We present JWSTNIRSpec highresolution G395HF290LP spectroscopy of MACS0647JD a gravitationally lensed galaxy merger at z  10.167. The new spectroscopy which is acquired for the two lensed images JD1 and JD2 detects and resolves emission lines in the restframe ultraviolet and blue optical including the resolved O II  3726 3729 doublet Ne III 3870 He I 3890 H H and O III 4363. This is the first observation of the resolved O II  3726 3729 doublet for a galaxy at z gt 8. We measure a line flux ratio O II 37293726  0.9  0.3 which corresponds to an estimated electron density of inlineformula mmlmath overflowscrollmmlmilogmmlmimmlmo stretchyfalsemmlmommlmsubmmlmrowmmlminmmlmimmlmrowmmlmrowmmlmiemmlmimmlmrowmmlmsubmmlmrowmmlmo stretchytruemmlmommlmrowmmlmsupmmlmrowmmlmicmmmlmimmlmrowmmlmrowmmlmommlmommlmn3mmlmnmmlmrowmmlmsupmmlmo stretchyfalsemmlmommlmommlmommlmn2.9mmlmnmmlmommlmommlmn0.5mmlmnmmlmath inlineformula. This is significantly higher than the electron densities of local galaxies reported in the literature. We compile measurements from the literature and further analyze the redshift evolution of n SUB e SUB. We find that the redshift evolution follows the powerlaw form of n SUB e SUB  A  1  zSUP p SUP with inlineformula mmlmath overflowscrollmmlmiAmmlmimmlmommlmommlmsubsupmmlmrowmmlmn54mmlmnmmlmrowmmlmrowmmlmommlmommlmn23mmlmnmmlmrowmmlmrowmmlmommlmommlmn31mmlmnmmlmrowmmlmsubsupmmlmath inlineformula cmSUP3SUP and inlineformula mmlmath overflowscrollmmlmipmmlmimmlmommlmommlmsubsupmmlmrowmmlmn1.2mmlmnmmlmrowmmlmrowmmlmommlmommlmn0.4mmlmnmmlmrowmmlmrowmmlmommlmommlmn0.4mmlmnmmlmrowmmlmsubsupmmlmath inlineformula. This powerlaw form may be explained by a combination of metallicity and morphological evolution of galaxies which become on average more metal poor and more compact with increasing redshift.
['Galaxies', 'High-redshift galaxies', 'Early universe', 'Strong gravitational lensing', 'Galaxy spectroscopy', '573', '734', '435', '1643', '2171', 'Astrophysics - Astrophysics of Galaxies']
JWST NIRSpec Highresolution Spectroscopy of MACS0647JD at z  10.167 Resolved O II Doublet and Electron Density in an Early Galaxy
{'JWST NIRSpec High-resolution Spectroscopy of MACS0647 -JD at z = 10 . 167 : Resolved [OII] Doublet and Electron Density in an Early Galaxy': "<!-- image -->  \nAdi Zitrin  \n1 Department of Physics and Astronomy, The Johns Hopkins University, 3400 N Charles St. Baltimore, MD 21218, USA 2 Space Telescope Science Institute (STScI), 3700 San Martin Drive, Baltimore, MD 21218, USA 3 School of Physics and Astronomy, Rochester Institute of Technology, 84 Lomb Memorial Drive, Rochester, NY 14623, USA 4 Association of Universities for Research in Astronomy (AURA), Inc. for the European Space Agency (ESA) 5 Centro de Astrobiolog'ıa (CAB), CSIC-INTA, Ctra. de Ajalvir km 4, Torrej'on de Ardoz, E-28850, Madrid, Spain 6 Department of Astronomy, The Oskar Klein Centre, Stockholm University, AlbaNova, SE-10691 Stockholm, Sweden  \n- 7 European Space Agency (ESA), European Space Astronomy Centre (ESAC), Camino Bajo del Castillo s/n, 28692 Villanueva de la Ca˜nada, Madrid, Spain\n- 8 Department of Astronomy, Stockholm University, Oscar Klein Centre, AlbaNova University Centre, 106 91 Stockholm, Sweden 9 Jodrell Bank Centre for Astrophysics, University of Manchester, Oxford Road, Manchester UK  \n10  \nKapteyn Astronomical Institute, University of Groningen, 9700 AV Groningen, The Netherlands  \n- 11 Instituto de F'ısica de Cantabria (CSIC-UC). Avda. Los Castros s/n. 39005 Santander, Spain 12 The University of Texas at Austin, Department of Astronomy, Austin, TX, United States\n- 13 Physics Department, Ben-Gurion University of the Negev, P.O. Box 653, Be'er-Sheva 84105, Israel\n- 14 Observational Cosmology Lab, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  \n15  \nSpace Telescope Science Institute, 3700 San Martin Drive Baltimore, MD 21218, United States  \n16 Instituto de Estudios Astrof'ısicos, Facultad de Ingenier'ıa y Ciencias, Universidad Diego Portales, Av. Ej'ercito 441, Santiago 8370191, Chile  \n- 17 Kapteyn Astronomical Institute, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands 18 Department of Astronomy, University of Maryland, College Park, 20742, USA  \n19 INAF - OAS, Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, via Gobetti 93/3, I-40129 Bologna, Italy 20 School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA 21 Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208, USA", 'ABSTRACT': "We present JWST/NIRSpec high-resolution spectroscopy G395H/F290LP of MACS0647 -JD, a gravitationally lensed galaxy merger at z = 10 . 167. The new spectroscopy, which is acquired for the two lensed images (JD1 and JD2), detects and resolves emission lines in the rest-frame ultraviolet (UV) and blue optical, including the resolved [O ii ] λλ 3726,3729 doublet, [Ne iii ] λ 3870, HeI λ 3890, H δ , H γ , and [O iii ] λ 4363. This is the first observation of the resolved [O ii ] λλ 3726,3729 doublet for a galaxy at z > 8. We measure a line flux ratio [O ii ] λ 3729/ λ 3726 = 0 . 9 ± 0 . 3, which corresponds to an estimated electron density of log( n e / cm -3 ) = 2 . 9 ± 0 . 5. This is significantly higher than the electron densities of local galaxies reported in the literature. We compile the measurements from the literature and further analyze the redshift evolution of n e . We find that the redshift evolution follows  \nCorresponding author: Abdurro'uf  \nthe power-law form of n e = A × (1 + z ) p with A = 54 +31 -23 cm -3 and p = 1 . 2 +0 . 4 -0 . 4 . This power-law form may be explained by a combination of metallicity and morphological evolution of galaxies, which become, on average, more metal-poor and more compact with increasing redshift.  \nKeywords: Galaxies (573), High-redshift galaxies (734), Early universe (435), Strong gravitational lensing (1643), Galaxy spectroscopy (2171)", '1. INTRODUCTION': "Understanding the physical conditions in star-forming galaxies, including the interstellar medium (ISM), is essential for a complete picture of the evolution of the stellar and gaseous content of galaxies. Spectroscopy of galaxies in the rest-frame ultraviolet (UV) and optical provides a wealth of emission line diagnostics for characterizing the ISM in galaxies (e.g., see review by Kewley et al. 2019b). The relative strengths of the emission lines are mainly driven by the ISM properties, including the chemical abundance, shape of the ionizing radiation field, ionization state, gas density, and temperature (e.g., Kewley & Dopita 2002; Dopita et al. 2006a,b).  \nBefore the launch of the JWST, the observations of rest-frame UV and optical spectra of high-redshift ( z ≳ 3) galaxies were very challenging because of the lack of highly sensitive (i.e., deep) near-infrared (NIR) spectroscopy. Only a few spectroscopic surveys have been conducted to observe rest-frame UV and optical spectroscopy of highz galaxies out to z ∼ 4 using 8-10 mclass telescopes (e.g., Kriek et al. 2015; Le F'evre et al. 2015; Bacon et al. 2017; Pentericci et al. 2018; Urrutia et al. 2019).  \nSince the launch of JWST (Rigby et al. 2023; Gardner et al. 2023), with its NIR and mid-infrared (MIR) spectroscopic capabilities, the rest-frame UV and optical emission lines of z > 2 galaxies have become easily accessible, enabling the study of the ISM properties in galaxies at high redshift (toward the reionization era). Several studies use JWST/Near Infrared Spectrograph (NIRSpec) spectroscopy (Jakobsen et al. 2022; Boker et al. 2023) to study the properties of ISM in galaxies up to z ∼ 9 (e.g., Fujimoto et al. 2022; Curti et al. 2023; Fujimoto et al. 2023; Tang et al. 2023; Bunker et al. 2023; Heintz et al. 2023a,b; Reddy et al. 2023; Nakajima et al. 2023; Hsiao et al. 2023a; Isobe et al. 2023; Jung et al. 2023; Cameron et al. 2023; Sanders et al. 2024; Backhaus et al. 2024). Those studies found that highz galaxies have significantly lower gas-phase metallicity (e.g., Fujimoto et al. 2023; Heintz et al. 2023a; Nakajima et al.  \n2023; Williams et al. 2023) and higher electron density ( n e ; e.g., Reddy et al. 2023; Isobe et al. 2023) than lowz galaxies.  \nThe electron density of the H ii regions is one of the important properties of the ISM because together with ISM pressure, they govern the emission from H ii regions, such that the derived quantities from the nebular emission lines depend critically on assumptions about n e and pressure of the nebula (Kewley et al. 2019a). This quantity can be estimated using density-sensitive emission line ratios, including [O ii ] λ 3729/ λ 3726, [S ii ] λ 6716/ λ 6731, C iii ] λ 1909/ λ 1907 (e.g., Kewley et al. 2019b). In starforming regions, the excitation energy between the two lines of those doublets is proportional to the thermal electron density. Therefore, the relative excitation rates depend only on the collision strengths of the electrons (Osterbrock 1989). This makes the flux ratio between the two lines in the doublets a perfect diagnostic for the electron density. While they are all density tracers, the derived n e from those lines are not necessarily comparable with each other because they are tracing different ionization regions. For instance, [O ii ] λ 3729/ λ 3726 and [S ii ] λ 6716/ λ 6731 trace low-ionization regions, while C iii ] λ 1909/ λ 1907 traces intermediate-ionization regions (e.g., Berg et al. 2021; Mingozzi et al. 2022).  \nBefore JWST, several large spectroscopic surveys investigated the evolution of the electron density based on [O ii ] λλ 3726,3729 and [S ii ] λλ 6716,6731 (i.e., from low-ionization regions). They found that n e declines from ∼ 200 cm -3 at z ∼ 3 to ∼ 30 cm -3 at z ∼ 0 (e.g., Steidel et al. 2014; Sanders et al. 2016; Kaasinen et al. 2017; Kashino et al. 2017; Harshan et al. 2020; Davies et al. 2021; Berg et al. 2022). Due to the lack of highly sensitive NIR spectroscopy, there was a lack of n e studies at z ≳ 3. A few exceptions come from studies that estimated n e based on doubly-ionized regions, such as Killi et al. (2023) who observed a galaxy at z = 7 . 133 with Atacama Large Millimeter Array (ALMA) and estimated n e ≲ 500 cm -3 based on the [O iii ] λ 52 µ m/[O iii ] λ 88 µ m ratio. However, this diagnostic probes a very different ISM region  \n(i.e., dust-obscured) and ionization level compared to the [O ii ] λλ 3726,3729 and [S ii ] λλ 6716,6731 doublets.  \nAfter the launch of JWST, several studies have already explored n e out to z ∼ 9 using various diagnostics. Isobe et al. (2023) used the spectroscopic data from public JWST surveys to measure n e of 14 galaxies at z = 4 . 02 -8 . 68. Among the sample, only three galaxies (with the highest z = 7 . 87) observed with NIRSpec high-resolution grating by the GLASS survey (Treu et al. 2022) showed resolved [O ii ] λλ 3726,3729 doublet, while the doublet remains unresolved in the rest of the sample. They estimated n e ≳ 300 cm -3 . Reddy et al. (2023) investigated the connections between the ionization parameter ( U ), electron density, and star formation rate (SFR) based on 48 galaxies at 2 . 7 < z < 6 . 3. They measured n e based on the [S ii ] λλ 6716,6731 doublet resolved in NIRSpec medium-resolution spectra from the Cosmic Evolution Early Release Science (CEERS; Finkelstein et al. 2023; Fujimoto et al. 2023). Using stacked spectra of two equal-number bins of O32=[O iii ] λλ 4959,5007/[O ii ] λλ 3726,3729, they estimated that galaxies with higher O32 have average n e ≃ 500 cm -3 that are ≳ 5 times larger than that of lowerO32 galaxies. The two bins have an average O32 of 1 . 978 ± 0 . 057 and 6 . 055 ± 0 . 174, while the entire sample has an average O32 of 3 . 457 ± 0 . 074. They also found a highly significant positive correlation between U and SFR surface density (Σ SFR ), which appears to be independent of redshift at 1 . 6 ≲ z ≲ 6 . 3.  \nWhile JWST/NIRSpec prism spectroscopy cannot resolve [O ii ] λλ 3726,3729 and [S ii ] λλ 6716,6731 lines due to low spectral resolution ( R ∼ 30 -300), some studies have combined [O iii ] λ 5007 observed by this instrument with [O iii ] λ 88 µ m observed with ALMA to indirectly estimate n e of galaxies at z = 9 . 11 ( ∼ 400 cm -3 ; Stiavelli et al. 2023) and z = 8 . 496 ( ∼ 220 cm -3 ; Fujimoto et al. 2022) using photoionization modeling. Until now, no studies have directly measured n e from resolved [O ii ] λλ 3726,3729 doublet at z > 8, while [S ii ] λλ 6716,6731 is redshifted beyond the wavelength coverage of NIRSpec. Detecting [O ii ] λλ 3726,3729 doublet remains challenging because most galaxies at such high redshift are faint. More importantly, those galaxies typically have a high O32 ratio and ionization parameter, such that more oxygen atoms are ionized to [OIII], thereby making [OII] relatively weaker, even for the same observed brightness. Moreover, high-resolution ( R > 2000) spectroscopy is needed to be able to resolve the doublets, which is only achievable using the NIRSpec high-resolution grating. Recently, the [O ii ] λλ 3726,3729 doublet has been observed in the spectrum of GN-z11 by Bunker et al. (2023), one of the brightest galaxies  \nknown at z > 10 (Oesch et al. 2016; Tacchella et al. 2023). However, the NIRSpec medium-resolution grating cannot resolve the single lines.  \nIn this paper, we present NIRSpec high-resolution ( R ∼ 2700) spectroscopy of MACS0647 -JD, a triplylensed galaxy at z = 10 . 167 (Coe et al. 2013; Hsiao et al. 2023b,a). Previously, JWST/NIRCam imaging and NIRSpec prism spectroscopy have been obtained for this galaxy by GO 1433 (PI Coe). The NIRCam imaging resolved the galaxy into two components A and B, suggesting a possible galaxy merger (Hsiao et al. 2023b). NIRSpec prism spectra of JD1 and JD2 (the two brightest lensed images of MACS0647 -JD) were presented in Hsiao et al. (2023a), revealing 7 strong emission lines and becoming one of the highest redshift galaxies with detected rest-frame UV emission lines besides GHZ2/GLASS-z12 (Castellano et al. 2024), GNz11 (Bunker et al. 2023), and JADES-GS-z11-0 (Hainline et al. 2024). Here, we observe JD1 and JD2 with the high-resolution G395H/F290LP setting to further resolve the lines and obtain better measurements of their fluxes and widths. We resolve [O ii ] λλ 3726,3729 doublet for the first time at z > 8 and use it to estimate n e .  \nThe paper is organized as follows. We describe the NIRSpec data and its reduction in Section 2. The measurements of emission lines are described in Section 3. We present and discuss our results in Section 4, and finally conclude in Section 5. Throughout, we assume the cosmological parameters of Ω m = 0 . 3, Ω Λ = 0 . 7, and H 0 = 70 km s -1 Mpc -1 .", '2.1. NIRSpec MSA Spectroscopy': "The NIRSpec micro-shutter assembly (MSA) Spectroscopy Ferruit et al. (2022) observation was conducted on January 14, 2024, as part of GO 4246 (PI Abdurro'uf), which focuses on MACS0647 -JD at z = 10 . 17. We use the high-resolution grating G395H/F290LP that covers a wavelength range of 2 . 87-5 . 14 µ m with spectral resolution ranges from R ∼ 1900 to 3500 over the wavelength range. The total exposure time was 2.43 hours. Half of that time was observed with standard 3-slitlet nods. With the other half, we used single slitlets and performed two dithers. The slitlets on JD1 and JD2 mainly cover the brightest Component A (see Figure 1). This is similar to the NIRSpec prism observation previously performed (Hsiao et al. 2023a). The data are all publicly available on  \nMAST, but not the reduction we analyzed in this paper which will be described below. 1", '2.2. NIRSpec Data Reduction': "The data were reduced with the JWST pipeline version 1.12.5 (Bushouse et al. 2023), using CRDS version 11.17.6 and jwst 1183.pmap with the 2D spectra obtained from the Mikulski Archive for Space Telescopes (MAST). The 2D frames were visually inspected for artifacts and the snowballs and residual cosmic rays were manually masked. Additional sigma clipping with a threshold of 6 σ was then applied to the 2D spectra to remove any additional spurious pixels. The source's onedimensional (1D) spectra were obtained via an optimal extraction (Horne 1986) with a spatial weight profile from the trace of the source in the masked 2D spectrum such that the pixels near the peak of the trace are maximally weighted. To create the extraction profile, the 2D signal-to-noise (SNR) spectrum was collapsed in the spectral direction, taking the median value at each spectral pixel and fitting a Gaussian to the positive trace. While the NIRSpec shutter includes flux from both Component A and Component B for JD1 (ID 3593), the orientation is such that Component B falls completely out of the shutter for JD2 (ID 3349). The source is effectively spatially unresolved at all wavelengths (intrinsic size is less than the JWST point spread function full width at half maximum, PSF FWHM), and there was only a single detectable trace in both observations at the expected location of Component A. An attempt to extract a spectrum for both Component A and Component B from JD1 yielded no discernible detections for Component B, which was affected by the location of the upper negative trace in the 2D spectrum.  \nFigure 1 shows 2D and 1D spectra of JD1 (top right) and JD2 (bottom right) along with the slitlet positions overlaid on 1 . 6 '' × 1 . 6 '' NIRCam color images (left). We detect several emission lines, including [O ii ] λλ 3726,3729 doublet, [Ne iii ] λ 3870, HeI λ 3890, H δ , H γ , and [O iii ] λ 4363. However, we do not detect the spectral continuum. The positions of emission lines are indicated with orange dashed lines and blue labels. The gray shaded area represents the flux uncertainties produced by the pipeline. These uncertainties might be underestimated (see e.g., Ferruit et al. 2022; Christensen et al. 2023). Therefore, we check it by calculating the standard deviations of the spectral fluxes after removing the emission lines ( ± 50 ˚ A). The green lines in Figure 1 show the standard deviation level, which is higher by a  \nfactor of ∼ 2 from the estimated flux uncertainties from the pipeline. The red lines represent the flux uncertainties multiplied by a factor of two, which we use for our analysis in this paper. The reprocessed spectra will be publicly available on our Cosmic Spring website 2 .", '3. ANALYSIS': 'Most of the emission lines that were previously detected with the NIRSpec prism data (see Hsiao et al. 2023a) are also detected with the current NIRSpec highresolution data, except C iii ] λ 1907 which is beyond the wavelength coverage of the current data. With the highresolution grating, we can resolve [O ii ] λλ 3726,3729 doublet for the first time at z > 8. At the central wavelength of [O ii ] λλ 3726,3729, the G395H/F290LP grating has R ∼ 2855 (Jakobsen et al. 2022) which corresponds to a rest-frame dispersion of ∼ 1 . 3 ˚ A per spectral resolution element. Besides this, HeI λ 3890 is separated from [Ne iii ] λ 3870, which were blended in the NIRSpec prism spectra. We describe the emission line analysis in this section.', '3.1. Stacking and Emission Line Measurements': "We stack (i.e., sum) the spectra of JD1 and JD2 to get a good overall S/N ratio. The stacked spectrum has a total lensing magnification ( µ ) of 13 . 3 (8 . 0 + 5 . 3; see Hsiao et al. 2023a,b). We do not de-lense the spectra of JD1 and JD2 before the stacking because the true line ratios of MACS0647 -JD are expected to be preserved. We measure the emission line flux and width in the individual spectra (JD1 and JD2) and the stacked spectrum. We fit the emission lines individually with a Gaussian function using piXedfit 3 (Abdurro'uf et al. 2021, 2022, 2023). The code uses the Markov Chain Monte Carlo (MCMC) method through the emcee package (Foreman-Mackey et al. 2013) for sampling the posterior probability distributions of free parameters in the fitting.  \nFirst, we determine the systemic redshift by fitting the strongest line [Ne iii ] λ 3870 as it also has the highest S/N ratio. The spectroscopic redshift of MACS0647 -JD has been previously determined by Hsiao et al. (2023a) using NIRSpec prism data to be 10 . 17. Here, we put a stronger constraint on the redshift using NIRSpec high-resolution data. We obtain z = 10 . 1672 +0 . 0003 -0 . 0003 , 10 . 1685 +0 . 0004 -0 . 0004 , and 10 . 1674 +0 . 0002 -0 . 0002 for JD1, JD2, and stacked spectrum, respectively. For each spectrum, we use the systemic redshift to estimate the observed central wavelength of  \nFigure 1. NIRSpec G395H/F290LP spectra of MACS0647 -JD lensed images JD1 and JD2 (IDs 3593 and 3349, respectively, in the catalog used for preparing the observation). Left panel : Slitlet positions overlaid on 1 . 6 '' × 1 . 