Search for Optically Dark Infrared Galaxies without Counterparts of Subaru Hyper Suprime-Cam in the AKARI North Ecliptic Pole Wide Survey Field

Yoshiki Toba, Tomotsugu Goto, Nagisa Oi, Ting-Wen Wang, Seong Jin Kim, Simon C.-C. Ho, Denis Burgarella, Tetsuya Hashimoto, Bau-Ching Hsieh, Ting-Chi Huang, et al.

► To cite this version:

Yoshiki Toba, Tomotsugu Goto, Nagisa Oi, Ting-Wen Wang, Seong Jin Kim, et al. Search for Optically Dark Infrared Galaxies without Counterparts of Subaru Hyper Suprime-Cam in the AKARI North Ecliptic Pole Wide Survey Field. The Astrophysical Journal, 2020, 899 (1), pp.35. 10.3847/1538-4357/ab9cb7. hal-02894400

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# Search for Optically Dark Infrared Galaxies without Counterparts of Subaru Hyper Suprime-Cam in the AKARI North Ecliptic Pole Wide Survey Field

Yoshiki Toba¹,²,³ ID, Tomotsugu Goto⁴, Nagisa Oi⁵ ID, Ting-Wen Wang⁴ ID, Seong Jin Kim⁴ ID, Simon C.-C. Ho⁴,

Denis Burgarella⁶ ID, Tetsuya Hashimoto⁴,⁷ ID, Bau-Ching Hsieh² ID, Ting-Chi Huang⁸,⁹ ID, Ho Seong Hwang¹⁰ ID,

Hiroyuki Ikeda¹¹,¹² ID, Helen K. Kim¹³, Seongjae Kim¹⁴,¹⁵, Dongseob Lee¹⁶, Matthew A. Malkan¹³ ID, Hideo Matsuhara⁸,⁹,

Takamitsu Miyaji¹⁷,¹⁸,<fnref n="27" /> ID, Rieko Momose¹⁹ ID, Youichi Ohyama² ID, Shinki Oyabu²⁰, Chris Pearson²¹,²²,²³,

Daryl Joe D. Santos⁴ ID, Hyunjin Shim¹⁶ ID, Toshinobu Takagi²⁴, Yoshihiro Ueda¹ ID, Yousuke Utsumi²⁵,²⁶ ID, and Takehiko Wada⁹

¹Department of Astronomy, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan; toba@kusastro.kyoto-u.ac.jp

²Academia Sinica Institute of Astronomy and Astrophysics, 11F of Astronomy–Mathematics Building, AS/NTU, No.1, Section 4, Roosevelt Road, Taipei 10617, Taiwan

³Research Center for Space and Cosmic Evolution, Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan

⁴Institute of Astronomy, National Tsing Hua University, No. 101, Section 2, Kuang-Fu Road, Hsinchu City 30013, Taiwan

⁵Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

⁶Aix Marseille Univ. CNRS, CNES, LAM Marseille, France

⁷Centre for Informatics and Computation in Astronomy (CICA), National Tsing Hua University, 101, Section 2, Kuang-Fu Road, Hsinchu, 30013, Taiwan

⁸Department of Space and Astronautical Science, The Graduate University for Advanced Studies, SOKENDAI, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan

⁹Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan

¹⁰Korea Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea

¹¹National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

¹²National Institute of Technology, Wakayama College, Gobo, Wakayama 644-0023, Japan

¹³Department of Physics and Astronomy, UCLA, 475 Portola Plaza, Los Angeles, CA 90095-1547, USA

¹⁴University of Science and Technology, Daejeon 34113, Republic of Korea

¹⁵Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea

¹⁶Department of Earth Science Education, Kyungpook National University, Daegu 41566, Republic of Korea

¹⁷Instituto de Astronomía sede, Ensenada, Universidad Nacional Autónoma de México (UNAM), Km 107, Carret. Tij.-Ens., Ensenada, 22060, BC, Mexico

¹⁸Leibniz Institut für Astrophysik Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany

¹⁹Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

²⁰Institute of Liberal Arts and Sciences, Tokushima University, Minami Jousanjima-Machi 1-1, Tokushima, Tokushima 770-8502, Japan

²¹RAL Space, STFC Rutherford Appleton Laboratory, Didcot, Oxfordshire OX11 0QX, UK

²²Oxford Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UK

²³The Open University, Milton Keynes MK7 6AA, UK

²⁴Japan Space Forum, 3-2-1, Kandasurugadai, Chiyoda-ku, Tokyo 101-0062, Japan

²⁵SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA

²⁶Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, 452 Lomita Mall, Stanford, CA 94035, USA

Received 2020 March 27; revised 2020 June 8; accepted 2020 June 12; published 2020 August 10

## Abstract

We present the physical properties of AKARI sources without optical counterparts in optical images from the Hyper Suprime-Cam (HSC) on the Subaru telescope. Using the AKARI infrared (IR) source catalog and HSC optical catalog, we select 583 objects that do not have HSC counterparts in the AKARI North Ecliptic Pole wide survey field (~5 deg²). Because the HSC limiting magnitude is deep ($g_{AB}$ ~ 28.6), these are good candidates for extremely red star-forming galaxies (SFGs) and/or active galactic nuclei (AGNs), possibly at high redshifts. We compile multiwavelength data out to 500 µm and use them for fitting the spectral energy distribution with CIGALE to investigate the physical properties of AKARI galaxies without optical counterparts. We also compare their physical quantities with AKARI mid-IR selected galaxies with HSC counterparts. The estimated redshifts of AKARI objects without HSC counterparts range up to $z \sim 4$, significantly higher than for AKARI objects with HSC counterparts. We find that (i) 3.6 – 4.5 µm color, (ii) AGN luminosity, (iii) stellar mass, (iv) star formation rate, and (v) V-band dust attenuation in the interstellar medium of AKARI objects without HSC counterparts are systematically larger than those of AKARI objects with counterparts. These results suggest that our sample includes luminous, heavily dust-obscured SFGs/AGNs at $z \sim 1–4$ that are missed by previous optical surveys, providing very interesting targets for the coming era of the James Webb Space Telescope.

*Unified Astronomy Thesaurus concepts: Active galactic nuclei (16); Infrared galaxies (790); Infrared photometry (792); Bayesian statistics (1900)*

## 1. Introduction

In the last two decades, it has become clear that dusty star-forming galaxies (SFGs) and active galactic nuclei (AGNs) play an important role in galaxy formation and evolution, and

in the co-evolution of galaxies and supermassive black holes (SMBHs) (see, e.g., Goto et al. 2011; Casey et al. 2014; Hickox & Alexander 2018; Chen et al. 2020, and references therein). They are particularly numerous in the high-$z$ universe ($z > 2$), the key epoch where the cosmic star formation rate (SFR) density and BH mass accretion rate density reach a maximum (e.g., Madau & Dickinson 2014; Ueda et al. 2014;

<footnote n="27">²⁷On sabbatical leave from UNAM.</footnote>
Aird et al. 2015). Blecha et al. (2018) conducted a smoothed-particle hydrodynamics and N-body simulation and reported that infrared (IR) color (3.4 and 4.6 µm color) correlates with AGN activity and nuclear obscuration in the framework of galaxy merger events—a redder system tends to have large AGN luminosity and hydrogen column density (see also Ricci et al. 2017; Ellison et al. 2019; Gao et al. 2020). Since dusty SFGs/AGNs often have redder color in the optical and near-IR (NIR), they could correspond to the maximum phase of SF/AGN activity. They would thus be the crucial population to understanding how the galaxies and their SMBHs co-evolve behind a large amount of dust (see also Hopkins et al. 2008; Narayanan et al. 2010).

