ${}_{-0.087}^{+0.084}$
Counterimage | — | — | 24.164 ${}_{-0.297}^{+0.233}$ | 22.705 ${}_{-0.127}^{+0.105}$ | 23.074 ${}_{-0.793}^{+0.453}$ | 23.774 ${}_{-1.545}^{+0.613}$

Note. — Magnitudes calculated via GALFIT, with output in AB system.
$griz$-band imaging from Magellan/PISCO simultaneous multi-band imager. JH
band imaging from Magellan/FOURSTAR infrared imager.

###  4.2 Model Photometry with GALFIT

We used the parametric fitting code GALFIT (Peng et al., 2002, 2010) to create
a model of the arc, its candidate counterimage, the central lens galaxy, and
other nearby contaminating objects, as well as to extract relevant photometry.
Point-spread functions (PSFs) were measured directly from the images; these
are simply small cutouts of two isolated and bright but unsaturated point
sources near the modeled region. Differences in photometry from choices of PSF
are substantially smaller than all uncertainties below. Multiple two-
dimensional Sérsic components were used to model each image. Model
construction proceeded iteratively, with bright objects fit first, and further
components added until the residual was consistent with the background noise.

To estimate statistical photometric uncertainties we added the final fitted
model to blank sky regions around the image, and re-fit the models on these
new images. The measured magnitude distribution of each object then gives an
uncertainty. If the flux distribution had significant outliers (presumably due
to poor convergence of the model instance) we computed the uncertainty from
the flux distribution iteratively clipped at 3$\sigma$. Additionally, to
estimate the systematic uncertainty caused by modeling choices, three co-
authors independently created models for the $z$-band data, and the range in
final fitted magnitudes for these models was taken as an estimate of the
systematic uncertainty for the PISCO images. Additionally these models were
re-optimized to fit the H-band image, and provide an estimate of the
systematic uncertainty in the J- and H-bands.

Finally, calibration zeropoint uncertainties, and the statistical and
systematic uncertainties estimated as above, were combined in quadrature to
compute total uncertainties for each measurement of each physical object.

The i-filter image, GALFIT model and residuals for the lens field are shown in
Figure 3. Table 1 gives the model magnitudes for the arc and the candidate
counter-image.

####  4.2.1 Lens Galaxies

As part of the modeling, we have measured photometry for the central lens
galaxy, as well as two other nearby galaxies to the east that have similar
apparent colors and morphologies (and are visible in Figure 1). These two
other galaxies were fit together, but independently of other objects. These
two galaxies have colors similar to the apparent central lens galaxy, as is
indicated also by the DECaLS photometry of these galaxies. Independent of
strong-lensing mass modeling, this suggests that the lens is a lower-mass
galaxy cluster.

####  4.2.2 Arc and Possible Counterimage

The lensed source is absent in the $g$-band and nearly so in the $r$-band,
both due to absorption from the intergalactic medium (IGM). It is not possible
to fit a model directly in the $g$-band. Rather, we took the initial $i$-band
model, solved for any residual astrometric shift between the two bands using
visible objects in the modeled region, and then performed a constrained refit
of the model allowing only the magnitudes to vary of any components that
describe the arc. This model was pushed through the same statistical error
analysis as other filters, though in the case of the $g$-band image the
distribution of notional measured magnitudes represents an upper limit, and we
report the 95th percentile value.

In the $r$-, J-, and H-band data, the arc is visible but measured at a
markedly lower SNR than the $i$\- and $z$-bands. In each of these cases we
explored both direct modeling, and re-optimized models taken from bands with
larger SNR detections of the arc, and the measurements we report come from the
latter. Note that in all of these cases, including the $g$-band, components
which describe well-detected objects were allowed to vary structurally, as
well as in brightness.

The suggested counter-image (see Figure 1) is photometrically consistent with
the arc; it has consistent colors across filters where both objects are
visible, and the apparent surface brightness of this object matches much of
the arc. The candidate counter image was observed via LDSS-3C optical long
slit spectroscopy (and not with GNIRS), but given that the lensed source has
no emission lines in the rest-frame UV, we have not attempted to extract a
spectrum of this much fainter source. We note, however, that there is no
evidence in the 2D spectral image of any emission lines from this object that
would be inconsistent with the identification of it as a lensed counterimage.

