# The Sunburst Arc with JWST: III. An Abundance of Direct Chemical Abundances

Brian Welch Department of Astronomy, University of Maryland, College Park, MD
20742, USA  Astrophysics Science Division, Code 660, NASA Goddard Space Flight
Center, 8800 Greenbelt Rd., Greenbelt, MD 20771, USA  Center for Research and
Exploration in Space Science and Technology, NASA/GSFC, Greenbelt, MD 20771
T. Emil Rivera-Thorsen The Oskar Klein Centre, Department of Astronomy,
Stockholm University, AlbaNova 10691, Stockholm, Sweden  Jane R. Rigby
Astrophysics Science Division, Code 660, NASA Goddard Space Flight Center,
8800 Greenbelt Rd., Greenbelt, MD 20771, USA  Taylor A. Hutchison Astrophysics
Science Division, Code 660, NASA Goddard Space Flight Center, 8800 Greenbelt
Rd., Greenbelt, MD 20771, USA  Grace M. Olivier Department of Physics and
Astronomy and George P. and Cynthia Woods Mitchell Institute for Fundamental
Physics and Astronomy, Texas A&M University, 4242 TAMU, College Station, TX
77843-4242, USA  Danielle A. Berg Department of Astronomy, The University of
Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712, USA  Keren
Sharon Department of Astronomy, University of Michigan, 1085 S. University
Ave, Ann Arbor, MI 48109, USA  Håkon Dahle Institute of Theoretical
Astrophysics, University of Oslo, P.O. Box 1029, Blindern, NO-0315 Oslo,
Norway  M. Riley Owens Department of Physics, University of Cincinnati,
Cincinnati, OH 45221, USA  Matthew B. Bayliss Department of Physics,
University of Cincinnati, Cincinnati, OH 45221, USA  Gourav Khullar Department
of Physics and Astronomy and PITT PACC, University of Pittsburgh, Pittsburgh,
PA 15260, USA  John Chisholm Department of Astronomy, The University of Texas
at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712, USA  Matthew Hayes The
Oskar Klein Centre, Department of Astronomy, Stockholm University, AlbaNova
10691, Stockholm, Sweden  Keunho J. Kim IPAC, California Institute of
Technology, 1200 E. California Boulevard, Pasadena, CA 91125, USA

###### Abstract

We measure the gas-phase abundances of the elements He, N, O, Ne, S, Ar, and
Fe in the Lyman-continuum emitting region of the Sunburst Arc, a highly
magnified galaxy at redshift $z=2.37$. We detect the temperature-sensitive
auroral lines [Sii]$\lambda\lambda 4069,4076$, [Oiii]$\lambda 4363$,
[Siii]$\lambda 6312$, [Oii]$\lambda\lambda 7320,7330$, and [Neiii]$\lambda
3343$ in a stacked spectrum of 5 multiple images of the Lyman-continuum
emitter (LCE), from which we directly measure the electron temperature in the
low, intermediate, and high ionization zones. We also detect the density-
sensitive doublets of [Oii]$\lambda\lambda 3727,3729$, [Sii]$\lambda\lambda
6717,6731$, and [Ariv]$\lambda\lambda 4713,4741$, which constrain the density
in both the low- and high-ionization gas. With these temperature and density
measurements, we measure gas-phase abundances with similar rigor as studies of
local galaxies. We measure a gas-phase metallicity for the LCE of
$12+\log(\textrm{O}/\textrm{H})=7.97\pm 0.05$, and find an enhanced nitrogen
abundance $\log(\textrm{N}/\textrm{O})=-0.65^{+0.16}_{-0.25}$. This nitrogen
abundance is consistent with enrichment from a population of Wolf-Rayet stars,
additional signatures of which are reported in a companion paper. Abundances
of sulfur, argon, neon, and iron are consistent with local low-metallicity HII
regions and low-redshift galaxies. This study represents the most complete
chemical abundance analysis of a galaxy at Cosmic Noon to date, which enables
direct comparisons between local HII regions and those in the distant
universe.

Chemical abundances, Gravitational lensing, galaxies

††facilities: JWST††software: Astropy (Astropy Collaboration et al., 2013,
2018, 2022), Matplotlib (Hunter, 2007), Scipy (Virtanen et al., 2020), emcee
(Foreman-Mackey et al., 2013), PyNeb (Luridiana et al., 2015)

##  1 Introduction

As stars shed mass in their late evolutionary stages and explode as
supernovae, they recycle newly synthesized elements into the surrounding gas,
enriching the nebula. Analysis of the chemical abundance patterns in nebulae
thus give insight into the evolution of stars and the star formation histories
of galaxies.

Recent measurements of high redshift galaxies have found unusual abundance
patterns, including anomalously high nitrogen abundances (N/O, Cameron et al.,
2023; Senchyna et al., 2023; Marques-Chaves et al., 2024; Castellano et al.,
2024) and carbon abundances (C/O, D’Eugenio et al., 2023). Meanwhile similar
carbon abundance measurements at slightly lower redshifts ($z=4-6$) find much
lower abundances (Citro et al., 2023; Jones et al., 2023). The anomalous
abundance patterns in the highest redshift galaxies may be indicative of
chemical evolution via e.g. Wolf-Rayet (WR) stars or extremely metal poor
stars, as the standard production pathway for nitrogen and carbon via
intermediate-mass AGB stars would not have time to develop.

One of the most robust methods to determine chemical abundance patterns in
galaxies is the so-called “direct” method, which directly measures electron
temperature ($T_{e}$) and density from the strengths of auroral emission lines
relative to bright collisionally-excited lines. These temperatures and
densities are then used in conjunction with the strengths of the bright lines
to calculate the abundance of each ion within the nebula (Dinerstein, 1990).

The auroral lines are intrinsically faint, making this measurement difficult.
Direct $T_{e}$ abundances have been well studied in nearby galaxies (e.g., van
Zee & Haynes, 2006; Berg et al., 2015; Croxall et al., 2015, 2016; Berg et
al., 2020; Rogers et al., 2021, 2022). In these local galaxies, multiple
auroral lines are detected, allowing direct measurements of the electron
temperature in multiple ionization zones within the nebular gas. This
eliminates the need for empirical temperature relations to infer the physical
conditions of different zones within the gas, thereby making the final
abundance determinations more accurate. Additionally, including muliple
ionization zones minimizes the impact of empirically-calibrated ionization
corrections, which account for unobserved ionization states of a given element
(e.g., Izotov et al., 2006; Amayo et al., 2021). In the best case, all
relevant ionization states of each element are observed, resulting in the most
accurate determinations of elemental abundances.

