ALMA Detections of [O iii] and [C ii] Emission Lines From A1689-zD1 at z=7.13

A1689-zD1 is one of the most distant galaxies, discovered with the aid of gravitational lensing, providing us with an important opportunity to study galaxy formation in the very early universe. In this study, we report the detection of [ C II ] 158 μ m and [ O III ] 88 μ m emission lines of A1689-zD1 in the Atacama Large Millimeter / submillimeter Array ( ALMA ) Bands 6 and 8. We measure the redshift of this galaxy as z sys = 7.133 ± 0.005 based on the [ C II ] and [ O III ] emission lines, consistent with that adopted by Bakx et al. The observed L [ O III ] / L [ C II ] ratio is 2.09 ± 0.09, higher than that of most of the local galaxies, but consistent with other z ∼ 7 galaxies. The moderate spatial resolution of ALMA data provided us with a precious opportunity to investigate spatial variation of L [ O III ] / L [ C II ] . In contrast to the average value of 2.09, we ﬁ nd a much higher L [ O III ] / L [ C II ] of ∼ 7 at the center of the galaxy. This spatial variation of L [ O III ] / L [ C II ] was seldom reported for other high-z galaxies. It is also interesting that the peak of the ratio does not overlap with optical peaks. Possible physical reasons include a central active galactic nucleus, shock heating from merging, and a starburst. Our moderate spatial resolution data also reveal that in addition to the observed two clumps shown in previous Hubble Space Telescope images, there is a redshifted segment to the west of the northern optical clump. This structure is consistent with previous claims that A1689-zD1 is a merging galaxy, but with the northern redshifted part being some ejected material, or that the northern redshifted material stems from a third more highly obscured region of the galaxy.


Introduction
Studies of high-redshift (high-z) galaxies are crucial for understanding the early phase of galaxy formation and evolution.The gravitationally lensed galaxy A1689-zD1 is one of the most distant sources (z ∼ 7.13) discovered so far; it is strongly lensed by a factor of μ = 9.3 (Bradley et al. 2008).It is therefore a useful probe to study the early universe.Recently, Bakx et al. (2021) adopted a new redshift of the galaxy z = 7.13, and our measurement confirms the redshift.
Having a high dust mass as compared to the Milky Way makes A1689-zD1 unusual among high-redshift dust emitters.It is also a sub-L * galaxy (Watson et al. 2015).The massive amount of dust may indicate a gas-rich system that makes the emission lines from the interstellar medium (ISM) detectable.According to Bradley et al. (2008), A1689-zD1 is a system composed of two clumps, which are likely separate starforming regions within the galaxy, but they could conceivably be interpreted as small star-forming galaxies merging at high redshift.
Previously, A1689-zD1 was detected in the dust continuum with the Atacama Large Millimeter/submillimeter Array (ALMA) in the absence of emission lines (Knudsen et al. 2017;Bakx et al. 2021), except for a slight excess in [C II]158 μm (Knudsen et al. 2017).Using the dust continuum, the sizes of the two detected clumps were estimated to be 0.4-1.7 kpc, and the dust temperature was approximated to be T dust ∼ 35-45 K.A recent update of the dust temperature and mass of A1689-zD1 using the continuum estimated with the 7 M e (Bakx et al. 2021).
In Watson et al. (2015), the redshift was measured from the X-shooter spectra taken on the Very Large Telescope, using the Lyman break due to the lack of Lyα and other emission lines.However, the redshift measurement based on the Lyman break is less certain than that using high-excitation lines.Moreover, the break is close to the spectrographʼs near-infrared/visual arm split.Thus, the redshift needs to be measured more accurately.Using [C II] and [O III] emission lines, the redshift of 7.13 by spectral measurement adopted by Bakx et al. (2021) is confirmed in this work.
Since [O III]88 μm is bright for some galaxies at z > 6 (e.g., Inoue et al. 2016;Carniani et al. 2017;Harikane et al. 2020), the [O III] line is one of the most useful tracers of ISM properties.In addition, [O III] has a higher ionization potential (35.1 eV) than [C II] (11.3 eV).Therefore, the [O III]/[C II] ratio is useful to investigate the ionization state.
In this paper, we present an analysis of archival ALMA data of [C II]158 μm and [O III]88 μm in Cycles 3 and 5 with a higher spatial resolution (∼0 2) than ever before (∼0 9 Knudsen et al. 2017;0 6-0 7 Watson et al. 2015).With this higher spatial resolution, the data can be used to examine the line emissions, to resolve structures inside the galaxy, and to investigate velocity structures and so on in comparison with the Hubble Space Telescope (HST) images.For example, this higher spatial resolution allows us to examine the kinematic properties of A1689-zD1.We can also investigate the ratio of [O III]/[C II] as a function of positions within the galaxy.This is important because, as some previous studies discussed, the observed high [O III]/[C II] may be due to the difference in their spatial distributions (Carniani et al. 2017).
This paper is organized as follows.In Section 2 we describe the ALMA data set used in the study; Section 3 presents the main results, and discussions are provided in Section 4. Finally, we present our conclusions in Section 5. Throughout this paper, we assume the Planck15 cosmology (Planck Collaboration et al. 2016) as a fiducial model, i.e., a Λ cold dark matter cosmology with (Ω m , Ω Λ , Ω b , h) = (0.308, 0.682, 0.0486, 0.678).