Owing to the heavy extinction by so much dust, some high-z dusty AGNs/SFGs are optically faint or even optically “dark”. For example, dust-obscured galaxies (DOGs: Dey et al. 2008; Toba et al. 2015, 2017c; Noboriguchi et al. 2019) are characterized by a large mid-IR (MIR) – optical color; their optical flux density is about $10^3$ times fainter than that in the MIR band (see also Hwang et al. 2013; Hwang & Geller 2013). They are considered as dusty SFGs or AGNs at $z \sim 1-2$—the relative proportion of AGNs could increase with IR luminosity (Melbourne et al. 2012; Toba et al. 2017a, 2017b; Riguccini et al. 2019). A more extreme DOG population, Hot DOGs (Eisenhardt et al. 2012; Wu et al. 2012) known as dusty AGNs at $z > 2$, also tend to be optically faint. Recently, some galaxies detected by the Atacama Large Millimeter/submillimeter Array have been recognized as invisible SFGs without optical/NIR counterparts (e.g., Franco et al. 2018; Wang et al. 2019; Williams et al. 2019; Yamaguchi et al. 2019).

AKARI, the first Japanese space satellite dedicated to IR astronomy (Murakami et al. 2007), also has a great potential to find such optically dark objects. In addition to all-sky surveys in the MIR and far-IR (FIR) (Ishihara et al. 2010; Yamamura et al. 2010), AKARI performed deep and wide observations of the North Ecliptic Pole (NEP) over a total area of 5.4 deg² (Matsuhara et al. 2006). The AKARI NEP survey consists of two layers: NEP Wide (NEP-W; Lee et al. 2009; Kim et al. 2012) and NEP Deep (NEP-D; Wada et al. 2008; Takagi et al. 2010; Murata et al. 2013).<fnref n="28" /> AKARI NEP regions were observed with the Infrared Camera (IRC: Onaka et al. 2007), using its nine filters that continuously cover 2–25 µm. They are called N2, N3, and N4 for the NIR bands, S7, S9W, and S11 for the shorter part of the MIR band (MIR-S), and L15, L18W, and L24 for the longer part of the MIR band (MIR-L). The effective wavelengths of the N2, N3, N4, S7, S9W, S11, L15, L18W, and L24 filters are about 2.4, 3.2, 4.1, 7.0, 9.0, 11.0, 15.0, 18.0, and 24.0 µm, respectively. These continuous NIR-MIR filters are critical to trace dust emission heated by AGNs and/or polycyclic aromatic hydrocarbon (PAH) emission associated with SF activity. This makes AKARI/NEP data quite powerful for selecting AGNs and measuring the SF activity up to $z \sim 2$ (e.g., Goto et al. 2011; Murata et al. 2014; Huang et al. 2017; Kim et al. 2019; Poliszczuk et al. 2019).

Recently, the AKARI NEP-W has been observed with Hyper Suprime-Cam (HSC; Miyazaki et al. 2018) (see also Furusawa et al. 2018; Kawanomoto et al. 2018; Komiyama et al. 2018) on the Subaru telescope (PI: T. Goto). Oi et al. (2020) reduced the

data and used them to construct a five-band HSC catalog that contains 3,251,792 sources. The 5σ detection limit for *g*, *r*, *i*, *z*, and *y* bands is about 28.6, 27.3, 26.7, 26.0, and 25.6 mag, respectively. Oi et al. (2020) cross-identified the HSC catalog with the AKARI NEP-W catalog and found that ~90,000 AKARI objects have HSC counterparts (hereafter AKARI-HSC objects) (see also S. J. Kim et al. 2020, in preparation). Using the AKARI-HSC objects, Goto et al. (2019) derived their IR luminosity function at $0.35 < z < 2.2$ and measured IR luminosity density as a function of redshift up to $z \sim 2$. Recently, Ho et al. (2020) calculated photometric redshifts ($z_{\text{photo}}$) of AKARI-HSC objects, and demonstrated how the deep HSC data improve their accuracy. Wang et al. (2020) investigated the physical properties of AKARI-HSC objects based on fitting the spectral energy distribution (SED) with CIGALE<fnref n="29" /> (Code Investigating GALaxy Emission: Burgarella et al. 2005; Noll et al. 2009; Boquien et al. 2019) (see also Chiang et al. 2019).

However, those works focused on AKARI sources that have optical (i.e., HSC) counterparts. In this work, we shed light on the remaining objects: AKARI sources without HSC counterparts in the AKARI NEP-W. Since the limiting magnitude of the HSC is deep, these sources are expected to be extremely red SFGs/AGNs at high redshifts. We carefully select the candidates and investigate their physical properties.

The structure of this paper is as follows. Section 2 describes the data set, sample selection of AKARI sources without HSC counterparts, and our SED modeling of them. In Section 3, we present the results of our SED fitting and the derived physical quantities. In Section 4, we compare the resultant physical properties with AKARI sources that have HSC counterparts (Wang et al. 2020). We summarize the results of the work in Section 5. Throughout this paper, the adopted cosmology is a flat universe with $H_0 = 70.4 \text{ km s}^{-1} \text{ Mpc}^{-1}$, $\Omega_M = 0.272$, and $\Omega_\Lambda = 0.728$ (the Wilkinson Microwave Anisotropy Probe 7 cosmology: Komatsu et al. 2011), which are the same values as those adopted in Wang et al. (2020). Unless otherwise noted, all magnitudes refer to the AB system and an initial mass function (IMF) from Salpeter (1955) is assumed.

## 2. Data and Analysis

### 2.1. Data Set

To select AKARI sources without HSC counterparts securely and investigate their physical properties, we compile multiwavelength data. AKARI NEP-W was observed by many facilities, and thus we have abundant data sets from ultraviolet (UV) to radio (see, e.g., Kim et al. 2012; Oi et al. 2020, and references therein for a full description). In addition to the AKARI NEP-W catalog (Kim et al. 2012) and HSC catalog (Oi et al. 2020) we particularly utilized the data sets that are summarized in Table 1. The area coverage of each data set is summarized in Figure 1.

We used NIR data provided by Jeon et al. (2014), who conducted deep imaging with *J* and *H* bands taken by the Florida Multi-object Imaging Near-IR Grism Observational Spectrometer (FLAMINGOS: Elston et al. 2006) on the Kitt Peak National Observatory (KPN0) 2.1 m telescope. This photometric catalog contains 295,383 sources with 5σ detection limits of 21.6 and 21.3 mag in the *J* and *H* bands, respectively.

