Searching for C ii Emission from the First Sample of z ∼ 6 O i Absorption-associated Galaxies with the Atacama Large Millimeter/submillimeter Array

Cosmological reionization occurs when hydrogen transitions from its neutral to ionized state in the early universe. Investigating the behavior of neutral hydrogen (H i) can help to reveal the astrophysics driving reionization and its timing. Unfortunately, H i in the circumgalactic medium (CGM) is quite difficult to observe because of the Gunn–Peterson effect (Gunn & Peterson 1965), the nearly complete absorption of photons with rest-frame excitation energy higher than that of Lyα by the intergalactic medium (IGM). Moreover, the absorption caused by the gas in the CGM, with λ_rest < 1216 Å, will also fall into the Gunn–Peterson trough and will blanket in the Lyα-caused absorption and then be undetectable (Simcoe et al. 2020). Thus, alternative tracers are required. Because neutral oxygen has a similar ionization energy as H i, it is regarded as a possible tracer for cosmological reionization (Oh 2002; Finlator et al. 2013; Doughty & Finlator 2019).

Metal absorption is commonly observed in QSO spectra. Thanks to the rapid development of the recent high −z QSO surveys (e.g., Bañados et al. 2016; Wang et al. 2019; Yang et al. 2019), ∼260 QSOs have been identified at z = 6–7.5, which enables us to search for metal absorbers systematically (e.g., Becker et al. 2019; Cooper et al. 2019; Zou et al. 2021). Additionally, the early universe is proposed to be in a metal-poor state. Therefore, at high redshift (z ≳ 6), the existence of metal absorption systems (e.g., O i, Mg ii, and C iv) constrains the nature and location of the source galaxies that contribute to the early-metal enrichment. Then, connecting galaxies with the gaseous reservoirs plays a crucial role in understanding galaxy formation at the end of the epoch of reionization.

Cosmological simulations suggest that galactic winds from typical star-forming galaxies can eject metals into the CGM/IGM (e.g., Keating et al. 2014; Pallottini et al. 2014; Davé et al. 2016). Inspired by these works, star formation rates (SFRs) and impact parameters of source galaxies are two key parameters that need to be measured to test models of galaxy formation. As such, the direct imaging of absorption-associated galaxies is necessary because it provides measurements of these two parameters simultaneously. Díaz et al. (2011) found a C iv absorption-associated Lyman α emitter (LAE) at z = 5.791 with Lyα-based SFR of 1.4 M_⊙ yr⁻¹and at the distance of 79 kpc. Additionally, Díaz et al. (2014, 2015) observed LAEs around a sample of C iv absorbers with imaging and follow-up spectroscopic analysis with the detection limit of SFR_Lyα ≈ 5 M_⊙ yr⁻¹. They surmised that the LAE distribution may potentially trace large-scale outflows. To further constrain the possibility of faint sources as C iv absorber host galaxies, Cai et al. (2017) used Hubble Space Telescope (HST) narrow band-imaging observations to constrain the detection limit down to 2 M_⊙ yr⁻¹. Moreover, Díaz et al. (2021) used the Very Large Telescope and Multi Unit Spectroscopic Explorer (MUSE) to search for LAEs around 11 C iv absorbers and found these LAEs have impact parameters ranging from 11–200 kpc and Lyα luminosity of $0.18\mbox{--}1.15{{\rm{L}}}_{\mathrm{Ly}\alpha }^{* }$. However, Lyα can easily be scattered due to the resonant scattering effect (e.g., Dijkstra et al. 2006; Zheng et al. 2010), which causes the Lyα-derived star formation rates to be uncertain.

Due to the limitation of treating Lyα emission as galaxy tracers, only a few candidate galaxies in the field of absorbers have been identified. Because [C ii]-158 μm emission is one of the best ISM indicators (e.g., Wang et al. 2013; Decarli et al. 2017; Neeleman et al. 2019), it is an alternative tracer at z ∼ 6. To trace H i at z ≳ 6, we choose to use O i absorption as an alternative. As such, we develop our approach following this methodology. To further investigate the connection between absorbers and their host galaxies, we use the Atacama Large Millimeter/submillimeter Array (ALMA) to search for O i absorber-[C ii] emitter pairs in QSO fields.