Only a handful of auroral line detections were available for galaxies at
higher redshifts ($z\sim 1-3$) prior to the launch of JWST (Christensen et
al., 2012; James et al., 2014; Bayliss et al., 2014; Ly et al., 2015; Kojima
et al., 2017; Sanders et al., 2020, 2023b; Citro et al., 2023). The
sensitivity and wavelength coverage of JWST (Gardner et al., 2023; Rigby et
al., 2023a) have changed the landscape of direct $T_{e}$ chemical abundance
measurements in distant galaxies. The auroral [Oiii]$\lambda 4363$ line was
detected out to $z\sim 8$ for the first time in the first data release from
the Early Release Observation (ERO, Pontoppidan et al., 2022) of the lensing
cluster SMACS0723 (Arellano-Córdova et al., 2022; Schaerer et al., 2022;
Taylor et al., 2022; Brinchmann, 2023; Curti et al., 2023; Katz et al., 2023;
Rhoads et al., 2023; Trump et al., 2023; Trussler et al., 2023). This line has
since been clearly detected out to $z\sim 8.7$ in a field galaxy (Sanders et
al., 2023a), and at $z=10.17$ in a gravitationally lensed galaxy (Hsiao et
al., 2024).

Each of the aforementioned studies have relied on detection of a single
auroral line for their abundance measurements. Several early JWST observing
programs have detected multiple auroral lines in galaxies at Cosmic Noon,
enabling more robust studies of abundance patterns in distant galaxies. The
CECILIA program (PID 2593, PI Strom, Co-PI Rudie) targeted the [Nii]$\lambda
5755$, [Siii]$\lambda 6312$, and [Oii]$\lambda\lambda 7320,7330$ lines in a
sample of galaxies at $z\sim 2-3$, aiming to measure multiple ionization
states and thus obtain more accurate abundances. This program has so far
yielded an analysis of the stacked sample (Strom et al., 2023), and
measurements of all three lines in a single galaxy at $z\sim 3$ with a notably
sub-solar S and Ar abundance (Rogers et al., 2024). Meanwhile the TEMPLATES
ERS program (PID 1355, PI Rigby, Co-PI Viera) has detected [Oiii]$\lambda
4363$, [Siii]$\lambda 6312$, and [Oii]$\lambda\lambda 7320,7330$ in a lensed
galaxy at $z\sim 1.3$, finding a slightly enhanced nitrogen abundance (Welch
et al., 2024). These studies measuring multiple ionization states at $z\sim
1-3$ represent a positive step towards applying the same detailed methods used
in local galaxies to high redshift. However none have managed to reach the
complete standard set by studies of local galaxies.

This paper presents the analysis of direct $T_{e}$ abundances in the Sunburst
Arc (Dahle et al., 2016), a highly magnified gravitationally lensed galaxy at
redshift $z=2.37$ (Sharon et al., 2022; Diego et al., 2022; Pignataro et al.,
2021). We focus on a single physical region of the galaxy that is leaking
ionizing photons (Rivera-Thorsen et al., 2019), which we refer to as the
Lyman-continuum emitter (LCE). This region is a compact star cluster (Vanzella
et al., 2022) hosting a young stellar population with a light-weighted age of
$\sim 3.6$ Myr (Chisholm et al., 2019; Rivera-Thorsen et al., 2024) and a
steep UV slope $\beta\simeq-3$ (Kim et al., 2023). Several authors have found
evidence of very massive stars in the LCE (Chisholm et al., 2019; Meštrić et
al., 2023; Pascale et al., 2023). A companion paper presents evidence that the
LCE hosts a population of Wolf-Rayet stars (Rivera-Thorsen et al., 2024).

In this paper, we report the detection of the [Sii]$\lambda\lambda 4069,4076$,
[Oiii]$\lambda 4363$, [Siii]$\lambda 6312$, [Oii]$\lambda\lambda 7320,7330$,
and [Neiii]$\lambda 3343$ auroral lines, from which we measure $T_{e}$
directly in the low, intermediate, and high ionization zones of the nebula. We
also measure the electron temperature in ionized hydrogen gas from the Balmer
jump. We measure abundances for seven elements (He, N, O, Ne, S, Ar, Fe). For
three of these (O, S, Ar) we measure multiple ionization states, which
minimizes the impact of ionization corrections in our abundance
determinations. With this set of diagnostics, for the first time we apply the
same level of rigor used in local galaxies to an object at Cosmic Noon,
bridging the gap between local abundance measurements and those at high
redshift.

This paper is organized as follows. The data are presented in Section 2. Our
emission line measurements and reddening corrections are described in Section
3. We describe our electron temperature, density, and chemical abundance
measurements and results in Section 4, and discuss the context of these
results in Section 5. We summarize our conclusions in Section 6. We assume
flat $\Lambda$CDM cosmology with $\Omega_{\Lambda}=0.7$, $\Omega_{m}=0.3$, and
$H_{0}=70$ km s-1 Mpc-1.

##  2 Data

The Sunburst Arc was observed by JWST in Cycle 1 using NIRCam (Rieke et al.,
2023) and the Integral Field Spectroscopy (IFS) mode of NIRSpec (Böker et al.,
2023), taken in program GO-02555 (PI: Rivera-Thorsen). NIRCam data were taken
in six broadband filters (F115W, F150W, F200W, F277W, F356W, and F444W).
NIRSpec data were taken with two grating settings (G140H/F100LP,
G235H/F170LP). The IFS data were taken in three pointings, shown in Figure 1
of Rivera-Thorsen et al. (2024). The observations and data reduction are
described in greater detail in Rivera-Thorsen et al., in prep; we briefly
summarize the relevant steps here. The NIRSpec IFS data were reduced following
the methods described in Rigby et al. (2023b), using the TEMPLATES NIRSpec
data reduction notebook (Rigby et al., 2024). We used the JWST data reduction
pipeline version 1.11.4 (Bushouse et al., 2023), along with calibration
reference files from pmap_1105. After running the main JWST pipeline, we use
the baryon-sweep111https://github.com/aibhleog/baryon-sweep code to remove any
remaining outliers from the final data cubes (Hutchison et al., 2023, 2024).

In this work, we analyze a spatially-integrated spectrum that consists of 5
multiple images of the LCE covered by the three IFU pointings. We extract
spectra of the LCE images from $5\times 5$ spaxel apertures, using a flux-
weighted sum. The spectra are normalized, no magnification correction is
applied, however all results presented herein rely exclusively on flux ratios
which are unaffected by magnification or normalization. The full extraction
method is documented in greater detail in Rivera-Thorsen et al. (2024).

##  3 Methods

###  3.1 Continuum Subtraction

Prior to fitting emission lines, we first remove the continuum. We mask known
emission lines and sigma-clip the remaining continuum to remove any artifacts
that passed our previous artifact removal steps described in Section 2. The
remaining continuum is then smoothed with a running median to produce a smooth
continuum model. The smooth model is subtracted from the original spectrum
prior to fitting any emission lines. This method of continuum subtraction will
not account for features such as Balmer absorption. However, we do not expect
significant Balmer absorption in the young stellar population seen in the LCE
($\lesssim 4$ Myr, Chisholm et al., 2019; Rivera-Thorsen et al., 2024), and
visual inspection of the original spectrum shows no sign of Balmer absorption
features.

