ALMA Reveals Extended Cool Gas and Hot Ionized Outflows in a Typical Star-forming Galaxy at Z = 7.13

We utilize ALMA observations of A1689-zD1 (R.A. 13^h 11^m 299, decl. $-1^\circ \,19^{\prime} \,18\buildrel{\prime\prime}\over{.} 7$) in bands 3, 6, 7, 8, and 9. The observations in bands 6 and 8 (ALMA program IDs 2015.1.01406.S and 2017.1.00775.S, respectively) will be presented in K. Knudsen et al. 2022 (in preparation). We use archival observations for bands 7 (Knudsen et al. 2017), and 9 (Bakx et al. 2021), and refer the reader to these papers for more details. While previous studies of A1689-zD1 have adopted the optical redshift of z = 7.5 determined from an apparent continuum break (interpreted as the Lyα; Watson et al. 2015), new observations of the [C II] and [O III] lines at high S/N place the spectroscopic redshift at z = 7.132. As such, the band 6 observations were tuned to the [C II] 158 μm line at ν_obs = 233.71 GHz. Similarly, bands 8 and 9 were tuned to the [O III] 88 μm, and [O III] 52 μm lines, respectively. Analysis of the [O III] 52 μm line will be presented in a separate, upcoming paper. Band 3 observations were tuned to cover the CO(7-6) and CO(6-5) lines.

The Common Astronomy Software Applications package (CASA; McMullin et al. 2007) was used for reduction, calibration, and imaging. The data were first processed via the standard ALMA pipeline reduction, which was sufficient for these observations. All images were produced with the tclean task in CASA, using natural weighting to maximize sensitivity. Cleaning was done using the "auto-multithresh" automasking algorithm (Kepley et al. 2020), initially down to the 3σ level but expanded to a lownoisethreshold of 1σ. In order to image both compact and extended emission, we apply the multiscale deconvolver (Cornwell 2008) with scales of zero (delta-function) one, and three times the beam size (i.e., the psf). Continuum maps were produced using the multifrequency synthesis (mfs; Conway et al. 1990) mode in CASA over a frequency range identified as lacking line emission. To produce moment 0 maps for the [C II] and [O III] lines, we first subtract the continuum using the CASA task uvcontsub, with order 0, and produce a map using the mfs mode. While this mode is typically used for continuum imaging, we employ it to produce an average line intensity map, as a pseudo-moment 0 map, in order to maximize the signal-to-noise ratio of the map prior to cleaning and ensure that we detect and deconvolve any faint and/or diffuse signals in the tclean process. We integrate channels between 233.4 and 234.0 GHz for the [C II] map and between 416.6 and 417.8 GHz for the [O III] map. Both ranges correspond to roughly ±400 km s⁻¹ from the line center.

For the [C II] and [O III] line intensity maps, we obtain an rms of 18.8 μJy beam⁻¹ and 63.0 μJy beam⁻¹. For the band 3, 6, 7, 8, and 9 continuum maps, we obtain respective rms values of 10.4, 5.3, 44.9, 24.5, and 181.2 μJy beam⁻¹. All maps are primary beam corrected, though the reported rms is derived prior to primary beam correction. All ALMA and HST images are aligned astrometrically using the reproject package in Python.

With natural weighting, the synthesized beam sizes for band 6 and 8 observations are 030 × 028 and 046 × 041, respectively. To perform a fair comparison based on the same spatial resolution, we apply a uv-taper of 03 for the band 6 data, which increases the beam size to 044 × 040. For the analysis of extended emission (Section 3.2), we apply a uv-taper of 05 (07) to observations in band 8 (band 6). Table 1 summarizes the beam size and depth of both the fiducial (uv-taper of 03 for band 6, untapered for other bands) and tapered (07 for band 6, 05 for other bands) continuum data in each band.

Table 1. Summary of ALMA Continuum Observations for A1689-zD1

Band	λrest	${\lambda }_{\min }$, ${\lambda }_{\max }$	θfid	θtap	σfid	σtap	References
	(μm)	(μm)	(arcsec)	(arcsec)	(μJy beam−1)	(μJy beam−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
3	402.5	375.8, 429.2	0.55 × 0.46	⋯	10.4	⋯	K. Knudsen et al. 2022 (in preparation)
6 a	163.0	156.2, 169.9	0.44 × 0.40	0.82 × 0.73	5.3	8.3	K. Knudsen et al. 2022 (in preparation) b
7	107.2	104.7, 109.7	0.62 × 0.58	0.78 × 0.74	44.9	47.1	Knudsen et al. (2017)
8	89.5	87.8, 91.1	0.46 × 0.42	0.72 × 0.69	24.5	28.7	K. Knudsen et al. 2022 (in preparation) b
9	53.0	52.6, 53.4	0.52 × 0.43	0.67 × 0.61	181.2	205.0	Bakx et al. (2021)

Notes. Columns: (1) ALMA band, (2 and 3) Central wavelength and range, (4 and 5) Beam size, for "fiducial" maps (with no uv-taper) and "tapered" maps (with a uv-taper of 05), (6 and 7) rms noise, (8) Reference for ALMA data.

