$\langle$2022 April 20$\rangle$ $\langle$2022 August 22$\rangle$
$\langle$publication date$\rangle$

galaxies: active — infrared: galaxies —methods: observational

# Optical IFU Observations of GOALS Sample with KOOLS-IFU on Seimei Telescope:
Initial results of 9 U/LIRGs at $z<$ 0.04

Yoshiki Toba 11affiliation: National Astronomical Observatory of Japan, 2-21-1
Osawa, Mitaka, Tokyo 181-8588, Japan 22affiliation: Department of Astronomy,
Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
33affiliation: Department of Physics, Nara Women’s University, Kitauoyanishi-
machi, Nara, Nara 630-8506, Japan 44affiliation: Academia Sinica Institute of
Astronomy and Astrophysics, 11F of Astronomy-Mathematics Building, AS/NTU,
No.1, Section 4, Roosevelt Road, Taipei 10617, Taiwan 55affiliation: Research
Center for Space and Cosmic Evolution, Ehime University, 2-5 Bunkyo-cho,
Matsuyama, Ehime 790-8577, Japan ${}^{\ast}$\thanks{NAOJ
Fellow}${}^{\ast}$\thanks{NAOJ Fellow}affiliationmark:  Satoshi Yamada
66affiliation: RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako,
Saitama 351-0198, Japan 22affiliationmark:  Kazuya Matsubayashi 77affiliation:
Institute of Astronomy, Graduate School of Science, The University of Tokyo,
2-21-1 Osawa, Mitaka,Tokyo 181-0015, Japan 88affiliation: Okayama Observatory,
Kyoto University, Honjo 3037-5, Kamogata-cho, Asakuchi, Okayama 719-0232,
Japan Koki Terao 99affiliation: Subaru Telescope, National Astronomical
Observatory of Japan, 650 North A’ohoku Place, Hilo, HI 96720, USA
1010affiliation: Astronomical Institute, Tohoku University, Aramaki, Aoba-ku,
Sendai, 980-8578, Japan Aoi Moriya 33affiliationmark:  Yoshihiro Ueda
22affiliationmark:  Kouji Ohta 22affiliationmark:  Aoi Hashiguchi
33affiliationmark:  Kazuharu G. Himoto 1111affiliation: Graduate School of
Science and Engineering, Ehime University, Bunkyo-cho, Matsuyama 790-8577,
Japan Hideyuki Izumiura 1212affiliation: Okayama Branch Office, Subaru
Telescope, National Astronomical Observatory of Japan, NINS, Kamogata,
Asakuchi, Okayama 719-0232, Japan Kazuma Joh 1111affiliationmark:  Nanako Kato
1111affiliationmark:  Shuhei Koyama 77affiliationmark:  55affiliationmark:
Hiroyuki Maehara 1212affiliationmark:  Rana Misato 33affiliationmark:  Akatoki
Noboriguchi 1313affiliation: School of General Education, Shinshu University,
3-1-1 Asahi, Matsumoto, Nagano 390-8621, Japan 1010affiliationmark:
1111affiliationmark:  Shoji Ogawa 22affiliationmark:  Naomi Ota
33affiliationmark:  Mio Shibata 33affiliationmark:  Nozomu Tamada
1111affiliationmark:  Anri Yanagawa 33affiliationmark:  Naoki Yonekura
1111affiliationmark:  Tohru Nagao 55affiliationmark:  Masayuki Akiyama
1010affiliationmark:  Masaru Kajisawa 55affiliationmark:  1111affiliationmark:
Yoshiki Matsuoka 55affiliationmark<EMAIL_ADDRESS>
###### Abstract