###  3.2 Emission Line Measurements

Emission lines are fit using Gaussian profiles, utilizing the publicly-
available tools developed by the TEMPLATES team and available on
GitHub.222github.com/JWST-Templates We initially attempt to fit each line with
a single Gaussian component, and iteratively add up to two additional
components if visual inspection determines the fit to be poor. We find that
the brightest lines (e.g. [Oiii]$\lambda\lambda 4959,5007$, H$\alpha$) require
three components - one narrow (unresolved) component, one medium component
with a full-width at half maximum (FWHM) of $\sim 200-300$ km s-1, and one
broad component with a FWHM of $\sim 600-700$ km s-1. As line strengths
decrease, the broadest component is the first to become lost in the noise.
Thus for many lines, only the unresolved and the medium width components are
used in fitting. For the faintest lines (including all of the auroral lines),
only a single unresolved component is sufficient to obtain a good fit. When
fitting both single- and multi-component lines, we allow the centroids of each
component to vary within $\pm 2$ Å in the observed frame to allow for possible
velocity offsets from our assumed systemic redshift ($z=2.371062\pm 6\times
10^{-6}$ Rivera-Thorsen et al., 2024). For bright multi-component lines, the
amplitude and width of the Gaussians are left unconstrained. For the faintest
emission features, we choose to fix the line widths to the instrumental
resolution at the observed wavelength, as is observed in the narrow components
of the brighter emission lines. This prevents noise around the edge of the
lines from artificially broadening the Gaussian fits. Final line fluxes are
obtained by integrating the Gaussian fits. For line fits with two components,
we sum the Gaussian integrals to obtain the total line flux. For three
component fits, we choose to not include the broadest component in our total
flux measurements, as the velocities ($\sim 600-700$ km s-1) are such that
this gas has likely traveled far from the main nebula. This only affects the
H$\alpha$ and [Oii]$\lambda\lambda 3727,3729$ lines. Uncertainties in measured
line fluxes are propagated through from fitting uncertainties on the Gaussian
amplitude and width.

Figure 1: Stacked spectrum of 5 multiple images of the Lyman-continuum emitter
in the Sunburst Arc, zoomed in to highlight detected auroral emission lines.
The extracted spectrum is shown in blue, and the continuum fit is shown in
orange. Flux errors are shown in grey, offset by the continuum fit to show the
SNR of the continuum-subtracted lines. The [Ariv]$\lambda\lambda 4713,4741$
lines abut the blue Wolf-Rayet bump (Rivera-Thorsen et al., 2024). Our
continuum fit treats this broad feature similar to the continuum, so it is
removed prior to fitting the argon emission lines.

Blended emission lines (e.g., H$\alpha$ and [Nii]$\lambda\lambda 6548,6584$)
are fit simultaneously, using the same priors and uncertainty calculations
described above. One notable exception in our fitting process is the
[Oii]$\lambda\lambda 3727,3729$ doublet. These lines are blended together, and
because of the high signal-to-noise ratio (SNR) of this spectrum, the H13 and
H14 lines of hydrogen are also blended with the [Oii]$\lambda\lambda
3727,3729$ doublet. We find that the [Oii]$\lambda\lambda 3727,3729$ lines
require two components each to fit properly. The combination of six blended
Gaussian profiles leads to a large degeneracy in model parameters,
particularly within the [Oii]$\lambda\lambda 3727,3729$ doublet. We choose to
fix the parameters of the H13 and H14 lines to improve the accuracy of the
[Oii]$\lambda\lambda 3727,3729$ fit. The fluxes of H13 and H14 are calculated
from our measured fluxes of the H11 and H12 lines, which are well separated
from other nearby lines. We use a simple mean of the line fluxes predicted
from H11 and H12 as our estimates for the H13 and H14 line flux. We fix the
line widths of the H13 and H14 lines to be unresolved, and fix the observed
wavelengths using the systemic redshift of the system. This process leads to a
reliable [Oii]$\lambda\lambda 3727,3729$ fit, however the degeneracy between
parameters in these blended lines still leads to unreasonably large flux
uncertainties. To estimate the true uncertainty on the fluxes of these two
lines, we run a MCMC ensemble using the python package emcee (Foreman-Mackey
et al., 2013). We calculate the total flux of each line from each step of the
MCMC, and use the standard deviation of the resulting distribution as our
estimate of the flux uncertainty.

Table 1: Emission Line Fluxes Line Name | Wavelength | $F(\lambda)/F(\textrm{H}\beta)$ | $I(\lambda)/I(\textrm{H}\beta)$
---|---|---|---
[Ne III] 3343 | $3343.50$ | $0.003\pm 0.001$ | $0.003\pm 0.001$
[O II] 3727 | $3727.09$ | $0.28\pm 0.03$ | $0.29\pm 0.03$
[O II] 3730 | $3729.88$ | $0.22\pm 0.03$ | $0.22\pm 0.03$
[Ne III] | $3869.86$ | $0.56\pm 0.03$ | $0.58\pm 0.03$
[Ne III] 3969 | $3968.59$ | $0.17\pm 0.02$ | $0.18\pm 0.03$
H$\epsilon$ | $3971.20$ | $0.14\pm 0.03$ | $0.15\pm 0.03$
[S II] 4069 | $4069.75$ | $0.006\pm 0.001$ | $0.006\pm 0.001$
S II] 4076 | $4075.79$ | $0.002\pm 0.001$ | $0.003\pm 0.001$
H$\delta$ | $4102.89$ | $0.24\pm 0.02$ | $0.25\pm 0.02$
H$\gamma$ | $4341.68$ | $0.52\pm 0.07$ | $0.53\pm 0.07$
[Fe II] 4360 | $4359.59$ | $0.010\pm 0.002$ | $0.010\pm 0.002$
[O III] 4363 | $4364.44$ | $0.135\pm 0.006$ | $0.138\pm 0.006$
He I 4473 | $4472.70$ | $0.04\pm 0.01$ | $0.04\pm 0.01$
[Fe III] 4658 | $4659.35$ | $0.008\pm 0.002$ | $0.008\pm 0.002$
[Ar IV] 4713 | $4712.69$ | $0.010\pm 0.003$ | $0.010\pm 0.003$
[Ar IV] 4741 | $4741.45$ | $0.010\pm 0.002$ | $0.010\pm 0.002$
H$\beta$ | $4862.68$ | $1.0\pm 0.1$ | $1.0\pm 0.1$
[O III] 4960 | $4960.30$ | $2.2\pm 0.3$ | $2.2\pm 0.3$
[O III] 5008 | $5008.24$ | $6.8\pm 0.4$ | $6.8\pm 0.4$
[N II] 5756 | $5756.24$ | $<0.0004$ | $<0.0004$
He I 5878 | $5877.59$ | $0.142\pm 0.007$ | $0.139\pm 0.007$
[O I] 6302 | $6302.05$ | $0.026\pm 0.004$ | $0.025\pm 0.004$
[S III] 6312 | $6313.80$ | $0.010\pm 0.001$ | $0.010\pm 0.001$
[N II] 6550 | $6549.85$ | $0.040\pm 0.004$ | $0.039\pm 0.004$
H$\alpha$ | $6564.61$ | $3.0\pm 0.3$ | $2.9\pm 0.3$
[N II] 6585 | $6585.28$ | $0.113\pm 0.005$ | $0.109\pm 0.005$
He I 6679 | $6680.00$ | $0.04\pm 0.02$ | $0.04\pm 0.02$
[S II] 6718 | $6718.29$ | $0.040\pm 0.003$ | $0.039\pm 0.003$
[S II] 6733 | $6732.67$ | $0.044\pm 0.003$ | $0.043\pm 0.003$
He I | $7064.21$ | $0.08\pm 0.01$ | $0.08\pm 0.01$
[Ar III] 7138 | $7137.80$ | $0.062\pm 0.007$ | $0.059\pm 0.006$
[O II] 7322 | $7322.01$ | $0.031\pm 0.002$ | $0.030\pm 0.002$
[O II] 7332 | $7331.68$ | $0.023\pm 0.001$ | $0.022\pm 0.001$
[Ar III] 7753 | $7753.20$ | $0.015\pm 0.001$ | $0.014\pm 0.001$
[S III] 9071 | $9071.10$ | $0.151\pm 0.007$ | $0.139\pm 0.007$