<footnote n="28">²⁸ AKARI NEP-D is a part of NEP-W as shown in Figure 1. But each catalog in NEP-W and NEP-D was independently created. Therefore, we ensure a uniform survey depth even for objects in the NEP-D as long as we use the NEP-W catalog.</footnote>

<footnote n="29">²⁹ https://cigale.lam.fr/2018/11/07/version-2018-0/</footnote>
<figure><img src="image_3.png" /><figcaption>**Figure 1.** The footprint of each observation. Red, orange, and yellow shaded regions represent AKARI NEP-W (Kim et al. 2012), NEP-D (Murata et al. 2013), and IRAC/Spitzer (Nayyeri et al. 2018), respectively. Blue, green, black, and magenta lines represent HSC/Subaru (Oi et al. 2020), FLAMINGOS/KPNO (Jeon et al. 2014), PACS/Herschel (Pearson et al. 2019), and SPIRE/Herschel (Pearson et al. 2017, C. Pearson 2020, in preparation), respectively.</figcaption></figure>

<table><caption>**Table 1**
Multiwavelength Data Set</caption><thead><tr><th>Catalog<br>(Number of sources)</th><th>Band</th><th>5σ Detection Limit (unit)</th></tr></thead><tbody><tr><td rowspan="5">HSC<br>(3,251,792)</td><td>g</td><td>28.6 (AB mag)</td></tr><tr><td>r</td><td>27.3 (AB mag)</td></tr><tr><td>i</td><td>26.7 (AB mag)</td></tr><tr><td>z</td><td>26.0 (AB mag)</td></tr><tr><td>y</td><td>25.6 (AB mag)</td></tr><tr><td rowspan="2">FLAMINGOS<br>(295,383)</td><td>J</td><td>21.6 (AB mag)</td></tr><tr><td>H</td><td>21.3 (AB mag)</td></tr><tr><td rowspan="2">Spitzer/IRAC<br>(380,858)</td><td>Ch1</td><td>6.45 (μJy)</td></tr><tr><td>Ch2</td><td>3.95 (μJy)</td></tr><tr><td rowspan="9">AKARI NEP-W<br>(114,794)</td><td>N2</td><td>15.42 (μJy)</td></tr><tr><td>N3</td><td>13.30 (μJy)</td></tr><tr><td>N4</td><td>13.55 (μJy)</td></tr><tr><td>S7</td><td>58.61 (μJy)</td></tr><tr><td>S9W</td><td>67.30 (μJy)</td></tr><tr><td>S11</td><td>93.76 (μJy)</td></tr><tr><td>L15</td><td>133.1 (μJy)</td></tr><tr><td>L18W</td><td>120.2 (μJy)</td></tr><tr><td>L24</td><td>274.4 (μJy)</td></tr><tr><td rowspan="3">Herschel/SPIRE<br>(4820)</td><td>250 μm</td><td>9.0 (mJy)</td></tr><tr><td>350 μm</td><td>7.5 (mJy)</td></tr><tr><td>500 μm</td><td>10.8 (mJy)</td></tr></tbody></table>

For MIR data, we used a catalog of Nayyeri et al. (2018), who provided 3.6 µm (ch1) and 4.5 µm (ch2) data taken with the Infrared Array Camera (IRAC: Fazio et al. 2004) on board the Spitzer Space Telescope (Werner et al. 2004). This photometric catalog contains 380,858 sources with 5σ

detection limits of 6.45 and 3.95 µJy in the 3.6 µm and 4.5 µm bands, respectively.

Regarding the FIR data, we utilized a recent catalog of 250, 350, and 500 µm data (Pearson et al. 2017, C. Pearson 2020, in preparation). The data were taken with the Spectral and Photometric Imaging Receiver instrument (SPIRE: Griffin et al. 2010) on board the Herschel Space Observatory (Pilbratt et al. 2010). This SPIRE catalog contains 4820 sources with 5σ detection limits of 9.0, 7.5, and 10.8 mJy at 250, 350, and 500 µm, respectively (Barrufet et al. 2020). Note that AKARI NEP-D was observed by the Photoconductor Array Camera and Spectrometer (PACS: Poglitsch et al. 2010) at 100 and 160 µm, and the catalog (including 1384 and 630 sources detected at 100 and 160 µm, respectively) is available (Pearson et al. 2019). But since the survey footprint is not so large (~0.7 deg², see Figure 1), we did not use the catalog in this work.<fnref n="30" />

Eventually, we used 21 photometric data in total; g, r, i, z, y, J, and H bands and 2.4 (N2), 3.2 (N3), 3.6 (ch1), 4.1 (N4), 4.5 (ch2), 7.0 (S7), 9.0 (S9W), 11.0 (S11), 15.0 (L15), 18.0 (L18W), 24.0 (L24), 250, 350, and 500 µm, even though some of them are often upper limits (e.g., HSC five-bands).

## 2.2. Sample Selection

The procedure for sample selection is summarized in Figure 2. The candidates for AKARI sources without HSC counterparts were drawn from the AKARI NEP-W sample in Kim et al. (2012), who provided 114,794 sources detected by the IRC. The 5σ detection limits of N2, N3, N4, S7, S9W, S11, L15, L18W, and L24 are 15.42, 13.30, 13.55, 58.61, 67.30, 93.76, 133.1, 120.2, and 274.4 µJy, respectively. Note that we selected candidates and obtained their multiwavelength information by cross-matching with several catalogs in which coordinates in the AKARI NEP-W catalog were always quoted. In this work, we attempt a cross-matching with a catalog by using a search radius that is much larger than the typical size of a point-spread function for objects in the catalog. We then determine a search radius for cross-matching with a catalog as a 3σ deviation from mean separation (ΔR.A. and Δdecl.) between AKARI NEP-W and that catalog, in the same manner as S. J. Kim et al. (2020, in preparation).

We first narrowed the sample to sources within the footprint observed by the HSC. This is because the HSC data do not cover quite the whole region of the AKARI NEP-W (see Figure 1), and hence some objects are just unobserved by the HSC. As a result, 109,734 objects were left out. We then removed 84,076 objects with nm<fnref n="31" /> > 0 that were reported as having optical counterparts in Kim et al. (2012). They used optical catalogs provided by Hwang et al. (2007) and Jeon et al. (2010) in which the optical data were taken with MegaCam (Boulade et al. 2003) on the Canada-France-Hawaii Telescope (CFHT) and SNUCAM (Im et al. 2010) at the Maidanak observatory, respectively. Following that, we cross-identified the sample with the HSC catalog (Oi et al. 2020), which has a sensitivity roughly five times deeper than optical catalogs used in Kim et al. (2012),

<footnote n="30">³⁰ The AKARI NEP-W was also partly observed in X-rays with Chandra (Krumpe et al. 2015), in the ultraviolet with GALEX (Buat et al. 2017), at 1.4 GHz with the Westerbork Radio Synthesis Telescope (White et al. 2010), and at 850 µm with the Submillimeter Common User Bolometer Array 2 on the James Clerk Maxwell Telescope (Shim et al. 2020). But we focus on physical properties of our sample based on the uniform optical-IR data in this work.</footnote>

<footnote n="31">³¹ It provides the number of optical sources matched to an AKARI source within 3" (see Kim et al. 2012).</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Flow chart of the process to select AKARI sources without HSC counterparts.</figcaption></figure>

providing optically faint AKARI sources. By adopting a search radius of 1.′′8, 20,446 objects were cross-identified.