^a For band 6, the "fiducial" and "tapered" maps have uv-tapers of 03 and 07, respectively, to more closely match the other bands in resolution. ^b Band 6 and band 8 data are also presented in Wong et al. (2022).

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In addition to deep ALMA observations of FIR line and continuum emission, we use archival Hubble Space Telescope (HST) data to probe the rest-frame UV continuum of A1689-zD1 (Watson et al. 2015). We obtain images taken with Hubble WFC3/IR in the J (F125W) and H (F160W) bands. At z = 7.13, these bands trace the UV continuum at 1350 Å < λ < 2050Å. These wavelengths are redder than the Lyman limit and unaffected by the Lyα forest, making this a good probe of the rest-frame UV continuum and the unobscured SFR.

Recent works (e.g., Rujopakarn et al. 2016; Dunlop et al. 2017; Fujimoto et al. 2019; Tamura et al. 2019; Herrera-Camus et al. 2021) have shown that there sometimes exist offsets of 01–03 between HST and ALMA astrometry, which can significantly impact results of comparisons between high-resolution observations. The HST data we use in this work have been corrected for this astrometric offset by comparison to astrometry from the Gaia survey (Gaia Collaboration Collaboration et al. 2018), which is accurate to ALMA astrometry to the milliarcsecond scale. The correction shifts the HST astrometry − 011 in R.A. and + 006 in decl.

As noted in previous analyses of A1689-zD1 (Watson et al. 2015; Knudsen et al. 2017), there is an additional source ∼ 15 westward of the target that has been identified as a low-redshift (z ∼ 2) galaxy. Other sources near A1689-zD1 can be identified as low-z interlopers galaxies by their detection in shorter-wavelength ACS/F814W observations, where A1689-zD1 disappears due to the Lyman-break nature of the galaxy. If a pixel has S/N > 3 in F125W+F160W, is more than 11 from A1689-zD1, and is also detected in ACS/F814W, we regard it as an interloper. We replace all such interlopers with randomly drawn values from the image rms noise. Finally, in order to present a fair comparison with the same spatial resolution between HST and ALMA images of A1689-zD1, we convolve the HST map with a Gaussian kernel constructed to match the idealized (i.e., Gaussian model) ALMA beam for the band 8 data. For the fiducial (tapered) maps, this kernel has a size of 044 × 039 (070 × 067).

To analyze the intrinsic ISM morphology of A1689-zD1, we reconstruct the ALMA and HST images into the source plane, correcting for the lens magnification and deflection.

The magnification of A1689-zD1 is derived to be a factor of μ = 9.3 ± 0.5 based on the mass model originally published in Limousin et al. (2007), and refined to include spectroscopic information of multiple systems as described in Bina et al. (2016). This parametric strong lensing model is constructed using the lenstool (Jullo et al. 2007) software, which provides a set of models sampling the posterior distribution of each parameter of the mass distribution, allowing us to derive the statistical error on the magnification. The uncertainty of 0.025 dex of the magnification at the location of the source was also confirmed independently as described in Watson et al. (2015), and the magnification is quite uniform across the source, with variations around 5% (see Figure A1 in Appendix). We show source plane reconstructed maps for each emission in Figure A2; we employ these source plane maps when measuring distance scales (i.e., Sections 3.2.2 and 3.2.3). This is because the asymmetrical deflection of the source confuses a simple relation between angular and physical scale in the image plane—the full reconstruction is necessary to assess the size/shape of the source.

When quoting the luminosity or flux from the source, we employ the notation that, for example, L_IR represents the observed IR luminosity and L_IR μ⁻¹ represents the intrinsic IR luminosity, corrected for magnification.

The top row of Figure 1 presents intensity maps of the [O III] and [C II] lines as well as the dust continuum at ∼90 μm and ∼163 μm and the UV continuum as probed by stacking the HST J and H bands. Blue crosses in the maps indicate the positions of the two UV continuum peaks, one in the southwest and one in the northeast. The peaks of the [O III] and [C II] maps are likely to be co-spatial with the southwest UV-bright region. This is also where the peak of the dust continuum emission lies, suggesting that this southwest component is the more actively star-forming region of the two. The consistency of the peak positions of the [O III] and [C II] with the FIR and UV continuum indicates that the majority of the line emission likely arises from the young star-forming regions visible in UV.

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These images indicate that the [C II] emission is likely extended relative to the [O III], FIR, and UV. [C II] emission is detected at >2σ out to r ∼ 2–$3^{\prime\prime}$ from the galaxy center. Furthermore, the dust continuum at 90 μm (band 8) appears more compact than at 163 μm (band 6), which we will revisit in Section 3.3.

