# Serendipitous discovery of an optically dark ultra-luminous infrared galaxy at z = 3.4

Natsuki Hayatsu, Zhi-Yu Zhang, R. J. Ivison, Chao-Wei Tsai, Ping Zhou, Katsuya Okoshi, Chentao Yang, Yuri Nishimura, Kotaro Kohno, Nobunari Kashikawa, et al.

► To cite this version:

Natsuki Hayatsu, Zhi-Yu Zhang, R. J. Ivison, Chao-Wei Tsai, Ping Zhou, et al. Serendipitous discovery of an optically dark ultra-luminous infrared galaxy at z = 3.4. Monthly Notices of the Royal Astronomical Society, 2025, 543 (4), pp.3967-3974. 10.1093/mnras/stf1655. hal-05495877

HAL Id: hal-05495877

https://hal.science/hal-05495877v1

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# Serendipitous discovery of an optically dark ultra-luminous infrared galaxy at $z = 3.4$

Natsuki H. Hayatsu<sup>1,★</sup>, Zhi-Yu Zhang<sup>2,3</sup>, R. J. Ivison<sup>1,4</sup>, Chao-Wei Tsai,<sup>5,6,7</sup> Ping Zhou<sup>1,2,3</sup>

Katsuya Okoshi,<sup>8</sup> Chentao Yang<sup>9</sup>, Yuri Nishimura,<sup>10,11,12,13</sup> Kotaro Kohno<sup>10,14</sup>, Nobunari Kashikawa,<sup>15</sup> Masahiro Nagashima,<sup>16</sup> Junfeng Wang<sup>17</sup> and Denis Burgarella<sup>18</sup>

Accepted 2025 September 19. Received 2025 September 18; in original form 2022 November 17

## ABSTRACT

Dusty, submillimeter-selected galaxies without optical counterparts contribute a non-negligible fraction of the star formation in the early universe. However, such a population is difficult to detect through classical optical/UV-based surveys. We report the serendipitous discovery of such an optically dark galaxy, behind the quadruply lensed $z = 2.56$ quasar, H1413+117, offset to the north by $6''$. From $^{12}$CO $J = 4–3$, $J = 6–5$, and part of the $J = 13–12$ transitions, which all spatially coincide with a compact submillimeter continuum emission, we determine an unambiguous spectroscopic redshift, $z = 3.386 \pm 0.005$. This galaxy has a molecular mass $M_{mol} \sim 10^{11}$ M$_{\odot}$ and a black hole mass $M_{BH} \sim 10^{8}$ M$_{\odot}$, estimated from $^{12}$CO $J = 4–3$ and archival *Chandra* X-ray data ($L_{2–10,keV} \sim 4 \times 10^{44}$ erg s$^{-1}$), respectively. We also estimate a total infrared luminosity of $L_{FIR} = (2.8 \pm 2.3) \times 10^{12}$ L$_{\odot}$ and a stellar mass of $M_{*} \lesssim 10^{11}$ M$_{\odot}$, from spectral energy distribution fitting. According to these simple mass estimations, this gas-rich and X-ray bright galaxy might be in a transition phase from starburst to quasar offering a unique case for studying galaxy-black hole co-evolution under extremely dusty conditions.

**Key words:** methods: observational – galaxies: distances and redshifts – galaxies: high-redshift – galaxies: individual: (H1413+117) – submillimetre: galaxies – X-rays: galaxies.

## 1 INTRODUCTION

The most active galaxies at high redshift often harbour large amounts of molecular gas, stellar populations, and supermassive black holes (SMBHs) and they are expected to evolve into massive elliptical galaxies in the local universe (e.g. D. Thomas et al. 2010; S. Toft et al. 2014). Such systems are usually starbursts that are luminous at far-infrared (FIR) wavelengths and faint at ultraviolet (UV) wavelengths

because of dust obscuration. The obscuring material absorbs UV and optical photons emitted from young stars and the accretion discs of SMBHs; i.e. the active galactic nucleus (AGN), and re-emits at IR wavelengths. This produces a population of UV/optically dark galaxies that shine at IR and radio wavelengths (e.g. T. Wang et al. 2019). The most luminous quasars (QSOs)/AGNs at the peak epoch for galaxy and BH growth, $z \approx 2$, are also the most dust-reddened, often or always coincident with merging events (e.g. E. Glikman et al. 2015).

The mid-IR all-sky survey undertaken by WISE found a population of dust-obscured AGNs, which dominate the global spectral energy

<footnote n="1"><sup>1</sup>Waseda Research Institute for Science and Engineering, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan</footnote>

<footnote n="2"><sup>2</sup>School of Astronomy and Space Science, Nanjing University, Nanjing 210023, People's Republic of China</footnote>

<footnote n="3"><sup>3</sup>Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210023, People's Republic of China</footnote>

<footnote n="4"><sup>4</sup>European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching, Germany</footnote>

<footnote n="5"><sup>5</sup>National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Beijing 100101, China</footnote>

<footnote n="6"><sup>6</sup>Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University, Beijing 102206, China</footnote>

<footnote n="7"><sup>7</sup>School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China</footnote>

<footnote n="8"><sup>8</sup>Institute of Arts and Sciences, Tokyo University of Science, 6-3-1, Niijyuku, Katsushika, Tokyo 125-8585, Japan</footnote>

<footnote n="9"><sup>9</sup>Department of Space, Earth and Environment, Onsala Space Observatory, Chalmers University of Technology, SE-439 92 Onsala, Sweden</footnote>