###  3.3 Extinction Correction

Emission line fluxes are first corrected for Milky Way dust reddening using
the dust law of Cardelli et al. (1989). We query the Milky Way dust map of
Schlafly & Finkbeiner (2011) via the NASA/IPAC Infrared Science
Archive333https://irsa.ipac.caltech.edu/applications/DUST/ to obtain the ISM
reddening correction. We find the Galactic $E(B-V)=0.0812\pm 0.003$.

We next correct for dust within the LCE itself. This correction is done using
an iterative process using the H$\alpha$, H$\beta$, H$\gamma$, and H$\delta$
line strengths. We start by calculating the expected Balmer line ratios,
assuming an initial electron temperature of $10^{4}$ K, and an initial
electron density of $10^{3}$ cm-3. The measured line ratios are then compared
to the predicted values to calculate $E(B-V)$, assuming the dust law of
Cardelli et al. (1989). We then apply the error-weighted average dust
correction, weighted by the uncertainty on the Balmer line ratios, to relevant
emission lines, and calculate the electron temperatures using the
[Oiii]$\lambda 4363$, [Oii]$\lambda\lambda 7320,7330$, and [Siii]$\lambda
6312$ lines. The electron density is calculated using the [Sii]$\lambda\lambda
6717,6731$ doublet ratio, as that is the best-measured of the density-
sensitive doublets used in this study. We update the electron temperature
using an error-weighted average of the three calculated temperatures and
repeat the dust correction measurement. This process is continued iteratively
until the change in error-weighted electron temperature is less than 15 K. The
reddening that we calculated from this iterative process is $E(B-V)=0.04\pm
0.1$. The reddening-corrected line intensities are reported in Table 1.

As a consistency check, we also calculated the reddening correction assuming
the dust law of Gordon et al. (2003), calculated for the Large Magellanic
Cloud, to see if low metallicity alters the reddening result. We find
$E(B-V)=0.06\pm 0.1$ in this case, consistent with the value calculated using
Cardelli et al. (1989).

##  4 Direct Electron Temperatures and Chemical Abundances

###  4.1 Electron Temperature and Density

The broad wavelength coverage (rest-frame $\sim 2900-9400$Å) and high SNR of
the stacked LCE spectrum enables calculations of direct electron temperatures
and densities from multiple ions. We detect the auroral emission lines of
[Oiii]$\lambda 4363$, [Oii]$\lambda\lambda 7320,7330$, [Siii]$\lambda 6312$,
and [Sii]$\lambda\lambda 4069,4076$, which are shown in Figure 1. These let us
use the temperature-sensitive auroral-to-nebular line ratios to calculate the
electron temperatures for O++, O+, S++, and S+. Our spectra do not go red
enough to cover the [Siii]$\lambda 9532$ line, so the S++ temperature is
measured from [Siii]$\lambda 6312/\lambda 9069$. While we detect both
[Sii]$\lambda\lambda 4069,4076$ lines, the redder line is barely detected
($<3\sigma$). We therefore choose to use the ratio [Sii]$\lambda
4069/\lambda\lambda 6717,6731$ to calculate the temperature for this ion. We
do not detect the [Nii]$\lambda 5755$ line, and instead set an upper limit on
its strength. This sets an upper limit on the ratio [Nii]$\lambda 5755/\lambda
6584$, and thus an upper limit on the N+ temperature. We also detect the
density-sensitive lines [Sii]$\lambda\lambda 6717,6731$, [Oii]$\lambda\lambda
3727,3729$, and [Ariv]$\lambda\lambda 4713,4741$. We calculate the electron
temperatures and densities from these lines using the getTemDen function from
the python package PYNEB (Luridiana et al., 2015). The resulting measurements
are presented in Table 3.

Uncertainties on temperatures and densities are calculated following the same
method as Welch et al. (2024). We draw 300 points from a Gaussian distribution
centered on the measured line ratio, with standard deviation equal to the
uncertainty on the line ratio. We calculate the temperature or density for
each point, then take the standard deviation of the resulting
temperature/density distribution as our uncertainty. In cases where the final
distribution is highly asymmetric, we use the 16th and 84th percentiles as our
$1\sigma$-low and $1\sigma$-high uncertainties.

We calculate the electron temperatures assuming a fixed density. We use the
best fit value from the [Sii]$\lambda\lambda 6717,6731$ ratio ($n_{e}=1200$
cm-3) as our fiducial density for temperature calculations. Similarly, we use
a fixed temperature for our density calculations. We adopt the O++ temperature
($T_{e}=14000$ K) as our fiducial value for density calculations. The
temperatures and densities are not strongly dependent on each other. We find
that any reasonable change in density (within $\sim 1\sigma$ of the S+
density) does not change our temperature estimates beyond the quoted
uncertainty range, and any reasonable change in temperature (within $\sim
1\sigma$ of the O++ temperature) does not change the density estimate beyond
the quoted uncertainty range.