3.2.1. uv-plane Visibility Profiles

3.2.2. Image-based Radial Profiles

We derive radial surface brightness profiles, based on images for both emission lines and the UV and FIR continuum. We conduct this analysis in the source plane, as described in Section 2.3. For the radial profiles, we use the midpoint between the two UV-bright peaks as the center.

Figure 2 shows radial profiles in the source plane for [C II], [O III], and UV continuum (top) and for the dust continuum at 90 μm and 163 μm (bottom), normalized at their peaks. Points show the mean surface brightness in circular annuli whose widths increase at increasing distances, from 0.4 kpc to 1 kpc. Error bars show the standard error of the mean. For ease of readability, we show these radial profiles out to the first point at which the mean surface brightness drops below 0. At this point and beyond, we consider the profile dominated by noise fluctuation and instead show only 1σ upper limits.

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Both [O III] and UV continuum emission are compact (though extended relative to the PSF), dropping to below 0 at radii of ∼4.5 and ∼3 kpc, respectively. In contrast, [C II] emission is detected out to r ∼ 12 kpc. Furthermore, the [C II] profile shape is inconsistent with the [O III] profile out to ∼6 kpc, and inconsistent with the UV profile out to ∼8 kpc.

Dust continuum emission appears to be extended with a radial profile similar to that of the [C II] line. This is true at both 163 μm and 90 μm, though the latter wavelength drops to 0 at ∼8 kpc while the former extends out to ∼12 kpc. ¹⁴ Both continuum profiles are inconsistent with UV and [O III] at radii of r ∼ 2–4 kpc, more in line with the [C II] profile. As with the visibility-based profiles, the large error bars at larger scales prevent robust evidence of extended emission. Nevertheless, the consistent positive surface brightness in the dust continuum may suggest some real extended emission. The presence of such extended dust continuum emission would be in contrast to previous ALMA results for star-forming galaxies at z ∼ 4–7, and we discuss this further in Section 4.

3.2.3. Gini Coefficients

While radial profiles give a quantitative sense as to the extent of [C II] emission, they may also be sensitive to the "clumpiness" of the emission. Recent analysis has shown that A1689-zD1 is a highly clumpy object, requiring multiple spatial/spectral components to fit its [C II] and [O III] data cubes (Wong et al. 2022, Knudsen et al. in prep). As such, the precise choice of center may impact the shape of the surface brightness profile. In the imaging analysis presented thus far, we have adopted the midpoint between the two UV-bright peaks as the center; however, in order to test against this possible bias, we additionally compute the Gini coefficient for each emission. The Gini coefficient (G) is a metric borrowed from econometrics, and was originally created to summarize the degree of income inequality in a population. It was first used to assess galaxy morphology by Abraham et al. (2003), who showed that it can, to first order, be interpreted similarly to other morphological indicators such as concentration. The advantage of using G in this work is that it is nonparametric: it does not depend on the galaxy having a well-defined center, but rather only indicates whether the bulk of the total intensity is contained within a few pixels or spread evenly across many. A high value of G (∼0.75) indicates that the emission from the object is concentrated in one or more bright nuclei, while a low value of G (∼0.25) indicates that the emission is more uniform.

We compute the Gini coefficient following Lotz et al. (2004) by first sorting all n pixel values X_i into increasing order and then computing

$$\begin{eqnarray}&&G=\displaystyle \frac{1}{\bar{X}n(n-1)}\sum _{i}^{n}(2i-n-1){X}_{i}.\end{eqnarray} \tag{ 1 }$$

We compute the error on G in a Monte Carlo fashion by varying the underlying map by a randomized "noise map," convolved with the ALMA beam. Since the Gini coefficient is sensitive to the number of pixels included, we compute G based on all pixels within a circular aperture of radius r = 2'' for each map. Moreover, while the Gini coefficient can be sensitive to the S/N of the map, this effect is negligible above a per-pixel S/N of ∼10 (Lisker 2008), and the sensitivity to the S/N is accounted for by the Monte Carlo error computation.

Figure 3 shows the Gini coefficient computed in the source plane for each map. Our Gini coefficient results reaffirm the conclusions from the radial profiles: [O III] and UV emission are compact and concentrated in one or two bright nuclei, while [C II] and dust continuum emission are spread more evenly. Interestingly, the Gini coefficient for the dust continuum suggests a difference between the different wavelengths: the dust continuum at shorter wavelengths is more concentrated than at higher wavelengths. This may suggest that the dust temperature may vary in space, with hotter dust (which peaks at shorter wavelengths) more concentrated than colder dust (which peaks at higher wavelengths). The spatially resolved dust temperature distribution is addressed further in Section 3.3.