For 25,658 – 20,446 = 5212 AKARI sources, we removed contaminants. Because objects with magnitude brighter than ~16 may be saturated in the MegaCam/SNUCAM/HSC images, they were removed from those catalogs before the cross-matching with the AKARI NEP-W catalog. Therefore, some AKARI sources in our sample are expected to be bright stars/galaxies. In order to remove bright objects, we cross-identified the sample with Gaia DR2 (Gaia Collaboration et al. 2016, 2018) using a search radius of 1.′′6. The Gaia DR2 catalog contains point sources with a g-band magnitude of 3–16. As a result, 534 bright objects were removed. We then extracted AKARI objects with 5σ detections in at least one AKARI band and with clean photometry flag<fnref n="32" /> (i.e., flag_bandname_mag = 0). We also applied nfl = 0 to select objects unaffected by cosmic rays and/or multiplexer bleed trails in the NIR bands (see Section 2.2 in Kim et al. 2012), which yielded 3734 objects.

Finally, we conducted a visual inspection to select reliable candidates in which we supplementarily used multiwavelength images in J and H bands (FLAMINGOS) and ch1 and ch2 (IRAC) in addition to HSC and AKARI images. Consequently, 583 objects were selected as AKARI sources without HSC counterparts. Figure 3 shows examples of postage stamp images for our sample. Why were 3734 – 583 = 3151 objects removed? One reason is that the edges of the fields of view of HSC may be degraded by artifacts. The AKARI NEP-W consists of 4–7 exposures by the HSC with a field of view of 1.′5 in diameter through dithering observations. Therefore, objects around the edges of each exposure frame would be missed from the HSC catalog created by the HSC pipeline (Bosch et al. 2018) although they exist on the HSC image (see Oi et al. 2020 for details). Nevertheless, we should note that the visual inspection might be highly dependent on the classifier. The number of objects selected in this work may have an uncertainty. Hence, the population census results such as number counts and volume density of AKARI sources without HSC counterparts should be addressed in future work, and we focus on an overview of their physical properties in this work.

For those AKARI sources without HSC counterparts, we compiled a multiwavelength data set up to 500 µm. We cross-identified the sample with FLAMINGOS, IRAC/Spitzer, and SPIRE/Herschel. In our sample, AKARI coordinates of each source were always used for the cross-matching. We employed 1.′′9, 2.′′3, and 6.′′6 as the search radius for cross-matching with FLAMINGOS, IRAC, and SPIRE, respectively. As stated, these search radii were determined to be 3σ deviations from the mean separation between AKARI objects without HSC counterparts and FLAMINGOS/IRAC/SPIRE catalogs. Accordingly, 70, 338, and 35 objects were cross-identified with FLAMINGOS, IRAC, and SPIRE, respectively. We found that 2/70, 4/338, and 2/35 AKARI objects have two candidate counterparts for FLAMINGOS, IRAC, and SPIRE, respectively. In this study, we chose the closest object as the counterpart for such cases. Among AKARI bands, 425/583 (73%), 109/583 (19%), and 59/583 (10%) objects are detected in the NIR, MIR-S, and MIR-L, respectively. We note that 23 objects with L24 detection naturally satisfy the DOG criterion, $(r - [24 \ \mu\text{m}])_{\text{AB}} > 7.5$ (Dey et al. 2008), owing to the limiting

<footnote n="32">³² Kim et al. (2012) employed SExtractor (Bertin & Arnouts 1996) for source detection and photometry (see Section 3 in Kim et al. 2012, for more details).</footnote>
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Examples of multiwavelength images (g, r, i, z, y, J, H, ch1, ch2, N2, N3, N4, S7, S9W, S11, L15, L18W, and L24, from top left to bottom right) for AKARI sources without HSC counterparts. R.A. and decl. are relative coordinates with respect to objects in the AKARI NEP-W catalog (Kim et al. 2012). White circles in the images also correspond to the coordinates of the AKARI NEP-W catalog.</figcaption></figure>
magnitude in the HSC *r* band (26.7) and AKARI 24 µm (17.8), suggesting that our sample selection may preferentially select dusty galaxies (see also Section 4.2).

## 2.3. SED Fitting with CIGALE

We employed CIGALE to conduct detailed SED modeling in a self-consistent framework by considering the energy balance between the UV/optical and IR. This code enables us to handle many parameters, such as star formation history (SFH), single stellar population (SSP), attenuation law, AGN emission, dust emission, and radio synchrotron emission (see, e.g., Boquien et al. 2014, 2016; Buat et al. 2014, 2015; Ciesla et al. 2017; Lo Faro et al. 2017; Toba et al. 2019a, 2020b; Burgarella et al. 2020). Note that one of the purposes of this work is to compare the physical properties between AKARI sources with and without HSC counterparts. Wang et al. (2020) constructed an AKARI L18W-selected sample with HSC counterparts, and also conducted the SED fitting with CIGALE to derive their physical properties. Therefore, to compare the resultant quantities under the same conditions, we chose the same models with the same parameter ranges as those that Wang et al. (2020) adopted, except for AGN fraction in the AGN module and $\gamma$ in the dust module (see below). Parameter ranges used in the SED fitting are tabulated in Table 2.

We used a delayed SFH model, assuming a single starburst with an exponential decay (Ciesla et al. 2015, 2016), where we fixed *e*-folding times of the main stellar population ($\tau_{\text{main}}$) and the late starburst population ($\tau_{\text{burst}}$), while we parameterized the age of the main stellar population in the galaxy.

We utilized the stellar templates with solar metallicity provided by Bruzual & Charlot (2003) assuming the IMF of Salpeter (1955), and the standard default nebular emission model included in CIGALE (see Inoue 2011).

Dust attenuation is modeled by using the model of Charlot & Fall (2000) with two different power-law attenuation curves that are parameterized by the power-law slope of the attenuation in the interstellar medium (ISM) and birth clouds (BC). We also separately parameterized the V-band attenuation in the ISM ($A_{V}^{\text{ISM}}$).

For AGN emission, we used models provided by Fritz et al. (2006). In order to avoid a degeneracy of AGN templates in the same manner as in Ciesla et al. (2015) and Toba et al. (2019b), we fixed certain parameters that determine the number density distribution of the dust within the dust torus, i.e., ratio of the maximum to minimum radii of the torus ($R_{\text{max}}/R_{\text{min}}$), density profile along the radial and the polar distance coordinates parameterized by $\beta$ and $\gamma$ (see Equation (3) in Fritz et al. 2006), and opening angle ($\theta$). We parameterized the optical depth at 9.7 µm ($\tau_{9.7}$) and $\psi$ parameter (the angle between the equatorial axis and the line of sight) that corresponds to our viewing angle of the torus. We further parameterized AGN fraction ($f_{\text{AGN}}$), which is the contribution of AGNs to the total IR luminosity (Ciesla et al. 2015). Note that we adopted a discrete interval for $f_{\text{AGN}}$, unlike Wang et al. (2020), where $f_{\text{AGN}}$ is a key parameter to investigate the dependence of the fractional AGN contribution on IR luminosity and redshift. Our sample is basically detected in only a few AKARI bands (and the remaining bands give upper limits). This may often not be enough to constrain $f_{\text{AGN}}$ precisely. Hence we reduced the number of possible values of $f_{\text{AGN}}$ considered.