<footnote n="10"><sup>10</sup>Institute of Astronomy, School of Science, The University of Tokyo, 2-21-1, Osawa, Mitaka, Tokyo 181-0015, Japan</footnote>

<footnote n="11"><sup>11</sup>Institute of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan</footnote>

<footnote n="12"><sup>12</sup>Tomonaga Center for the History of the Universe, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan</footnote>

<footnote n="13"><sup>13</sup>Tsukuba Institute for Advanced Research (TIAR), University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan</footnote>

<footnote n="14"><sup>14</sup>Research Center for the Early Universe, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan</footnote>

<footnote n="15"><sup>15</sup>Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan</footnote>

<footnote n="16"><sup>16</sup>Faculty of Education, Bunkyo University, 3337 Minami-Ogishima, Koshigaya-shi, Saitama 343-8511, Japan</footnote>

<footnote n="17"><sup>17</sup>Department of Astronomy, Xiamen University, Xiamen, Fujian 361005, People's Republic of China</footnote>

<footnote n="18"><sup>18</sup>Laboratoire d'Astrophysique de Marseille, Aix Marseille University, CNRS, CNES, 38, rue Frédéric Joliot-Curie, F-13388 Marseille, cedex 13, France</footnote>

<footnote>*E-mail: hayatsu@aoni.waseda.jp</footnote>
distributions (SEDs) of their host galaxies and can reach bolometric luminosities of ≈10¹³–10¹⁴ L⊙ (Hyper- or Extremely Luminous IR Galaxy; P. R. M. Eisenhardt et al. 2012; J. Wu et al. 2012; C.-W. Tsai et al. 2015). Their extraordinary mid-IR luminosity is due to hot dust, with little rest-frame optical emission due to the high extinction (2 ≲ E(B − V ) ≲ 25; R. J. Assef et al. 2015). Near-IR (NIR) spectroscopic studies suggest that SMBH masses can exceed 10⁹ M⊙, with an accretion rate close to the Eddington limit (C.-W. Tsai et al. 2018; J. Wu et al. 2018). This population of hot, dust-obscured galaxies (HotDOGs; J. Wu et al. 2012) resides at the massive end of the black hole – stellar mass relation (J. Magorrian et al. 1998; R. J. Assef et al. 2015; J. Wu et al. 2018).

The predecessors of the most massive galaxies are also expected
to be dust-obscured starburst/AGN host galaxies, which are likely
triggered by major mergers that boost star formation and AGN
activity, which then blow out the surrounding dust and gas via
AGN outflows and stellar winds (D. B. Sanders et al. 1988; P. F.
Hopkins et al. 2008; Y. Tamura et al. 2010; T. Díaz-Santos et al.
2018). Although large FIR and submillimeter (submm) surveys, e.g.
H-ATLAS and the SPT survey, have discovered submm galaxies
(SMGs) without optical counterparts (S. Eales et al. 2010; T. R.
Greve et al. 2012) – indeed, I. Smail et al. (2021) point out that
this population is rediscovered regularly – it is extremely resource
intensive and time consuming to determine their redshifts and
intrinsic properties in blind line searches (e.g. A. Weiß et al. 2009; F.
Walter et al. 2012), unless the survey is designed highly efficiently
using wideband receivers and/or targeting clustering fields (A. Weiß
et al. 2013; R. Neri et al. 2020).

In this paper, we report the serendipitous discovery of an optical
and NIR dark galaxy, which has a small angular separation from
a lensed QSO known as the Cloverleaf at z = 2.56 (P. Magain
et al. 1988). In Section 2, we describe ALMA observations and data
reduction, and in Section 3 we present the serendipitous detection of
line emission in the ALMA data and multiwavelength data including
new imaging from *Spitzer*. In Section 4, we discuss the determination
of the spectroscopic redshift and molecular and BH mass estimations.
In Section 5, we summarize our result and discuss future prospects.

Throughout this paper, we adopt a standard Lambda cold dark mat-
ter cosmological model with the following parameters: Ω_m = 0.30,
Ω_Λ = 0.70, and the Hubble constant, H_0 = 70 km s⁻¹ Mpc⁻¹.

## 2 ALMA OBSERVATIONS AND DATA REDUCTION

**2.1 Band 3 observation**

ALMA Cycle 3 band 3 observations (ID: 2015.1.01309.S; PI: Z. Zhang) were taken during 2016 April, with the pointing centred on the Cloverleaf: right ascension (RA) and declination (Dec.) (J2000) = 14h15m46.25s, +11d29m43.4s.

The observing frequency consists of four spectral windows (SPWs), covering frequency ranges of 91.87–93.74, 93.77–95.75, 103.88–105.86, and 105.77–107.75 GHz. The synthesized beam is 2.′72 × 1.′56. The exposure time is 29.23 min, with a precipitable water vacuum (PWV) of 3.12 mm. The details of the observations are described in Z.-Y. Zhang et al. (2018).

**2.2 Follow-up band 4 observation**

We performed ALMA band 4 observations in ALMA Cycle 7
(ID: 2019.1.00883.S; PI: N. H. Hayatsu). The frequency cover-
age, 136.86–147.81, 148.86–152.60, and 156.06–159.81 GHz, al-

lowed us to look for line emission at possible redshifts: z =
2.3, 3.4, 4.5, or 5.6. The observation was centred on RA and Dec.
(J2000) = 14h15m46.279s, 11d29m49.815s.

The exposure time is 25.7 min, with a PWV of ~0.75 mm.
The spectral resolution and the median angular resolution are
1953.09 kHz and 0.85 × 0.78, respectively.