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The rich FIR continuum data for A1689-zD1 facilitates accurate determinations of the dust temperature. Importantly, band 9 (rest-frame 53 μm) data are taken, which helps significantly to constrain the FIR SED at shorter wavelengths. However, the low S/N of the band 9 observations prohibits using this lower-wavelength data to constrain the dust temperature in a spatially resolved sense. We opt instead to use the ratio between bands 6 (163 μm) and 8 (90 μm) to spatially resolve the dust temperature; however, this method depends on the assumed dust emissivity index, β, which usually ranges from 1 to 2.5 (Casey 2012). Therefore, we first determine the best-fit β value via a modified blackbody fit on the galaxy as a whole, using continuum data from bands 3, 6, 7, 8, and 9. We then derive the spatially resolved dust temperature map, assuming that β remains constant in space.

Figure 4 shows the FIR SED of A1689-zD1. Measurements of the dust continuum flux from bands 6 (163 μm), 7 (107 μm), 8 (90 μm), and 9 (53 μm) are shown, and a 3σ upper limit is shown for the continuum in band 3 (∼400 μm), which is not detected. All photometry is computed in the 28 × 18 elliptical aperture shown over the dust continuum images on the right. This aperture is adopted consistently across all bands and is determined by eye to correspond roughly to the [O III]-emitting region. The aperture is large enough to cover the bulk of the dust continuum in bands 6–8, but not so large as to include outskirt noise fluctuation in band 9 and significantly reduce the S/N in that band. Since band 9 holds most of the constraining power in our MBB fit, it is critical to focus on this central region where the band 9 continuum is robustly detected. Error bars in Figure 4 show the combined uncertainty, including both statistical uncertainty measured from the image rms and an additional systematic uncertainty of 10% (20% in band 9) arising from flux calibration, as specified in the ALMA Cycle 8 proposer's guide. ¹⁵ We fit a modified blackbody spectrum to the data points, correcting for the decreasing temperature contrast between the target and background due to the heating of dust by the CMB following da Cunha et al. (2013). We perform this fitting using a Monte Carlo approach, allowing T_dust and β to vary freely with flat priors. We determine a best-fit dust temperature of ${T}_{\mathrm{dust}}={41}_{-14}^{+17}$ K and dust emissivity index $\beta ={1.7}_{-0.7}^{+1.1}$. The inset panel shows the distribution of T_dust and β values derived from the MCMC fitting, and highlights the inherent degeneracy between the two parameters. The larger uncertainty in our T_dust and β measurements compared to Bakx et al. (2021) is due to our use of a 20% uncertainty on the band 9 measurement.

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To extend the analysis in a spatially resolved fashion, we then fix β = 1.7 as a fiducial value. We note that, with variations in the dust chemical composition and crystallinity, it would be possible for β to vary in space with T_dust fixed. However, we have fit the full FIR SED in two spatially resolved apertures and found <1σ difference in β between the two. Therefore, we consider it reasonable to fix β and explore the resulting variation in T_dust. We do so by deriving a relationship between the observed rest-frame 90 μm to 163 μm continuum ratio (corrected for CMB effects) and the dust temperature. Figure 5 shows the spatially resolved dust temperature map for pixels where the dust continuum is detected (at 2σ) at both 163 μm and 90 μm. We show in the right panel the fractional uncertainty on the inferred dust temperature. While we see three regions of high dust temperature, the two on the far northeast and northwest sides of the galaxy are likely a product of noise fluctuation, as the uncertainty is >60%.

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We overplot contours showing the stacked HST J + H-band image. The southeast UV-bright region corresponds to a peak in the dust temperature of ∼50 K, while the northwest region corresponds primarily to a noisy peak. However, the high dust temperature in the galaxy center stretches out toward both noisy peaks, with low errors. Similarly, the far southwest of the map shows a higher temperature than the minimum, with low errors. These regions likely correspond to distinct clumps in the galaxy ISM, which have been identified in the galaxy spectrum (Wong et al. 2022, Knudsen et al. in prep).

In addition to estimating T_dust on a pixel-by-pixel basis, we also endeavor to estimate the spatially resolved T_dust on kpc scales. Figure 6 shows the inferred dust temperature as a function of distance, in arcsec, based on image-plane radial profiles of the continuum maps at both wavelengths. We use circular annuli of variable width out to 2'' from the galaxy center, which corresponds to ∼7 kpc when accounting for the gravitational lensing. We use image-plane maps for this analysis, to minimize any additional uncertainty brought about by the source-plane reconstruction. Error bars show 1σ uncertainty on the dust temperature. The radial profile suggests that the dust temperature decreases with increasing distance from the galaxy center, starting at ∼50 K within 025 and dropping to ∼30 K beyond 1''. At further distances, it appears to increase again, though our signal-to-noise becomes too low to robustly measure the dust temperature.

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We explore the feasibility of a T_dust gradient by applying a constant model in which the dust temperature is fixed at the best-fit spatially integrated value (T_dust = 41 K) everywhere. This model results in a reduced chi-squared of ${\chi }_{\nu }^{2}=3.4$. In contrast, a simple linear model for the decreasing trend agrees within the error in every annulus. These results indicate that a model with constant T_dust is unlikely to be consistent with the data. While the errors in our results are large, this analysis suggests that deep ALMA observations, with the aid of gravitational lensing, may be able to observe the T_dust gradient at z > 7.