6 '' NIRCam color images (blue:F115W; green:F150W; red:F200W). Right panel : 2D and 1D NIRSpec high-resolution spectra of JD1 (top) and JD2 (bottom). Several emission lines are detected while the continuum is not. Emission lines are indicated with blue-colored labels and orange vertical dashed lines. The gray shaded area represents the uncertainties obtained from the pipeline. The green lines represent the standard deviations of the spectral fluxes after removing the emission lines. We multiply the flux uncertainties by a factor of two to match the overall level of the standard deviations. This is shown with a red line. These rescaled uncertainties are used for the analysis in this paper.  \n<!-- image -->  \nthe other emission lines and set the initial positions of the MCMC walkers. To better constrain the FWHM of the lines, we use the FWHM posterior distribution function derived from the fitting of [Ne iii ] λ 3870 as an additional prior. For [O ii ] λλ 3726,3729 doublet, we set the two lines to have the same FWHM, while the value is allowed to vary during the fitting process.  \nFor each emission line, we fit the spectrum region within ± 100 ˚ A around the expected peak wavelength to minimize the influence of noise. We estimate the continuum level by taking the median of fluxes within the fitting region after excluding the emission line (i.e., masked around ± 40 ˚ A from the expected peak wavelength). We then subtract the continuum from the spectrum and fit the emission line. We scale up the flux uncertainties by a factor of two to match the overall level of the standard deviation (see Figure 1).  \nWe do not use the measured continuum fluxes from the NIRSpec prims spectra because of the differences in the slitlet position and coverage. In Hsiao et al. (2023a), the measurements of emission lines were performed to a stacked spectrum, which is summed of the JD1 and JD2 spectra from two observations (Obs 21 and Obs 23). In  \nAppendix D, we perform emission line measurements of the individual NIRSpec prism spectra and the stacked one using the updated reductions and fitting method.", '3.2. Measured Emission Line Properties': 'The results of the emission-line fitting for the stacked spectrum is shown in Figure 2, while the measured line properties are summarized in Table 1. For comparison, we also show the fitting results of the JD1 and JD2 spectra in Appendix A (see Figures 6 and 7). In Figure 2, the first row shows the full spectrum, while cutouts in the second and third rows show fitting results of the emission lines. The red line and shaded area in each cutout show the Gaussian model drawn from the median posteriors and the range between the 16th and 84th percentiles, respectively. For the [O ii ] λλ 3726,3729 doublet, the best fits of the individual lines are shown by the blue and green dashed lines, while the red line shows the total. The flux uncertainties shown in the cutout spectra have been scaled up by a factor of two.  \nWe detect and resolve [O ii ] λλ 3726,3729 doublet with S/N of ∼ 3 -4 on the individual lines. The flux ratio between the two lines, R [OII] ≡ [O ii ] λ 3729/ λ 3726, is 0 . 91 +0 . 29 -0 . 27 for the stacked spectrum. For comparison, the  \nFigure 2. Top : Fitting results of the emission lines in the stacked spectrum. The gray shaded area shows the original flux uncertainties, while the red line represents a factor of two scale-up, which is used in the fitting. This matches with the overall level of standard deviations as shown by the green line. The detected emission lines are indicated with orange vertical dashed lines and blue labels. Middle and bottom : cutouts showing the detected emission lines and the best-fit Gaussian model drawn from the posteriors obtained from the MCMC fitting. The best-fit models are shown by the red lines (median) and red-shaded areas (range between 16th and 84th percentiles). The best fits of the individual [O ii ] λλ 3726,3729 lines are shown in blue and green, while the total is shown in red. The flux uncertainties in the cutouts have been scaled up by a factor of two.  \n<!-- image -->  \nline ratios of JD1 and JD2 are 0 . 71 +0 . 32 -0 . 22 and 1 . 04 +0 . 27 -0 . 30 , respectively. The flux ratios are consistent within their uncertainties, though the median values are slightly different. This is likely caused by the noise and the different slit coverage on JD1 and JD2 (see Figure 1). The stacked [O ii ] λλ 3726,3729 has an observed FWHM of 183 +15 -15 kms -1 , or 150 +18 -19 kms -1 intrinsic after correcting for instrumental line broadening of 105 km s -1 .  \nThe strongest line [Ne iii ] λ 3870 is detected with a high S/N of 11 . 2 and 6 in JD1 and JD2, while it is 16 . 6 in the stacked spectrum. The observed systemic FWHMfrom the stacked [Ne iii ] λ 3870 is 176 +16 -14 kms -1 , or 144 +19 -17 kms -1 intrinsic after correcting for instrumental broadening of 101 kms -1 . The good detection of [Ne iii ] λ 3870 and [O ii ] λλ 3726,3729 allows us to measure Ne3O2 ≡ [Ne iii ] λ 3870/[O ii ] λλ 3726,3729 ratio. From the NIRSpec high-resolution data, we obtain Ne3O2 of 2 . 1 +0 . 7 -0 . 4 , 0 . 7 +0 . 2 -0 . 2 , and 1 . 2 +0 . 2 -0 . 1 for JD1, JD2, and stacked spectrum, respectively. We also determine  \nNe3O2 from NIRSpec prism data (see Appendix D) and obtain 1 . 2 +0 . 6 -0 . 4 , 1 . 0 +0 . 3 -0 . 2 , 1 . 1 +0 . 2 -0 . 1 , 1 . 7 +0 . 4 -0 . 3 for the JD1 Obs 21, JD1 Obs23, JD2 Obs21, JD2 Obs23, respectively. Again, the discrepancies can be caused by the difference in the slit coverage and noise (in the case of the high-resolution data). Recent studies of high redshift (3 ≲ z ≲ 9) galaxies using JWST/NIRSpec data measured Ne3O2 in the range of ∼ 0 . 2 -3 (e.g., Tang et al. 2023; Reddy et al. 2023; Cameron et al. 2023; Sanders et al. 2024; Backhaus et al. 2024), in agreement with the values determined for MACS0647 -JD.', '4.1. Measurement of Electron Density': 'We measure n e from the line ratio R [OII] based on the photoionization models adopted from Kewley et al. (2019a), which were generated using the MAPPINGS  \nTable 1. Measured Emission Line Properties of the Stacked Spectrum  \nversion 5.1 photoionization code (Binette et al. 1985; Sutherland & Dopita 1993; Dopita et al. 2015). We perform interpolations to the model grids from Kewley et al. (2019a) and construct a functional formula for converting R [OII] to n e that takes into account the electron temperature ( T e ). We describe this in detail in Appendix B.  \nFigure 3 shows the model R [OII] ( n e ) curves for 9 values of T e calculated using the constructed formula (Equations B1 and B2). Different electron temperatures are indicated with different colors. The vertical gray dashed lines mark the range of electron densities for which the line ratio is a useful density diagnostic according to Kewley et al. (2019a). The black dashed line shows the relation from Sanders et al. 2016 (Eq. 6 therein). It perfectly matches the curve from Kewley et al. (2019a) for T e = 10000 K, which was indeed assumed in Sanders et al. (2016).  \nWe use the new formula for calculating the n e of MACS0647 -JD system. From our fitting (see Sections 3.1 and 3.2), we obtain R [OII] of 0 . 71 +0 . 32 -0 . 22 , 1 . 04 +0 . 27 -0 . 30 , and 0 . 91 +0 . 29 -0 . 