## 2.3 ALMA archival band 7 data

We searched the ALMA archive for data targeting the Clover-
leaf, finding proposal IDs 2011.0.00747.S, 2012.1.00175.S,
2012.1.01081.S, 2017.1.01232, and 2017.1.00963.S.

In the ALMA Cycle 1 band 7 data (ID: 2012.1.00175.S, PI: P. van der Werf), we found the continuum and line emission coinciding with the new source, as described Section 3.3. The exposure time and the angular resolution are 9.4 min and 0.′30 × 0.′18, respectively. The frequency resolution is 15.625 MHz after re-binning, with frequency coverages of 325.84–327.83, 327.28–329.27, 338.41–340.41, and 339.47–341.46 GHz.

No significant continuum or line emission was detected in the
other archival data sets.

## 2.4 ALMA data reduction

All ALMA data, including the archival data were reduced and analysed with the Common Astronomy Software Application (CASA) ver. 5.6.1–8 (J. P. McMullin et al. 2007). We calibrated the data with the default pipeline scripts. The rms noise was estimated using *imstat* in the region with primary beam response >0.5. We subtracted the continuum with *uvcontsub*, then cleaned the data with *tclean* with briggs weighting and robust = 0.5.

We fitted a two-dimensional Gaussian profile to the 3 mm contin-
uum data corrected for the primary beam with *imfit*. Line fluxes are
measured with *specflux*. The measured values are summarized in
Table 1, combining with the photometry measurements discussed in
Section 3.4. There are no significant atmospheric features within the
frequency ranges covered by the data used in this paper.

3 DATA ANALYSIS AND SOURCE DETECTION

3.1 Line detection in ALMA band 3

The noise level of the band 3 continuum image is ≈75 µJy beam⁻¹.
We re-bin the spectral channels from 976.51 kHz to 15.625 MHz
(≈45 km s⁻¹), which then reaches a noise level of ≈0.23 mJy beam⁻¹
per channel.

We performed a systematic blind line search in our previous ALMA band 3 data (N. H. Hayatsu et al. 2017), and discovered a strong emission line at 105 GHz, coincident spatially with continuum, ~6 arcsec away from Cloverleaf. The peak position is RA = 14h15m46.30s, Dec. = 11d29m49.8s. The best-fitting parameters are: flux density, 218 ± 75 µJy, with the major and minor axes of 2.′72 and 1.′72, respectively, indicating an unresolved source.

We then extracted a spectrum of the source with an aperture size matched to the beamsize. As shown in Fig. 1, the 105-GHz line profile is doubly or triply peaked, with a full-width zero power (FWZP) ~1000 km s⁻¹. The two striking peaks lie at 105.00 and 105.22 GHz, and we take the central frequency as the mean value, 105.11 GHz. The velocity-integrated flux yields 1.27 ± 0.10 Jy km s⁻¹, with the mean of the peaks of 1.73 ± 0.30 mJy. The peak SN ratio achieves 6.7 σ at a 45 km s⁻¹ resolution. The moment-0 image in Fig. 1 indicates that the line-emitting region is also unresolved.
<table><caption>**Table 1.** Position, line total flux, and multiband photometry of the new source.</caption><thead><tr><th>Parameter</th><th>Value</th><th>Comment or unit</th></tr></thead><tbody><tr><td>RA</td><td>14:15:46.279</td><td>ALMA, J2000<sup>a</sup></td></tr><tr><td>Dec.</td><td>11:29:49.815</td><td>ALMA, J2000<sup>a</sup></td></tr><tr><td>redshift</td><td>3.386 ± 0.005</td><td>from CO J = 4–3<sup>a</sup></td></tr><tr><td>CO J = 4–3</td><td>1.27 ± 0.10</td><td>Jy km s<sup>-1a</sup></td></tr><tr><td>CO J = 5–6</td><td>1.40 ± 0.40</td><td>Jy km s<sup>-1b</sup></td></tr><tr><td>CO J = 12–11</td><td>0.24 ± 0.06</td><td>Jy km s<sup>-1c</sup></td></tr><tr><td>0.5–10 keV</td><td>45</td><td>counts, Chandra<sup>d</sup></td></tr><tr><td>0.8 µm</td><td>&lt;2.0</td><td>µJy, HST/F814W<sup>e</sup></td></tr><tr><td>1.6 µm</td><td>&lt;1.2</td><td>µJy, HST/F160W<sup>f</sup></td></tr><tr><td>1.8 µm</td><td>&lt;1.1</td><td>µJy, HST/F180M<sup>g</sup></td></tr><tr><td>2.3 µm</td><td>&lt;2.6</td><td>µJy, VLT/ISAAC K<sub>s</sub><sup>h</sup></td></tr><tr><td>3.6 µm</td><td>31 ± 7</td><td>µJy, Spitzer/IRAC1<sup>i</sup></td></tr><tr><td>4.5 µm</td><td>38 ± 6</td><td>µJy, Spitzer/IRAC2<sup>i</sup></td></tr><tr><td>340 GHz</td><td>4.0 ± 0.2</td><td>mJy, ALMA/band 7</td></tr><tr><td>140 GHz</td><td>368 ± 70</td><td>µJy, ALMA/band 4</td></tr><tr><td>100 GHz</td><td>218 ± 75</td><td>µJy, ALMA/band 3</td></tr><tr><td>33 GHz</td><td>&lt;15</td><td>µJy, VLA<sup>j</sup></td></tr></tbody></table>

Note. All upper limits are 3σ.