Figure 4: (Left) Best fit SED model with nebular line emission (blue) and
corresponding Residual ($\chi$) values (green) for COOL J1241+2219 ,
calculated via Prospector, and using $z$JH photometry and IR spectroscopy.
Best-fit SED model without nebular line emission is displayed as short-dashed
grey curve. Best-fit photometry for $z$JH data is shown as black squares.
Photometric projections for the masked $ri$ data corresponding to the model
with and without nebular line emission are shown as blue ’plus’ and black
’plus’ symbols, respectively. (Right) Best-fit model spectrum with nebular
line emission (blue) zoomed into the observed wavelength range corresponding
to the blended [O II] 3727, 3729Å emission, with IR spectroscopic data
(orange) and uncertainties (dotted green), with model $\chi$ values (in green)
displayed in the bottom panel. Two black vertical lines mark the locations of
the [O II] 3727,3729Å doublet peaks.  Figure 5: (Top left) Corner plot with
posterior distributions and correlations for inferred parameters in the
Prospector SED fitting analysis for the lensed source, with contours
corresponding to 1$\sigma$ (in dark blue) and 2$\sigma$ (in light blue). (Top
right) The star formation history i.e. the SFR as a function of age bins; the
uncertainties in the SFR as a function of age are calculated by Monte Carlo
(MC)-sampling the SFR in the SED fitting chains. (Bottom) The posterior
probability distributions of the remnant stellar mass of COOL J1241+2219 , the
star formation rate (SFR) in the youngest age bin, and the specific star
formation rate (sSFR) in the same age bin.  Table 2: Prospector Analysis: Free
Parameters in Galaxy SED Model

Parameter | Description | Priors | Best Fit Value
---|---|---|---
$\log(M_{\rm tot}/M_{\odot})$ | Total stellar mass formed | Tophat: [10, 13] | $11.77_{-0.25}^{+0.20}$
$\log(\mathrm{SFR}_{\rm ratio})$ | Ratio of the SFRs in adjacent age bins: | Student-T: Bin 1: mean=0.0,scale=0.3, $\nu=2$ | $0.10_{-0.26}^{+0.33}$
| non-parametric SFH | Bin 2: mean=0.0,scale=0.3,$\nu=2$ | $0.10_{-0.28}^{+0.34}$
$\log(Z/Z_{\odot})$ | Stellar metallicity in units of $\log(Z/Z_{\odot})$ | Tophat: [-2, 0.5] | $-1.32_{-0.40}^{+0.56}$
$\tau_{\lambda,2}$ | Diffuse dust optical depth | Tophat: [0.01, 1.00] | $0.14_{-0.09}^{+0.13}$
$\mathrm{spec}_{\rm norm}^{*}$ | Factor by which to scale the spectrum to match photometry | Tophat: [0.1, 3.0] | $1.94_{-0.51}^{+0.53}$
$\mathrm{gas}_{\log(Z/Z_{\odot})}^{*}$ | Gas-phase metallicity in units of $\log(Z/Z_{\odot})$ | Tophat: [-2, 0.5]; depends on $\log(Z/Z_{\odot})$ | $-0.94_{-0.73}^{+0.90}$
$\log(U)^{*}$ | Gas Ionization Parameter $U=n\gamma/n_{H}$ | Tophat: [-4.0, -1.0] | $-2.48_{-1.09}^{+1.00}$

Note. — Data in AB magnitudes. $griz$ band imaging from Magellan/PISCO
simultaneous multi-band imager. JH band imaging from Magellan/FOURSTAR
infrared imager. *Considered as nuisance parameters.

###  4.3 SED Fitting with Prospector

Using the model photometry in $griz$JH filters, we perform spectral energy
distribution (SED) fitting for the central lens galaxy and the COOL J1241+2219
arc using the Markov Chain Monte Carlo (MCMC) — based stellar population
synthesis (SPS) and parameter inference code, Prospector. Prospector is based
on the the Python-FSPS framework, with the MILES stellar spectral library and
the MIST set of isochrones (Conroy & Gunn, 2010; Johnson & Leja, 2017; Leja et
al., 2017; Foreman-Mackey et al., 2013; Falcón-Barroso et al., 2011; Choi et
al., 2016). We exclude the LDSS3 spectrum from the fitting procedure because
at its low signal-to-noise ratio, it mostly samples saturated interstellar
absorption lines that are not directly constrained by Prospector libraries.