Spatially resolving the dust temperature facilitates robust estimates of the spatially resolved total IR luminosity (8–1000 μm) and obscured SFR. For each pixel, we compute the total IR luminosity by integrating a modified blackbody with β = 1.7 and T_dust set to the inferred dust temperature shown in Figure 5, or if the temperature was not well-determined, ¹⁶ with T_dust = 30 K. We then compute the obscured SFR following the Murphy et al. (2011) calibration as

$$\begin{eqnarray}&&{\mathrm{SFR}}_{\mathrm{IR}}\,[{M}_{\odot }/\mathrm{yr}]=3.88\times {10}^{-44}\times {L}_{\mathrm{IR}}\,{\mu }^{-1}\,[\mathrm{erg}/{\rm{s}}].\end{eqnarray} \tag{ 2 }$$

We additionally compute the unobscured (UV-based) SFR following the Murphy et al. (2011) calibration as

$$\begin{eqnarray}&&{\mathrm{SFR}}_{\mathrm{UV}}\,[{M}_{\odot }/\mathrm{yr}]=4.42\times {10}^{-44}\times {L}_{\mathrm{UV}}\,{\mu }^{-1}\,[\mathrm{erg}/{\rm{s}}],\end{eqnarray} \tag{ 3 }$$

where L_UV is the UV luminosity measured from the stacked HST J+H-band image. This probes the rest-frame wavelength range 1350 Å < λ < 2050Å, comparable to the GALEX FUV transmission curve used in the calibration of Murphy et al. (2011). The calibrations from Murphy et al. (2011) assume a Kroupa (2001) IMF and a constant star formation history with an age of ∼100 Myr. Uncertainties on the derived SFRs include the uncertainties on the ALMA/HST maps as well as the uncertainty in the dust temperature (for SFR _IR). Summing over the elliptical aperture used for photometry in Section 3.3, and assuming β = 1.7, we derive an obscured SFR of SFR_IR = 32 ± 1M_⊙yr⁻¹ and an unobscured SFR of SFR_UV = 4.95 ± 0.03M_⊙yr⁻¹, resulting in a total SFR of ∼ 37 ± 1M_⊙yr⁻¹ and an obscured fraction of ∼87%. The high obscured SFR is in line with recent estimates for A1689-zD1 from Bakx et al. (2021). We derive a total infrared luminosity of L_IR μ⁻¹ = (2.16 ± 0.07) × 10¹¹ L_⊙.

To compare the derived SFR to [C II] and [O III] emission, we place circular annuli of varying width across the tapered maps, and compute the SFR and line surface densities in each annulus. Figure 7 shows the spatially resolved Σ_{[O III]}–Σ_SFR and Σ_{[C II]}–Σ_SFR relations with the empirical, local universe relation from De Looze et al. (2014) and (for Σ_{[C II]}) the results for z ∼ 2–6 dusty star-forming galaxies from Spilker et al. (2016). We see that the [O III] line roughly traces the SFR following the relation for local, low-Z, dwarf galaxies, with a slight (∼0.3 dex) excess in regions with high Σ_SFR (i.e., the galaxy center). By contrast, we see a ∼0.7 dex deficit of [C II] in the galaxy center, relative to local dwarfs. This deficit is consistent with the [C II]-FIR deficit in high-redshift DSFGs observed by Spilker et al. (2016), which has also been observed in local IR luminous galaxies (Díaz-Santos et al. 2014). The deficit at high Σ_SFR diminishes at lower Σ_SFR, with the two largest annuli showing [C II] detections despite nondetections of UV or IR continua. The [O III] line is also not detected in these annuli.

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We also investigate the [C II] and [O III] line profiles in a spatially resolved manner. In these emission line spectra, high-velocity outflows in different gas phases may be identified via the "broad wings" that extend past the extent of the best-fit Gaussian profile (see, e.g., Veilleux et al. 2020). We produce line profiles from the [C II] and [O III] cubes in a small (025 radius) aperture centered at the the peak of the Σ_SFR map, i.e., over the UV+FIR-bright region. This small radius is roughly the beam size of the fiducial ALMA maps. We focus on this region for two reasons: 1) the clumpy nature of A1689-zD1 confuses identification of the broad-wing feature with distinct spectral components, and 2) in a SF-driven outflow scenario, the faint broad-wing feature would be most easily detected in regions of highest Σ_SFR (Davies et al. 2019). We have verified that this aperture is small enough to probe only one of the five kinematic component components identified in Knudsen et al. (in prep). Moreover, as the same aperture is applied to both the [C II] and [O III] maps, any differences in the line profiles corresponds to different kinematics between [C II] and [O III] rather than contamination from different components, which would be seen in both emission lines.