27 for the JD1, JD2, and stacked spectrum, respectively. Assuming T e = 17000 K for MACS0647 -JD as calculated in a companion paper (Hsiao et al. 2024), we obtain electron densities of log( n e / cm -3 ) = 3 . 3 +0 . 6 -0 . 5 , 2 . 7 +0 . 5 -0 . 6 , and 2 . 9 +0 . 5 -0 . 5 , respectively. In Figure 3, those values are indicated with blue, red, and black circles, respectively. With the current measured R [OII] , we check that changing the assumptions of electron temperature from T e = 10000 to 30000 K increases n e by a factor of ∼ 1 . 7.  \nWe also estimate n e using pyneb (Luridiana et al. 2015) task getCrossTemDen and combine measured R [OII] from the stacked spectrum and [O iii ] λ 5007/ λ 4363 = 40 ± 5 line ratio measured in a companion paper (Hsiao et al. 2024). We obtain log( n e ) = 2 . 9 +0 . 3 -0 . 4 , which is consistent with the value derived above.  \nWe highlight the fitting results of [O ii ] λλ 3726,3729 in Figure 4. Even though JD1 and JD2 are lensed images of the same galaxy, there is an opposite trend of R [OII] between JD1 and JD2 if we examine the median values. However, they are consistent within the range given their uncertainties. With the MCMC method performed here, we propagate the uncertainty from the spectra to the posterior probability distribution of n e in a self-consistent way. We show the posterior distributions of n e (along with the fluxes of the two lines in [O ii ] λλ 3726,3729 doublet, and FWHM) in Appendix C (Figure 9). The posteriors of these parameters are converged, indicating a good fitting. The apparent cut (i.e., envelope) in the 2D posterior between the two line fluxes is due to the range given by the R [OII] within which n e is physically realistic. From the Equations B1 and B2, this range is between 0 . 3729 and 1 . 4556 for T e = 17000 K. We note that this range is not imposed from the beginning (i.e., in the fitting process).  \nR [OII] is also a good indicator of the ISM pressure, which is defined as the pressure within the ionized gaseous nebulae surrounding young hot stars (e.g., Kewley et al. 2019a). Using the photoionization models of Kewley et al. (2019a, Figure 10 therein) and assuming  \nFigure 3. The relationship between [O ii ] λ 3729/ λ 3726 and the electron density drawn from the photoionization models generated by Kewley et al. (2019a). The curves for different temperatures are shown with different colors. Equations B1 and B2 give the formulas to reconstruct these curves. The black dashed line represents the model from Sanders et al. (2016), which perfectly matches the Kewley et al. (2019a) model for T e = 10000 K. The vertical gray dashed lines mark the range of electron densities for which the line ratio is a useful density diagnostic according to Kewley et al. (2019a). Given the [O ii ] λ 3729/ λ 3726 line ratio and measured T e = 17000 K (Hsiao et al. 2024), the estimated n e of JD1, JD2, and the stacked spectrum are shown by the red, blue, and black circles, respectively.  \n<!-- image -->  \n12 + log(O / H) = 7 . 79 ± 0 . 09 (Hsiao et al. 2024), we estimate ISM pressure of log( P/ k) = 7 . 3 +0 . 4 -0 . 3 .', '4.2. Redshift Evolution of Electron Density': "Here, we put the measured electron density of MACS0647 -JD into the context of galaxy evolution by comparing it with the measurements at lower redshifts. We compile measured electron densities at z = 0 -9 reported in the literature and plot them in Figure 5. Different symbols represent various emission-line diagnostics used in deriving n e , while different colors represent different studies. Three emission-line diagnostics have been used in the literature to derive n e : R [OII] (square), R [SII] (plus), and an indirect method using [O iii ] λ 88 µ m/ λ 5007 ratio (cross). Some observations do not resolve [O ii ] λλ 3726,3729 doublet because of the insufficient spectral resolution. We indicate the results from those studies with open squares. For studies that  \nreported n e of the individual galaxies, we show those values with transparent symbols, in addition to the median values shown with thick symbols. The measured n e of JD1, JD2, and stacked spectrum are shown with the blue, red, and black squares, respectively. The rest of the data points are listed in the following, classified based on the redshift range.  \n- · z ≲ 0 . 2: Berg et al. (2022) measured n e of 45 local star-forming galaxies at 0 . 002 < z < 0 . 182 as part of the CLASSY survey (Berg et al. 2022; James et al. 2022) which aims to study the ISM properties of local highz analogs. They derived n e based on R [SII] =[S ii ] λ 6716/ λ 6731 and obtained a wide range of n e ∼ 10 -900 cm -3 , with a median of 100 cm -3 . Using the same CLASSY sample, Mingozzi et al. (2022) explored multiple UV and optical diagnostics for measuring the properties of ISM, including n e , in which they applied multiple line ratios representing low- and high-ionization regions. We take n e measured based on R [SII] whose T e is derived based on [O iii ] λ 4363/ λ 5007. Davies et al. (2021) measured n e of galaxies in a wide redshift range by stacking the spectra of the galaxies in four redshift bins: z ≲ 0 . 1 (471), 0 . 6 ≲ z ≲ 1 . 1 (39), 1 . 1 ≲ z ≲ 1 . 9 (36), and 1 . 9 ≲ z ≲ 2 . 6 (65). The data for local galaxies are taken from SAMI survey (Croom et al. 2012). They estimated n e = 32 +4 -9 cm -3 from R [SII] . Kashino et al. (2017) and Kaasinen et al. (2017) measured n e of galaxies at z ∼ 1 . 5 and z ∼ 0. For the local sample, they used data from the SDSS Data Release 7 (Abazajian et al. 2009), specifically the MPA-JHU catalogs (Kauffmann et al. 2003; Brinchmann et al. 2004). For the local sample, Kaasinen et al. (2017) obtained a median of n e 26 . 8 +0 . 2 -0 . 2 cm -3 , while Kashino et al. (2017) obtained n e in the range of ∼ 10 -100 cm -3 . Shirazi et al. (2014) studied the ISM properties in 14 star-forming galaxies at 2 . 6 < z < 3 . 4 and local galaxies matched in stellar mass and sSFR. They used emission lines from the MPA-JHU catalogs for the local sample, and estimated n e based on R [SII] , finding a range of ∼ 60 -250 cm -3 .\n- · 0 . 2 ≲ z ≲ 4: Davies et al. (2021) used data from the KMOS 3D survey (Wisnioski et al. 2015) to measure n e of galaxies in 3 highz bins (mentioned above). Based on the R [SII] of the stacked spectra, they estimated n e = 101 +59 -85 , 79 +120 40 , and 187 +140 -132 cm -3 for the samples at z ∼ 0 . 9, ∼ 1 . 5, and ∼ 2 . 2, respectively. Swinbank et al. (2019) used data from the KROSS survey (Stott et al.  \nFigure 4. Resolved [O ii ] λλ 3726,3729 doublet of JD1 (left), JD2 (middle), and the stacked spectrum (right). The two lines are resolved in the three spectra. Green dashed and blue dashed lines are the best-fit Gaussian of [O ii ] λ 3726 and [O ii ] λ 3729 respectively, while the solid red line represents the total. Derived R [OII] of JD1, JD2, and stacked spectrum are 0 . 71 +0 . 32 -0 . 22 , 1 . 04 +0 . 27 -0 . 30 , and 0 . 91 +0 . 29 -0 . 27 , respectively. Assuming T e = 17000 K (Hsiao et al. 2024), we estimate n e of log( n e ) = 3 . 