We have chosen to perform the SED fitting on the observed photometry, a choice
which assumes that there are no correlations within the SED fitting that
couple parameters that are magnification-dependent (such as stellar mass, star
formation rate) with those that are not magnification-dependent (such as
metallicity, dust extinction). This assumption has been tested by arbitrarily
rescaling the input photometry by the measured mean magnification (see Section
4.5),and the resulting SED fits are entirely consistent with the results
presented below.

In these models, we assume a non-parametric star formation history (with age
bins with $[0-50]$, $[50-100]$, and $[100-1000]$ Myr in lookback time),
represented by the parameters SFRratio, referring to the ratio of total star
formation in adjacent time bins. These bins correspond to redshift bins
[5.04-5.22], [5.22-5.41] and [5.41- 20.50]. The priors for the star-formation
rate ratios in adjacent time-bins is the continuity prior, that fits directly
for the change in log(SFR) between the bins and weights against sharp
transitions in SFR (see Leja et al., 2019).

We also fit for dust attenuation — using the Calzetti et al. (2000)
attenuation — applied to all light from the galaxy (in units of opacity at
5500Å), stellar metallicity $log(Z/Z_{\odot})$ (where $Z_{\odot}=0.0142$), gas
ionization parameter $U$, gas-phase metallicity (linked to stellar
metallicity) and total mass formed in the galaxy (Mtot,in units of M⊙), as
free parameters. For each chain in the MCMC analysis, the remnant stellar mass
M∗,remnant after compensating for mass loss from post main sequence stars, and
stellar mass locked in stellar remnants. The dust extinction and metallicities
have flat and liberal priors, roughly covering the range allowed by the
spectral model libraries. These models each assumed a Kroupa IMF (Kroupa,
2001). Nebular continuum and line emission are present, and a nominal velocity
smoothing of 250 kms-1 was used for the spectrum, informed by and consistent
with both an SED fit with this as a free parameter as well as a direct fit of
the spectrum using a simple Gaussian (see below).

The arc is not visible in $g$, and the $r$\- and $i$-bands sample the
Ly$\alpha$ forest and Ly$\alpha$ and Ly$\beta$ in the arc. To avoid biases
arising from a lack of correlation between star formation activity and the
complexity of Ly$\alpha$ absorption/emission in galaxies, which is not
captured in the stellar population synthesis models, we use only $z$JH
photometry for the arc SED fitting. We add to this the IR spectroscopy
sampling the [O II] 3727,3729Å doublet. The spectrum and photometry are fit
here simultaneously.

We assume that the [O II] equivalent width is uniform across COOL J1241+2219
in the source plane, and we scale the emission line spectrum to be
representative of the whole arc by considering the entire arc flux against the
portion contained within the slit, in the $i-$band. This flux normalization is
uncertain in practice, quite apart from the underlying assumption of uniform
equivalent width, so we include a nuisance parameter, specnorm (spectrum
normalization factor), to capture any unresolved differences between model
photometry and spectroscopy. This parameter is simultaneously fit with other
parameters within Prospector. Note however, that fits computed without this
parameter in place are consistent with conclusions from models (e.g., stellar
mass) that include specnorm.

The best fit SED model is shown in Figure 4. We also show corner plots
constructed via pyGTC (Bocquet & Carter, 2016), with one and two dimensional
projections of the posterior probability functions (to demonstrate both one
dimensional marginalized probabilities and two dimensional covariance) in
Figure 5 for the free parameters fit in the arc SED modeling (see Table 2).

It is also crucial to note that the best fit SED model fits a nominal Gaussian
to the observed wavelength range where we expect [O II] emission. The result
here – mean, width and amplitude – of the [O II] emission feature, is
consistent with results from fitting a 1D Gaussian profile to just the
spectroscopic data (see Section 4.4 for details).

The parameter Mtot, total stellar mass formed, converges to a tailed Gaussian
posterior distribution for these sources, which corresponds to a model-
generated remnant stellar mass distribution, displayed in the bottom panel of
Figure 5. The median value for the remnant stellar mass (M∗) in the image
plane (i.e., the magnified value) is logM (M⊙)) = $11.63^{+0.19}_{-0.24}$. The
precision of this result may surprise the reader, given that it is based on
rest-UV photometry, which is under most circumstances — e.g. at lower
redshifts, and in the presence of significant extinction — insufficient to
constrain stellar mass reliably. However, only modest dust columns are allowed
by the data, and at $z=5.043$ the Universe was not old enough to conceal much
stellar mass in older stars that do not produce significant UV flux.