####  4.1.1 Balmer Jump Temperature

Figure 2: The spectrum of the Sunburst LCE shows a clear Balmer jump at 3646 Å
(marked with the vertical dashed line). The strength of this jump is sensitive
to the electron temperature in the ionized hydrogen gas. The jump is measured
by fitting the continuum on either side of the discontinuity, as described in
Section 4.1.1. The wavelength region used to fit the continuum blueward of the
jump is shown in blue, while the region used to fit the continuum redward of
the jump is shown in red. Linear fits to each continuum region are shown in
the corresponding colors.

Our spectrum covers the Balmer jump at $\lambda 3646$Å, and the high SNR of
the stacked spectrum allow us to detect this continuum feature. The strength
of the jump is sensitive to the electron temperature of the ionized hydrogen
in the nebula. We measure the jump following the procedure of Liu et al.
(2001). The continuum redward and blueward of the jump is measured with a
linear fit (shown in Figure 2). On the red side of the jump, we mask emission
lines prior to fitting. We also mask the region between the jump at $\lambda
3646$Å and the H12 line, where blended high-order Balmer lines will bias the
continuum level. We evaluate the blue linear fit at 3643Å, and the red linear
fit at 3681Å.

Following Equation 3 of Liu et al. (2001), the Balmer jump temperature depends
on the ratio of the jump strength to the H11 line flux, and the helium
abundances He+/H+ and He++/H+. Our helium abundance measurements are described
in greater detail in the following section. We do not detect nebular
Heii$\lambda 4686$; while the line is present, we only see evidence of a broad
component originating in the WR stars (see Rivera-Thorsen et al., 2024). We
therefore assume the He++/H${}^{+}=0$. The dependence on helium abundance is
weak (see also Fig. 9 of Liu et al., 2001). As a test of this weak dependence,
if we assume the He++ abundance is 50% of the He+, the calculated temperature
does not change beyond our quoted $1\sigma$ uncertainties.

With this method, we measure a Balmer jump temperature of
$T_{e}(\textrm{Bal})=12000\pm 300$ K. This temperature is largely consistent
with our other measured electron temperatures.

####  4.1.2 Comparison of Electron Temperatures & Densities

Figure 3: Comparison of electron temperatures measured from auroral lines of
different ions in the Sunburst Arc (black point), plotted alongside local HII
regions from CHAOS (blue points, Berg et al., 2020). The black dashed line
represents equal temperatures. The electron temperature for O+ is biased high
due to significant contribution to the [Oii]$\lambda\lambda 7320,7330$ flux
from dielectronic recombination. We therefore do not consider the O+
temperature reliable. The upper limit placed on the N+ temperature does not
offer a strong constraint when compared to expectations based on other well-
measured temperatures.

We have measured electron temperatures and densities from multiple ionization
zones within the Sunburst LCE nebula. The densities we measure are generally
consistent within $1\sigma$ uncertainties, however there is some evidence that
the high-ionization gas density is higher than the lower ionization states.
While the low ionization estimates from S+
($n_{e}=1200^{+500}_{-300}\textrm{cm}^{-3}$) and O+
($n_{e}=1600^{+1500}_{-200}\textrm{cm}^{-3}$) are very consistent, the density
measured from [Ariv]$\lambda\lambda
4713,4741$($n_{e}=4500^{+10000}_{-2500}\textrm{cm}^{-3}$) is somewhat higher.
However, the [Ariv]$\lambda\lambda 4713,4741$ lines are much fainter than
either [Sii]$\lambda\lambda 6717,6731$ or [Oii]$\lambda\lambda 3727,3729$,
leading to a much larger uncertainty on the resulting density estimate. The
high density reported from [Ariv]$\lambda\lambda 4713,4741$ could thus be
evidence that the high ionization gas is denser than the surrounding low-
ionization gas, however the large uncertainty means that we cannot rule out
these two ionization states having equal density.

Electron temperature measurements show greater variation across ionization
zones and across diagnostics. The lower-ionization gas probed by
$T_{e}(\textrm{S}^{+})$ (10.36–23.34 eV) and $T_{e}(\textrm{S}^{++})$
(23.34–34.86 eV) favors slightly lower electron temperatures ($10000\pm 1000$
and $10300\pm 600$ K, respectively). Meanwhile, the higher ionization states
observed with $T_{e}(\textrm{O}^{++})$ (35.12–54.94 eV) and
$T_{e}(\textrm{Ne}^{++})$ (40.96–63.42 eV) show slightly higher temperatures
($15100\pm 500$ and $15400\pm 1500$ K, respectively). These differences
between ionization zones highlight the value of obtaining $T_{e}$ measurements
from ions at different ionization energies, as empirical temperature relations
do not fully capture such variations.

One notable exception to this trend is $T_{e}(\textrm{O}^{+})=28000\pm 3000$
K, which is an outlier in our measurements. At high densities
($n_{e}>10^{3}\textrm{cm}^{-3}$), dielectronic recombination contributes
substantially to the [OII] emission (Liu et al., 2001); this artificially
increases the inferred O+ electron temperature. All of our densities are above
this threshold, thus we conclude that the O+ temperature is not reliable for
this object.

We also have a measurement of the Balmer jump, which is sensitive to the
electron temperature in the hydrogen gas across the whole nebula. We find that
the Balmer temperature is closer to the measurements from low ionization gas,
though the larger uncertainty on the Balmer temperature means that it is still
consistent with the high ionization temperatures within $1\sigma$ uncertainty.

###  4.2 Abundances and Ionization Corrections

Ionic abundances relative to hydrogen are calculated using

$\frac{N(X^{i})}{N(H^{+})}=\frac{I_{\lambda(i)}}{I_{\textrm{H}\beta}}\frac{j_{\textrm{H}\beta}}{j_{\lambda(i)}}.$
(1)

The emissivity coeffecients $j_{\lambda(i)}$ are temperature dependent. We
calculate these coeffecients using the getIonAbundance function from PYNEB
(Luridiana et al., 2015). We use the temperature from the nearest ionization
zones for each ionic abundance calculation, as described below.

Atomic data used in our calculations are tabulated in Table 2.

Table 2: Atomic Data Sources Ion | Transition Probabilities | Collision Strengths
---|---|---
O+ | Froese Fischer & Tachiev (2004) | Kisielius et al. (2009)
O++ | Froese Fischer & Tachiev (2004) | Aggarwal & Keenan (1999)
N+ | Froese Fischer & Tachiev (2004) | Tayal (2011)
S+ | Rynkun et al. (2019) | Tayal & Zatsarinny (2010)
S++ | Tayal et al. (2019) | Grieve et al. (2014)
Ar++ | Mendoza & Zeippen (1983) | Munoz Burgos et al. (2009)
Ar+3 | Rynkun et al. (2019) | Ramsbottom et al. (1997)
Ne++ | Froese Fischer & Tachiev (2004) | McLaughlin & Bell (2000)

####  4.2.1 Oxygen Abundance

We calculate the total oxygen abundance
$\textrm{O}/\textrm{H}=\textrm{O}^{+}/\textrm{H}^{+}+\textrm{O}^{++}/\textrm{H}^{+}$.
We use the electron temperature $T_{e}(\textrm{O}^{++})$ determined from
[Oiii]$\lambda 4363$ to calculate the $\textrm{O}^{++}/\textrm{H}^{+}$ ionic
abundance.