<sup>a</sup>ALMA band 3 data (2015.1.01309.S).

<sup>b</sup>ALMA band 4 data (2019.1.00883.S).

<sup>c</sup>ALMA band 7 data (2012.1.00175.S).

<sup>d</sup>ID: 930, 5645, and 14960.

<sup>e</sup>The ID is 8268 and the instrument is WFPC2/PC.

<sup>f</sup>The ID is 7495 and the instrument is NICMOS.

<sup>g</sup>The ID is 9439 and the instrument is NICMOS.

<sup>h</sup>Co-add data.

<sup>i</sup>ID:14252.

<sup>j</sup>ID:13B-051.

## 3.2 Line detection in ALMA band 4

The sensitivities of the band 4 achieves 24 µJy beam⁻<fnref n="1" /> and 0.24 mJy beam⁻<fnref n="1" /> at a 21.1 MHz or ~40 km s⁻<fnref n="1" /> resolution, for continuum and line, respectively.

We measure a continuum flux density of 368 ± 70 µJy as a point source. We extracted a spectrum at the continuum position and the FWZP of the line is ≈1200 km s⁻<fnref n="1" />, similar to the line found in the band 3 data. We detected a double or triple peaked emission line at 157.6 GHz in the band 4 datacube covering 156.06–159.81 GHz. The total flux of the line emission is 1.40 ± 0.40 Jy km s⁻<fnref n="1" /> with a peak S/N of 8.64 σ.

## 3.3 Additional detection in ALMA band 7

The sensitivity of the band 7 continuum achieves 61 µJy beam⁻<fnref n="1" />. We found a continuum emission at ~340 GHz, with a flux of 4.0 ± 0.2 mJy at the peak position of 14h15m46.31s, 11d29m50.1s with an apparent size of 0.38 × 0.36.

We obtained the spectrum in the continuum region with the SPWs covering 339.47–341.46 GHz. The median sensitivity of the datacube was ≈0.6 mJy beam⁻<fnref n="1" /> at 15.6 MHz or ~13.8 km s⁻<fnref n="1" /> resolution. Weak line emission appears at ~340.8 GHz. Unfortunately, this SPW covers only half of the necessary velocity range, and only shows a narrow feature. The measured total flux of the line is 0.24 ± 0.06 Jy km s⁻<fnref n="1" /> with a peak S/N of 2.74σ.

## 3.4 Photometric counterparts

To check whether the detected lines arise from a known source, we compare the source position of the new source with those of the

<figure><img src="image_2.png" /><figcaption>**Figure 1.** CO Spectra, submm continuum, and CO moment-0 maps of the newly discovered source at 6'' north-east to the Cloverleaf QSO. Top: CO spectra J = 4–3, 6–5, and 13–12 from the detected source at ~40–45 km s⁻<fnref n="1" /> resolution. We label the line emission velocity range in yellow. The vertical line represents $v_{sys} = 0$. The CO J = 13–12 spectrum covers only part of the velocity range at the edge of the SPW. Bottom: Moment-0 map of the CO J = 4–3 line detected in ALMA band 3, shown with greyscales. The green and bold contours represent the band 3 continuum data at levels 2, 3, and 4σ. The red abd cyan contours with medium and thin thickness represent band 4 and 7 continuum data, respectively, at 5, 10, and 20σ levels. The beam size for each data set is shown with its corresponding colour (2.72 × 1.56, 0.85 × 0.78, and 0.30 × 0.18, from top to bottom, respectively).</figcaption></figure>

surrounding galaxies reported by J. P. Kneib et al. (1998a) and J. P. Kneib, D. Alloin & R. Pello (1998b). We also check the NASA/IPAC Extragalactic Data base.<fnref n="1" /> There is no known source within a radius of 1 arcsec of the position of the new source. Note that we checked the

<footnote n="1">¹The website of the data base: https://ned.ipac.caltech.edu/.</footnote>
<figure><img src="image_3.png" /><figcaption>**Figure 2.** NIR (left and middle) and X-ray (right) snapshots of the new source. The red contours show the ALMA 850 µm continuum emission, at 5, 10, and 20σ. The residual image from *Spitzer* 4.5 µm shows marginal detection, while the *HST* 1.6 µm band shows non-detection. The new source is detected in the archival *Chandra* X-ray data (integrated within in 0.8–10 keV), which originally targeted the Cloverleaf.</figcaption></figure>

optically detected absorption line toward the Cloverleaf reported by E. M. Monier, D. A. Turnshek & O. L. Lupie (1998) and there is no corresponding absorption system associated with the newly detected source.

The Cloverleaf field has been observed at multiple wavelengths from radio to X-ray, using, e.g. *Hubble Space Telescope (HST)*, the Very Large Telescope (VLT), *Spitzer*, *WISE*, *Herschel*, VLA, ALMA, and *Chandra*. We searched for counterparts to the detected source using these archival data, as well as in our newly acquired *Spitzer* data (Fig. 2). Our measured values and proposal IDs are summarized in Table 1. In this section, we focus on the non-detections in *HST*, VLT, and VLA data and detections in the *Spitzer* and *Chandra* data.