We further test different models to check the robustness of our results. The
stellar mass of the arc is found to be robust when varying parameters as
follows:
1.Stellar metallicity fixed at the median best fit value in Figure 5.
2\. Removing nebular line emission from the model.
3\. Altering the number of age bins from three to four, which is recommended
by (Leja et al., 2019) (as well as from three to two), spanning the same time
period.
4\. Changing mean and standard deviation of the star formation history priors.
5\. Assuming a parametric star formation history (decayed-tau with a single
burst).
6\. Constraining SFH only to 0-500 Myr, as opposed to 0-1000 Myr.
7\. Using velocity smoothing as a free parameter for the [O II] emission line
fitting.
8\. Fixing gas ionization parameter to -2 and -2.5, as well as gas-phase
metallicity to that of the stellar value (i.e. 0).

We use the Bayesian Information Criterion (BIC) to quantify our model
selection, for the greater penalty imposed by BIC on the number of free
parameters used in our fitting procedure. Given a candidate model and M models
to compare with, the magnitude of $\Delta$BIC (BICM — BICcandidate) can be
inferred as evidence against a candidate model being the best model (Kass &
Raftery, 1995). The candidate best-fit model has a BIC value of -1245.5, and
the models discussed above have a |$\Delta$BIC| $<$ 5, which implies that the
evidence against our candidate best-fit model is positive, albeit low.
Qualitatively, all models constrain stellar mass and dust attenuation, while
leaving metallicities and the gas ionization parameter unconstrained (albeit
used here as nuisance parameters).

It is important to note that the SED fitting model contains contribution by
nebular line emission in order to fit [O II] emission, and hence depicts
Ly$\alpha$ in emission even though it is absent in the spectrum and photometry
(as indicated by mismatch between observed photometry and the synthetic
magnitudes marked by plus symbol in Figure 4). This does not impact our
results since the photometry sampling Ly$\alpha$ is not included in our
candidate best-fit model, and M∗ derived from removing nebular emission
contribution is within uncertainties consistent with that derived from our
best-fit model.

To cross-check the complete end-to-end pipeline from raw data to SED fits, we
have also applied a Prospector-based analysis to measurements of the central
lens galaxy and two likely cluster members discussed in Section 4.2.1 above,
and find that these galaxies are well fit by passively aging old stellar
populations at the notional lens redshift — as expected.

###  4.4 Instantaneous SFR: [O II]

Distinct from the simultaneous spectro-photometric SED fit to the data, we
cross-check our SFR result by calculating the [O II] 3727,3729Å doublet line
flux to characterize the instantaneous SFR (Rosa-González et al., 2002) for
COOL J1241+2219 from a scaling relation. We fit a 4 parameter 1-D Gaussian
profile (with mean, width, amplitude and continuum pedestal) to the
spectroscopic data, in the rest-frame region 3720-3735Å, to capture the
blended-doublet emission line. The observed [O II] line flux, corrected for
the entire arc, is $4.5^{+2.1}_{-2.0}\times 10^{-16}\ ergscm^{-2}s^{-1}$. The
redshift derived from blended-doublet line is $5.041\pm 0.001$.

Using the oft-used Kennicutt-calibrated [O II]-SFR relation (Kennicutt, 1992):

$SFR([OII],M_{\odot}yr^{-1})=1.4\times 10^{-41}L_{[OII]}(ergs^{-1})$ (1)

in the image plane we find the SFR for COOL J1241+2219 to be
$1700^{+800}_{-800}$ M⊙ yr-1. Instead, if we use the SFR-[O II] relation
empirically corrected for stellar metallicity and takes as input the galaxy
stellar mass (Equation 8 in Gilbank et al., 2010), we find the calculated SFR
to be $4600^{+3400}_{-2400}$ M⊙ yr-1.