We present ionized gas properties of 9 local ultra/luminous infrared galaxies
(U/LIRGs) at $z<$ 0.04 through IFU observations with KOOLS-IFU on Seimei
Telescope. The observed targets are drawn from the Great Observatories All-sky
LIRG Survey (GOALS), covering a wide range of merger stages. We successfully
detect emission lines such as H$\beta$, [O iii]$\lambda$5007, H$\alpha$, [N
ii]$\lambda\lambda$6549,6583, and [S ii]$\lambda\lambda$6717,6731 with a
spectral resolution of $R$ = 1500–2000, which provides (i) spatially-resolved
($\sim$200–700 pc) moment map of ionized gas and (ii) diagnostics for active
galactic nucleus (AGN) within the central $\sim$3–11 kpc in diameter for our
sample. We find that [O iii] outflow that is expected to be driven by AGN
tends to be stronger (i) towards the galactic center and (ii) as a sequence of
merger stage. In particular, the outflow strength in the late-stage (stage D)
mergers is about 1.5 times stronger than that in the early-state (stage B)
mergers, which indicates that galaxy mergers could induce AGN-driven outflow
and play an important role in the co-evolution of galaxies and supermassive
black holes.

##  1 Introduction

In the last two decades, galaxy mergers have been recognized as a key
phenomenon for understanding galaxy evolution (e.g., [Conselice (2014)] and
reference therein). Star formation (SF) and/or active galactic nucleus (AGN)
activity in galaxies are often triggered by galaxy mergers111We note that
major mergers are not the only triggering mechanism of SF/AGN activity. Non-
merger processes such as secular mechanisms may also trigger SF/AGN activity
(see e.g., [Schawinski et al. (2011), Draper & Ballantyne (2012), Sharma et
al. (2021)], and references therein) (see also Section 3.4)., which enhances
the inflow of material from galactic scales into the close environments of the
nuclear region. The galaxy merger also enhances infrared (IR) luminosity
($L_{\rm IR}$222$L_{\rm IR}$ is empirically defined as the luminosity
integrated over a wavelength range of 8–1000 $\mu$m (e.g., [Sanders & Mirabel
(1996), Chary & Elbaz (2001)]).) (e.g., [Sanders et al. (1988), Veilleux et
al. (2002), Imanishi et al. (2007), Imanishi (2009), Toba et al. (2015), Toba
& Nagao (2016), Toba et al. (2017a)]). These are observed as luminous IR
galaxies (LIRGs) and ultraluminous IR galaxies (ULIRGs) with $L_{\rm IR}$
greater than 1011 and 1012 $L_{\odot}$, respectively (Sanders & Mirabel,
1996). Recent works also suggested that the relative strength of SF and AGN
activity in U/LIRGs may be varied in the course of galaxy mergers (e.g.,
Narayanan et al. (2010); Ricci et al. (2017); Blecha et al. (2018); Yamada et
al. (2019, 2021)). In particular, radiation from an AGN is expected to
interact with the interstellar medium (ISM) and lead to the ejection or
heating of the gas, which could be tightly associated with the growth of the
galaxy and its supermassive black hole (SMBH) (e.g., Cazzoli et al. (2016);
Toba et al. (2017b); Harrison et al. (2018); Chen et al. (2019); Finnerty et
al. (2020); Jun et al. (2020); Fluetsch et al. (2021)). That AGN-driven
outflow is often observed in U/LIRGs: recent observations reported that dusty
IR luminous AGN often shows a strong ionized gas outflow, and its strength
seems to be correlated with $L_{\rm IR}$ (Bischetti et al., 2017; Toba et al.,
2017c; Chen et al., 2019; Jun et al., 2020). Therefore, U/LIRGs are a good
laboratory to examine how AGN-driven outflow could influence the host galaxy
and its SMBH. However, those works are often limited to handling a whole
galaxy as a system. To address, from a spatially-resolved point of view, how
the SF and AGN activity could be enhanced/quenched as a function of merger
sequence, Integral Field Unit (IFU) observation is a quite powerful tool that
may trace the gas kinematics and energetics (e.g., Bae et al. (2017); Shin et
al. (2019); Pan et al. (2019)).

In this work, we focus on the Great Observatories All-sky LIRG Survey (GOALS;
Armus et al. (2009)) that provides a complete, flux-limited (i.e., flux
density at 60 $\mu$m $>$ 5.24 Jy) U/LIRG sample in the local universe. In
addition to their multi-wavelength follow-up observations, Stierwalt et al.
(2013) divided the GOALS U/LIRGs into sub-samples regarding the merger stage,
based on a visual inspection of the IRAC/Spitzer 3.6 $\micron$ images and/or
higher resolution images taken by e.g., Hubble Space Telescope (see also Haan
et al. (2011)). Therefore, the GOALS sample is an ideal laboratory to
investigate the role of galaxy mergers in the co-evolution of galaxies and
SMBHs.