Dust grain emission is modeled by Draine et al. (2014). The model is parameterized by the mass fraction of PAHs ($q_{\text{PAH}}$), the

<table><caption>**Table 2**
Parameter Ranges Used in the SED Fitting with CIGALE</caption><thead><tr><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td colspan="2"><strong>Delayed SFH</strong></td></tr><tr><td>τ<sub>main</sub> (Myr)</td><td>5000.0</td></tr><tr><td>τ<sub>burst</sub> (Myr)</td><td>20000</td></tr><tr><td>f<sub>burst</sub></td><td>0.00, 0.01</td></tr><tr><td>Age (Myr)</td><td>1000, 5000, 10000</td></tr><tr><td colspan="2"><strong>SSP (Bruzual & Charlot 2003)</strong></td></tr><tr><td>IMF</td><td>Salpeter (1955)</td></tr><tr><td>Metallicity</td><td>0.02</td></tr><tr><td colspan="2"><strong>Dust Attenuation (Charlot & Fall 2000)</strong></td></tr><tr><td>log (A<sub>V</sub><sup>ISM</sup>)</td><td>-2, -1.7, -1.4, -1.1, -0.8, -0.5,<br>-0.2, 0.1, 0.4, 0.7, 1.0</td></tr><tr><td>slope_ISM</td><td>-0.9, -0.7, -0.5</td></tr><tr><td>slope_BC</td><td>-1.3, -1.0, -0.7</td></tr><tr><td colspan="2"><strong>AGN Emission (Fritz et al. 2006)</strong></td></tr><tr><td>R<sub>max</sub>/R<sub>min</sub></td><td>60</td></tr><tr><td>τ<sub>9.7</sub></td><td>0.3, 6.0</td></tr><tr><td>β</td><td>-0.5</td></tr><tr><td>γ</td><td>4.0</td></tr><tr><td>θ</td><td>100.0</td></tr><tr><td>ψ</td><td>0.001, 60.100, 89.990</td></tr><tr><td>f<sub>AGN</sub></td><td>0.1, 0.3, 0.5, 0.7, 0.9</td></tr><tr><td colspan="2"><strong>Dust Emission (Draine et al. 2014)</strong></td></tr><tr><td>q<sub>PAH</sub></td><td>0.47, 1.77, 2.50, 5.26</td></tr><tr><td>U<sub>min</sub></td><td>0.1, 1.0, 10, 50</td></tr><tr><td>α</td><td>1.0, 1.5, 2.0, 2.5, 3.0</td></tr><tr><td>γ</td><td>0.01, 0.1, 1.0</td></tr><tr><td colspan="2"><strong>Photometric Redshift</strong></td></tr><tr><td>z<sub>photo</sub></td><td>0.8, 1.0, 1.5, 2.0, 2.2, 2.4, 2.6, 2.8, 3.0,<br>3.2, 3.4, 3.6, 3.8, 4.0, 4.2</td></tr></tbody></table>

minimum radiation field ($U_{\text{min}}$), and the power-law slope of the radiation field distribution ($\alpha$) (see Equation (4) in Draine et al. 2014). We also parameterized the fraction illuminated with a variable radiation field ranging from $U_{\text{min}}$ to $U_{\text{max}}$ ($\gamma$), although Wang et al. (2020) fixed this at $\gamma = 1$. We confirmed that parameterizing $\gamma$ gives a better fit to the FIR parts of the spectra.

We also parameterized redshift to estimate photometric redshift ($z_{\text{photo}}$), because by definition our sample is optically too faint to obtain spectroscopic redshifts. Since the optically dark galaxies tend to be located at $z > 2$ (e.g., Franco et al. 2018; Wang et al. 2019; Williams et al. 2019; Yamaguchi et al. 2019), we optimized the range of $z_{\text{photo}}$, which reduces the computing time. Aside from being an excellent SED-fitting tool, CIGALE is known to be a good estimator of $z_{\text{photo}}$, since it utilizes a large number of models covering the whole SED including the MIR-FIR regime. For example, Malek et al. (2014) calculated $z_{\text{photo}}$ for AKARI sources in the AKARI Deep Field South. They demonstrated the accuracy of $z_{\text{photo}}$ by using the normalized median absolute deviation defined as $\sigma_{\Delta z/(1+z_{\text{spec}})} = 1.48 \times \text{median}(|\Delta z|/(1+z_{\text{spec}}))$ in the same manner as Ilbert et al. (2006). The resultant $\sigma_{\Delta z/(1+z_{\text{spec}})}$ is 0.056, lower than what was obtained by software using mainly optical to NIR data (Ilbert et al. 2006; see also Barrufet et al. 2020). On the other hand, the above AKARI sources have optical
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Normalized histogram of [3.6]–[4.5] color (in Vega magnitude) of AKARI sources with (black) and without (red) HSC counterparts.</figcaption></figure>

counterparts, i.e., they are moderately bright in the optical, and the sample is limited to the local universe ($z < 0.25$). Since we constrain the optical SEDs based only on upper limits, we need to investigate the influence of our lack of optical data points on the accuracy of $z_{\text{photo}}$ (see Section 4.6.1).

In order to ensure the reliability of the derived physical quantities including $z_{\text{photo}}$, we extracted AKARI sources with $5\sigma$ detections in at least five bands between the NIR and FIR, which yields 142/583 objects for SED fitting. If the signal-to-noise ratio (S/N) at a certain band is greater than 5.0, we used the photometry at that band. Otherwise, we placed $10\sigma$ upper limits<fnref n="33" /> that are drawn from each catalog (see Section 2.1).

# 3. Results

## 3.1. Comparison of IRAC Color

Before the SED fitting, we check the IRAC ch1 and ch2 color ([3.6]–[4.5] in Vega magnitudes) of our sample objects. Figure 4 shows the IRAC color of 338 AKARI sources without HSC counterparts. We also plotted IRAC colors of AKARI sources with HSC counterparts where we used a multiwavelength merged AKARI catalog provided by S. J. Kim et al. (2020, in preparation). We removed stars with stellarity parameter (which was measured from CFHT r-band or Maidanak R-band images) greater than 0.8 (see Kim et al. 2012). This left 42,264 objects for the comparison.

We find that [3.6]–[4.5] colors of AKARI sources without HSC counterparts (i.e., our sample) are systematically redder than those of AKARI sources with HSC counterparts. Blecha et al. (2018) reported that W1 (3.4 µm) and W2 (4.6 µm) color (almost the same as IRAC ch1 and ch2 color) taken with the Wide-field Infrared Survey Explorer (Wright et al. 2010) is a good indicator of AGN activity and nuclear obscuration. The AGN luminosity and hydrogen column density peak during the galaxies’ coalescence, where W1–W2 color ranges from 0.8 to 1.6 (see Figure 1 in Blecha et al. 2018). This suggests that a fraction of objects in our sample could correspond to a luminous, obscured AGN phase.

## 3.2. Result of SED Fitting

Figure 5 shows examples of the SED fitting with CIGALE. We confirm that 91/142 (~64%) objects have reduced $\chi^2 < 3.0$ while 112/142 (~79%) objects have reduced $\chi^2 < 5.0$. This means that the data are moderately well fitted with the combination of the stellar, AGN, and SF components by CIGALE. We also confirm that the probability distribution function (PDF) of redshift does not have prominent secondary peaks for ~90% of our sample, where a peak that is 30% of the primary peak is considered to be a secondary peak (see top panels for objects that show no secondary peak and bottom panels for objects that do show a secondary peak in the PDF in Figure 5). The typical uncertainty of $z_{\text{photo}}$ is about 20% (see also Section 4.6.1). Hereafter, we will focus on a subsample of 112 AKARI galaxies with reduced $\chi^2$ of their SED fitting smaller than 5.0, in the same manner as Toba et al. (2019b).