Without stronger constraints on metallicity and dust in our SED posterior
distributions, their impact on the systematic uncertainties in the SFR-[O II]
flux scaling relations cannot be mitigated (e.g., Kewley et al., 2004; Bicker
& Fritze-v. Alvensleben, 2005). It is important to note that current
constraints are within the metallicity values observed for local universe
galaxies.

Figure 6: Lens model of the low-mass cluster lens based on ground-based
imaging, using the positional constraints indicated in green. We include two
halos — a galaxy-scale (smaller cyan ellipse) and cluster-scale halo (larger
cyan ellipse) to explain the observed lensing. The size of the ellipses
represent, on an arbitrary scale, the relative masses of the halos. The
tangential critical curve in red trisects the arc – this is a classic 3-image
arc with a counter image. This mass configuration is also informed by the
bright knot along the arc, which we set as a critical curve crossing in the
model (green cross).  Figure 7: (Left) Distribution of magnification values,
from a sample of 1000 magnification maps generated via an MCMC LENSTOOL
analysis of the lens model fit to the data. Note that distribution is strongly
asymmetric about the best fit value, which is in part a consequence of the
choice to identify the brightest peak on the arc as a location of the critical
curve. (Right) Current SFR in the source plane.

###  4.5 Lens Modeling and Magnification

We provide a brief summary of the gravitational lensing analysis used in this
work here, and we refer the reader to Kneib & Soucail, 1996; Richard et al.,
2010; Verdugo et al., 2011 for a more in depth discussion of the lensing
algorithm used. We adopt a parametric approach using LENSTOOL (Jullo et al.,
2007) to model the mass distribution with dual pseudo-isothermal ellipsoids
(dPIEs, Elíasdóttir et al., 2007), using an MCMC method to estimate the
parameters and their uncertainties. The lens modeling strategy generally
follows Sharon et al. (2020) (with a cosmology with $\Omega_{M}$ = 0.3,
$\Omega_{\Lambda}$ = 0.7). We model the lens plane with two dPIE potentials,
one to represent a group-scale dark matter halo, and one that represents the
contribution from the main lens galaxy. The geometric parameters of the
galaxy-scale halo are fixed to its observed properties (position, ellipticity,
and position angle), while the slope and overall normalization are allowed to
vary. The choice of two halos is motivated by the arc radius, which suggests
the presence of a mass structure larger than a single massive galaxy, and the
presence of other luminous early-type galaxies with colors consistent with the
apparent central lens galaxy, again indicative of a more complex structure.
Hence, the two dPIE clumps used here are combined to map the dark matter (DM)
at the cluster scale and the central lens galaxy.

The smooth appearance of the arc in the ground based data limits the
availability of lensing constraints; a more complex lens plane, with
additional galaxy-scale halos, is not required in order to satisfy these
constraints. Hence, we do not include any other galaxy-scale halos in this
initial model (see Figure 6). We choose to use the peak of the galaxy core as
a constraint (see system 1 with four images in Figure 6), the surroundings of
the star-forming clump merging on the critical curve (system 2), and a
critical curve constraint (see green cross). The precision assumed for the
location of the constraints in the lens model is 0.1", with an RMS of the
optimized model in the image plane of 0.12".

To estimate the magnification, we calculate the ratio of flux in the image
plane using the GALFIT modeling image of the arc and its pixel-matched source
plane reconstruction for 100 realisations of the lens model posterior
probability distribution, resulting in an estimate of the magnification of
$32^{+8}_{-5}$. We apply this as a division factor to the arc imaging in the
image plane, to convert the derived physical parameter values to the source
plane.

The uncertainties used in the SED fitting do not include the system-wide
magnification uncertainty, which when combined with the statistical
uncertainties, yields a final stellar mass for COOL J1241+2219 of logM (M⊙) =
$10.11^{+0.21}_{-0.26}$. Similarly, the demagnified current star formation
rate (SFR, in units of M⊙/yr) is calculated to be $27^{+13}_{-9}$ (see Figure
7), which makes this an active star-forming galaxy, given the constraints of
the SED and lens modeling. This is assuming that the SFR in the age bin 0-50
Myr is a proxy for current star forming activity in COOL J1241+2219 .