Observation
Two ALMA bands, Bands 6 and 8, are chosen in this study in order to characterize the physical properties of A1689-zD1.Because it is a dusty galaxy (Watson et al. 2015), it is important to measure the star formation rate (SFR) derived from farinfrared (FIR) observations, using its relation with  1.
The calibration of visibility data from the ALMA archive was conducted with the pipeline versions 4.7 and 5.4 for Bands 6 and 8, respectively, provided by the ALMA project using the Common Astronomy Software Applications (CASA).For the Band 6 data, targeting [C II], the channel width of the observation is 1.95 MHz.For the Band 8 data, targeting [O III], the channel width is 3.91 MHz.The total exposure time on source for the Band 6 ([C II]) observation is 28,123 s ∼ 7.81 hr, while that for the Band 8 ([O III]) observation is 12,337 s ∼ 3.43 hr.The maximum recoverable scales (MRS) for the Band 6 and Band 8 data are 5 32 and 4 58, respectively, which are larger than the detected signals, as we discuss below.
Using the calibrated measurement set (MS), we create image cubes for the [C II] and [O III] lines with a spectral resolution of 10 km s −1 .The beam size is controlled by the robustness parameter of the Briggs weighting and uv-tapering in the CASA task tclean().First, we subtract the continuum in each band using the CASA task uvcontsub by selecting the frequency ranges without line detection, i.e., 232.000 ∼ 233.420GHz for Band 6,and 416.342 ∼ 416.823 GHz and 417.588 ∼418.178GHz for Band 8. Next, in order to investigate both the morphology and photometry of A1689-zD1, we produce two sets of image cubes for each of the bands (Hashimoto et al. 2019a).Since we are interested in the extent of [C II] and [O III] emissions of the galaxy, we adopt a Briggs robust weighting of R = 0.5, achieving a beam size of 0 271 × 0 243 (0 387 × 0 332), with a position angle at −80°(−89°) for Band 6 (8) data.As presented in Section 3.1.1,the extended structure does not exceed the MRS in the two bands.Hence, we use the image cube sets with Briggs robust parameter R = 0.5 for the morphology analysis of A1689-zD1.To maximize the sensitivity of collecting the flux as a point source, we use natural weighting by setting R = 2, and further apply uv-tapering to 2″ so as to obtain the maximum flux of the extended source.The beam size is dramatically increased to 2 640 × 2 337 (1 874 × 1 790) at −63°(−70°) for Band 6 (8) data.This set of data is used for flux and related calculations of the galaxy.The characteristics of the calibrated images are summarized in Table 2.

Spatial Distribution
Using the CASA task immoments, we obtain moment-0 maps of the Band 6 and Band 8 (Briggs) data by stacking the cube channels along the spectrum, covering ∼400 km s −1 (∼1.2 FWHM).This is done to ensure that the detections of the emission lines are valid (Novak et al. 2019).This range of frequency is comparable to that in previous studies (Inoue et al. 2016;Matthee et al. 2017;Hashimoto et al. 2019b;Novak et al. 2019).Figure 1 shows the [C II] (white contours) line emission at 3, 7, 11, and 15σ levels and the [O III] (magenta contours) line emission at 3, 7, 11, 15, and 19σ levels, overlaid on the combined HST color image.For the purpose of color display, we stack the HST filters with F105W as blue, F125W as green, and F160W as red (proposal ID: 11802, P.I.: Ford).There is a known coordinate offset between their ALMA image and HST image as an average value of 0 4 ∼ 0 45 (Watson et al. 2015).We therefore measure the position difference of the peaks between the ALMA Bands 6 and 8 data and the HST image we use, and shift the ALMA contours by 0 386 along  From the HST image shown in Figure 1, we see that there are two clumps: one in the northeast (clump A), and one in the southwest (clump B).We refer to them as clump A and clump B throughout.