We chose to use ALMA because it also provides us with deep continuum observations, which will allow us to investigate the source densities/environment of these high-z QSOs. Previously, Wu et al. (2021) reported the results in the field of QSO J2054−0005. Here, we follow up on work and present observations of the additional four fields. These five systems also form the first sample to study metal absorber–submillimeter galaxy interactions. Simulations predict that QSOs at z ∼ 6 with a black hole mass of M_BH ≈ 10⁹ M_⊙ are primarily embedded in massive halos and located in overdense regions (Costa et al. 2014). Observationally, Decarli et al. (2017) and Trakhtenbrot et al. (2017) conducted ALMA observations in QSO fields and found several continuum sources and [C ii] companions at the redshifts of QSOs. After comparing blind-field number counts, Decarli et al. (2017) concluded that the cumulative number of companion galaxies are excesses in QSO fields. Neeleman et al. (2019) observed more QSOs at this redshift and then obtained the same conclusion. Furthermore, at z ∼ 4, García-Vergara et al. (2022) detected five CO(4–3) emitters around 17 QSOs, while only 0.28 CO(4–3) detections are expected with the same volume, suggesting that QSO fields have clustering properties with emitters. Conversely, except for line emitters, Champagne et al. (2018) used ALMA to search for continuum sources in 35 bright QSOs fields at 6 < z < 7 and found no spatial overabundances at the scale of (<1 cMpc). Conducting our ALMA observations, we can further discuss the continuum overabundances in QSO fields.

This paper is organized as follows. In Section 2, we describe the composition of our sample, data reduction, and source-detection details. In Section 3, we present the [C ii]-intensity, continuum map and compare our observations with simulations. In Section 4, we provide further discussions about the physics behind our observations. In this paper, we assume a flat cosmological model with Ω_M = 0.3, Ω_λ = 0.7, and H₀ = 70 km s⁻¹ Mpc⁻¹, 1'' = 5.7 kpc at z = 6.

2.1. Survey Description

We used ALMA in its compact configuration (C43-1) to search for [C ii] 158 μm emission of absorber-associated galaxies at z ∼ 6 (ALMA 2017.1.01088.S, 2019.1.00466.S; PI: Cai). Our sample is composed of five QSO fields containing six strong O i absorbers with $\mathrm{log}({N}_{\mathrm{OI}}/{\mathrm{cm}}^{-2})\gt 14$ (Becker et al. 2011; Cooper et al. 2019). The detailed redshift, column density, and source time are collected in Table 1. Each individual ALMA observation was done using four 1.875 GHz spectral windows (SPWs). In general, in each spectral tuning, we use one SPW to center on the [C ii] emission at the redshift of the O i absorber, while the remaining SPWs were used to obtain a continuum image of the field. Specifically, in the field QSO J0100+2802, because two absorbers are located at very similar redshifts, we used our SPW-setting strategy to observe [C ii] emission. Our sample contains five (six) QSO (absorber) fields. Combined with Wu et al. (2021), we describe the observations of all five QSO fields in this paper.

Table 1. O i Absorber and QSO Information

QSO Field Name	zOI	$\mathrm{log}({N}_{\mathrm{OI}}/{\mathrm{cm}}^{-2})$	ton (hr)
(1)	(2)	(3)	(4)
J2054−0005	5.978	14.2	2.3
J2315−0023	5.7529	14.5	2.8
J0100+2802 (F1)	6.144	14.7	2.5
J0100+2802 (F2)	6.112	14.4	2.5
PSO J183+05	6.064	14.4	2.0
PSO J159-02	6.238	14.5	1.4

Notes. Columns: (1) QSO field name: F1 is the first absorber field, while F2 is the second one from the same sightline; (2) redshift of O i absorber; (3) O i column density; (4) on-source time.

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2.2. Data Reduction

2.3. Source-detection Algorithm

3.1. O i Asorber-associated [C ii] Emitters Sample

3.1.1. [C ii] Emitter Detection

Our primary science goal is to survey the [C ii] emission from galaxies that could host strong O i absorbers. We strictly followed a popular method called FINDCLUMPS (Walter et al. 2016; Decarli et al. 2020; González-López et al. 2020). The basic idea of this algorithm is to detect 2D sources on different moment-zero maps with different line widths at different frequencies. For the first step, the potential [C ii]-intensity images are generated by floating averages of a given number of channels with different window sizes (e.g., three-, four-, and five-channel windows) at different frequencies. Then, to search for candidates, we performed the source-detection algorithm (Section 2.3) on these moment-zero maps.