##  5 Discussion

###  5.1 Luminosity Function

We compare the brightness of COOL J1241+2219 to M${}^{*}_{UV}$, the
characteristic luminosity in the parametric luminosity function (Schechter,
1976). As a proxy for the UV absolute magnitude we compute $M_{1600}$,
calculated from synthetic photometry applied to the best fit SED model, using
a top-hat filter from 1550-1650 Å. The UV continuum is roughly flat, and hence
differences in definitions of UV magnitudes in the literature do not
significantly impact the comparison of our reported absolute magnitude to
published values.

Taking into account the lensing magnification, MUV for COOL J1241+2219 is
$-22.2^{+0.2}_{-0.2}$. Bouwens et al. (2015) give a characteristic
M${}^{*}_{UV}$ at $z$ = 5 of -21.1$\pm$0.2 (see Table 6 in Bouwens et al.,
2015; we use the higher uncertainty value). Hence, we find that for COOL
J1241+2219 , M${}^{*}_{UV}$ — MUV= $1.0^{+0.5}_{-0.4}$. In other words, COOL
J1241+2219 is $\sim$ 2-4 times more luminous than an object with the
characteristic UV luminosity at these redshifts.

###  5.2 The UV Continuum Slope

The observed UV continuum slope of star-forming galaxies is closely related to
emission from massive stellar populations, as well as dust extinction in the
galaxy. We fit the best-fit SED model for COOL J1241+2219 with a power law in
fλ, i.e., fλ $\simeq$ ${\lambda}^{\beta}$, between rest-frame 1268-2580Å (the
entirety of the fitting windows described initially by Calzetti et al., 1994).
For COOL J1241+2219 , the best-fit UV continuum slope is calculated to be
$\beta$ = -2.2$\pm$0.2. This is on the blue side of the distribution of
$\beta$ observed in (albeit fainter) galaxies at $z=5$ in (e.g., Finkelstein
et al., 2012) but consistent with their measured distribution. However, the
mean relation between $\beta$ and UV luminosity (Bouwens et al., 2014) for
galaxies at $z=5$ predicts a value of $\beta$ for COOL J1241+2219 of
$\sim$-1.6, significantly shallower than we observe. The observed $\beta$ is
in fact consistent with that for galaxies $\sim$ 4 magnitudes fainter,
emphasizing that COOL J1241+2219 is unusually blue for its total UV
luminosity.

###  5.3 Star-forming Main Sequence

The relationship between SFR and stellar mass of a galaxy is a well-studied
relationship in galaxy populations and large samples, known as the star-
forming main sequence (SFMS; Noeske et al., 2007; Rodighiero et al., 2011). It
is informative to place these properties of COOL J1241+2219 in relation to the
SFMS of a galaxy sample in the same epoch of observation. We compare the SFR
and stellar mass of COOL J1241+2219 with galaxies at 4 < $z$ < 6 in the Hubble
Space Telescope Frontier Fields. The SFMS for galaxies in this field in the
redshift bins 4 < $z$ < 5, and 5 < $z$ < 6 has been reported in Santini et al.
(2017). We direct the reader to the solid lines in bottom panels in Figure 2
of that publication, which reflect the best-fit SFMS, corrected for Eddington
bias. The demagnified SFR and stellar mass of COOL J1241+2219 (logM (M⊙) =
$10.11^{+0.21}_{-0.26}$ and SFR (M⊙/yr) = $27^{+13}_{-9}$), are consistent
with these power-law fits for the SFMS within 1$\sigma$, but incompatible with
high SFRs corresponding to bursty mode(s) of star formation during major
mergers or in the densest regions. It is also important to note that the
source plane properties of COOL J1241+2219 place this galaxy among the highest
mass values reported in those data.

###  5.4 Stellar Populations in COOL J1241+2219

COOL J1241+2219 has a stellar mass consistent within a factor of a few of that
of the present-day Milky Way (Licquia & Newman, 2015), and is forming stars
$\sim$ 1-2 orders of magnitude faster. This rate of star formation is not
surprising, given that the available time to build this galaxy at $z=5.04$ is
only $\sim$1 Gyr. COOL J1241+2219 is extremely UV-bright with little apparent
extinction. This stands in strong contrast to some similarly massive galaxies
known from this early epoch (e.g., Riechers et al., 2013; Strandet et al.,
2017; Casey et al., 2019) which tend to be much dustier with SFRs an order of
magnitude larger. This difference is of course due to the selection process
used to identify these objects. What is less clear, however, is whether COOL
J1241+2219 looked like these dust-enshrouded examples of early star formation
at any point in its history. The relative contribution of dust-enshrouded star
formation to the total star formation rate at this epoch is not well-measured
(Casey et al., 2019) and so objects like COOL J1241+2219 that are bright
enough to allow detailed studies are of particular interest.