For O+, the electron temperature measured from the [Oii]$\lambda\lambda
7320,7330$ lines is not reliable at the densities measured, as discussed in
the Section 4.1.2. We therefore use the S+ temperature as our low-density
electron temperature, as the [Sii]$\lambda\lambda 4069,4076$ lines are not
similarly inflated. Calculating the $\textrm{O}^{+}/\textrm{H}^{+}$ abundance
using the high O+ temperature leads to a $\sim 10\times$ reduction in the
inferred ionic abundance.

The final oxygen ion abundances are reported in Table 3. We find a total
metallicity for this object of $12+\log(\textrm{O}/\textrm{H})=7.97\pm 0.05$.

####  4.2.2 Nitrogen Abundance

We make the assumption that N/O $\simeq\textrm{N}^{+}/\textrm{O}^{+}$, based
on the similar ionization zones of the N+ and O+ ions (Peimbert, 1967). This
assumption has been found to be valid within $\sim 10\%$ (Nava et al., 2006;
Amayo et al., 2021).

Because we do not detect the [Nii]$\lambda 5755$ line, we use the temperature
from the [Sii]$\lambda 4069/\lambda\lambda 6717,6731$ ratio as our low-
ionization temperature when calculating the nitrogen abundance. One potential
caveat when using the S+ temperature is that the lower bound of the S+
ionization energy (10.36 eV) is lower than the hydrogen ionization energy
(13.6 eV). Thus S+ can form outside the H+ boundary. We note however that the
Balmer jump, sensitive to the electron temperature of H+, yields a temperature
that is consistent within uncertainties of the S+ temperature. Thus we would
not expect a significant change in our measured N+ abundance from this effect.

####  4.2.3 Sulfur Abundance

Our spectrum contains the temperature sensitive lines for both S+ and S++,
which we use to calculate the abundance of the lower ionization states of
sulfur. We do not have a measurement of a higher ionization state of sulfur,
so we must correct for the unobserved high ionization sulfur. There may be a
small contribution from S+3 ($34.86-47.22$ eV ionization energy). We use the
ionization correction factor (ICF) of Izotov et al. (2006), specifically the
“low-Z” component of their Equation 20, to make this correction. We find that
the ICF is consistent with 1 within uncertainties, indicating that we have
measured the primary states of sulfur within the nebula.

We use the direct S+ and S++ temperatures to measure the abundances of these
sulfur ions.

####  4.2.4 Argon Abundance

We detect both [Ariii]$\lambda 7138$ and [Ariv]$\lambda\lambda 4713,4741$,
allowing us to calculate the ionic abundances of both Ar++ and Ar+3. We
correct for unobserved higher ionization states of argon using the ICF in
Equation 23 of Izotov et al. (2006), specifically using the “low-Z” component
based on our measured oxygen abundance. Most of the gas-phase argon is in the
two ionization states which we have measured, resulting in an ICF of $1\pm
0.2$ and a decreased systematic uncertainty on the total argon abundance.

The ionization energy range of Ar++ does not neatly align with any ion for
which we have a temperature measurement; it lies between the S++ and O++
zones. The overlap with S++ is slightly greater, so we choose to use
$T_{e}(\textrm{S}^{++})$ when calculating Ar++/H+. We did test the effect of
using the O++ temperature, and found that the resulting Ar++/H+ ionic
abundance is lower by a factor $\sim 2$. Ar+3 better aligns with O++, so we
use $T_{e}(\textrm{O}^{++})$ when calculating Ar3+/H+.

####  4.2.5 Neon Abundance

We only detect neon in the Ne++ state, requiring a correction for unobserved
ionization states. We again use the ICF of Izotov et al. (2006) for this
correction. The neon abundance and ICF are reported in Table 3. We use the
electron temperature from O++ to calculate the neon ionic abundance. While we
have a direct measurement of $T_{e}(Ne^{++})$, this temperature has a
relatively large uncertainty (owing to the faintness of the [Neiii]$\lambda
3343$ line). Additionally, it is consistent within $1\sigma$ uncertainties of
$T_{e}(O^{++})$. Thus using the doubly ionized oxygen temperature reduces the
statistical uncertainty on the neon abundance measurement without introducing
any additional systematic uncertainty, as the two temperatures have been found
to be consistent.

We find that the ionization correction for neon is $1.1\pm 0.1$, indicating
that the majority of the neon is contained within the measured Ne++ state.

####  4.2.6 Iron Abundance

We calculate the gas-phase iron abundance based on the strength of the nebular
[Feiii]$\lambda 4658$ line. To account for the unobserved ionization states of
iron, we use the ICF from Equation 24 of Izotov et al. (2006). The ionization
energy of Fe++ (16.2–30.7 eV) overlaps both the low and intermediate
ionization zones. We choose to use the low-ionization temperature from S+ for
the iron abundance calculation, though the final result would not change
significantly if we instead used the S++ temperature.

The iron abundance here relies on only a single ionization state, and as such
the ICF ($6\pm 2$) is large. This abundance is thus subject to additional
systematic uncertainties. While we detect [Feii]$\lambda 4360$, this line is
strongly affected by flourescence and is thus not suitable for abundance
determinations. The [Feii]$\lambda 4288$ line appears to be partially
detected, however it straddles the detector gap in the NIRSpec IFS data so we
cannot measure a reliable flux. We do not detect any higher-ionization iron
lines, though we may expect some contribution from Fe+3, which has similar
ionization energy to O++.

###  4.3 Helium Abundance

We measure a variety of He I lines that allow us to calculate the helium
abundance, which is needed for the Balmer jump temperature calculation. While
we detect Heii$\lambda 4686$ emission, we only see evidence of the broad
stellar component, without significant contribution from a narrow nebular
component. We therefore assume that the He${}^{++}/$H+ abundance is small
relative to He${}^{+}/$H+, and thus He/H = He${}^{+}/$H+.

The He I ionization energy is most similar to that of O++, so we use
$T_{e}(\textrm{O}^{++})$ when calculating the helium abundance. We have a
number of He I lines available to calculate the ionic abundance. We find that
the various lines give similar abundance results (reported in Table 3. For our
final value, we use an error-weighted average of the abundance measurements
from each line.