After having these candidates, we selected reliable targets. As mentioned previously, all O i absorbers have column densities of $\mathrm{log}({N}_{\mathrm{OI}}/{\mathrm{cm}}^{-2})\gt 14$. Guided by theoretical works, at z ≈ 6, strong absorbers are generally linked to massive dark-matter (DM) haloes ($\mathrm{log}({M}_{h}/{M}_{\odot })\gtrsim 11$; Finlator et al. 2013; Keating et al. 2016), corresponding to stellar masses of $\mathrm{log}({M}_{* }/{M}_{\odot })\gtrsim 9$ (Ma et al. 2018). To search for such galaxies, we aim to detect [C ii] emission from data cubes by constraining three key parameters: the line width of [C ii] emission, the velocity offset, and the projected impact parameters between [C ii] emitters and O i absorbers.

To begin with, following Le Fèvre et al. (2020), the line width of a reliable [C ii] emitter at z ∼ 6 should be ≳250 km s⁻¹, as measured by Capak et al. (2015). Similar line width justification is also reported in (e.g., Aravena et al. 2016; Fujimoto et al. 2019; Béthermin et al. 2020). Furthermore, the relative velocity offset between the absorber and its host galaxy should be within the range of ±200 km s⁻¹, because typical star-forming galaxies at z ≈ 6 have been shown to have outflow velocities of v ≲ 200 km s⁻¹ (e.g., Steidel et al. 2010; Keating et al. 2016; Díaz et al. 2021). We also note that due to projection effects, the projected velocity along the line of sight should be one component of the outflow velocity. As such, it is safe to constrain the velocity offset, our second constrained parameter, from −200 to 200 km s⁻¹. For the projected impact parameter, cosmological simulations suggest that star formations and galactic outflows from star-forming galaxies are the primary mechanisms (Oppenheimer et al. 2009). These metal-enriched gases (particularly for strong absorbers, e.g., $\mathrm{log}({N}_{\mathrm{OI}}/{\mathrm{cm}}^{-2})\gt 14$) are reasonably gravitationally bounded in the circumgalactic medium (CGM) scale (Finlator et al. 2013; Keating et al. 2014). Guided by these theoretical models, the hosts of strong O i absorbers tend to reside in dark-matter halos with masses of M_h ≈ 10¹¹⁻¹² M_⊙, corresponding to virial radii of <50 proper kpc (pkpc) at z ∼ 6 (Keating et al. 2016). Therefore, the impact parameter between absorbers and hosts should be smaller than 50 pkpc. We select candidates with a fidelity level of 30%, which corresponds to the S/N ≥ 4. To summarize, we constrain the following parameters

• 1.  
  Line Width ≳ 250 km s⁻¹
• 2.  
  −200 km s⁻¹ ≤ Velocity Offset ≤ 200 km s⁻¹
• 3.  
  Impact parameter ≤ 50 kpc
• 4.  
  S/N ≥ 4

We also discuss [C ii]-emitter candidates with large velocity offset and impact parameters in Section 4.2.2.

After completing all three steps, except the first detection (called [C ii]2054 below) reported by Wu et al. (2021), there are no emitters passing our criteria. In the case of nondetections, we used five-channel width windows, corresponding to the typical line width closing to ∼300 km s⁻¹(Aravena et al. 2016), centered on the expected frequency of [C ii] emission to obtain final velocity-integrated flux maps. The detection and nondetection [C ii] maps of our samples are shown in Figure 1. Although only one out of six showed a positive detection, we constrained the velocity-integrated flux (SΔv_{[C II]}) of [C ii] emitters to be within 3σ upper limits. Additionally, the [C ii] luminosity (L_{[C II]}) and the derived star formation rate (SFR_{[C II]}; e.g., Wang et al. 2013; Schaerer et al. 2020) can be further constrained. The results are reported in Table 2. We conclude that, for the nondetection fields, the average 3σ upper limits of the various parameters are SΔv_{[C II]} < 0.06 Jy km s⁻¹, L_{[C II]} < 5.8 × 10⁷ L_⊙, and SFR_{[C II]} < 5.5 M_⊙ yr⁻¹. Note that several emitters with larger impact parameters in Figure 1 are further discussed in Sections 4.2.2 and 4.3.

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Table 2. [C ii] Moment-zero Map Properties

Field Name	SΔv[C II]	L[C II]	SFR[C II]
	(Jy km s−1)	(107 L⊙)	(M⊙ yr−1)
(1)	(2)	(3)	(4)
J2054−0005*	0.0758 ± 0.0177	7.0 ± 1.7	6.8 ± 1.7
J2315−0023	<0.03	<2.7	<2.5
J0100+2802 (F1)	<0.07	<7.1	<6.8
J0100+2802 (F2)	<0.08	<7.9	<7.6
PSO J183+05	<0.05	<5.0	<4.8
PSO J159-02	<0.06	<6.2	<5.9

Notes. Columns: (1) QSO field name; (2) integrated [C ii] flux (3σ upper limit); (3) [C ii] luminosity; (4) [C ii]-based star formation rate; ∗ means the field with detection and shows the results of the targets ([C ii]2054).