The current constraints from SED fitting (see Figures 5 and 7) imply that the
SFH of COOL J1241+2219 is consistent with a constant SFR across the $\sim$1
Gyr available. The current data however are insufficient to say more; the non-
parametric model forms the bulk of its stars in the oldest (and widest) bin,
and a briefer and much elevated star-formation episode in that interval is
certainly possible.

Despite significant ongoing star-formation, and a blue UV slope that suggests
little extinction, COOL J1241+2219 shows no evidence for Ly$\alpha$ emission
in the extracted spectrum. In addition, we carefully examine the stacked 2D
spectrum, and see no evidence of spatially-extended Ly$\alpha$ emission
outside of the continuum. This complete lack of emission indicates the
presence of sufficient dust to suppress Ly$\alpha$, as one would expect in a
massive galaxy with a sustained SFH and resulting enrichment. These results
are somewhat in tension. However, note that the measured scatter in galaxies
between the Ly$\alpha$ escape fraction and continuum extinction is large
(Hayes et al., 2011) and suppression of Ly$\alpha$ emission is possible even
with extremely sparse dust columns.

##  6 Summary and Future Work

We report the discovery of COOL J1241+2219 , a strongly lensed galaxy at
$z$=5.043$\pm$0.002 that is lensed by a moderate-mass galaxy cluster at
$z$=1.00$\pm$0.001. In this first work by the COOL-LAMPS collaboration, we
characterise the lensed galaxy using $griz$JH band photometry and optical and
NIR spectroscopy. Using Prospector, we perform a stellar population synthesis
analysis spectro-photometrically, to constrain the stellar mass, SFH, stellar
metallicity and dust properties. Our dPIE-halo-based lens mass modeling from
LENSTOOL, based on ground-based imaging, implies a median source magnification
of at least $\sim$30, which puts the stellar mass and star formation rate (in
the youngest age bin, closest to the epoch of observation) at logM∗ =
$10.11^{+0.21}_{-0.26}$ and SFR = $27^{+13}_{-9}$ M⊙/yr, respectively. This
places this galaxy on the star-forming main sequence, at the massive end of
that relation, and we find that COOL J1241+2219 is 2-4x more luminous than a
galaxy with the characteristic UV luminosity at these redshifts. We constrain
a star formation history for COOL J1241+2219 starting at $z\sim 20$ that is
consistent with constant star formation across $\sim$1 Gyr of cosmic time.

Current data are insufficient to constrain the metallicity and star formation
history robustly. Also, as is almost always true, the lens model built on
ground-based data limits the precision and accuracy of some aspects of our
analysis; a lens model built from much sharper imaging (e.g., with HST) will
provide insights into fluxes, flux variations, and identification of a variety
of faint spatial features within this galaxy much more comprehensively via a
proper source plane reconstruction. Moreover, our current spectroscopy only
samples the apparently brightest clump in this galaxy. Once lensed into the
observed giant arc, COOL J1241+2219 is the brightest galaxy at $z>5$ currently
known, and thus presents a unique opportunity for the detailed study of a
massive galaxy immediately after the epoch of reionization. COOL J1241+2219 is
bright enough that precise high resolution observations will be possible
across a broad range of wavelengths.