# 4. Discussions

Wang et al. (2020) constructed an 18 µm (L18W)-selected AKARI sample with HSC counterparts, among which 443 objects have Herschel detections (SPIRE 250 µm or PACS 100 µm) and spectroscopic redshifts (Shim et al. 2013; Oi et al. 2017; Kim et al. 2018; Shogaki et al. 2018). In order to derive their physical properties such as AGN luminosity and SFR, Wang et al. performed SED fitting with CIGALE.<fnref n="34" /> What is the difference in the physical properties between AKARI objects with and without HSC counterparts? To ensure the relatability of the SED fitting, we will use 317 sources with reduced $\chi^2 < 5.0$ in the sample provided by Wang et al. (2020) for the following discussion.

## 4.1. Stellar Mass

Figure 6 shows the stellar mass for AKARI sources with and without HSC counterparts. We find that the stellar mass of our sample galaxies is systematically larger than that of AKARI sources with HSC counterparts (Wang et al. 2020). The average stellar mass of AKARI sources with and without HSC counterparts is $\log(M_*/M_{\odot}) = 10.8$ and 11.3, respectively. A two-sided Kolmogorov–Smirnov (K-S) test rules out the hypothesis that the two samples are drawn from the same distribution at >99.9% significance.

One caution here is that the procedure of sample selection in this work differs from that in Wang et al. (2020); AKARI–HSC objects in Wang et al. (2020) require both L18W and Herschel detections, while our sample is not necessarily detected by them. Therefore, we extracted 22 objects that satisfy the sample selection criteria in Wang et al. (2020). Their average $\log(M_*/M_{\odot})$ is 11.7, also significantly larger than for the sample in Wang et al. (2020), which is also confirmed by the K-S test with >99.9% significance.

Figure 6 also shows objects with the Bayesian information criterion (BIC; Schwarz 1978) greater than 2, which indicates that those objects need the AGN component to give a better SED fitting (see Section 4.6.2 for more detail). We confirmed that there is no systematic difference between those objects and others.

<footnote n="33">³³ CIGALE can handle SED fitting of photometric data with upper limits when using the method presented by Sawicki (2012). This method computes $\chi^2$ by introducing the error function (see Equations (15) and (16) in Boquien et al. 2019).</footnote>

<footnote n="34">³⁴ We parameterized $\gamma$ in the dust emission model as described in Section 2.3. For a fair comparison, we re-performed the SED fitting with parameterization of $\gamma$ for the sample provided by Wang et al. (2020).</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Examples of the SED fitting. The black points are photometric data. The contributions from the stellar, AGN, and SF components to the total SED are shown as blue, yellow, and red lines, respectively. The black solid line represents the resultant best-fit SED. The inset shows the probability density distribution of redshift.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 6.** Histogram of the stellar mass of AKARI sources with (blue) and without (yellow) HSC counterparts. The red line represents the stellar mass of our sample with L18W and SPIRE detections. The green line represents our sample with ΔBIC > 2.0 (see Section 4.6.2).</figcaption></figure>

## 4.2. Dust Attenuation in the ISM

We then compare the V-band attenuation in the ISM ($A_V^{ISM}$) for AKARI sources with and without HSC counterparts. Before the comparison, we should note that the dust attenuation may depend

on the stellar mass (e.g., Buat et al. 2012, 2015), and the stellar mass distributions in the two samples are different as discussed in Section 4.1. Therefore, we extracted objects in an overlapped stellar mass range, i.e., $10 < \log(M_*/M_\odot) < 12$, in the AKARI sample with/without HSC counterparts (see Figure 6).

Figure 7 shows $A_V^{ISM}$ for AKARI sources with and without HSC counterparts. These objects are samples matched by stellar mass. The average $A_V^{ISM}$ of AKARI sources with and without HSC counterparts is 1.26 and 5.16 mag, respectively. We find that the attenuation of our sample is systematically much larger than that of AKARI sources with HSC counterparts (Wang et al. 2020), which is supported by the K-S test with >99.9% significance. This result seems to be reasonable, given the fact that our sample is undetected even by the HSC, and its optical light is expected to be suppressed heavily by enshrouding dust.

One caution is that the redshift distributions of AKARI objects in Wang et al. (2020) and in this study are different (see Section 4.3). Given an overlapped redshift range ($0.8 < z < 2.0$) between two samples (see Figure 8), the average $A_V^{ISM}$ of the sample in Wang et al. (2020) is 1.77 mag and that in this work is 5.23 mag. This suggests that our sample is intrinsically affected by dust extinction compared with AKARI with HSC counterparts.
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Histogram of the V-band attenuations in the ISM of AKARI sources with (blue) and without (yellow) HSC counterparts. The red line represents $A_{\odot}^{\text{ISM}}$ of our sample with L18W and SPIRE detections. The green line represents our sample with $\Delta\text{BIC} > 2.0$. The objects with $10 < \log(M_*/M_{\odot}) < 12$ are plotted in each sample.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 8.** IR luminosity contributed by AGNs as a function of redshift. Blue and yellow points represent AKARI sources with and without HSC counterparts, respectively. Yellow points with red circles represent our sample with L18W and SPIRE detections. Yellow points with green circles represent our sample with $\Delta\text{BIC} > 2.0$.</figcaption></figure>

### 4.3. AGN Luminosity as a Function of Redshift

Figure 8 shows the IR luminosity contributed by AGNs as a function of redshift. We find that AKARI objects without HSC counterparts tend to be located at higher redshifts than those with HSC counterparts: the mean redshift of AKARI objects with and without HSC counterparts is $z \sim 0.46$ and 1.34, respectively. We also find that objects with L18W and SPIRE detections tend to have larger AGN luminosity than others in our sample.

Note that the parent sample for these objects is the same, i.e., a flux-limited sample drawn from the AKARI NEP-W catalog (Kim et al. 2012). Thus AKARI sources are expected to lie in the same sequence on the redshift–luminosity plane, regardless of HSC detection. We confirm that samples in Wang et al. (2020) and this work are continuously distributed in that plane, indicating that CIGALE securely estimated redshift and luminosity. Indeed, given the overlapped redshift range of $0.8 < z < 2.0$, the mean AGN luminosity of our sample is

<figure><img src="image_11.png" /><figcaption>**Figure 9.** Histograms of AGN fraction for AKARI sources with (blue) and without (yellow) HSC counterparts. The red line represents $f_{\text{AGN}}$ of our sample with L18W and SPIRE detections. The green line represents $f_{\text{AGN}}$ of our sample with $\text{BIC} > 2.0$ (see Section 4.6.2).</figcaption></figure>

$\log(L_{\text{IR}}(\text{AGN})/L_{\odot}) \sim 11.2$, comparable to the sample in Wang et al. (2020).

The total IR luminosity of AKARI sources without HSC counterparts is also larger than that of those with HSC counterparts, with mean $\log(L_{\text{IR}}/L_{\odot})$ of 11.4 and 12.2, respectively. Actually, about 65% and 15% of our sample are ultraluminous IR galaxies (ULIRGs: Sanders & Mirabel 1996) and hyperluminous IR galaxies (HyLIRGs: Rowan-Robinson 2000) with $L_{\text{IR}}$ greater than $10^{12}$ and $10^{13} L_{\odot}$, respectively. This is in good agreement with the fact that dusty galaxies with extreme optical–IR color tend to be luminous in the IR (e.g., Tsai et al. 2015; Toba & Nagao 2016; Toba et al. 2018, 2020a; Fan et al. 2020).