Spectra
Using elliptical apertures of 8 5 × 7 5 and 6 5 × 5 5 (both approximately 3 beams), we extracted spectra from the natural and uv-tapered Band 6 and Band 8 image cubes, respectively.The spectra are shown in blue in Figure 2.This is to include all the flux obtainable by covering the area within which spatially extended emission may exist, for instance, the [C II]158 μm halos around z ∼ 6 galaxies reported by Fujimoto et al. (2019).Taking the average of the redshifts obtained from [Cii] and [Oiii] spectra, we obtain a systemic redshift z sys = 7.133 ± 0.005.This matches the adopted redshift z = 7.13 in Bakx et al. (2021).The new redshift derived from FIR fine structure [C II] and [O III] lines, and hence is a better measurement than the previous estimate of z ∼ 7.5 based on the Lyman break with no detection of any emission line (Watson et al. 2015).
We measure the widths of the emission lines with their FWHMs in terms of velocity (km s −1 ).Details of the measured and derived parameters, corrected with a lensing magnification factor of μ = 9.3 (Bradley et al. 2008), of the galaxy, are summarized in Table 3.We also include the 1σ uncertainty of the parameters in Table 3.The emission-line fluxes of [C II] and [O III] are measured by integrating the flux density along the velocity, obtaining a total of 548 ± 56 mJy km s −1 for [C II], and 640 ± 69 mJy km s −1 for [O III].We note that each flux error mentioned above is calculated by a quadrature sum of (i) the fitting error of the emission line and (ii) the 10% error due to the uncertainty in the absolute flux scale of ALMA data.With total line fluxes and systemic redshift deduced, we derive the line luminosities with the equation Notes.
a The beam PA is in degrees east of north, by which the major axis is rotated.b Sensitivity is defined as the rms value of the cube image with 10 km s −1 channel width.With the obtained L [C II] , we can also revise the SFR of the system using the relation This is one of the rare cases that a spatial distribution of the ratio is highest around the center of the galaxy with a value of ∼7, and it gradually decreases toward the outer parts of the galaxy, reaching a ratio of one.We further discuss the implications in Section 4.1.
In Figure 4 we show the [O III]/[C II] luminosity ratio as a function of the bolometric luminosity, which is defined as the summation of the UV and total infrared (TIR) luminosities, i.e., L bol = L UV + L TIR (Hashimoto et al. 2019a;Harikane et al. 2020).For comparisons, we also plot the ratios for z = 6-9 galaxies in the literature plotted in Carniani et al. (2020) before applying surface brightness dimming (SBD), as well as those of local galaxies studied in the Dwarf Galaxy Survey (Madden et al. 2013;De Looze et al. 2014;Cormier et al. 2015) and the Great Observatories All-sky LIRG Survey (GOALS: Howell et al. 2010;Díaz-Santos et al. 2017).The orange line is the fitting function of z = 6-9 galaxies without A1689-zD1, adopted from Equation (7) in Harikane et al. (2020), as a comparison.Although as suggested in Carniani et al. (2020), SBD may affect the flux measurements gravely with ALMA, we do not apply the same correction because of the high S/N of [C II] emission of A1689-zD1 (∼17.1).Such an effect was predicted to be weak at high S/N (Carniani et al. 2020).We  find that A1689-zD1 and other z = 6-9 galaxies show systematically higher [O III]/[C II] ratios than most of the local galaxies, which is consistent with previous results (Inoue et al. 2016;Laporte et al. 2019).

Velocity Fields
In this section, we investigate the kinematic properties of A1689-zD1 using [O III] and [C II] emissions.With the CASA task immoments, we create flux-weighted velocity (i.e., moment-1) maps of [C II] and [O III] emission lines (Figure 5), using pixels with >2σ detections of Briggs data.Note that we do not consider the beam-smearing effect for the velocity fields.
Comparing clumps A and B we observe in Figure 1, we see that clump A consists of a blueshifted component on the upper left (east side) and a redshifted component on the upper right (west side), while clump B is a cloud of a redshifted and blueshifted mixture, but not as intense as the components in clump A.
We only investigate the [C II] field because (1) the Band 6 data ([C II]) have a better S/N than Band 8 data ([O III]), and (2) the patterns and the values of velocity field in [C II] and [O III] are similar.
A1689-zD1 might be a merger due to the parallel isovelocity lines found between clump A and clump B, as has been claimed (Bradley et al. 2008;Knudsen et al. 2017).A comparison to Figure 1 shows that the two peaks of [C II] are consistent with clump B and the blueshifted part of clump A, while the redshifted part of clump A might be (1) some ejected material from the merger, or (2) material from a highly obscured component of the galaxy.Similar discussions can be found in Jones et al. (2017) and Hashimoto et al. (2019a), while further comparisons to other targets are presented in Section 4.2.