### 3.4.1 HST and VLT

We perform an aperture photometry for an aperture of 1 arcsec in diameter for both *HST and VLT* data. The *HST* multiband optical/NIR data (F814W, F160W, F180M) are obtained from Hubble Legacy Archive<fnref n="2" />, with project IDs 8268, 7495, and 9439. The exposure time is 5200, 2560, and 4096 s for the F814W, F160W, and F180M data, respectively. We first masked all strong sources in a 10 arcsec radius region, then fit the background and subtracted it. Then we randomly draw 20 000 times of 1 arcsec-diameter circles and measure their fluxes. The final noise levels were obtained by fitting these fluxes with a Gaussian distribution. The non-detections put upper limits of <1.1–2.0 µJy, corresponding to ~23–24 AB magnitude at 0.8–1.8 µm.

The VLT/ISAAC data (programme ID:67.A-0502; PI: Courbin, F.) in K band shows no detection of the source, to a 3σ upper limit of <2.6 µJy at 2.3 µm. The total exposure time is 1 h 50 min.

### 3.4.2 VLA

We obtained the K-a band (33 GHz) JVLA data from the NRAO archival system. The project ID is 13B-051 (PI: Sharon, Chelsea), and was taken from 2013 October 27 to 2014 January 5, with the B-array configuration. The total on-source time is ~6.8 h on-source.

The data were calibrated and imaged with CASA 5.6.2–2 using the standard pipeline. The noise level is $\sigma \sim 4.5 \times 10^{-6}$ Jy beam$^{-1}$, with a beam size of ~0".25.

### 3.4.3 Spitzer/IRAC

We obtained *Spitzer* observations with 500 s of on-source time in IRAC band 1 (3.6 µm), and 1080 s in the IRAC band 2 (4.5 µm), with the proposal ID:14252 (PI: N. H. Hayatsu). This source was observed on 2019 October 28.

The observation yielded an rms noise level of 0.39 µJy at 3.6 µm and 0.42 µJy at 4.5 µm. Our target is covered and overpowered by the halo of the Cloverleaf because of the large PSF of IRAC images. The residual IRAC image was generated after the subtraction of the contribution of the Cloverleaf. The IRAC subtraction was performed using the *HST/F180M* image as a model for Cloverleaf. We convolve the point sources in the F180M image with the IRAC PSFs rotated to the observing position angle to make the Cloverleaf model in both IRAC images. The aperture corrections were applied.

After removing the Cloverleaf using the models, we performed aperture photometry on the location of the new source. We adopted the sky subtraction value from the further out region (with a ~20 arcsec annulus radius) and the mean statistics clipped to avoid contamination from the residual of the Cloverleaf. The error was estimated by combining the sky variation within the sky annulus and the residual variation near the new source. We also propagate the calibration errors into the error estimate.

The source was detected in the residual map with flux densities of 31 ± 7 µJy and 38 ± 6 µJy for the IRAC band 1 and band 2, respectively.

### 3.4.4 Chandra

We have identified the X-ray counterpart from the archival *Chandra* data targeting at Cloverleaf with a total exposure time of 147 ks after removing 38.2 ks of exposure affected by a solar flare in 2000 April. We extracted *Chandra* X-ray spectra from a 1 arcsec radius circular region centred at the new source, and selected the background from an annular region surrounding the new source. By merging all the

<footnote n="2">²https://hla.stsci.edu/hlaview.html</footnote>
observations, Our analysis yields 45 counts of X-ray photons in 0.5–10 keV, which were grouped to have a minimum of 5 counts per bin. There was no positional offset between the X-ray and submm dust continuum emission from ALMA (within 0".8).

# 4 RESULT AND DISCUSSION

## 4.1 Redshift identification

From the frequency ratios of the detected line emission, we identify the line species are CO J = 4–3, 6–5, and 13–12 for the 105.1, 157.6, and 340.8 GHz lines, respectively. Therefore, we obtain the redshift of this system, from the first detection at 105.11 ± 0.11 GHz, corresponding to z = 3.386 ± 0.005. Note that other redshift possibilities from z = 0–10 are excluded by the non-detection of line emission in our other observed frequency range.

## 4.2 CO emissions and molecular mass

The line width, FWZP ~ 1000 km s⁻¹, and the double-peaked CO J = 4–3 and 6–5 lines, are suggestive of an interacting system (e.g. P. Salomé et al. 2012; E. Treister et al. 2012; T. Díaz-Santos et al. 2018). The frequency coverage of CO J = 13–12 line covers only part of the low-J velocity range (Fig. 1). Note that alternative explanations for the double-peaked emission profile, such as a disc-like galaxy, should be investigated in future high-angular resolution observations.

We estimate its molecular gas mass $M_{mol}$ from the CO J = 4–3 line using conversion factors for mass-to-light ratio and CO line ratio. We use a formula from A. D. Bolatto, M. Wolfire & A. K. Leroy (2013):

$$M_{mol} = 1.05 \times 10^4 \left( \frac{X_{CO(1-0)}}{2 \times 10^{20} \frac{\text{cm}^{-2}}{\text{kmms}^{-1}}} \right) \frac{S_{CO(1-0)} \Delta v D_L^2}{(1+z)} M_{\odot},$$

where $X_{CO}$, $S_{CO}\Delta v D_L^2$, and z are CO-to-H₂ conversion factor in cm⁻² K⁻¹ km⁻¹ s, integrated flux density for CO J = 1–0 in Jy km s⁻¹, luminosity distance in Mpc, and redshift.

We assume a $X_{CO(1-0)} = 0.5 \times 10^{20} \text{cm}^{-2} \text{K}^{-1} \text{km}^{-1} \text{s}$, a typical value for high-redshift starburst galaxies (A. D. Bolatto et al. 2013). We refer to the high-z CO J = 4–3/CO J = 1–0 line brightness temperature ratio $r_{41} = 0.63 \pm 0.44$ from M. Frias Castillo et al. (2023), assuming the same line profile between the two CO line emissions.