In this paper, we present the initial results of our follow-up campaign of
GOALS sample with an optical IFU, the Kyoto Okayama Optical Low-dispersion
Spectrograph with optical-fiber IFU (KOOLS-IFU; Yoshida (2005); Matsubayashi
et al. (2019)) on the Okayama 3.8 m, Seimei Telescope (Kurita et al., 2020).
The structure of this paper is as follows. Section 2 describes the sample
selection, observations, and data reduction of observed targets. In Section 3,
we present the results of our optical IFU observations and discuss the
dependence of ionized gas outflow on distance from the galaxy center and
merger stage. We summarize the results of this work in Section 4. Throughout
this paper, the adopted cosmology is a flat universe with $H_{0}$ = 70 km s-1
Mpc-1, $\Omega_{\rm M}$ = 0.28, and $\Omega_{\Lambda}$ = 0.72, which are the
same as those adopted in a series of GOALS papers that are relevant to this
work (e.g., Armus et al. (2009); Rich et al. (2015)).

##  2 Data and analysis

###  2.1 Target selection

The observed targets were drawn from the GOALS sample, which is itself a
subset of the IRAS Revised Bright Galaxy Sample (Sanders et al., 2003),
providing a 60 $\micron$ flux-limited sample of U/LIRGs at $z<0.088$. The
GOALS sample has been extensively examined by multi-wavelength observations
from X-ray (e.g., Iwasawa et al. (2011); Ricci et al. (2017); Torres-Albà et
al. (2018); Yamada et al. (2020); Ricci et al. (2021); Yamada et al. (2021)),
ultraviolet (UV) (e.g., Howell et al. (2010); Petty et al. (2014)), optical-
NIR (e.g., Haan et al. (2011); Kim et al. (2013); Linden et al. (2017); Jin et
al. (2019); Larson et al. (2020)), mid-IR (MIR)–far-IR (FIR) (e.g., Inami et
al. (2013); Stierwalt et al. (2013, 2014); Chu et al. (2017); Díaz-Santos et
al. (2017); Inami et al. (2018); Yamada et al. (2019); Armus et al. (2020)) to
radio (e.g., Privon et al. (2015); Barcos-Muñoz et al. (2017); Yamashita et
al. (2017); Herrero-Illana et al. (2019); Linden et al. (2019); Condon et al.
(2021)) (see also Casey (2012); U et al. (2012) for SED analysis). We employed
the merger classifications provided by Stierwalt et al. (2013), which have
five categories from N (no signs of merger activity or massive neighbors), to
stage A (galaxy pairs prior to a first encounter), B (post-first encounter
with galaxy disks that are still symmetric and intact but with signs of tidal
tails), C (showing amorphous disks, tidal tails, and other signs of merger
activity), and D (two nuclei in a common envelope), as a sequence of merger
stage (see Section 2.5 in Stierwalt et al. (2013) for more detail) (see also
e.g., Figure 1 in Ricci et al. (2017) for an example image of each merger
stage).

Figure 1: Histograms of (a) redshift, (b) IR luminosity, and (c) merger stage
of the GOALS sample (black/gray), GOALS sample with WiFeS provided in (Rich et
al., 2015) (blue), and GOALS sample with KOOLS-IFU, i.e., our sample (red).