### 4.4. AGN Fraction

Figure 9 shows the AGN fraction ($f_{\text{AGN}}$), $L_{\text{IR}}(\text{AGN})/L_{\text{IR}}$. The mean AGN fraction of AKARI sources with and without HSC counterparts is 0.06 and 0.22, respectively, indicating that our sample tends to harbor AGNs. We also find that $f_{\text{AGN}}$ of objects with L18W and SPIRE detection is 0.16, smaller than the average of all objects in our sample. On the other hand, given the overlapped redshift range ($0.8 < z < 2.0$), the mean $f_{\text{AGN}}$ of AKARI sources with and without HSC counterparts is 0.12 and 0.23, respectively. This could indicate that one of the reasons for the difference in $f_{\text{AGN}}$ between the two samples may be the difference in sample selection and redshift. Other possible uncertainties caused by a limited number of MIR data are discussed in Section 4.6.2.

### 4.5. Star Formation Rate

Finally, we compare the SFR in two samples as shown in Figure 10. The SFR is converted from dust luminosity using a relation provided by Kennicutt (1998; see also Hirashita et al. 2003).

We find that the SFR of our sample is systematically higher than that of AKARI with HSC objects. The average SFR of AKARI objects with and without HSC counterparts is about 91 and $758 M_{\odot} \text{ yr}^{-1}$, respectively. If we focus on our sample with L18W and SPIRE detections, the mean SFR is $2240 M_{\odot} \text{ yr}^{-1}$ because of the requirement of FIR detection. These results are consistent with previous works reporting that SFRs of dusty
<figure><img src="image_12.png" /><figcaption>**Figure 10.** Histograms of SFR for AKARI sources with (blue) and without (yellow) HSC counterparts. The red and green lines represent the SFR of our sample with L18W and SPIRE detections, and with $\Delta$BIC > 2.0, respectively.</figcaption></figure>

galaxies tend to be high (e.g., Ikarashi et al. 2017; Toba et al. 2017d; Yamaguchi et al. 2019; Fan et al. 2020). On the other hand, if we compare SFRs of the sample in this work and Wang et al. (2020) in an overlapped redshift range ($0.8 < z < 2.0$), the mean SFR of AKARI with and without HSC counterparts is 319 and 207 $M_{\odot} \text{ yr}^{-1}$, respectively. This indicates that the observed difference in SFR may be due to the difference in redshift.

## 4.6. Reliability of the SED Analysis

### 4.6.1. Influence of Data Set without Optical Photometry on the SED-based Photometric Redshift

We showed that our estimate of $z_{\text{photo}}$ is expected to be secure in some ways (see Sections 2.3 and 4.3), but these arguments are indirect. Although Małek et al. (2014) demonstrated the accuracy of $z_{\text{photo}}$ based on CIGALE for an AKARI sample at $z_{\text{spec}} < 0.25$, they utilized optical data points for $z_{\text{photo}}$ estimation, and the redshift range for their sample differs from that for our sample. We need to investigate how the lack of optical data affects the accuracy of $z_{\text{photo}}$ for AKARI objects at $z > 0.8$. Hence, we estimate $z_{\text{photo}}$ of AKARI objects with $z_{\text{spec}}$ in the band-merged catalog (S. J. Kim et al. 2020, in preparation). In order to calculate $z_{\text{photo}}$ under the same condition as we performed so far, we extracted objects with $z_{\text{spec}} > 0.8$ and with five-band detections in NIR-FIR, yielding 100 objects. Note that although the sample is detected by the HSC, we “artificially” multiplied the HSC flux densities by 10 and treated them as $10\sigma$ upper limits. We then executed the SED fitting with CIGALE in exactly the same manner as what we described in Section 2.3.

Figure 11 shows the relative difference between $z_{\text{photo}}$ and $z_{\text{spec}}$, i.e., $(z_{\text{spec}} - z_{\text{photo}})/(1+z_{\text{spec}})$ as a function of $z_{\text{spec}}$. The mean and standard deviation of $(z_{\text{spec}} - z_{\text{photo}})/(1+z_{\text{spec}})$ is $0.09 \pm 0.45$, and the accuracy of $z_{\text{photo}}$, $\sigma_{\Delta z}/(1+z_{\text{spec}})$ is 0.23, which are worse than those reported by Małek et al. (2014). We find that ~56% of objects have $|(z_{\text{spec}} - z_{\text{photo}})/(1+z_{\text{spec}}) < 0.2$. This may be partly because the AKARI-HSC objects at $z > 0.8$ are biased toward optically bright type 1 AGNs, for which $z_{\text{photo}}$ is harder to estimate precisely than for other galaxy types. Actually, ~90% of objects plotted in Figure 11 are spectroscopically confirmed type 1

<figure><img src="image_13.png" /><figcaption>**Figure 11.** Relative difference between $z_{\text{photo}}$ and $z_{\text{spec}}$, $(z_{\text{spec}} - z_{\text{photo}})/(1+z_{\text{spec}})$ as a function of $z_{\text{spec}}$. The red solid line represents $z_{\text{photo}} - z_{\text{spec}} = 0$ and the dotted lines represent $(z_{\text{spec}} - z_{\text{photo}})/(1+z_{\text{spec}}) = \pm 0.2$. The inset shows the histogram of $(z_{\text{spec}} - z_{\text{photo}})/(1+z_{\text{spec}})$.</figcaption></figure>

AGNs, which may induce a large deviation of $(z_{\text{spec}} - z_{\text{photo}})/(1+z_{\text{spec}})$.

### 4.6.2. Bayesian Information Criterion

Another potential issue raised by the SED fitting with a limited number of data points in the MIR may be an uncertainty in the AGN contribution to the total SED, although we used upper limits at an MIR band if an object is not detected at that band. To test the requirement to add an AGN component to the SED fitting, we compute the BIC for two fits that are derived with and without an AGN component. The BIC is defined as $\text{BIC} = \chi^2 + k \times \ln(n)$, where $\chi^2$ is nonreduced chi-square, $k$ is the number of degrees of freedom (DOF), and $n$ is the number of photometric data points used for the fitting. We then compare the results of two SED fittings without/with an AGN model by using $\Delta$BIC = $\text{BIC}_{\text{WOAGN}} - \text{BIC}_{\text{WAGN}}$. The resultant $\Delta$BIC tells whether the AGN model is required to give a better fit when taking into account the difference in DOF (e.g., Ciesla et al. 2018; Buat et al. 2019, see also Aufort et al. 2020).

Figure 12 shows the histogram of $\Delta$BIC for AKARI sources without HSC counterparts. If $\Delta$BIC is larger than two, this indicates that adding the AGN component provides a better fit than not adding it (Liddle 2004; Stanley et al. 2015; see also Ciesla et al. 2018; Buat et al. 2019, who set a higher threshold for $\Delta$BIC). Otherwise, there is no significant difference between two fits with/without an AGN model. We find that only 31% of object fits satisfy $\Delta$BIC > 2. This suggests that it may be difficult to constrain the AGN activity for many cases, and thus AGN fraction may have a large uncertainty given a limited number of photometric detections in the MIR regime. On the other hand, Figures 6–10 also show objects with $\Delta$BIC > 2. We find that there is no systematic difference between objects with $\Delta$BIC > 2 and others, especially for AGN fraction (see Figure 9), which suggests that overall trends discussed in Section 4.4 may not be changed even if taking the BIC into account.