Although the value differs by the selection of the conversion factor and the assumption of the line profile, the estimate indicates that the source has a massive molecular gas budget $M_{mol} \sim 4–23 \times 10^{10} M_{\odot}$, which is consistent with the typical value of high-z ULIRGs.

## 4.3 X-ray emission and BH mass

To fit the X-ray spectrum, we first applied an absorbed power-law model zpowerlaw, tbabs, and ztbabs in XSPEC (K. A. Arnaud 1996) and employed a C-statistic (W. Cash 1979) for fitting statistics. The redshift is fixed to 3.39 and the photon index is fixed $\Gamma = 1.7$, a typical value for AGN.

The X-ray spectrum suggests an intrinsic absorption column density $N_H$ of $(5 \pm 2) \times 10^{23} \text{cm}^{-2}$, which consistent with the estimate from the ALMA dust measurement discussed in Appendix A. X-ray flux are estimated $4.6 \times 10^{-15} \text{ erg cm}^{-2} \text{ s}^{-1}$ and the total X-ray luminosity is $\sim 4 \times 10^{44} \text{ erg s}^{-1}$ in 0.5–10 keV. From this value, we can obtain an estimate of black hole mass $M_{BH} \sim 10^8 M_{\odot}$ from the empirical correlation reported in J. A. Mayers et al. (2018). The hard

X-ray data show a point source, suggesting a dust-enshrouded AGN (Fig. 2).

The non-detection at the optical wavelength indicates that this system, no matter whether it is powered by starburst or AGN, is highly obscured. Although the non-detections at the optical wavelength suggest that the AGN is obscured (e.g. T. Wang et al. 2019), the X-ray detection indicates that the foreground material is not Compton thick for X-ray. It is suspected that the AGN has not yet reached its peak accretion capacity and is not fully cocooned by dust. The molecular gas has not yet been impacted by radiative feedback. This scenario is similar to that of extremely luminous Hot DOGs in a similar redshift range (C.-W. Tsai et al. 2015), although these Hot DOGs usually reach the Eddington limits (C.-W. Tsai et al. 2018; J. Wu et al. 2018) and lack AGN features in their optical wavebands and X-ray emissions (F. Vito et al. 2018). Therefore, it is possible that the new source is in the progenitor stage of the hot DOG phase, perhaps evolving towards the naked AGN phase and then the elliptical galaxy in the local universe (D. Thomas et al. 2010; S. Toft et al. 2014).

We present SED analysis and stellar mass estimation in Appendix A.

# 5 SUMMARY

We discovered a new galaxy located 6 arcsec away from the well-known Cloverleaf quasar (H1413+117) at z = 2.56. The spectroscopic redshift of this system was determined to be z = 3.386 ± 0.005 based on detections of the CO J = 4–3, 6–5, and 13–12 lines from ALMA band 3, 4, and 7 data, respectively.

The double-peaked CO profiles suggest that the molecular gas in this system has not yet settled dynamically, likely due to a gas-rich major galaxy merger in its early stages. Therefore, the source is likely destined to continue as a starburst, with its rich molecular budget, triggered by the merging process (e.g. E. Glikman et al. 2015). In addition, the strong X-ray emission provides evidence of an accreting AGN in this system.

The central mystery of this source compared to typical SMGs is how it can display bright dust continuum and X-rays alongside extremely weak NIR/optical. The newly confirmed system at z = 3.39 is thus an interesting target to study galaxy–BH co-evolution in extremely dusty conditions. To infer the evolutionary stage of such an optically dark galaxy, be it massive starburst, QSO, or HotDOG, it is essential to clarify the physical state of the gas, especially the dense molecular gas that provides the fuel for star formation, and this will be the subject of future follow-up studies. The uncertainty of the mass estimates should be discussed and improved after obtaining new constraints for NIR and FIR wavelengths using e.g. James Webb Space Telescope and ALMA.

# ACKNOWLEDGEMENTS

We would like to express our sincere gratitude to the anonymous reviewers for their valuable comments and suggestions, which significantly improved the manuscript.

NHH acknowledges the support of European Southern Observatory (ESO) through its PhD Studentship Programme. NHH is grateful to the NAOJ ALMA project for financial support for the ALMA workshops (2020b, 2023a). This work was initiated and conducted during NHH’s time at ESO, the University of Tokyo, Bunkyo University, and Ecole Normale Supérieure, and was submitted while she was affiliated with the Ishigakijima Astronomical Observatory, NAOJ.
ZYZ acknowledges the support of NSFC (grants 12041305, 12173016, 1257030642, 12533003). ZYZ acknowledges the Programme for Innovative Talents, Entrepreneur in Jiangsu. ZYZ acknowledges the science research grants from the China Manned Space Projects with no. CMS-CSST-2021-A08 and CMS-CSST-2021-A07. Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2094–390783311.

CWT acknowledges support from the NSFC grant 11973051.

CY acknowledges support from an ERC Advanced grant 789410.

DB acknowledges the CNRS International Research Network France-Japan NECO'.

This work was supported by JSPS KAKENHI grant nos JP18H05437, JP20H01950 (MN), JP17H06130, JP23K20035, and JP24H00004 (KK), and the NAOJ ALMA Scientific Research grant number 2017–06B (YN, KK).

JW acknowledges support from the NSFC grant 12033004.