Basic properties of observed targets in GOALS sample.  Object Name IRAS Name
R.A. Decl. redshift $D_{\rm L}$ physical scale $B$-mag $\log\,(L_{\rm
IR}/L_{\odot})$ Merger Stage (J2000.0) (J2000.0) (Mpc) (kpc/arcsec) (1) (2)
(3) (4) (5) (6) (7) (8) (9) (10) NGC 1614 F04315$-$0840 04:34:00.03
$-$08:34:44.57 0.01594 69.12 0.32 14.7 11.65 D CGCG 468$-$002W F05054+1718_W
05:08:19.71 +17:21:48.09 0.01748 75.89 0.36 15.4 (11.22) B NGC 3690 West
F11257+5850_W 11:28:30.78 +58:33:42.90 0.01017 43.90 0.21 11.8 (11.93) C NGC
3690 East F11257+5850_E 11:28:33.39 +58:33:46.40 0.01036 44.74 0.21 11.8
(11.93) C Mrk 273 F13428+5608 13:44:42.07 +55:53:13.17 0.03734 164.61 0.74
15.7 12.21 D NGC 6786 F19120+7320_W 19:10:53.75 +73:24:36.60 0.02524 110.27
0.51 13.7 (11.49) C NGC 6921 20264+2533_W 20:28:28.84 +25:43:24.19 0.01447
62.67 0.30 14.4 (11.11) A NGC 7674 F23254+0830 23:27:56.70 +08:46:44.24
0.02903 127.17 0.58 13.9 11.56 A NGC 7679 23262+0314_W 23:28:46.67
+03:30:40.99 0.01715 74.45 0.35 13.2 11.11 A Columns: (1) object name from
SIMBAD Astronomical Database or NASA/IPAC Extragalactic Database (NED). (2)
IRAS name. (3–4) right ascension (R.A.) and declination (Decl.) (J2000.0). (5)
spectroscopic redshift in NED. (6–7) luminosity distance and physical size in
1 arcsec in the assumed cosmology. (8) $B$-band magnitude from SIMBAD or NED.
(9) IR luminosity from Armus et al. (2009), where values in brackets denote
the total IR luminosity for a system. (10) merger stage from Stierwalt et al.
(2013).

Figure 2: The $i$-band postage stamps ($60\arcsec\times 60\arcsec$) of our
sample taken by Pan-STARRS. The footprint of the KOOLS-IFU with 127 fibers is
overlaid as red circles. R.A. and decl. are relative coordinates with respect
to those in Table 2.1 in which ($\Delta$R.A, $\Delta$Decl.) = (0, 0) also
corresponds to the center of the field of view for KOOLS-IFU (i.e., fiber ID =
37, see Figure 3). North is up and east is left in all images.

We selected 9 objects as the target by taking into account the magnitude in
optical bands ($r$-mag $<$ 16.0), merger stage, previous IFU observations, and
visibility from the Seimei telescope. The basic information of observed
targets is summarized in Table 2.1. Figure 1 shows distributions of redshift,
IR luminosity, and merger stage of our sample. We also present those
distributions for all the GOALS sample (Armus et al., 2009) and sub-sample
reported in Rich et al. (2015), who performed the IFU observations of 27
southern U/LIRGs from the GOALS sample with the Wide Field Spectrograph
(WiFeS) installed on a 2.3 m telescope that capability is similar to KOOLS-
IFU. We confirm from Figure 1 that our sample is widely distributed in terms
of IR luminosity and merger stage while that is biased toward low-$z$
($z<0.04$). Figure 2 shows $i$-band images of our sample taken by Pan-
STARRS333https://ps1images.stsci.edu/cgi-bin/ps1cutouts (Chambers et al.,
2016).