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3.1.2. Statistical Results

To constrain the galaxy absorber cross-correlation function, we constructed it as follows:

$\begin{eqnarray}&&{\xi }_{{\rm{g}}-\mathrm{abs}}=\displaystyle \frac{1}{{n}_{0}}\displaystyle \frac{{\rm{\Delta }}N(r)}{{\rm{\Delta }}V}-1={\left(\displaystyle \frac{r}{{r}_{0}}\right)}^{-\gamma }.\end{eqnarray} \tag{ 1 }$

In Equation (1), n₀ is the mean number density of galaxies, which can be obtained from the Luminosity function (LF) proposed by Loiacono et al. (2021). By integrating the LF to the bright end (L > L_{[C II]_obs}), we then obtain n₀ = 1.3 × 10⁻⁴ cMpc⁻³. Similarly, ΔN(r) represents the number of galaxies in a spherical shell of survey volume ΔV, where r is the distance between an absorber and a galaxy. r₀ and γ are the correlation length and power-law slope, respectively. Here, we recall the initial detection results. We have one [C ii] emitter with SFR_[CII] ≈ 7 M_⊙ yr⁻¹ that is located approximately 20 kpc from OI-enriched gas at z = 5.978. Combined with our larger sample, however, only one [C ii] emitter in six O i absorber fields is detected. Plugging in the final survey volume and one detected [C ii] emitter into Equation (1) (r = 20 kpc and ΔN(r) = 1, and ΔV is the total survey volume of six fields), we get the relation between r₀ and γ. We add detailed calculations in Appendix B. This result is shown in the left panel of Figure 2. Although we only detect one [C ii] emitter, the observed r₀ and γ relation is statistically greater than that of cosmological simulations (Finlator et al. 2020).

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In addition to comparisons between the measured SFR and impact parameter, the properties of dark-matter halos that host O i absorbers can also strongly constrain cosmological simulations. Here, we do not directly compare the observed host halo properties with simulations because of the mismatching problem. It is inevitable to mismatch absorbers and their host galaxies in cosmological simulations. Usually, the host-halo-match algorithm is based on the closest match method, i.e., the metal-enriched gas is naturally assumed to be hosted by the nearest halo. However, massive halos can reasonably blow out metal-enriched gas far away, which may result in a relatively small halo being closer to the blownout gas. An example of this scenario can be found in Figure 16 in Keating et al. (2016). Therefore, we compare the number of galaxies clustered with O i absorbers to that predicted by simulations. In the right panel of Figure 2, we show how many galaxies are around O i absorbers within our given impact parameters. The gray line shows the results in Technicolor Dawn simulations (Finlator et al. 2020), while the blue line is a best-fit linear relation. Simulations suggest that the number of associated [C ii] emitters is ≈10^−2.5 within 50 kpc around O I absorbers. However, the identification of [C ii]2054 suggests 1/6 of our O i absorber sample (red square), which is 1–2 orders of magnitude more abundant than that predicted by simulations. Considering the Poisson uncertainty at the 99% single-sided confidence level (Gehrels 1986), the observed number of [C ii] emitters at our detection is 10^−2.77 (red triangle). Given these results, although there is only one detected [C ii] emitter in six absorber fields, the detection of such a bright [C ii] emitter is unexpected. But, considering the lower limit, our results are also consistent with those predicted by simulations. More discussions on the detection and nondetection of [C ii] emitters can be found in Section 4.2.

3.2. Continuum Observations

Our deep ALMA observations also yield several continuum-source detections. Continuum images of five QSO fields are shown in Figure 3. In this section, we further analyze the properties of these targets.

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To obtain the number of continuum sources, we run the source-detection algorithm on the continuum images. The effective search areas of our data are defined by regions where the primary beam limit was higher than 20% and are represented by dashed lines in Figure 3. Again, sources with peak S/N higher than 4σ are regarded as detections. Here, we give a quick summary. Our five-field observations yield continuum images at 260.0, 286.6, 259.9, 262.4, and 256.0 GHz, respectively. The standard deviations of these fields are 0.012, 0.009, 0.018, 0.016, and 0.014 mJy/beam. Excluding the five identified QSOs, there are nine sources detected with a mean flux density of 0.19 mJy and S/N of 7.6. The sources catalog is presented in Table 3. We note that these newly detected continuum sources in our observations have no redshift information.