We would like to express gratitude towards the staff and workers at the 6.5m
Magellan Telescopes at the Las Campanas Observatory, Chile, and the Gemini-
North telescopes at Mauna Kea, Hawaii, USA, for their valuable labor. The
authors wish to recognize and acknowledge the very significant cultural role
and reverence that the summit of Mauna Kea has always had within the
indigenous Hawaiian community. The authors are most fortunate to have the
opportunity to conduct observations via the NOIRLab-operated Gemini-North
facility from this mountain. GK acknowledges the impact of astrophysical
observatories and research on this sacred Native Hawaiian land, and directs
the reader towards resources on this matter for further consumption (e.g.,
Kahanamoku et al., 2020; Prescod-Weinstein et al., 2020, and references
therein). We would like to thank the anonymous reviewer for their thoughtful
and helpful comments, that improved the quality of this manuscript and the
robustness of ther results herein, substantially. GK thanks Joel Leja and
Benjamin Johnson for their responses, guidance and input related to specifics
of the Prospector framework. This work is supported by The College
Undergraduate program at the University of Chicago, and the Department of
Astronomy and Astrophysics at the University of Chicago. Magellan/PISCO
operations are supported by NSF AST-1814719. This research was supported by an
appointment to the NASA Postdoctoral Program at the NASA Goddard Space Flight
Center administered by Universities Space Research Association through a
contract with NASA. Work at Argonne National Lab is supported by UChicago
Argonne LLC,Operator of Argonne National Laboratory (Argonne). Argonne, a U.S.
Department of Energy Office of Science Laboratory, is operated under contract
no. DE-AC02-06CH11357. The Legacy Surveys consist of three individual and
complementary projects: the Dark Energy Camera Legacy Survey (DECaLS; Proposal
ID #2014B-0404; PIs: David Schlegel and Arjun Dey), the Beijing-Arizona Sky
Survey (BASS; NOAO Prop. ID #2015A-0801; PIs: Zhou Xu and Xiaohui Fan), and
the Mayall z-band Legacy Survey (MzLS; Prop. ID #2016A-0453; PI: Arjun Dey).
DECaLS, BASS and MzLS together include data obtained, respectively, at the
Blanco telescope, Cerro Tololo Inter-American Observatory, NSF’s NOIRLab; the
Bok telescope, Steward Observatory, University of Arizona; and the Mayall
telescope, Kitt Peak National Observatory, NOIRLab. The Legacy Surveys project
is honored to be permitted to conduct astronomical research on Iolkam Du’ag
(Kitt Peak), a mountain with particular significance to the Tohono O’odham
Nation. NOIRLab is operated by the Association of Universities for Research in
Astronomy (AURA) under a cooperative agreement with the National Science
Foundation. This project used data obtained with the Dark Energy Camera
(DECam), which was constructed by the Dark Energy Survey (DES) collaboration.
Funding for the DES Projects has been provided 19 by the U.S. Department of
Energy, the U.S. National Science Foundation, the Ministry of Science and
Education of Spain, the Science and Technology Facilities Council of the
United Kingdom, the Higher Education Funding Council for England, the National
Center for Supercomputing Applications at the University of Illinois at
Urbana-Champaign, the Kavli Institute of Cosmological Physics at the
University of Chicago, Center for Cosmology and Astro-Particle Physics at the
Ohio State University, the Mitchell Institute for Fundamental Physics and
Astronomy at Texas A&M University, Financiadora de Estudos e Projetos,
Fundacao Carlos Chagas Filho de Amparo, Financiadora de Estudos e Projetos,
Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro,
Conselho Nacional de Desenvolvimento Cientifico e Tecnologico and the
Ministerio da Ciencia, Tecnologia e Inovacao, the Deutsche
Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy
Survey. The Collaborating Institutions are Argonne National Laboratory, the
University of California at Santa Cruz, the University of Cambridge, Centro de
Investigaciones Energeticas, Medioambientales y Tecnologicas-Madrid, the
University of Chicago, University College London, the DES-Brazil Consortium,
the University of Edinburgh, the Eidgenossische Technische Hochschule (ETH)
Zurich, Fermi National Accelerator Laboratory, the University of Illinois at
Urbana-Champaign, the Institut de Ciencies de l’Espai (IEEC/CSIC), the
Institut de Fisica d’Altes Energies, Lawrence Berkeley National Laboratory,
the Ludwig Maximilians Universitat Munchen and the associated Excellence
Cluster Universe, the University of Michigan, NSF’s NOIRLab, the University of
Nottingham, the Ohio State University, the University of Pennsylvania, the
University of Portsmouth, SLAC National Accelerator Laboratory, Stanford
University, the University of Sussex, and Texas A&M University. The Legacy
Surveys imaging of the DESI footprint is supported by the Director, Office of
Science, Office of High Energy Physics of the U.S. Department of Energy under
Contract No. DE-AC02- 05CH1123, by the National Energy Research Scientific
Computing Center, a DOE Office of Science User Facility under the same
contract; and by the U.S. National Science Foundation, Division of
Astronomical Sciences under Contract No. AST-0950945 to NOIRLab.

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