We note that the WiFeS-GOALS IFU survey (Rich et al., 2011, 2012, 2015), the
VLT-VIMOS IFU survey (Arribas et al., 2008), the PMAS IFU survey (Alonso-
Herrero et al., 2009), the INTEGRAL IFU survey (García-Marín et al., 2009),
VLT-SINFONI IFU survey (Piqueras López, et al., 2012), Physics of ULIRGs with
MUSE and ALMA (PUMA; Perna et al. (2021)), and the Keck OSIRIS AO LIRG
Analysis (KOALA; U et al. (2019)) observed (a part of) GOALS sample (see also
García-Marín et al. (2006); Rodríguez-Zaurín et al. (2011); Bellocchi et al.
(2013); Arribas et al. (2014); Kakkad et al. (2022); Perna et al. (2022)). In
particular, the WiFeS-GOALS IFU survey provides specially-resolved maps for
emission-line ratios based on various emission lines, such as H$\beta$, [O
iii]$\lambda$5007, H$\alpha$, [N ii]$\lambda\lambda$6549,6583, and [S
ii]$\lambda\lambda$6716,6731 that are also targeted lines in this work (see
Section 3.2). The sample in this survey is observable from the southern
hemisphere, and thus our sample (that is observable from the northern
hemisphere) is complementary to those reported in Rich et al. (2015). For the
remaining projects, those basically focused on one emission line (e.g.,
H$\alpha$) and spatially-resolved emission-line ratios were not well
investigated444We also confirmed that our targets have not yet been cataloged
in the Calar Alto Legacy Integral Field Area Survey (CALIFA; Sánchez et al.
(2012)) Data Release (DR) 3 (Sánchez et al., 2016), the Sydney-AAO Multi-
object Integral-field spectrograph (SAMI) galaxy survey (Bryant et al., 2015)
DR3 (Croom et al., 2021), and the Sloan Digital Sky Survey (SDSS: York et al.
(2000)) Mapping Nearby Galaxies at Apache Point Observatory survey (MaNGA;
Bundy et al. (2015)) DR17 (Abdurro’uf et al., 2022)..

Observation log in 2019B, 2020A, and 2020B semester.  Name IRAS Name Observing
date Exposure time (minutes) Standard star VPH 495 VPH 683 CGCG 468-002W
F05054+1718_W Oct. 8, 2019 40 40 EGGR247 (=G191–B2B) NGC 1614 F04315-0840 Oct.
9, 27, 2019 50 50 HR9087, HD74280 (=HR3454) NGC 7679 23262+0314_W Oct. 25,
2019 30 30 HR7596 NGC 3690 West F11257+5850_W Apr. 20,21, 2020 40 40 HR5501,
EGGR98 (=HZ43) NGC 3690 East F11257+5850_E Apr. 22,23, 2020 36 38 EGGR98
(=HZ43) Mrk 273 F13428+5608 Apr. 23, 2020 36 36 HR5501 NGC 6786 F19120+7320_W
Aug. 16, 2020 40 40 HR7596 NGC 7674 F23254+0830 Aug 16-18, 2020 40 40 HR7596
NGC 6921 20264+2533_W Aug. 17, 18, 2020 80 80 HD15318 (=HR718)

###  2.2 Observations and data reduction

The targets were observed with the KOOLS-IFU on the Seimei Telescope in the
2019B, 2020A, and 2020B semesters (PI: Y.Toba with proposal IDs = 19B-N-CN01,
19B-K-0001, 20A-N-CN01, and 20B-K-0004). The Seimei is a new 3.8-meter
diameter optical-IR alt-azimuth mount telescope located at Okayama
Observatory, Kyoto University, Okayama prefecture in Japan, where the typical
seeing on this site is 1.2–1.4. The science operation was started in 2019. The
KOOLS-IFU consists of 127 fibers with a total field of view (FoV) of $\sim
15\arcsec$ in diameter555This configuration is valid until September 2020..
Each fiber is assigned a unique fiber ID as shown in Figure 3. The spatial
sampling is $\sim 1.2\arcsec$ per fiber, and the 10$\sigma$ limiting magnitude
is 17–18 AB mag given 10 minutes of exposure. We used the VPH 495 and VPH
683666We did not use an order-sorting filter O56 that is adopted for blocking
the light with $\lambda<5600$ Å. grisms among four grisms equipped with the
KOOLS-IFU. The wavelength coverage and the spectral resolution
($R=\lambda/\Delta\lambda$) of VPH 495 and VPH 683 are 4300–5900 Å and $R$
$\sim$1500 and 5800–8000 Å and $R$ $\sim$2000,
respectively777http://www.o.kwasan.kyoto-u.ac.jp/inst/p-kools/performance/.
The observational log is summarized in Table 2.1.

Figure 3: The schematic view of KOOLS-IFU with fiber ID.