Table 3. Continuum Sources

Target Name	R.A.	Decl.	Scont
	(J2000)	(J2000)	(mJy)
(1)	(2)	(3)	(4)
J2054−0005C1	20:54:05.325	−00:05:12.127	0.64 ± 0.06
J2054−0005C2	20:54:05.742	−00:05:10.890	0.12 ± 0.02
J2054−0005C3	20:54:06.358	−00:05:14.828	0.19 ± 0.01
J2054−0005Q (C4)	20:54:06.501	−00:05:14.435	3.37 ± 0.01
J2054−0005C5	20:54:06.649	−00:05:16.482	0.067 ± 0.014
J2054−0005C6	20:54:06.792	−00:05:17.915	0.069 ± 0.016
J2315−0023Q	23:15:46.601	−00:23:57.652	0.35 ± 0.01
J2315−0023C1	23:15:46.055	−00:23:46.697	0.13 ± 0.03
J0100+2802Q	01:00:13.021	+28:02:25.822	1.27 ± 0.02
J0100+2802C1	01:00:12.763	+28:02:25.678	0.076 ± 0.019
J0100+2802C2	01:00:12.156	+28:02:31.593	0.18 ± 0.04
PSO J183+05Q	12:12:26.976	+05:05:33.576	4.77 ± 0.02
PSO J159-02Q	10:36:54.184	−02:32:37.938	0.63 ± 0.01
PSO J159-02C1	10:36:54.718	−02:32:39.164	0.21 ± 0.02

Notes. Columns: (1) name of continuum source, where QSO host galaxies are appended by a Q after the field name, while continuum sources are appended by a C; (4) continuum flux density.

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4.1. Continuum-source Number Counts

To evaluate the number-count excess of continuum sources in our observed fields, we compare observed continuum-source numbers with those in random fields.

Our continuum observations are conducted around ∼266 GHz, corresponding to ∼1.1 mm. To date, there are a handful of deep submillimeter-continuum surveys that conduct random-field 1.1 mm continuum galaxy number counts (e.g., Fujimoto et al. 2016; Franco et al. 2018; González-López et al. 2020). To reveal the continuum-source excesses in our QSO fields, we compared the number of detected sources to the expected number in blank fields based on the 1.1 mm galaxy number counts. To do a proper analysis, our observed flux densities at different frequencies need to be converted to flux densities at 1.1 mm. We do this conversion by assuming a modified blackbody emission model, specifically, ${S}_{\nu }\,\propto {\nu }^{(3+\beta )}/(\exp (h\nu /{{kT}}_{\mathrm{dust}})-1)$ (Popping et al. 2020). For this model, we adopt β = 2.0 and T_dust = 38 K for star-forming galaxies at z ∼ 6 (Faisst et al. 2020). For QSO field, J2054, J2315, J0100, PSO J183 and PSO J159, the flux converted ratios are S_{1.1 mm}/S_{264.0 GHz} = 1.13, S_{1.1 mm}/S_{286.6 GHz} = 0.83, S_{1.1 mm}/S_{259.9 GHz} = 1.20, S_{1.1 mm}/S_{262.4 GHz} = 1.16, and S_{1.1 mm}/S_{256.0 GHz} = 1.27, respectively. For these models, the radii for the efficient searching area in these five fields are 165, 152, 167, 166, and 170. We note that the efficient searching areas are defined as primary beam limits >20%. From this analysis, we obtain the completeness-corrected continuum-source densities in five QSO fields (see Figure 4). We list details of completeness correction in Appendix B.

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In Figure 4, the different black symbols represent the observed continuum-source densities in different fields, while the blue star represents the five-field-averaged result. The measurement in the field of QSO J2054-0005 is shown in a red diamond. Error bars are estimated based on the Poissonian noise of the observed number of continuum sources. Our results suggest that within the field of view of ALMA, only the QSO J2054−0005 field shows a higher number density of continuum sources than the prediction from the continuum number counts function (González-López et al. 2020; Popping et al. 2020). Our observations are also consistent with that described in Champagne et al. (2018). However, we note that, due to the size of the ALMA field of view, one-pointing observations may miss the true number of excesses on the scale of ≳30''. Meyer et al. (2022) conducted multidithering ALMA observations to map the environments surrounding QSOs and also found an overabundance case of continuum sources in one of three QSO fields. This scenario is explained by a possible foreground overdensity caused by galaxies at the cosmic noon. This effect could also be suitable to the excess of dusty sources in J2054-0005. Although we only identify one overabundance, we conclude that more large-scale continuum observations in QSO fields will be necessary for future analysis of the environment around QSOs at high redshift or galaxy overdensities at any other redshift.