3 +0 . 6 -0 . 5 , 2 . 7 +0 . 5 -0 . 6 , and 2 . 9 +0 . 5 -0 . 5 , respectively.  \n<!-- image -->  \n2016) and performed stacking on the spectra of 529 star-forming galaxies at 0 . 6 < z < 1 . 0. They estimated n e from R [SII] in the stacked spectrum and decomposed it into broad-line and narrowline components. They estimated n e = 30 +40 -20 and 75 +55 -50 cm -3 for the narrow-line and broadline components, respectively. We take the mean of the two for our analysis. Kashino et al. (2017) used data from the FMOS-COSMOS survey (Silverman et al. 2015) to study the ISM properties of galaxies at 1 . 4 ≲ z ≲ 1 . 7. They measured an average n e = 220 +170 -130 cm -3 based on R [SII] . Kaasinen et al. (2017) measured n e of 21 star-forming galaxies at 1 . 4 ≲ z ≲ 1 . 7 using data from the COSMOS-[OII] survey. The estimated n e based on R [OII] ranges from ∼ 9 to 1000 cm -3 , with a median of 114 +28 -27 cm -3 . Harshan et al. (2020) used data from the ZFIRE survey (Nanayakkara et al. 2016) to calculate n e of z ∼ 1 . 5 galaxies, of which 6 are in the cluster environment and 2 are in the field. They found n e in the range of ∼ 57 -490 cm -3 for the cluster galaxies and ∼ 49 -160 cm -3 for the field galaxies. Sanders et al. (2016) measured n e of 97 galaxies at 2 . 0 < z < 2 . 6 using data from the MOSDEF survey (Kriek et al. 2015). They obtained a median n e = 225 +119 -4 cm -3 based on R [OII] . Steidel et al. (2014) estimated n e = 220 +380 -160 cm -3 from R [OII] of a stacked spectrum of 113 galaxies at 2 . 0 < z < 2 . 6. Shimakawa et al. (2015) measured n e of 14 H α -emitting galaxies at z ∼ 2 . 5 based on R [OII] . They obtained a median of n e ∼ 290 cm -3 . Gburek et al. (2019) measured n e ∼ 220 cm -3 in a lensed dwarf galaxy at z = 2 . 59 based on R [OII] . Onodera et al. (2016) derived n e of star-forming  \ngalaxies at 3 ≲ z ≲ 3 . 7 based on R [OII] , finding a median ∼ 420 cm -3 . Shirazi et al. (2014) obtained n e ∼ 110 -2700 cm -3 in star-forming galaxies at 2 . 6 < z < 3 . 4 based on R [SII] .  \n- · 4 ≲ z ≲ 9: Isobe et al. (2023) estimated n e of 14 star-forming galaxies at 4 . 02 < z < 8 . 68 using data from public JWST surveys that used the NIRSpec medium- and high-resolution spectroscopy. They observed [O ii ] λλ 3726,3729 doublet resolved in only three galaxies, but blended in the other galaxies. They carefully modeled the line spread function (LSF) of the NIRSpec to deconvolve the [O ii ] λλ 3726,3729 doublets. They obtained n e range of ∼ 39 -3100 cm -3 . Larson et al. (2023) studied the ISM properties in a galaxy CEERS 1019 at z = 8 . 679 using NIRSpec medium-resolution data. They carefully fit an unresolved [O ii ] λλ 3726,3729 doublet with two Gaussian models and derived n e 1 . 9 ± 0 . 2 × 10 3 cm -3 . Fujimoto et al. (2022) measured n e of a galaxy at z = 8 . 496 using indirect method based on the [O iii ] 88 µ m/ λ 5007 line ratio and obtained n e = 220 +230 -130 cm -3 . Using the same method as Fujimoto et al. (2022), Stiavelli et al. (2023) estimated n e of MACS1149-JD1 at z = 9 . 11 to be log( n e ) = 2 . 60 +0 . 25 -0 . 27 . With the [S ii ] λλ 6716,6731 doublets, Fujimoto et al. (2024) evaluated n e of a subL ⋆ main-sequence lensed galaxy at z = 6 . 07, the Cosmic Grapes , to be n e = 260 +400 -230 cm -3 .  \nAs shown in Figure 5, there is an indication of an increasing trend of n e with redshift from z = 0 to 10, especially for the median values in the redshift bins (thick symbols). To get a functional form out of the evolutionary trend, we fit the data with a power-law function in  \nFigure 5. Electron densities of galaxies measured from z = 0 to 10. Our measurements for JD1, JD2, and the stacked spectrum are shown by the blue, red, and black squares, respectively. The rest of the n e measurements are compiled from the literature. For local galaxies at z ≲ 0 . 2: Berg et al. (2022), Davies et al. (2021), Kashino et al. (2017), Kaasinen et al. (2017), Shirazi et al. (2014), and Mingozzi et al. (2022). For 0 . 2 ≲ z ≲ 4: Davies et al. (2021), Swinbank et al. (2019), Kashino et al. (2017), Kaasinen et al. (2017), Harshan et al. (2020), Sanders et al. (2016), Steidel et al. (2014), Shimakawa et al. (2015), Gburek et al. (2019), Onodera et al. (2016), and Shirazi et al. (2014). For 4 ≲ z ≲ 9: Isobe et al. (2023), Larson et al. (2023), Fujimoto et al. (2022), Stiavelli et al. (2023), and Fujimoto et al. (2024). Different colors represent different studies, while different symbols represent various emission-line diagnostics used to derive n e . Overall, there are three employed emission-line diagnostics to derive n e : R [OII] (square), R [SII] (plus), and an indirect method using [O iii ] λ 88 µ m/ λ 5007 ratio (cross). While [O ii ] λλ 3726,3729 doublet is resolved in the majority of the studies (indicated with closed squares), it is not resolved in some studies (indicated with open squares) because of the insufficient spectral resolution. For studies that reported n e of the individual galaxies, we show those with transparent symbols, in addition to the median values shown with thick symbols. The black dashed line represents the best-fit power-law function in the form of n e = A × (1 + z ) p with A = 54 +31 -22 cm -3 and p = 1 . 2 ± 0 . 4. The gray shaded area shows 2 σ uncertainty around the best-fit line.  \n<!-- image -->  \nthe form of n e = A × (1+ z ) p using the MCMC method. For the literature that reports electron densities of multiple individual galaxies in a redshift bin, we only use the median value for the fitting. For MACS0647 -JD, we only use the electron density derived from the stacked spectrum. We obtain A = 54 +31 -22 cm -3 and p = 1 . 2 +0 . 4 -0 . 4 . The median function obtained from the fitting result is shown with the black dashed line, while the gray shaded area shows 2 σ uncertainty. The fitting result can track the bulk of the data distribution quite well. Best-fit A suggests an electron density of ∼ 50 cm -3 in the lo-  \nuniverse. The n e of JD1, JD2, and stacked spectrum falls within the range of the best-fit line and 2 σ uncertainty. While the median n e values follow the increasing trend with redshift, we note the relatively wide scatter of the individual n e values around the best-fit function. Some CLASSY galaxies have n e that reach ∼ 10 3 cm -3 . This can be because those galaxies are local highz analogs.  \nPrevious studies have also hinted at a redshift evolution of electron density in the form of a power-law function, n e ∝ (1+ z ) p with p ∼ 1 -2 (e.g., Davies et al.  \n2021; Isobe et al. 2023). Isobe et al. (2023) compiled electron densities reported from the literature at z ≲ 3 and combined with their measurements at 4 ≲ z ≲ 9. They found that the majority of the data lie within the range given by the power-law function with p = 1 and 2. They further investigate the dependence of n e on the M ∗ , SFR, and sSFR, and found that n e seems to increase toward higher redshift at a given M ∗ , SFR, and sSFR, suggesting that n e evolution is not an implication of the evolution of those global properties. This somewhat contradicts the finding of Kaasinen et al. (2017) that shows a weak evolution of n e with redshift for a given SFR, suggesting that the redshift evolution of n e is mainly due to the cosmic evolution of SFR. To further investigate the driving factors of n e evolution, we need more data that cover a wide range of redshift and homogeneous methods in the measurements of the physical properties, which is beyond the scope of our current study. We do not investigate the dependence of n e on the global properties of galaxies because of the inhomogeneity of the methods for deriving those properties used in the literature.  \nThe values n e ≈ 10 3 cm -3 measured in JD1 and JD2 are in good agreement with the typical density of the ISM in the vicinity of massive stars, within star-forming regions, found in cosmological simulations of z ∼ 10 galaxies (e.g., see Fig. 12 in Sugimura et al. 2024). However, understanding the dominant driver of the redshift evolution of n e is more complicated. Although the mean density of the IGM and virialized halos scale as (1+ z ) 3 , the phase of the ISM probed by the [O ii ] λλ 3726,3729 emission is ionized gas around newly formed massive stars, which is several orders of magnitude denser than the mean gas density in halos. One intriguing interpretation of the redshift evolution of n e is in terms of the mean metallicity evolution of galaxies with redshift. This suggestion is based on two observations: i) Simulations of high-redshift galaxies find that the mean density of star-forming clumps roughly scales as n ∝ Z -1 , a result that is a direct consequence of their higher temperatures in lower-metallicity gas clouds (see Fig. 3 in Garcia et al. 2023); ii) The mean metallicity of the ISM in star-forming galaxies at redshifts z ∼ 0 -3, according to simulations (Dav'e et al. 2011) and observations (Yuan et al. 2012), decreases with increasing redshift roughly as Z ∝ (1+ z ) -1 , hence the relationship n e ∝ n ∝ (1+ z ).  \nAlternatively, the n e evolution in the form of n e ∝ (1 + z ) p may be related to the morphological evolution of galaxies which influences the density of the ISM. The increasing ISM density toward high redshift can be caused by the size evolution of galaxies, which are more compact at high redshift. The galaxy size has  \nbeen shown to decrease with redshift in the form of r ∝ (1 + z ) ∼-1 (e.g., Shibuya et al. 2015; Ono et al. 2023; Ormerod et al. 2024). The virial radius of the dark matter halo also evolves at a similar rate (e.g., Mo & White 2002). Assuming disk morphology, which is compatible with star-forming galaxies, the densities of stellar mass and dark matter halo mass are expected to evolve as r -2 ∝ (1 + z ) ∼ 2 . If n e is expected to evolve following the stellar mass and halo mass densities, it evolves as n e ∝ (1 + z ) ∼ 2 . Our result suggests a slightly lower power index of 1 . 2 +0 . 5 -0 . 4 .", '5. SUMMARY': 'We present JWST/NIRSpec high-resolution spectroscopy (G395H/F290LP grating) of MACS0647 -JD, a triply-lensed galaxy system at z = 10 . 167. We obtained spectra for the MACS0647-JD1 and -JD2. The new spectra detect and resolve emission lines in the rest-frame ultraviolet (UV) and blue optical, including resolved [O ii ] λλ 3726,3729 doublet, [Ne iii ] λ 3870, HeI λ 3890, H δ , H γ , and [O iii ] λ 4363. The [O ii ] λλ 3726,3729 is resolved for the first time at z > 8, revealing the two lines and providing an unprecedented opportunity to directly measure electron density ( n e ) in a galaxy at early cosmic time. We stack the spectra of JD1 and JD2 to get a higher overall signal-to-noise ratio. We measure n e from the [O ii ] λ 3729/ λ 3726 and obtained log( n e / cm -3 ) = 3 . 3 +0 . 6 -0 . 5 , 2 . 7 +0 . 5 -0 . 6 , and 2 . 9 +0 . 5 -0 . 5 for JD1, JD2, and stacked spectrum, respectively. We compare our n e measurements with those reported in the literature for galaxies in lower redshifts and study the evolutionary trend of n e . We see a clear trend of increasing n e with redshift. The redshift evolution follows a power-law function in the form of n e = A × (1 + z ) p with A = 54 +31 -22 cm -3 and p = 1 . 2 +0 . 4 -0 . 4 . This power-law form may be explained as the result of decreasing gasphase metallicity of galaxies with increasing redshift, the morphological evolution of galaxies, or the combination of the two. It has been known that lower-metallicity star-forming clouds tend to be denser and the morphological evolution of galaxies happened in such a way that galaxies were more compact at higher redshift.', '6. ACKNOWLEDGMENTS': "We thank the anonymous referee for providing valuable comments that helped to improve this paper. This work is based on observations made with the NASA/ESA/CSA James Webb Space Telescope ( JWST ). The JWST data presented in this article were obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space Telescope Science Institute. The specific observations analyzed can be accessed via DOI.  \nThe Association of Universities for Research in Astronomy (AURA), Inc. operates the MAST under NASA contract NAS 5-03127 for JWST .  \nA and TYYH are funded by a grant for JWST-GO01433 and JWST-GO-04246 provided by STScI under NASA contract NAS5-03127. TYYH appreciates the support from the Government scholarship to study abroad (Taiwan). We are grateful and indebted to the 20,000 people who worked to make JWST an incredible discovery machine. AA acknowledges support by the Swedish research council Vetenskapsr˚adet (202105559). PD acknowledges support from the NWO grant 016.VIDI.189.162 ('ODIN') and warmly thanks the European Commission's and University of Groningen's CO-FUND Rosalind Franklin program. M.K. was supported by the ANID BASAL project FB210003. AZ and LJF acknowledge support by Grant No. 2020750 from the United States-Israel Binational Science Foundation  \n(BSF) and Grant No. 2109066 from the United States National Science Foundation (NSF); by the Ministry of Science & Technology, Israel; and by the Israel Science Foundation Grant No. 864/23.", 'Facilities: JWST /NIRSpec': "Software: grizli (Brammer et al. 2022), astropy (Astropy Collaboration et al. 2013; The Astropy Collaboration et al. 2018; Astropy Collaboration et al. 2022), matplotlib (Hunter 2007), NumPy (Harris et al. 2020), SciPy (Virtanen et al. 2020), STScI JWST Calibration Pipeline (jwst-pipeline.readthedocs.io; Rigby et al. 2023, Bushouse et al. 2023), IDL Astronomy Library (idlastro.gsfc.nasa.gov; Landsman 1993), piXedfit (Abdurro'uf et al. 2021, 2022), msaexp (Brammer 2023), pyneb (Luridiana et al. 2015).", 'A. FITTING RESULTS OF THE EMISSION LINES IN THE JD1 AND JD2 SPECTRA': 'The results of emission-line fitting for the JD1 and JD2 spectra are shown in Figures 6 and 7, respectively. The measured properties of the emission lines are summarized in Tables 2 and 3.', 'B. GENERAL FORMULA FOR THE RELATIONSHIP BETWEEN R [OII] AND n e': 'We perform interpolation to the model grids of Kewley et al. (2019a) to construct a general functional formula for calculating n e from R [OII] given an electron temperature ( T e ). The model grids of Kewley et al. (2019a) give the relationship between n e and R [OII] for three different electron temperatures (log( T e / K) = 3 . 