##  5 Discussion

Table 3: Temperature, Density, and Abundance Measurements from the Ly-C Leaking Cluster Property | Measurement
---|---
$T_{e}(\textrm{O}^{++})$ ($10^{3}$K) | $15.1\pm 0.5$
$T_{e}(\textrm{O}^{+})$ ($10^{3}$K) | $28\pm 3$
$T_{e}(\textrm{S}^{++})$ ($10^{3}$K) | $10.3\pm 0.6$
$T_{e}(\textrm{S}^{+})$ ($10^{3}$K) | $10\pm 1$
$T_{e}(\textrm{N}^{+})$ ($10^{3}$K) | $<26.3$
$T_{e}(\textrm{Ne}^{++})$ ($10^{3}$K) | $15.4\pm 1.5$
$T_{e}$(Balmer) ($10^{3}$K) | $12\pm 3$
$n_{e}(\textrm{O}^{+})$ (cm-3) | $1600^{+1500}_{-200}$
$n_{e}(\textrm{S}^{+})$ (cm-3) | $1200^{+500}_{-400}$
$n_{e}(\textrm{Ar}^{+3})$ (cm-3) | $4500^{+10000}_{-2500}$
O+/H+ ($\times 10^{5}$) | $2.0^{+1.1}_{-0.7}$
O++/H+ ($\times 10^{5}$) | $7.3\pm 1.2$
$12+\log(\textrm{O}/\textrm{H})$ | $7.97\pm 0.05$
$\textrm{S}^{+}/\textrm{H}^{+}$ ($\times 10^{7}$) | $2.3\pm 0.7$
$\textrm{S}^{++}/\textrm{H}^{+}$ ($\times 10^{7}$) | $21\pm 4$
S ICF | $1.3\pm 0.3$
$12+\log(\textrm{S}/\textrm{H})$ | $6.48\pm 0.05$
log(S/O) | $-1.49\pm 0.14$
$\textrm{N}^{+}/\textrm{H}^{+}$ ($\times 10^{7}$) | $46\pm 7$
log(N/O) | $-0.65^{+0.16}_{-0.25}$
$\textrm{Ar}^{++}/\textrm{H}^{+}$ ($\times 10^{7}$) | $4.5\pm 0.9$
$\textrm{Ar}^{+3}/\textrm{H}^{+}$ ($\times 10^{7}$) | $0.7\pm 0.2$
Ar ICF | $1.0\pm 0.2$
$12+\log(\textrm{Ar}/\textrm{H})$ | $5.72\pm 0.04$
log(Ar/O) | $-2.24\pm 0.14$
$\textrm{Ne}^{++}/\textrm{H}^{+}$ ($\times 10^{5}$) | $1.5\pm 0.3$
Ne ICF | $1.1\pm 0.1$
$12+\log(\textrm{Ne}/\textrm{H})$ | $7.21\pm 0.04$
log(Ne/O) | $-0.66\pm 0.11$
$\textrm{Fe}^{++}/\textrm{H}^{+}$ ($\times 10^{7}$) | $3.1\pm 0.1$
Fe ICF | $6\pm 2$
$12+\log(\textrm{Fe}/\textrm{H})$ | $6.28\pm 0.06$
log(Fe/O) | $-1.7\pm 0.2$
$\textrm{He}^{+}/\textrm{H}^{+}(\lambda 4471)$ | $0.08\pm 0.01$
$\textrm{He}^{+}/\textrm{H}^{+}(\lambda 5876)$ | $0.09\pm 0.01$
$\textrm{He}^{+}/\textrm{H}^{+}(\lambda 6678)$ | $0.09\pm 0.01$
Mean $\textrm{He}^{+}/\textrm{H}^{+}$ | $0.08\pm 0.02$
$12+\log(\textrm{He}/\textrm{H})$ | $10.93\pm 0.09$

###  5.1 High-Quality Abundances of Multiple Species at $z=2.37$

We have detected the auroral lines [Sii]$\lambda\lambda 4069,4076$,
[Oiii]$\lambda 4363$, [Siii]$\lambda 6312$, and [Oii]$\lambda\lambda
7320,7330$, allowing us to measure the electron temperature in the low,
intermediate, and high ionization zones of the nebula. The resulting
temperatures are reported in Table 3, and plotted in Figure 3 alongside
temperature measurements from local HII regions from the CHAOS project (Berg
et al., 2015; Croxall et al., 2015, 2016; Berg et al., 2020). We do not detect
[Nii]$\lambda 5755$, so we only set an upper limit on the N+ temperature.

These electron temperatures allow us to calculate abundances of multiple
species via the direct method. The resulting ionic abundance, ICFs, and
abundances relative to oxygen are reported in Table 3. Our spectrum includes
emission lines from the dominant ionization states of oxygen, nitrogen,
sulfur, argon, and neon, minimizing the uncertainties propagated to our
abundances from ionization correction factors.

This combination of directly measured electron temperatures for each of the
low, intermediate, and high ionization zones, plus detection of the relevant
emission lines for the primary states of multiple elements, enables the same
quality of abundance measurements as has been used in nearby galaxies. We can
therefore directly compare the gas-phase abundances of this young star cluster
at $z=2.37$ to abundances measured in nearby HII regions. This is the first
time chemical abundance patterns have been measured to this level of precision
in a galaxy beyond the local universe.

We plot the abundances of nitrogen, sulfur, argon, neon, and iron relative to
oxygen in Figure 4. We compare our abundances to measurements from local HII
regions from CHAOS (Berg et al., 2015; Croxall et al., 2015, 2016; Berg et
al., 2020), low-redshift galaxies from SDSS (Izotov et al., 2006), and other
galaxies measured at cosmic noon (Sanders et al., 2023b; Rogers et al., 2024;
Welch et al., 2024). Solar abundances from Asplund et al. (2021) are also
marked. We find that our measured abundances of sulfur, argon, and neon are
all consistent with solar abundance patterns. Additionally, these elements are
consistent with local HII regions, indicating the enrichment of alpha elements
in the LCE is following standard patterns, in contrast with the low alpha
abundances for a $z\sim 3$ galaxy reported in Rogers et al. (2024). Our
nitrogen abundance is high compared to local HII regions, similar to the
$z\sim 2$ galaxies reported in Sanders et al. (2023b). We discuss this
enhanced nitrogen abundance in the following section. We find an iron
abundance that is slightly below the solar value, however it matches the Fe/O
abundances of low-redshift galaxies with similar oxygen abundances (Izotov et
al., 2006). Our measured Fe/O is still higher than what has been observed in
the Magellanic Clouds (Domínguez-Guzmán et al., 2022), however our measured
dust $E(B-V)$ is also lower, indicating that there is less dust available onto
which the iron can condense.

Figure 4: Abundances of the LyC leaking clump, compared to local HII regions
(Berg et al., 2020), low-redshift galaxies (Izotov et al., 2006), and other
galaxies at Cosmic Noon (Rogers et al., 2024; Sanders et al., 2023b; Welch et
al., 2024). Solar abundances from Asplund et al. (2021) are shown as black
dashed lines. We find an enhanced nitrogen abundance, while other elements are
consistent with local HII regions and low-redshift star-forming galaxies.