This paper makes use of the following ALMA data: ADS/JAO.ALMA#2011.0.00747.S, 2012.1.00175.S, 2015.1.01309.S, 2017.1.00963, 2017.1.01081.S, 2017.1.01232.S and 2019.1.00883.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. This research has made use of the NASA/IPAC Extragalactic Data base (NED), which is funded by the National Aeronautics and Space Administration and operated by the California Institute of Technology.

## DATA AVAILABILITY

The data underlying this article were accessed from

(i) HST: https://hla.stsci.edu/hlaview.html,

(ii) VLT: https://archive.eso.org/scienceportal/home,

(iii) VLA: https://data.nrao.edu/portal/#/,

(iv) Spitzer: https://sha.ipac.caltech.edu/applications/Spitzer/SH A/,

(v) Chandra: https://cda.harvard.edu/chaser/,

(vi) ALMA: https://almascience.nrao.edu/aq/.

The derived data generated in this research will be shared on reasonable request to the corresponding author.

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## APPENDIX: SED PROPERTIES

We compile the SED of the new source with all data collected from the literature (see Fig. A1 left). These data cover a wide range of wavelengths, from radio to optical. We then attempt to infer the
<figure><img src="image_4.png" /><figcaption>**Figure A1.** Photometry of the new source. The measurements are shown in red circles and blue triangles. (Left:) Blue dashed, light green dotted, orange, cyan, and brown curves represent the SED templates of high-redshift radio galaxy, DKB07 (HzRG; H. Dannerbauer et al. 2014), AGN torus model constructed from Compton-thick AGNs (M. d. C. Polletta et al. 2006), hot dust-obscured galaxies (C.-W. Tsai et al. 2015), a Type-1 AGN (G. T. Richards et al. 2006), and an elliptical galaxy (R. J. Assef et al. 2010), respectively. The grey shaded region indicates the $1\sigma$ region for a large sample of SMGs from SCUBA-2 (following R. J. Ivison et al. 2019; U. Dudzevičiūtė et al. 2020). None of the templates are compatible with the SED of the new source. (Right:) The best-fitting model from the SED fitting code X-CIGALE (D. Burgarella, V. Buat & J. Iglesias-Páramo 2005; M. Boquien et al. 2019; G. Yang et al. 2020). The best-fitting model well explains the upper limits in the optical wavebands (black solid curve). The dashed lines show the corresponding SED components.</figcaption></figure>

global physical properties of the new source by comparing with a series of SED templates of a high redshift radio galaxy (HzRG; H. Dannerbauer et al. 2014), an AGN torus model constructed from Compton-thick AGNs (M. d. C. Polletta et al. 2006), hot dust-obscured galaxies (C.-W. Tsai et al. 2015), a Type-1 AGN (G. T. Richards et al. 2006), an elliptical galaxy (R. J. Assef et al. 2010), and SCUBA-2 SMGs (R. J. Ivison et al. 2019; U. Dudzevičiūtė et al. 2020), respectively. We manually adjusted the amplitude of the template to best match the observed data.

Overall, none of the SEDs is compatible with the optical darkness of the new source. This suggests that the emission in our deep Spitzer IRAC measurements is dominated by the torus emission constructed from a Compton-thick AGN (light green dotted curve in Fig. A1 left M. d. C. Polletta et al. 2006), but yet still suffers extinction which removes most of its rest-frame optical emission. The non-detection by HST naively suggests a host galaxy with $M_*$ smaller than that of elliptical galaxy ($10^{10} M_\odot$; the brown curves shown in Fig. A1 left), but of course this ignores the effects of dust obscuration.

For more discussion, we use SED fitting code CIGALE (Code Investigating GALaxy Emission<fnref n="3" />), which is capable of modelling the observed SED from X-ray to radio (D. Burgarella et al. 2005; M. Boquien et al. 2019; G. Yang et al. 2020) and returns the best-fitting model and the Bayesian-like analysis. We aim to obtain FIR luminosity ($L_{FIR}$), stellar mass, and AGN fraction from the result. We input fixed values for, e.g. redshift, X-ray power-law index so that the values are consistent with the observational result and the assumption. For some of the other parameters, such as visual extinction $E(B-V)$, or a fraction of the AGN luminosity to the total dust bolometric luminosity $f_{AGN}$, we input as a range of values. For example, we input $E(B-V) = 30-50$ assuming that the column density of H1 is the same as the column density from X-ray observation.

We run $\sim 3 \times 10^7$ models and the best model which contains six components; an attenuated stellar, a nebular, a dust, an AGN, and a radio component. For detailed information on the parameter sets, see Table A1. Note that we ignore the unreal cuts at the edge of the components. The best-fitting model with reduced $\chi^2 = 3.55$ explains the upper limits in the optical wavebands (black solid curve in Fig. A1 right). As the results, the Bayesian analysis yields large uncertainties in model parameters. However, we still consider the results for the rough estimates on the overall characteristics of the SED such as the luminosity or mass.

From the best-fitting model, we obtain $M_* = 5.4 \pm 0.8 \times 10^{10} M_\odot$. This large uncertainty indicates the model cannot constrain stellar mass. Note that this cannot be improved with the higher extinction ($E(B-V) > 100$). Thus we regard the value $M_* \lesssim 10^{11} M_\odot$ as an upper limit.

The dust bolometric luminosity is $L_{FIR} = 2.8 \pm 2.3 \times 10^{12} L_\odot$. The value from the best-fitting model is lower than a conservative estimate from the dust continuum flux, $\sim 10^{13} L_\odot$ (e.g. A. W. Blain et al. 2002).