High [O III]/[C II] Luminosity Ratio
From Section 3.2, we find a high [O III]/[C II] luminosity ratio of 2.17 ± 0.14.In the literature (e.g., Carniani et al. 2017;Laporte et al. 2019;Bakx et al. 2020), the [O III]/[C II] luminosity ratios of the 6 < z < 9 galaxies have been found to be systematically higher than those of z ∼ 0 galaxies, similar to A1689-zD1.Formerly, Harikane et al. (2020) also found high values of the ratio for their large samples of high-z galaxies.
From their simulations in Katz et al. (2022), when they assume a low C/O abundance, their core-collapse supernova model agrees well with observations with high [O III]/[C II] luminosity ratios at high redshift.Therefore, a low C/O abundance may account for the high [O III]/[C II] ratios for z ∼ 6 galaxies.
Moreover, as mentioned in Carniani et al. (2020), there might also be an underestimation of [C II] flux caused by high angular resolution.Often, [C II] emission is more spatially extended, and thus, such extended flux might be underestimated due to the interferometric nature of ALMA, which is why we further perform uv-tapering so as to increase the beam size of Band 6 data to ∼2″, with a peak S/N of 17.1.Comparing our results with those in Carniani et al. (2020), the value of L [O III] /L [C II] = 2.09 ± 0.09 of A1689-zD1 just touched the lower limit of the range of 2 < L [O III] /L [C II] < 8 measured with the nine observed high-z galaxies reported in Carniani et al. (2020).The comparatively high values of for the other z > 6 sources may possibly be due to observational limitations.Carniani et al. (2020) found that for the nine z > 6 galaxies, up to 40% of the extended [C II] component might be missed at an ALMA angular resolution of 0 8, implying that L [C II] might be underestimated by a factor of ∼2 in data at low S/N (<7).
In the models presented in Harikane et al. (2020), they suggested several possible mechanisms responsible for the high ratio of [O III]/[C II] luminosities that might match the case for the galaxy: (1) a higher ionization parameter (U ion ) in higherredshift galaxies, possibly due to the low-metallicity young stellar populations with larger volumes of [H II]   (Figure 15 From Figure 4, most of the discovered high-z galaxies (z = 6-9) have an overall L [O III] /L [C II] higher than that of A1689-zD1 (∼2).Thus, we expect that other z ∼ 7 galaxies might obtain even higher values of the luminosity ratio [O III]/[C II] at the center if they are observed with higher spatial resolution.
In addition, in Figure 3, we find that the [O III]/[C II] ratio is highest in between the optical peaks shown in the HST images (clumps A and B; Figure 1), but not at the peaks, with a ratio of ∼7, it then gradually decreases outward.This is a high value as compared to an average luminosity ratio of L [O III] /L [C II] = 2.09 ± 0.09.Thanks to the high spatial resolution of our ALMA data, we have the precious opportunity to investigate the spatial variation of the ratio within the galaxy.
A number of physical mechanisms could cause the high ratio at the center of the galaxy.If a central active galactic nucleus (AGN) is present, the ionization of neutral gas by an AGN may be one reason (Walter et al. 2018).Alternatively, if clumps A and B are in the process of merging, the excess [O III] may also be the heated ionized gas due to shock heating from mergers (Hopkins et al. 2007;Minsley et al. 2020).However, we might expect an extended shock front in this case, rather than the point-like high-ratio region we observe in Figure 3.The velocity difference between clumps A and B is also small, at least in the line-of-sight direction.Another explanation may be that A1689-zD1 has a central starburst region that gives rise to ionized gas (Silk 1997).However, this may not be the case for the sharp peak of [O III]/[C II] in A1689-zD1 because according to Weilbacher et al. (2018), ionized gas is diffuse in the H II region of starburst galaxies.