Figure 8 shows the line profiles for [C II] and [O III] in this small aperture, with Gaussian fits applied. Before performing any Gaussian fits, we determine the FWHM of each line and examine the differences in the line widths. ¹⁷ The [C II] line width of 252 ± 21 km s⁻¹ is significantly larger than the [O III] line width of 182 ± 31 km s⁻¹. The smaller line width for the [O III] line is consistent with hydrodynamic simulations (e.g., Katz et al. 2019b, 2022), as the [O III] tends to trace younger star-forming regions, which tend to have a lower velocity dispersion than the system as a whole. The larger line width for [C II] may also be related to the spatial extent of the [C II] emission. If the extended emission were spherically symmetric, then the larger volume of gas observed may capture more complicated kinematics along the line of sight and thus contribute to the larger line width.

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To test for the outflow signature, we fit a Gaussian to each line with the FWHM fixed at the measured value. We see that the [C II] line is fit well by a single Gaussian, with a reduced chi-squared value of ${\chi }_{\nu }^{2}\,=\,1.18$. By contrast, the [O III] line is not fit well by a single Gaussian, with a reduced chi-squared value of ${\chi }_{\nu }^{2}\,=\,2.16$ (p < 10⁻⁷). This is owed to significant excess flux in high-velocity regions, despite the narrow line width overall. We show in the bottom panels of Figure 8 the residuals on each Gaussian fit. For [O III], we find significant (>5σ) residuals when integrating across the high-velocity tails from ±100 to 400 km s⁻¹. As [C II] is fit well by a single Gaussian, we find no significant residuals in these high-velocity tails.

The results presented thus far are reminiscent of the "Lyα halo" universally identified around normal star-forming galaxies at z ∼ 3–6 (e.g., Momose et al. 2014; Leclercq et al. 2017). However, another possibility is that we are observing the outskirts of the central galaxy disk even out to r ∼ 10 kpc, and that star formation in this disk is the source of the extended [C II] emission (e.g., Novak et al. 2020). Due to the detection of extended FIR emission (Figure 2), we cannot immediately rule out the latter scenario.

While the rest-UV and [O III] sizes are similarly compact, we see potential evidence of extended dust emission in both uv- and image-based analyses (e.g., Figures 1 and 2). The presence of extended dust continuum emission would be in contrast to previous ALMA results for star-forming galaxies at z ∼ 4–7 (Fujimoto et al. 2019; Ginolfi et al. 2020a; Herrera-Camus et al. 2021), and would, at first glance, suggest significant obscured star formation in the outskirts of the galaxy.

One possible explanation for this inconsistency with previous observations is that this extended dust emission is common in the early universe, but too cold and faint to be detected, being embedded in the warm CMB (e.g., da Cunha et al. 2013; Vallini et al. 2015; Zhang et al. 2016; Pallottini et al. 2017; Lagache et al. 2018). The dust continuum profiles for A1689-zD1 are similar to the UV and [O III] line up to r ∼ 3 kpc, and only diverge at larger distances. This faint extended structure may have been missed in previous stacking results, especially if the observed dust temperature gradient is common, as it is in local galaxies (Hunt et al. 2015) and as is predicted in cosmological zoom-in simulations for early galaxies (e.g., Behrens et al. 2018; Sommovigo et al. 2020). For this study, the deep integration times in bands 6 and 8, combined with the strong lensing effect (with magnification μ ∼ 10) yield an effective sensitivity ∼10 times deeper than previous stacking results (e.g., Fujimoto et al. 2019; Ginolfi et al. 2020a). Under this interpretation, many high-z star-forming galaxies may host extended dust continuum emission corresponding to their extended [C II] emission. In fact, recent stacking results for z ≳ 6 massive quasar host galaxies find similar radial profiles for [C II] and dust (Novak et al. 2020), although the physical mechanisms producing extended dust emission might be different between massive quasar host galaxies and sub-L* galaxies.

It is worth noting that the detection of extended dust continuum emission implies a larger dust mass than what has previously been estimated (e.g., ${M}_{\mathrm{dust}}={1.7}_{-0.7}^{+1.3}\times {10}^{7}\,{M}_{\odot }$ from Bakx et al. 2021). Indeed, the elliptical aperture applied in Section 3.3 fails to capture ∼13% of the band 6 continuum flux observed out to r ∼ 15. Based on our spatially resolved T_dust estimates, fitting this excess flux to a modified blackbody with T_dust = 30 K and β = 1.7 yields a dust mass of M_dust ∼7 × 10⁶ M_⊙. This suggests that the dust mass estimate could be increased by ∼ 40% compared with the previous estimate of Bakx et al. (2021) by including the extended dust component. If the extended dust component ubiquitously exists around early galaxies, this additional, previously unaccounted for dust mass may have implications for dust evolution in the early universe (e.g., Mancini et al. 2015; Michałowski et al. 2019; Dayal et al. 2022).