4.2. Detection and Nondetection of [C ii] Emitters

4.3. The Role of Outflow Velocities

We analyze the impact parameters again to discuss the physics behind our observations. Theoretical work predicts that metal-line absorbers are blown out by galactic feedback (Muratov et al. 2015; Doughty & Finlator 2019; Finlator et al. 2020). In an effort to test the efficiency of galactic winds in transporting metals in our sample, following Díaz et al. (2021) and Galbiati et al. (2023), we assume the outflow starts at redshifts higher than those of the observed metal absorbers (z = 7–10, Galbiati et al. 2023). We then compare the observed and the expected impact parameters between galaxies and absorbers. The predicted impact parameters are calculated based on the assumption of the projected velocity of the galactic wind (〈v(z)〉) as the following equation:

$\begin{eqnarray}&&\mathrm{impact}\ \mathrm{parameter}=\langle v(z)\rangle \times \left[{t}_{{\rm{z}}\_\mathrm{start}}-t(z)\right],\end{eqnarray} \tag{ 2 }$

where t_{z_start} is the lookback time at the launching redshift of galactic outflow, and t is the lookback time at the observed redshifts.

This comparison allows us to test different feedback models (Keating et al. 2016) with different outflow velocities. Díaz et al. (2021) regarded LAEs that are located near C iv absorbers as the real absorber host galaxies and found eight C iv-LAE pairs at z = 5–6 in MUSE observations. Their results suggest that the 〈v〉 values of metal-line absorber-associated galaxies mostly range from 100–150 km s⁻¹. In Figure 5, we demonstrate the expected impact parameters as the combinations of different t_{z_start}, and 〈v〉. The gray-colored star and unfilled stars are our samples. We note that outflows launched more recently before the observations will be linked to more intense star formation activity, providing strong galactic winds with large velocities.

We present deep ALMA [C ii] and continuum observations in five QSO fields containing six strong O i absorbers at z ∼ 6. By performing a source-finder algorithm on the [C ii] moment-zero and continuum maps, we obtain nondetections of [C ii] emitters, while nine additional, new continuum sources are detected. Our findings are summarized as follows:

• 1.  
  If we constrain the velocity range of ±200 km s⁻¹ and impact parameter of 50 kpc, our ALMA observations yielded nondetections of five strong O i absorption ($\mathrm{log}({N}_{\mathrm{OI}}/{\mathrm{cm}}^{-2})\gt 14$) associated galaxies. Including the detection we reported in Wu et al. (2021), we have one detection per six O i absorber fields. Further, we also found 14 tentative detections with S/N of ≈4.3 and an averaged SFR of 17.4 M_⊙ yr⁻¹ at large impact parameters (>50 kpc) and having larger velocity offsets of within ±600 km s⁻¹. If these detections are confirmed in the future, then the scenario that massive galaxies blow out metals in larger distances with higher velocities may be favored from the theoretical side.
• 2.  
  Although we only detected one [C ii] emitter, the detection rate of bright sources is still much higher than that predicted from simulations. The observed correlation length (r₀) and power-law index γ of the galaxy absorber correlation function ξ_g−abs is 1–2 orders higher than that measured from cosmological simulations Finlator et al. (2020). Meanwhile, comparing the cumulative number of galaxies around absorbers with that in cosmological simulations, the detected [C ii] emitter is brighter at a factor of 10 than the expected one in simulations.
• 3.  
  Using the method proposed by Díaz et al. (2021) and Galbiati et al. (2023), we use the measured impact parameter to test the mean speeds 〈v〉 of galactic winds, based on different assumptions of the launching time of galactic outflows. For the typical outflow velocities of galactic wind (∼100–200 km s⁻¹), at the observed redshift, a more recently launched outflow will be more intense to eject the metal-enriched gas out to the observed impact parameter.
• 4.  
  ALMA observations provide us with deep continuum observations with a field of view with a diameter of ∼30''. No significant continuum-source number excesses are observed in QSO fields other than J2054. Our results suggest that QSOs do not directly trace overabundances, which is also consistent with Champagne et al. (2018). Nevertheless, future observations are required to further confirm the overabundances on a large scale (Meyer et al. 2022).