The data reduction was executed with a dedicated
software888http://www.o.kwasan.kyoto-u.ac.jp/inst/p-kools/ in which the Image
Reduction and Analysis Facility (IRAF: Tody (1986, 1993)) tasks are utilized
through the Python package (PyRAF: Science Software Branch at STScI (2012)).
In particular, the IRAF imred.hydra package (Barden et al., 1994; Barden &
Armandroff, 1995) was mainly used for spectrum extraction, flat fielding, and
wavelength calibration in a standard manner. Following Matsubayashi et al.
(2019), spectrum extraction was done by measuring the center position of a
spectrum at each pixel based on dome flat frames in which we summed the counts
within $\pm$2.5 pixels of the center position. The wavelength was calibrated
with arc (Hg and Ne) lamp frames. The flux calibration was carried out by
using an observed spectrum of a standard star (see Table 2.1). Since we
utilized all fibers of KOOLS-IFU for targets, we took sky frames separately
for sky subtractions.

###  2.3 Spectral fitting

In order to measure the properties of emission lines such as line flux and
line width for our GOALS sample, we conducted a spectral fitting to the
reduced spectra by using the Quasar Spectral Fitting package (QSFit
v1.3.0999https://qsfit.inaf.it; Calderone et al. (2017)). Following Toba et
al. (2021a), we fit KOOLS-IFU spectra with the following five components; (i)
AGN continuum with a single power law, (ii) Balmer continuum modeled by Grandi
(1982) and Dietrich et al. (2002), (iii) host galaxy component taken from an
empirical SED template in which a Spiral galaxy template101010We note that
choice of the galaxy templates does not significantly affect the result of the
fitting and our conclusion. (Polletta et al., 2007) is employed, (iv) iron
blended emission lines with UV-optical templates (Vestergaard & Wilkes, 2001;
Véron-Cetty et al., 2004), and (v) emission lines with Gaussian components.
QSFit allows us to fit all the components simultaneously based on a Levenberg-
Marquardt least-squares minimization algorithm with MPFIT (Markwardt, 2009)
procedure.

Since QSFit is optimized to optical spectra taken by the SDSS (e.g., Calderone
et al. (2017); Toba et al. (2021a, b)), we modified the code for general-
purpose, which allows us to do the spectral fitting to KOOLS-IFU data. We fit
the Balmer lines with narrow and broad components in which the FWHM of narrow
and broad components is constrained in the range of 100–1000 km s-1 and
900–15,000 km s-1, respectively, to allow a good decomposition of the line
profile, in the same manner as Toba et al. (2021a). Galactic extinction is
corrected according to Schlafly & Finkbeiner (2011). Since one of the purposes
of this work is to measure the kinematics of an ionized gas outflow, we also
account for a blue-wing component of [O iii]$\lambda\lambda$4959,5007 lines.
Following Calderone et al. (2017), the FWHM of the broad blue-wing component
is constrained to be larger than the narrow component in the range of 100–1000
km s-1 while the broad component is allowed to be blue-shifted up to 2000 km
s-1. The velocity offsets of [O iii]$\lambda$4959 and [O iii]$\lambda$5007 are
tied111111This tying could fail when the SN of the emission line is low (see
e.g., the middle panels of Figure 4). In this work, we employed the velocity
offset of [O iii]$\lambda$5007 as long as it was reasonably measured without
any warning, even if the velocity offset of [O iii]$\lambda$4959 might not be
securely estimated.. The measurement errors are estimated from the Monte Carlo
resampling method in which we adopted the 1$\sigma$ dispersion of each value
by measuring them 100 times for spectra while randomly adding the noise in the
same manner as in Toba et al. (2017b) (see Appendix B in Calderone et al.
(2017) for a full explanation of this procedure).

Figure 4: Examples of spectral fitting for our objects in fiber with VPH 495
(top) and VPH 683 (bottom). The black lines are observed data. The blue and
yellow curves show the narrow and broad components of emission lines,
respectively. The best-fit spectrum is shown with red lines. The vertical
green dashed lines correspond to the rest-frame wavelengths for H$\beta$, [O
iii]$\lambda\lambda$4959,5007, [N ii]$\lambda\lambda$6549,6583, H$\alpha$, and
[S ii]$\lambda\lambda$6716,6731 lines.