The extended [C II] and dust continuum emission could be explained by localized star formation, i.e., an extended SF disk rather than an independent halo component. Given that the dust temperature at the outskirts of the galaxy approaches the CMB temperature (Figure 6), it is possible that we underestimate Σ_IR in these regions despite correcting for the decreasing contrast following da Cunha et al. (2013). However, even in this scenario, the compact rest-UV size of the galaxy implies that the obscured fraction increases up to ∼100% toward the outskirts of the galaxy. We show in Figure 9 the UV and IR SFRs (top) and obscured fraction (bottom) as a function of radius in several circular annuli (as in Figure 7). While the obscured fraction decreases with increasing radius up to r ∼ 1'', the detections of IR SFR despite nondetections of UV SFR yield 3σ lower limits on the obscured fraction of ∼93%. Such a reversal of the decreasing trend is in contrast to the metallicity gradient expected from simulations, which would continue to decrease to ∼1% at the outskirts (Pallottini et al. 2017).

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Therefore, a realistic picture might include some dust heating mechanisms other than localized SF activity in the outskirts of the galaxy, such as heating from the interstellar radiation field (ISRF) or by hot outflows. In this scenario, we would need to correct the SFR estimates by removing the extended FIR emission counted as SFR. Then, the Σ_{[C II]}–Σ_SFR relation in the furthest annuli would deviate even more from the local relation, strengthening the interpretation that extended [C II] emission is powered by heating mechanisms other than the localized SF.

At the same time, the [C II] emission in the outskirts of the galaxy can also be suppressed by the CMB, depending on the gas temperature and density (Vallini et al. 2015; Kohandel et al. 2019). Since in general the gas temperature ( ≳10² K) is much higher than T_CMB, the detection of the extended [C II] emission may indicate (i) the extended C⁺ gas maintains a relatively high density that is sufficient to prevent it from being significantly affected by the CMB suppression, or (ii) the majority of the [C II] emission in the outskirt regions is actually suppressed and the intrinsic [C II] luminosity is even greater. The latter case would yield even further deviation from the local Σ_{[C II]}–Σ_SFR relation (right panel of Figure 7.

As A1689-zD1 is a low-mass ( ∼10⁹ M_⊙), sub-L* galaxy (Watson et al. 2015), the existence of an extended disk of r ∼ 10 kpc would be striking. The effective radius for such sub-L* galaxies is generally estimated to be <0.8 kpc (e.g., Shibuya et al. 2015). ¹⁸ Following studies of the Lyα halo (e.g., Hayes et al. 2014; Momose et al. 2014; Leclercq et al. 2017), we fit the [C II] and [O III] profiles using a combined Sérsic+exponential model to fit the central and halo components, respectively. Figure 10 shows these fits. For the [O III] line, we find that including a second component is unnecessary, as the emission is fit well by a single Sérsic profile with R_eff = 1.21 ±0.01 kpc and n = 0.59 ± 0.02. This is generally consistent with the rest-frame optical and UV sizes measured by Shibuya et al. (2015), though perhaps a bit more extended. For the [C II] line, the single Sérsic model fails to capture the extended emission; instead, we need a central component with ${R}_{\mathrm{eff}}^{\mathrm{central}}\,=1.36\pm 0.04\,\mathrm{kpc}$ and n = 0.55 ± 0.03 and an exponential halo component with ${R}_{\mathrm{eff}}^{\mathrm{halo}}=3.5\pm 0.3\,\mathrm{kpc}$. In addition to the visibility-based analysis (Section 3.2.1), the fitting clearly confirms the existence of two separate components, which is reminiscent of the Lyα halo identified around high-z SFGs.

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In summary, the extended dust continuum and [C II] emission might be explained by the outskirt of an extended galaxy disk. But this interpretation suggests an increasing trend of the obscured fraction as a function of radius up to ∼100% at large radii. Instead, the extended [C II] structure is more likely explained by an independent gaseous halo, which is evident from both visibility- and image-based profile fitting for the [C II] emission, and we may call it the "[C II] halo." The [C II] halo and the extended dust emission would have formed via some physical mechanism(s) other than localized SF, which we will discuss in the next section.

Assuming that the extended [C II] emission represents a distinct [C II] halo, we now discuss the physical origin of this feature. Fujimoto et al. (2019) present five possible explanations for [C II] emission on circumgalactic scales: A) star formation from satellite galaxies; B) circumgalactic-scale photodissociation region (CG-PDR); C) circumgalactic-scale H II region (CG-H II); D) cold streams; and E) outflow. For merging galaxies in the center of the protocluster, Ginolfi et al. (2020b) argue for a sixth possible explanation: F) turbulence and shocks associated with tidal stripping.