### 4.6.3. Mock Analysis

Finally, we check whether or not the derived physical properties in this work can actually be estimated reliably, given
<figure><img src="image_14.png" /><figcaption>**Figure 12.** Histogram of $\Delta$BIC = BIC<sub>WOAGN</sub> - BIC<sub>WAGN</sub> for AKARI sources without HSC counterparts. The red dotted line corresponds to $\Delta$BIC = 2.</figcaption></figure>

the uncertainty of the photometry. We conduct a mock analysis that is a procedure provided by CIGALE (see, e.g., Buat et al. 2012, 2014; Ciesla et al. 2015; Lo Faro et al. 2017; Boquien et al. 2019; Toba et al. 2019b, for more detail).

Figure 13 shows the differences in $z_{\text{photo}}$, V-band attenuation in the $A_V$ ISM, stellar mass, SFR, and $L_{\text{IR}}$(AGN) derived from CIGALE in this work and those derived from the mock catalog as a function of redshift. The mean and standard deviations of $\Delta z_{\text{photo}}$, $\Delta A_V^{\text{ISM}}$, $\Delta \log M_*$, $\Delta \log \text{SFR}$, and $\Delta \log L_{\text{IR}}$(AGN) are $\Delta z_{\text{photo}} = 0.03 \pm 0.47$, $\Delta A_V^{\text{ISM}} = -0.23 \pm 1.17$, $\Delta \log M_* = 0.08 \pm 0.37$, $\Delta \log \text{SFR} = 0.03 \pm 0.43$, and $\Delta \log L_{\text{IR}}$(AGN) =0.11 ± 0.30. In particular, we can see a large deviation for objects at $z < 1.5$. This trend can also be seen in Figure 11. These results indicate that any physical quantities derived by the SED fitting especially for objects at $z < 1.5$ may be significantly affected by the limited number of photometric data points. On the other hand, we could ensure reliable physical quantities for our sample at $z > 1.5$.

## 5. Summary

In this paper, we report the physical properties of AKARI sources that do not have optical counterparts in the HSC/Subaru catalog (Oi et al. 2020). The parent sample is drawn from IR sources in the AKARI NEP-W field (Kim et al. 2012). By using AKARI, HSC, Gaia, FLAMINGOS/KPNO, and IRAC/Spitzer catalogs and images, we select 583 objects as optically dark IR sources without HSC counterparts. Thanks to the continuous filters of AKARI in the MIR and multiwavelength data up to the FIR (SPIRE/Herschel), we successfully pin down their optical–FIR SEDs, even if flux densities in some bands are upper limits. We compare the physical properties derived by the CIGALE SED fitting between AKARI objects without HSC counterparts and mid-IR selected AKARI objects with HSC counterparts (Wang et al. 2020). We find that AKARI sources without HSC counterparts have systematically redder 3.6 – 4.5 µm color than AKARI sources with HSC counterparts. With all the caveats discussed in Section 4.6 in mind, we find that our sample tends to be located at high redshifts up to $z \sim 4$, and has larger stellar mass, AGN luminosity, SFR, and V-band dust attenuation in the ISM than AKARI sources with HSC counterparts. Although this is partly due to the Malmquist bias, these results indicate that AKARI objects without HSC counterparts are heavily

<figure><img src="image_15.png" /><figcaption>**Figure 13.** The differences between $z_{\text{photo}}$, V-band attenuation in the ISM, stellar mass, SFR, and $L_{\text{IR}}$(AGN) derived from CIGALE in this work and those derived from the mock catalog. (a) $\Delta z_{\text{photo}}$, (b) $\Delta A_V^{\text{ISM}}$, (c) $\Delta \log M_*$, (d) $\Delta \log \text{SFR}$, and (e) $\Delta \log L_{\text{IR}}$(AGN) as a function of redshift. The right panels show a histogram of each quantity. The red dotted lines show $\Delta = 0$.</figcaption></figure>

dust-obscured SFGs/AGNs at $z \sim 1-4$ that may be missed by the previous optical surveys.

The launch of the James Webb Space Telescope (JWST: Gardner et al. 2006) is approaching, and AKARI NEP should be an attractive field for JWST (e.g., Jansen & Windhorst 2018). Since the AKARI NEP has multiwavelength data from X-ray to radio, in which the filter sets of AKARI are similar to those of JWST, this work establishes a benchmark for forthcoming studies of dusty SFGs/AGNs with JWST and provides specially interesting optically dark IR sources for JWST study.

We gratefully acknowledge the anonymous referee for a careful reading of the manuscript and very helpful comments.

This research is based on observations with AKARI, a JAXA project with the participation of ESA.

This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.
This work is based on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. Support for this work was provided by NASA through an award issued by JPL/Caltech

Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.

Numerical computations/simulations were carried out (in part) using the SuMiRe cluster operated by the Extragalactic OIR group at ASIAA.

This work is supported by JSPS KAKENHI grant Nos. 18J01050 and 19K14759 (Y.T.), JP18J40088 (R.M.), and 17K05384 (Y.U.). Y.T. and T.G. acknowledge the support by the Ministry of Science and Technology of Taiwan, MOST 108-2112-M-001-014- and 108-2628-M-007-004-MY3. R.M. acknowledges a Japan Society for the Promotion of Science (JSPS) Fellowship at Japan. T.H. is supported by the Centre for Informatics and Computation in Astronomy (CICA) at National Tsing Hua University (NTHU) through a grant from the Ministry of Education of the Republic of China (Taiwan). T.M. is supported by CONACyT 252531 and UNAM-DGAPA (PASPA and PAPIIT IN111319).

*Facilities:* AKARI, Subaru, KPN0:2.1 m, Spitzer, Herschel.

*Software:* IDL, IDL Astronomy User's Library (Landsman 1993), CIGALE (Boquien et al. 2019), TOPCAT (Taylor 2006).

## ORCID iDs

Yoshiki Toba https://orcid.org/0000-0002-3531-7863

Nagisa Oi https://orcid.org/0000-0002-4686-4985

Ting-Wen Wang https://orcid.org/0000-0002-1151-7094

Seong Jin Kim https://orcid.org/0000-0001-9970-8145

Denis Burgarella https://orcid.org/0000-0002-4193-2539

Tetsuya Hashimoto https://orcid.org/0000-0001-7228-1428

Bau-Ching Hsieh https://orcid.org/0000-0001-5615-4904

Ting-Chi Huang https://orcid.org/0000-0001-7200-8157

Ho Seong Hwang https://orcid.org/0000-0003-3428-7612

Hiroyuki Ikeda https://orcid.org/0000-0002-1207-1979

Matthew A. Malkan https://orcid.org/0000-0001-6919-1237

Takamitsu Miyaji https://orcid.org/0000-0002-7562-485X

Rieko Momose https://orcid.org/0000-0002-8857-2905

Youichi Ohyama https://orcid.org/0000-0001-9490-3582

Daryl Joe D. Santos https://orcid.org/0000-0002-5687-0609

Hyunjin Shim https://orcid.org/0000-0002-4179-2628

Yoshihiro Ueda https://orcid.org/0000-0001-7821-6715

Yousuke Utsumi https://orcid.org/0000-0001-6161-8988

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