##  3 Results and discussion

###  3.1 Result of the spectral fitting

Figure 4 shows examples of the optical spectral fitting with QSFit. We confirm
that about 72% of the fibers are successfully fitted, of which $\sim 90$% have
reduced $\chi^{2}<1.2$. This indicates that the spectra of our sample taken by
KOOLS-IFU are well fitted by QSFit. The failure of the fitting is mainly due
to the low SN of spectra.

###  3.2 Line luminosity maps and line ratio diagnostics

Figure 5: Maps for several line luminosities (H$\beta$, [O iii]$\lambda$5007,
H$\alpha$, [N ii]$\lambda\lambda$6549,6583, and [S
ii]$\lambda\lambda$6716,6731 from left to right) for our sample. Gray circles
denote fibers for which line luminosity could not be estimated due to poor SN.
North is up and east is left in all images.

Figure 5 shows maps for line luminosity in units of erg s-1. Luminosity is the
sum of the broad and narrow emission line components as long as a broad
component is detected. Otherwise, a narrow component of the emission line is
used for estimating the line luminosity. Since each spectrum in fiber is
fitted 100 times via the Monte Carlo realization (see Section 2.3), their
weighted mean is used. Line luminosity is successfully estimated for over 95%
of fibers for most objects. We note that we did not correct for internal dust
extinction because it is quite hard to estimate the amount of attenuation
through the Balmer decrement in all fibers due to poor SN of H$\alpha$ and/or
H$\beta$ line in some fibers (see Figure 5). But this does not affect
estimating the outflow properties that are relevant to the conclusion of this
work (see Section 3.3).

Figure 6 shows a spatially resolved BPT diagram (Baldwin et al., 1981) in
which each fiber position is classified as Seyfert 2 (Sy2), low-ionization
nuclear emission-line region (LINER), composite, star-forming region (SF), and
Unknown. We employed diagnostics with line ratios of [N
ii]$\lambda$6583/H$\alpha$ and [O iii]$\lambda$5007/H$\beta$ provided by
Kauffmann et al. (2003) and Kewley et al. (2006) (see also Toba et al. (2013,
2014)), in which narrow component of each emission line is used. If we define
a fiber with Sy2 or composite classification as AGN-dominant, NGC 1614, CGCG
468-002W, Mrk 273, and NGC 7674 are AGN-dominated with 50-70% of fibers being
classified as Sy2/Composite. For NGC 3690 West and East (that is classified as
merger stage C), about 50% and 30% of fibers are classified as AGN,
respectively, which suggests that NGC 3690 is basically SF-dominated, but the
AGN contribution to the West part is larger than that of the East part for NGC
3690. Indeed, Alonso-Herrero et al. (2000) reported an interaction-induced
star formation for this system. Hard X-ray observations also supported the
presence of AGN in NGC 3690 West and the absence of AGN (or very faint AGN) in
NGC 3690 East (Yamada et al., 2021). A caution here is that obscured AGN often
lacks the signature of AGN emission from narrow-line regions (NLRs) in optical
spectra because NLR is not well developed, and hence those are even outside of
the AGN region in the BPT diagram (Hickox & Alexander (2018), and references
therein), which makes the diagnostics with line ratios difficult.

Figure 6: Spatially resolved BPT diagram for our sample. Red, green, yellow,
and blue circles correspond to Sy2, LINER, composite, and SF, respectively.
Gray circles denote “Unknown” fibers for which line ratio diagnostics could
not be executed because either or both lines for line ratio were undetected.
North is up and east is left in all images.