In all cases, some physical process is required in order to enrich the CGM with carbon and produce the halo of C⁺ that we observe. Assuming that cold streams are composed primarily of pristine gas, only scenarios A), E), and F) include some mechanism to enrich the CGM with carbon. Scenarios B) (CG-PDR) or C) (CG-H II) may certainly ionize the carbon and power [C II] emission, provided the CGM was pre-enriched by some other process. However, given that A1689-zD1 is a sub-L*, pre-mature galaxy at z = 7.13 whose formation history is relatively short, we assume that the metal-enrichment process is related to ongoing activity and focus our discussion on the three scenarios of (A) star formation, (E) outflow, and (F) tidal disruption.

4.2.1. Star Formation from Satellite Galaxies

4.2.2. Outflows

4.2.3. Tidal Stripping

4.2.4. Summary: Origin of the [C ii] Halo

Recent evidence from ALMA has shown that high-redshift galaxies tend to have (∼3–10 times) higher L_{[O III]}/L_{[C II]} ratios than local galaxies (Hashimoto et al. 2019; Bakx et al. 2020; Carniani et al. 2020; Harikane et al. 2020). This may suggest different properties of the ISM at high-z, such as a higher ionization parameter, PDR deficit, higher burstiness parameter (Vallini et al. 2021), or lower C/O abundance ratio than solar (Becker et al. 2011; Katz et al. 2022).

Using the best sensitivity [O III] and [C II] maps so far obtained at this redshift, we have shown the existence of the [C II] halo and [O III] outflows in A1689-zD1, both of which may be additional factors to explain the high L_{[O III]}/L_{[C II]} ratios in z > 6 galaxies. Although our results rely on one galaxy, A1689-zD1 is just one of the abundant population of sub-L* galaxies whose properties may be a representative picture in the Epoch of Reionization. Therefore, we discuss here the contribution from the [C II] halo and [O III] outflows to the L_{[O III]}/L_{[C II]} ratio in A1689-zD1. A full analysis of the spatially resolved L_{[O III]}/L_{[C II]} ratio in A1689-zD1 will be presented in K. Knudsen et al. 2022, (in preparation).

4.3.1. Contribution from [C ii] Halo

One possible explanation for the high L_{[O III]}/L_{[C II]} ratios in z > 6 galaxies is the systematic existence of, and failure to account for, the extended [C II] emission on CGM scales. This has been investigated by Carniani et al. (2020), who find that correcting for surface brightness dimming in high-resolution, low-S/N observations can lower the L_{[O III]}/L_{[C II]} ratios by a factor of ∼2.

Figure 11 shows the L_{[O III]}/L_{[C II]} ratio as a function of SFR for A1689-zD1, in multiple circular apertures of different sizes. These different apertures each encompass different amounts of the [C II] halo. We additionally show the nine galaxies studied in Harikane et al. (2020). By accounting for the full extent of the [C II] halo ( <35), we find a lower L_{[O III]}/L_{[C II]} ratio of ∼2, compared to ∼4 for the central region of the galaxy ( <05). That is, accounting for extended [C II] emission can help to reconcile the high L_{[O III]}/L_{[C II]} ratios with lower ratios found in local galaxies, but cannot bring these values completely in line with local relations.

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4.3.2. Contribution from [O iii] Outflows

Another possible explanation for the high L_{[O III]}/L_{[C II]} ratio, at least in the case of A1689-zD1, is the contribution of the "broad-wing" feature in the [O III] spectrum to the total [O III] luminosity. If this emission indeed corresponds to hot, ionized gas in outflows, rather than H II regions around massive stars, we would expect to see a higher L_{[O III]}/L_{[C II]} ratio here than in local universe galaxies not undergoing this outflow.

To examine this, we analyze the [O III] line profile in A1689-zD1. Since the single Gaussian fitting in [O III] shows significant residuals (Section 3.5), we perform two-component (narrow+broad) Gaussian fitting to the [O III] line profile. Figure 12 shows the [O III] line profile in the same central aperture as Figure 8, with a two-component Gaussian fit applied. We see that the broad component dominates the overall spectrum, with the narrow component responsible for only about 13% of the total luminosity.

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The bottom panel of Figure 12 shows how the L_{[O III]}/L_{[C II]} ratio changes when calculated using the total [O III] luminosity (narrow+broad) versus the luminosity of only the narrow component. We use the same SFR for both points, derived from the UV+FIR emission as described in Section 3.4. We see that, while this central region shows an overall L_{[O III]}/L_{[C II]} ratio of ∼3, the narrow component alone shows a ratio of ∼0.4. Assuming the low-Z dwarf galaxies in the De Looze et al. (2014) sample do not show significant outflows, this result suggests that outflowing gas in the hot, ionized phase could be a factor contributing to the high L_{[O III]}/L_{[C II]} ratios in high-z galaxies. While the outflow signature in the [O III] line is not universally identified around the high-z galaxies with high L_{[O III]}/L_{[C II]} ratios, it has been tentatively detected in the galaxy NB1006 (Inoue et al. 2016). Importantly, the S/N of the [O III] line in our data is at least 4–8 times greater than in previous studies (e.g., Harikane et al. 2020), which could explain the nondetections of the [O III] outflow signature.