Velocity Fields
The complexity of the velocity field of the galaxy A1689-zD1 shown in Figure 5 gives little indication of any existence of a rotating disk.W therefore, suggest that it may simply be a merging system, in agreement with previous analyses (e.g., Bradley et al. 2008;Knudsen et al. 2017).
Considering the observed high-z quasars (QSOs) in the literature, in Bañados et al. (2019), for instance, the host galaxy of the QSO ULAS J1342 + 0928 at z = 7.54 showed a velocity gradient in which the northern part was blueshifted and the southern part was redshifted.In spite of this, the velocity dispersion did not resemble a coherent rotating structure.Hence, they interpreted the velocity dispersion structure as that of a merger.On the other hand, Shao et al. (2017) found that the velocity dispersion of a QSO at z = 6.13, with a best-fit inclination angle of 34°, has a coherent rotating structure that is consistent with the rotation of the galaxy.Similarly, Wang et al. (2013) observed six QSOs at z ∼ 6 using ALMA and reported that their velocity gradients are consistent with rotating, gravitationally bound gas components.
For [C II] emitters, Smit et al. (2018) found rotating structures based on a simulation and their velocity fields in COS-3018555981 and COS-2987030247 at z = 6.8.Their results are consistent with rotationally supported galaxy disks, which were often found at z ∼ 2. Likewise, Bakx et al. (2020) found a Lyman-break galaxy (LBG) (MACS0416-Y1) at z ∼ 8.3 that shows a rotation-dominated disk given the observed velocity gradient.In addition, Hashimoto et al. (2019a) used ALMA and detected two clumps in B14-65666 at z = 7.15 with [O III] and [C II] emission lines.However, they thought that the galaxy is a starburst galaxy induced by a major merger because they did not see a smooth velocity field.
Given the complex velocity field of A1689-zD1 and the possibility that other dynamical interpretations would be equally valid as supported by the literature, further investigation is needed to make a conclusion.As mentioned in Section 3.3, A1689-zD1 may possibly be a merger with some northwestern ejected materials, or a merger with northwestern redshifted materials coming from a third, more highly obscured region of the galaxy.

Conclusions
Using the new ALMA Bands 6 and 8 data, we detect [C II] 158 μm and [O III]88 μm emission lines for A1689-zD1.Our findings are summarized as follows.
1. We measure the redshift of A1689-zD1 as z = 7.  III] include a central AGN, shock heating, and/or a starburst.5.The moment-1 maps of the ALMA Bands 6 and 8 data (Figure 5) show complex velocity fields of A1689-zD1, with the northeastern part being blueshifted, the southwestern part being redshifted, and an additional northwestern part being comparatively more highly redshifted.It is therefore suggested that the galaxy may be a merger with the northwestern redshifted part being (1) some ejected material from the merger, or (2) some components coming from a third, more highly obscured region of the galaxy.
We are grateful to the anonymous referee for all the insightful comments.This paper makes use of the following ALMA data: ADS/JAO.ALMA#2015.1.01406.S and ADS/ [C II]158 μm and [O III]88 μm emissions.At the redshift of A1689-zD1, Band 6 covers the [C II] emission line, and Band 8 covers the [O III] emission line.The Band 6 observation was carried out in 2016 from August 1 to 25 (Cycle 3) with the ALMA 12 m array and an antenna configuration of C36-(4)/5 and C36-(5)/6 (project ID: 2015.1.01406.S, P.I.: D. Watson), while the Band 8 data were obtained from observations in 2018 from April to December (Cycle 5), also with the 12 m array, but in an antenna configuration of C43-3 and C43-4 (project ID: 2017.1.00775.S, P.I.: D. Watson).The observational configurations are summarized in Table right ascension (R.A.) in order to match the peaks for a better comparison.Because the structures shown in Figure1extend to a 3σ detection that is within an area of ∼2 3 × 1 5 for both [C II] and [O III], which is much smaller than the MRS of 5 32 and 4 58 for [C II] and [O III], respectively, we confirm that the observed structures are not artificial.Both [C II] and [O III] emission lines are spatially well resolved with angular resolutions of 0 203 and 0 232, respectively.
At around the rest frequencies of [C II]158 μm and [O III] 88 μm, in Band 6 and Band 8 respectively, we detect a line emission with two peaks in each band, indicated as "redshifted" and "blueshifted", as shown in Figure 2.They may indicate two merging components.More analyses are presented in Sections 3.2 and 3.3.Here, we first fit the spectra with two Gaussians.We obtain two peaks of Gaussians centered at 233.58 ± 0.05 GHz and 233.72 ± 0.08 GHz for [C II] using Band 6 data in panel (a).Similarly, for Band 8 data, we find two peaks of [O III] at 416.98 ± 0.08 GHz and 417.23 ± 0.11 GHz, respectively, after applying a two-Gaussian fitting, as shown in panel (b).The fitted results are shown as dotted red lines in Figure 2. We acquire a redshift of z [C II]red = 7.137 ± 0.002 for the redshifted part and a redshift of z [C II]blue = 7.132 ± 0.003 for the blueshifted part for the [C II] line detections in Band 6. Accordingly, we obtain redshifts of z [O III]red = 7.137 ± 0.002 and z [O III]blue = 7.132 ±0.002 with Band 8 [O III] detections for the redshfited and blueshifted parts.We find that the redshifts we obtain from the [C II] and [O III] line detections agree well with each other for the two components.The signal-to-noise ratio (S/N), defined as the ratio of the peak flux of the source (moment-0 map) to the background noise of the image, is calculated for both Band 6 and Band 8 (natural and uv-tapered) data, with a value of S/N = 51.5 for [C II] and S/N = 22.3 for [O III].Note that for Briggs-weighted data, the S/N values are calculated as 16.1 for [C II] and 27.9 for [O III].