Absorbers discovered from QSO sightlines can directly trace gas that provides the fuel for star formation and regulates the formation of galaxies. Yet ALMA observations have provided constraints to early CGM/IGM enrichment theoretical models up to z ≈ 6. Our pilot results also suggest that future James Webb Space Telescope (JWST) observations of absorber-galaxy interaction at the epoch of reionization are necessary. We aim to use JWST, as JWST also plans to observe the same sightline with the slitless spectroscopic mode, which will enable us to detect the [O iii] emission λ λ4959, 5007 associated with the [C ii] emitter.

Y.W. thanks Wenshuo Xu, Xiaojing Lin, and Mingyu Li for the fruitful discussion. Z.C., Y.W., and S.Z. are supported by the National Key R&D Program of China (grant No. 2018YFA0404503) and the National Science Foundation of China (grant No. 12073014). The science research grants from the China Manned Space Project with No. CMS-CSST2021-A05, and Tsinghua University Initiative Scientific Research Program (No. 20223080023). The Cosmic Dawn Center is funded by the Danish National Research Foundation. K.F. gratefully acknowledges support from STScI Program #HST-AR-16125.001-A. This program was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Associations of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. K.F.'s simulation utilized resources from the New Mexico State University High Performance Computing Group, which is directly supported by the National Science Foundation (OAC-2019000), the Student Technology Advisory Committee, and New Mexico State University and benefits from inclusion in various grants (DoD ARO-W911NF1810454; NSF EPSCoR OIA-1757207; Partnership for the Advancement of Cancer Research, supported in part by NCI grants U54 CA132383 (NMSU)). M.N. acknowledges support from ERC Advanced grant 740246 (Cosmic_Gas). F.W. is thankful for the support provided by NASA through a NASA Hubble Fellowship (grant No. HST-HF2-51448.001-A) awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. L.K. was supported by the European Unions Horizon 2020 research and innovation program under the Marie Skodowska-Curie grant agreement No. 885990. For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) license to any Author Accepted Manuscript version arising from this submission.

Facility: ALMA - Atacama Large Millimeter Array.

Software: astropy (Astropy Collaboration et al. 2022), lenstronomy (Birrer & Amara 2018; Birrer et al. 2021), CASA v.5.6.1-8 (McMullin et al. 2007), DAOStarFinder (Bradley et al. 2020), CIGALE (Boquien et al. 2019), Qubefit (Neeleman et al. 2020), EAZY-py (Brammer et al. 2008), interferopy (Boogaard et al. 2021).

To get the fidelity of our [C ii] emitter detection, we use interferopy to search for both positive and negative targets in six O i absorber fields. The blue and orange lines in the left panel of Figure 6 show the cumulative distribution of positive and negative targets. To avoid the small number statistics at the tail of the distribution, following González-López et al. (2019), we regarded the number of negative sources as a function with the form of $N=1-\mathrm{erf}(\tfrac{{\rm{S}}/{\rm{N}}}{\sqrt{2}\sigma })$, where erf is the error function. We then integrated this function into the low-S/N end to get the cumulative distribution (red line in the left panel). Following Aravena et al. (2016), we define the fidelity P as $P(\gt {\rm{S}}/{\rm{N}})=1-\tfrac{{N}_{\mathrm{negative}}}{{N}_{\mathrm{postive}}}$, where N_positive and N_negative are the cumulative number of positive and negative targets, respectively. The measured values are shown in gray bars in the right panel of Response Figure 6. We also fitted the measured fidelity as a function of S/N with the form of ${\rm{P}}=1/2+\mathrm{erf}(\tfrac{{\rm{S}}/{\rm{N}}-{\rm{c}}}{\sigma }))/2$. The fitted result is shown as the dark-red line.

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To estimate the actual number of sources in our observations, we insert pseudo-continuum targets into each image of each field and then obtain the detection completeness. Details of the completeness estimation mostly follow the procedure described in Fujimoto et al. (2016), Franco et al. (2018), and Gómez-Guijarro et al. (2022).

We first mask continuum sources with S/N > 4 to avoid the contamination caused by tentative detections. The pseudo-continuum targets were generated using the flux-scaled synthesized beam with S/N ranging from 4 to 6 in steps of 0.1. For each S/N bin, we randomly insert 100 sources into each image and re-perform the source-detection algorithm. If the detected location of an artificial source is close to that inserted within a distance smaller than one beam size, we regard this detection as recovered. The completeness of these QSO fields is shown in Figure 7. The red line is fitted by the function of $1\ -\ \exp (a{\rm{S}}/{\rm{N}}-b)$. We find that sources with S/N ranging from 4-5 have a mean probability of being detected of ∼70%. The completeness-corrected number of continuum sources in fields J2054, J2315, J0100, PSO J183, and PSO J159 are 7.0, 2.8, 4.1, 1.0, and 2.0, respectively.