###  5.2 Nitrogen Enrichment from Wolf-Rayet Stars

The oxygen abundance of the LCE places it just below the point at which
measurements of local HII regions have begun to find significant contribution
from secondary nitrogen production. We might therefore expect it to only be
affected by primary nitrogen production, placing it along the N/O plateau for
low-metallicity galaxies and HII regions (e.g. within uncertainties of the
photoionization model prediction from Nicholls et al. (2017)). Additionally,
the young stellar age that has been previously reported for this star cluster
($<4$ Myr, Chisholm et al. (2019)) would typically be indicative of only
primary nitrogen production driving the N/O abundance. The elevated N/O
measured for the LCE is in tension with this interpretation, indicating
another source of nitrogen enrichment is driving the abundance.

Elevated nitrogen abundances have been observed previously in low-redshift
galaxies (e.g., Brinchmann et al., 2008; Amorín et al., 2010; Berg et al.,
2011), galaxies at cosmic noon (e.g., Masters et al., 2014; Sanders et al.,
2023b), and more recently in high redshift galaxies (Cameron et al., 2023;
Senchyna et al., 2023; Marques-Chaves et al., 2024; Castellano et al., 2024).
The elevated nitrogen has often been attributed to nitrogen enrichment from
Wolf-Rayet stars (Henry et al., 2000; Kobayashi & Ferrara, 2024). However it
has also been suggested that inflows of low-metallicity gas can dilute the
oxygen abundance, driving increases in the N/O ratio without requiring
enrichment from Wolf-Rayet stars (e.g., Köppen & Hensler, 2005; Amorín et al.,
2010; Andrews & Martini, 2013).

A companion paper utilizing the same stacked spectrum determined that the LCE
contains spectral signatures of Wolf-Rayet stars (Rivera-Thorsen et al.,
2024). Previous analyses of galaxies showing WR signatures at low redshift
have found that abundances of alpha elements (Ar & Ne) relative to oxygen were
not elevated (Brinchmann et al., 2008). Recent theoretical analysis of WR
abundance patterns from Kobayashi & Ferrara (2024) find a similar result, that
only the nitrogen abundance will change significantly with enrichment from WR
stars. We see a similar abundance pattern here, with only N/O elevated
relative to similarly low-O/H galaxies and HII regions. The similar abundance
pattern could be indicative of WR stars driving the elevated N/O in the
Sunburst LCE. However earlier studies have suggested that the WR stellar winds
driving the enhanced nitrogen abundance would also carry significant helium
(Kobulnicky et al., 1997). We find a helium abundance
$12+\log(\textrm{He}/\textrm{H})=10.93\pm 0.09$ that is consistent with solar
($12+\log(\textrm{He}/\textrm{H})_{\odot}=10.914\pm 0.013$, Asplund et al.,
2021). Brinchmann et al. (2008) also find no evidence for elevated helium
abundance in their WR galaxy sample, yet still conclude that the elevated N/O
is likely due to WR stellar winds. We thus make the same conclusion here, that
WR stellar winds are driving increased N/O abundance in the Sunburst LCE. A
recent analysis of several high-redshift ($z\sim 6$) galaxies with elevated
N/O also found evidence for elevated He/H (Yanagisawa et al., 2024). These
authors suggest that elevated densities ($n_{e}\sim 10^{3}-10^{4}$) could be
related to the high helium abundance. We measure a similar density ($n_{e}\sim
1200-4500$) but see no increase in helium abundance.

The type of WR stars present can also influence the measured chemical
abundances. Analyses of wind abundances in WN and WC stars found that WNs
exhibit fairly typical neon abundance, while WC stars show significantly
elevated levels of neon (Smith & Houck, 2005; Ignace et al., 2007). We see no
evidence of enhanced neon abundance here, which could be indicative of a
majority of the WR stars present being WN-type. In exploratory fitting by
Rivera-Thorsen et al. (2024), the best-fitting BPASS model had only 13% of the
WR stars of WC-type, offering some support to this hypothesis. However, more
detailed analysis would be required to constrain the relative quantities of WC
and WN stars.

A previous analysis of the LCE using rest-frame UV spectra also measured a
high N/O abundance (Pascale et al., 2023). However, their measurement
($\log(\textrm{N}/\textrm{O})=-0.21\pm 0.1$) is higher than our direct
measurement by $\sim 0.3$ dex, though the two are still consistent within
$2\sigma$. Pascale et al. (2023) hypothesize that the nitrogen enrichment is
most enhanced in the high-density, high-ionization regions of the cluster. Our
measurement using N+ being slightly lower than their measurement based on N++
would be consistent with this picture. However we also note that the [NII]
transitions used here have lower critical densities than the higher-ionization
lines, so collisional de-excitation could be lowering the measured flux. Given
the high measured densities here, it is possible that our measured N/O is
slightly low, owing to the effects of collisional de-excitation.

##  6 Conclusions

We have measured direct gas-phase chemical abundances in the stacked spectrum
of the Lyman-continuum emitting star cluster in the Sunburst Arc. We detect
the [Sii]$\lambda\lambda 4069,4076$, [Oiii]$\lambda 4363$, [Siii]$\lambda
6312$, and [Oii]$\lambda\lambda 7320,7330$ lines, allowing measurement of the
electron temperature in the low, intermediate, and high ionization zones of
the nebular gas. With these multiple temperature measurements, we measure
direct abundances of oxygen, nitrogen, sulfur, argon, neon, and iron,
following best practices established in nearby galaxies from the CHAOS
program. These measurements enable a direct comparison between well-studied
nearby HII regions and an object at Cosmic Noon ($z=2.37$).

These high-quality abundance measurements enable detailed studies of the
origins of abundance patterns in distant galaxies. In the Sunburst LCE, the
combination of these abundance measurements and the detection of Wolf-Rayet
features (Rivera-Thorsen et al., 2024) allow us to conclude that nitrogen-rich
Wolf-Rayet stars are responsible for increasing the nitrogen abundance.

Further high-quality abundance measurements of galaxies and galactic
substructures at Cosmic Noon and beyond will continue to drive our
understanding of how galaxies built up the chemical elements.

The authors wish to dedicate this paper to the memory of Prof. Liese Van Zee,
a pioneer of chemical abundance measurements in galaxies. This work was based
on observations taken with the NASA/ESA/CSA JWST. JWST is operated by the
Space Telescope Science Institute under the management of the Association of
Universities for Research in Astronomy, Inc., under NASA contract no. NAS
5-03127. These observations were taken as part of JWST GO program 2555,
support for which was provided by NASA through a grant from the Space
Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127.
BW is supported by NASA under award number 80GSFC21M0002.

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