5 , 4 . 0 , and 4 . 5). The model grids were generated using the MAPPINGS version 5.1 photoionization code (Binette et al. 1985; Sutherland & Dopita 1993; Dopita et al. 2015). To get a functional formula out of the curves, we fit each R [OII] ( n e ) curve with the following functional form adapted from Sanders et al. (2016):  \nn e = γR [OII] -αβ α -R [OII] . (B1)  \nWe then interpolate the R [OII] ( n e ) curves using the cubic spline method for 9 values of log( T e ) between 3 . 5 and 4 . 5. For each interpolated curve, we perform fitting with Eq. B1 to get the coefficients ( α , β , and γ ) and investigate their dependencies with T e . We show the relations between those coefficients and T e in Figure 8. The blue crosses represent the coefficients of the original curves from Kewley et al. (2019a), while the gray circles are from the interpolated curves. The relations can be well-fitted with a cubic polynomial function of the form  \nα, β, γ = a + bx + cx 2 + dx 3 (B2)  \nwith x = log( T e ). The best-fit cubic polynomial functions are shown as red dashed lines in Figure 8 and their coefficients are summarized in Table 4. We show models R [OII] ( n e ) for 9 values of T e in Figure 3.', 'C. CORNER PLOTS OF THE FITTING ON [O ii ] λλ 3726,3729 DOUBLET': 'Figure 9 shows the corner plots showing the posterior probability distributions from the MCMC fitting of the [O ii ] λλ 3726,3729 doublet of JD1 (top left), JD2 (top right), and the stacked spectrum (bottom). Only some parameters are shown in the corner plots, including the individual line fluxes of [O ii ] λλ 3726,3729 doublet, FWHM, and electron density. Among those parameters, only FWHM is a free parameter, while the others are dependent parameters. Other free parameters, including the peak wavelength and amplitude, are not shown in the corner plots.  \nFigure 6. Same as Figure 2 but for JD1 spectrum.  \n<!-- image -->', 'D. MEASURED EMISSION LINES FROM THE NIRSPEC PRISM SPECTRA': "The NIRSpec prism spectra of JD1 and JD2 were obtained by JWST program GO 1433 (PI Coe) and presented in Hsiao et al. (2023a). There were two separate NIRSpec multi-object spectroscopy (MOS) observations (Obs 21 and Obs 23) using the low-resolution ( R ∼ 30 -300) prism spanning a wavelength coverage of 0 . 6 -5 . 3 µ m. Obs 23 was performed with standard 3-slitlet nods, while Obs 21 was performed with single slitlets. Each observation had a total exposure time of 1.8 hours (3.6 hours). In Hsiao et al. (2023a), the emission lines were measured from the stacked spectrum of the four spectra (JD1 Obs 21, JD1 Obs 23, JD2 Obs 21, and JD2 Obs 23). Here, we revisit the analysis and measure the emission lines in the individual spectra. Moreover, we use the latest reduced spectra from The Dawn JWST Archive (DJA) 4 , which were reduced using the upgraded msaexp 5 version 0.6.7. The NIRSpec data reduction is described in Heintz et al. (2023b) and Heintz et al. (2024). We fit the NIRSpec prism spectra and measure the emission line fluxes using piXedfit . Besides the individual spectra, we also fit the stacked sum of the four spectra (i.e., JD1 Obs 21 + JD1 Obs 23 + JD2 Obs 21 + JD2 Obs 23).  \nThe fitting results for the individual spectra are shown in Figure 10 alongside the slitlets configurations overlaid on 1 . 6 '' × 1 . 6 '' NIRCam color images. We show the fitting result of the stacked spectrum in Figure 11. We note that most of the observations target the brighter component A. Only Obs 21 on JD2 covers both components A and B. We also note that slitlets do not cover the same area in the two observations, causing the differences in emission line fluxes. The black line and gray shaded area represent the observed spectra and their 1 σ uncertainties. The blue and red lines represent the best-fit continuum and Gaussian models of the detected emission lines. The spectra roll off gradually from ∼ 1 . 5 µ m (1343 ˚ Arest-frame) to the Lyman break observed at 1 . 36 µ m (1216 ˚ A), instead of a sharp break. This is due to the Lymanα damping wing (see Hsiao et al. 2023a; Heintz et al. 2023b). The continuum modeled here does", "Abdurro'uf et al.": 'Figure 7. Same as Figure 2 but for JD2 spectrum. The fitting results of [O iii ] λ 5007 and HeI λ 4473 are omitted because of the insignificant detection of the lines.  \n<!-- image -->  \nFigure 8. The dependence of the coefficients in Equation B1 to the electron temperature ( T e ; in logarithmic scale). The blue crosses represent the coefficients of the original R [OII] ( n e ) curves from Kewley et al. (2019a) at log( T e / K) = 3 . 5 , 4 . 0 , and 4 . 5. The gray circles show the coefficients of the interpolated curves at 9 values of T e . The red dashed lines show the best-fit cubic polynomial functions.  \n<!-- image -->  \nnot include the modeling of Lymanα damping wing which makes the discrepancy between the models and observed spectra around the wavelength range. The best-fit continuum is obtained from SED fitting on the spectrum after masking the emission lines and cutting at 1 . 5 < λ < 5 . 2 µ m.  \nTable 5 summarizes the measured emission line properties. The line fluxes are not corrected for the lensing magnifications (8 . 0 and 5 . 3 for JD1 and JD2, respectively) and slit loss. The slit loss corrections can be estimated by taking  \nFigure 9. Corner plots showing the posterior probability distributions of some parameters in the MCMC fitting of the [O ii ] λλ 3726,3729 doublet. The top left, top right, and bottom panels show the corner plots for JD1, JD2, and stacked spectrum, respectively. Other free parameters, including the central wavelength and amplitude, are not shown here. The fluxes of [O ii ] λ 3726 and [O ii ] λ 3729 are dependent parameters.  \n<!-- image -->  \nthe ratio between the total aperture photometry in NIRCam filters, obtained from the grizli pipeline (Brammer et al. 2022) (see Hsiao et al. 2023a), and pseudo photometry obtained by integrating the NIRSpec spectra through the NIRCam filters. Then the correction factors at the emission lines can be estimated by interpolating the wavelengthdependent flux ratio. The correction factors for the listed lines in Table 5 are the following. JD1 Obs 21 = [2.5, 3.7, 3.9, 4.0, 4.2, 4.6, 4.6, 4.6], JD1 Obs 23 = [2.2, 3.3, 3.4, 3.5, 3.7, 4.0, 4.0, 4.0], JD2 Obs 21 = [2.7, 2.4, 2.4, 2.4, 2.3, 2.0, 2.0, 2.0], and JD2 Obs 23 = [2.0, 2.5, 2.6, 2.6, 2.7, 2.8, 2.8, 2.8].  \nTable 2. Measured Emission Line Properties of the JD1 Spectrum  \nTable 3. Measured Emission Line Properties of the JD2 Spectrum  \nTable 4. Coefficients for the polynomial function in Eq. B2  \nTable 5. 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