The extinction and the AGN fraction $f_{AGN}$ shows $40 \pm 8$ and $0.5 \pm 0.3$ for the Bayesian-like analysis, respectively.

To compare the star-formation rate (SFR) with the known galaxies, we obtain SFR by considering the contribution from dust bolometric luminosity using the empirical relation from J. Kennicutt (1998) assuming G. Chabrier (2003) IMF, which is the same assumption to the SED analysis:

$$ \frac{\text{SFR}}{M_{\odot}\text{yr}^{-1}} \approx 1.52 \times 10^{-10} x_{\text{StoC}}(1 - f_{\text{AGN}}) \frac{L_{\text{FIR}}}{L_{\odot}}, $$

where the conversion factor from Salpeter to Chabrier IMF $x_{\text{StoC}} = 1.7$. The discovered source has an SFR $\sim 362_{-336}^{+693} M_{\odot}\text{yr}^{-1}$. The SFR from Cigale returns $\sim 83 M_{\odot}\text{yr}^{-1}$, which is consistent with the calculation.

<footnote n="3">³https://cigale.lam.fr</footnote>
<table><caption>**Table A1.** A range of models, free parameters and best-fitting model for the new source's SED, calculated by X-CIGALE.</caption><thead><tr><th>Model/parameter</th><th>Values</th><th>Best-fitting model</th></tr></thead><tbody><tr><td colspan="3"><strong>Star-formation history: double-exponentially decreasing (τ-decay) model</strong></td></tr><tr><td>e-folding time of the main stellar population (Myr)</td><td>500, 1000, 2000, 3000, 6000</td><td>6000</td></tr><tr><td>Age of the main stellar population (Myr)</td><td>100, 250, 500, 1000, 2500, 5000</td><td>1000</td></tr><tr><td>e-folding time of the late starburst population (Myr)</td><td>25, 50, 75, 100</td><td>50</td></tr><tr><td>Age of the late burst (Myr)</td><td>5, 10, 20, 50, 100</td><td>20</td></tr><tr><td>Mass fraction of the late burst population</td><td>0.01, 0.03, 0.1</td><td>0.01</td></tr><tr><td colspan="3"><strong>Stellar population synthesis model</strong></td></tr><tr><td>Simple stellar population</td><td>G. Bruzual & S. Charlot (2003)</td><td>G. Bruzual & S. Charlot (2003)</td></tr><tr><td>Initial mass function</td><td>E. E. Salpeter (1955) or G. Chabrier (2003)</td><td>E. E. Salpeter (1955); G. Chabrier (2003)</td></tr><tr><td>Metallicity</td><td>0.02</td><td>0.02</td></tr><tr><td colspan="3"><strong>Dust attenuation: Calzetti et al. (2000)</strong></td></tr><tr><td>Colour excess of stellar continuum light for young stars E(B-V)</td><td>30–60 (step 5)</td><td>50</td></tr><tr><td colspan="3"><strong>Dust emission: Dale et al. (2014)</strong></td></tr><tr><td>α slope in dM<sub>dust</sub> ∝ U<sup>-α</sup>dU<br>(IR power-law slope)</td><td>1.0, 2.0, 3.0</td><td>2.0</td></tr><tr><td colspan="3"><strong>AGN (UV-to-IR): SKIRTOR (Stalevski et al. 2012, 2016)</strong></td></tr><tr><td>Viewing angle (θ)<br>(face on: θ = 0°, edge on: θ = 90°)</td><td>30°, 30°</td><td>30°</td></tr><tr><td>Opening angle</td><td>20°, 50°, 70°</td><td>50°</td></tr><tr><td>a AGN fraction in total IR luminosity</td><td>0.1, 0.3, 0.5, 0.7, 0.9</td><td>0.9</td></tr><tr><td>Mass fraction of the late burst population</td><td>0.4, 0.5, 0.6</td><td>0.6</td></tr><tr><td>Extinction law of polar dust</td><td>SMC, Calzetti et al. (2000); Gaskell et al. (2004)</td><td>SMC</td></tr><tr><td>E(B-V) of polar dust</td><td>30, 40, 50</td><td>50</td></tr><tr><td>Temperature of polar dust (K)</td><td>100, 150, 200</td><td>100</td></tr><tr><td>Emissivity of polar dust</td><td>1.6</td><td></td></tr><tr><td colspan="3"><strong>AGN X-ray</strong></td></tr><tr><td>AGN photon index (Γ)</td><td>1.7</td><td></td></tr><tr><td>X-ray energy cut-off (E<sub>cut</sub>)</td><td>330 KeV</td><td></td></tr><tr><td>Maximum deviation from the α<sub>ox</sub>-L<sub>v</sub>(2500 Å) relation</td><td>0.2</td><td></td></tr><tr><td colspan="3"><strong>Radio</strong></td></tr><tr><td>The slope of the power-law synchrotron emission</td><td>0.7, 0.8, 0.9</td><td>0.9<sup>a</sup></td></tr></tbody></table>

The dust bolometric luminosity requires the contribution of an SMBH with $M_{BH} = 1.4^{+2.6}_{-1.3} \times 10^8 M_{\odot}$, assuming a typical Eddington ratio ~0.3 for $z \sim 2$ QSOs (R. J. Assef et al. 2015; C.-W. Tsai et al. 2015). The estimate has an agreement with $M_{BH}$ value from X-ray.

This paper has been typeset from a TeX/LATEX file prepared by the author.