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In this section, we show the detailed calculations of the correlation length and power-law index. The correlation function is defined as the number excess of galaxies around one metal absorber in a given survey volume.

$\begin{eqnarray}&&\begin{array}{l}{\xi }_{{\rm{g}}-\mathrm{abs}}=\displaystyle \frac{1}{{n}_{0}}\displaystyle \frac{{\rm{\Delta }}N(r)}{{\rm{\Delta }}V}-1.\,\mathrm{Thus}\ \mathrm{we}\ \mathrm{have},\\ {n}_{0}\left[1+{\xi }_{{\rm{g}}-\mathrm{abs}}(r)\right]=\displaystyle \frac{{\rm{\Delta }}N(r)}{{\rm{\Delta }}V}.\end{array}\end{eqnarray} \tag{ C1 }$

If we then assume a power-law function, ${\xi }_{{\rm{g}}-\mathrm{abs}}={\left(\tfrac{r}{{r}_{0}}\right)}^{-\gamma }$, we can then replace ξ_g−abs as a power law and get the following equation:

$\begin{eqnarray}&&{n}_{0}\left[1+{\left(\displaystyle \frac{r}{{r}_{0}}\right)}^{-\gamma }\right]=\displaystyle \frac{{\rm{\Delta }}N(r)}{{\rm{\Delta }}V}.\end{eqnarray} \tag{ C2 }$

We assumed a 3D spherical survey volume with a given radius of r. We then integrate this equation and obtain:

$\begin{eqnarray}&&4\pi {\int }_{0}^{r}{n}_{0}\left[1+{\left(\displaystyle \frac{r}{{r}_{0}}\right)}^{-\gamma }\right]=N(r).\end{eqnarray} \tag{ C3 }$

To justify the spherical approach, we use the following assumptions proposed by simulations. In simulations (Keating et al. 2016), strong O i absorbers are always included within the DM halo of galaxies. For the successfully detected system, the halo mass is 4 × 10¹¹ M_⊙ (Wu et al. 2021), corresponding to the virial radius of ∼20–30 pkpc at z ≈ 6. Further, the observed impact parameter (∼20 pkpc) is very close to the halo virial radius. Thus, to include this system in the DM halo, the line-of-sight distance will be small. A sphere-like survey volume with a radius of 20 pkpc will thus be large enough to include this target. In this work, we detect one galaxy at 20 pkpc. Thus, N(20 pkpc) = 1. We then obtained:

$\begin{eqnarray}&&4\pi {\int }_{0}^{r}{n}_{0}\left[1+{\left(\displaystyle \frac{r}{{r}_{0}}\right)}^{-\gamma }\right]=1,\mathrm{where}\ r=20\,\mathrm{pkpc}.\end{eqnarray} \tag{ C4 }$

By integrating this equation, we then obtain a relation between r₀ and γ:

$\begin{eqnarray}&&\begin{array}{l}\mathrm{log}({r}_{0})=\displaystyle \frac{\mathrm{log}\left[A(\gamma )\right]}{\gamma },\mathrm{where}\\ A\equiv \left(\displaystyle \frac{1}{4\pi {n}_{0}}-\displaystyle \frac{{r}^{3}}{3}\right)\times \left(\displaystyle \frac{3-\gamma }{{r}^{3}}\right),\mathrm{where}\ r=20\,{\rm{pkpc}}.\end{array}\end{eqnarray} \tag{ C5 }$

In this section, we show the comparison between our two sets of criteria. Our major criteria are guided by theoretical simulations and described in Section 3.1.1. Cosmological simulations suggest that these metal absorbers are mostly generated by star formations and galactic outflows (Oppenheimer et al. 2009). Therefore, the velocity offset between absorbers and the actual hosts should be close to the outflow velocity (∼200 km s⁻¹, Steidel et al. 2010). Further, these strong absorbers need to be gravitationally bounded in the circumgalactic medium (CGM) scale (Keating et al. 2014). The impact parameters thus need to be smaller than the virial radii of DM halos (<50 pkpc, at z ∼ 6 Keating et al. 2016). The criteria are shown in the dark-gray region in Figure 8. We note that galaxies in the dark-gray region could be more physically connected to the O i absorbers.

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