Figure 4 .
Figure 4. [O III]88 μm/[C II]158 μm luminosity ratio as a function of bolometric luminosity.The red triangle shows the data point for A1689-zD1.The bolometric luminosities of z = 6-9 galaxies are taken from Hashimoto et al. (2019a), while the orange line is adopted from Equation (7) in Harikane et al. (2020), which is the fitting function of z = 6-9 galaxies.The gray triangle and circles denote z ∼ 0 galaxies from the Dwarf Galaxy Survey (Madden et al. 2013; De Looze et al. 2014; Cormier et al. 2015) and from the Great Observatories All-sky LIRG Survey (GOALS: Howell et al. 2010; Díaz-Santos et al. 2017), respectively.The bolometric luminosity is estimated as the total of the UV and TIR luminosities.

Figure 5 .
Figure 5.The velocity field (moment-1 map) of the emission lines (top: [C II] 158 μm, and bottom: [O III]88 μm; using Briggs-weighted data).The gray contour in the top (bottom) panel is the same as the white (magenta) contour for [C II] ([O III]) emission in Figure.1.The color bar in each panel shows the velocity in the range of −225 km s −1 ∼ 135 km s −1 , as it is close to and covers the maximum and minimum values of both emissions.
Note.The PWV values for each of the band data are from separate measurement sets due to the long exposure time; therefore, we present the minimum and maximum of averages per execution block (EB).

Table 2
Summary of Image Characteristics ( Natural and uv-tapered) ( Briggs)( Natural and uv-tapered) PDF = 0 gives a decrease of L [C II] by ∼99%; and (3) a low C/O ratio due to a young stellar age.Since a higher U ion gives rise to a more extended H II and thus [O III] region PDFwhere C (b) of Harikane et al. 2020), it may not be able to explain the observed sharp peak of [O III] at the center of A1689-zD1.A low C PDF leads to a low [C II] luminosity.While it is impossible that no PDR overlaps the H II region (C PDF = 0), a low coverage of the PDR region ([C II] emission) together with a concentrated H II region may still explain the peaky [O III] as observed in Figure 3.A low C/O ratio due to production of C at a young stellar age may partially explain the high [O III]/[C II] ratio.But it does not indicate the spatial distribution of the ratio.
133 ± 0.005 based on [C II] and [O III] emission lines detected in Band 6 and Band 8 (natural and uv-tapered), respectively.The redshift is consistent with that adopted by Bakx et al. (2021).2. Using the derived L [C II] , we estimate a star formation rate of SFR [C II],Krou = 46.1 ± 0.8 M e yr −1 .Converting it from a Kroupa IMF into a Salpeter IMF, the value becomes SFR [C II],Sal = 68.8± 1.2 M e yr −1 , which is about a factor of 2 larger than the SED-fitting estimate SFR obsc,Sal = 33 ± 9 M e yr −1 in Bakx et al. (2021).However, the difference is still within a reasonable range according to Figure 4 of De Looze et al. (2011).3. The [O III]/[C II] luminosity ratio of this galaxy is 2.09 ± 0.09, which is similar to other high-z galaxies, but much higher than its local counterparts.4. Despite a number of average L [O III] /L [C II] ∼ 2, A1689-zD1 has an exceptionally high spatial ratio of L [O III] /L [C II] ∼ 7 at the center of the galaxy.This is because [C II] emission is significantly spatially extended, while [O III] is compact at the center.Possible reasons of the compactness of [O