###  3.3 Outflow properties as a function of distance from the galaxy center

We examine the spatial correlation of outflow properties in a galaxy and how
the outflow strength could be associated with the merger stage. The velocity
offset and/or velocity dispersion of [O iii]$\lambda$5007 have been
preferentially used for evaluating the strength of ionized gas outflow from
the rest-frame optical spectra (e.g., Zakamska et al. (2016); Rakshit & Woo
(2018); Chen et al. (2019); Jun et al. (2020)). But it is known that the
velocity offset or velocity dispersion alone is not always a good tracer of
the strength of AGN outflows because they are often affected by dust
extinction (Bae & Woo, 2014; Woo et al., 2016). To make a fair comparison of
outflow power for objects in any merger stage that may have different amounts
of dust (e.g., Ricci et al. (2017); Blecha et al. (2018); Ricci et al. (2021);
Yamada et al. (2021)), we employ the following quantity;

$\sigma_{0}=\sqrt{v_{\rm[OIII]}^{2}+\sigma_{\rm[OIII]}^{2}},$ (1)

where $v_{\rm[OIII]}$ and $\sigma_{\rm[OIII]}$ are velocity shifts of the
broad blue-wing component and its velocity dispersion, respectively. This
quantity minimizes the influence of dust extinction; Bae & Woo (2016)
demonstrated that $\sigma_{0}$ does not change significantly regardless of the
amount of dust extinction given a bicone inclination by assuming a biconical
outflow model (see Bae & Woo (2016) for details). This methodology is
applicable even to heavily dust-obscured galaxies (Toba et al., 2017b).

We then investigate how $\sigma_{0}$ could depend on the distance from the
galaxy center (i.e., fiber center). In order to obtain reliable $\sigma_{0}$
with a relatively small uncertainty, we estimate $\sigma_{0}$ in the following
three annular areas with an inner-outer radius of (i) 0–1 kpc, (ii) 1–2 kpc,
and (iii) 2–5 kpc. Figure 7 shows resultant $\sigma_{0}$ as a function of
galaxy center for various merger stages. The only object classified as merger
stage “B”, CGCG 468$-$002W, is shown only in the innermost area because
$\sigma_{0}$ could not be measured in the outer regions due to poor
SN121212Even in the innermost area, the uncertainty of $\sigma_{0}$ is about
0.3 dex (see Figure 7).. We find a negative correlation between distance from
the center and $\sigma_{0}$ regardless of the merger stage, with a coefficient
of $r\sim-0.4$ in which uncertainties of $\sigma_{0}$ are taken into account
(see e.g., Kelly (2007); Toba et al. (2019)). This result supports an AGN-
driven outflow; an ionized gas outflow is launched from the galactic nucleus.
Focusing on the galactic center, $\sigma_{0}$ in merger stage D is the
strongest that is comparable to dust-obscured AGN (Toba et al., 2017b) (see
also Section 3.4).

Figure 7: The outflow strength ($\sigma_{0}$) as a function of the galaxy
(fiber) center. Blue, green, yellow, and red data points represent the merger
stage of A, B, C, and D, respectively.

It should be noted that a starburst-driven outflow is also reported in some
galaxies and is reproduced by numerical simulations (e.g., Jogee al. (1998);
Leon et al. (2007); Schneider et al. (2020)). Hence $\sigma_{0}$ may not be
tracing purely AGN-driven outflow. To test this possibility, we utilize SDSS
spectra of nearby starburst galaxies and execute the spectral analysis. We
first select 430 objects from the SDSS DR17 with satisfying the following
criteria; (i) $0.01<z<0.04$, (ii) $r$-mag $<15$, and (iii) SUBCLASS =
“STARBURST”131313It labels a galaxy with being classified star-forming
galaxies (SFGs) in the BPT diagram but has an equivalent width of H$\alpha$
greater than 50 Å.. The redshift and magnitude ranges are similar to those in
our GOALS sample. The fiber diameter of the SDSS/BOSS Spectrograph is 2–3,
which corresponds to central 2–3 fibers in KOOLS-IFU. We then perform the
spectral fitting with QSFit in the same manner as what is described in Section
2.3 and estimate $\sigma_{0}$. As a result, a weighted mean of $\sigma_{0}$
for the starburst galaxy sample is $\log\,\sigma_{0}\sim 2.7$. This value is
smaller than those in the inner part of our GOALS sample, which means that it
could be difficult for starburst galaxies to produce such a strong outflow
with $\log\,\sigma_{0}>2.8$ as we observed for our sample (Figure 7). This
suggests that high $\sigma_{0}$ basically originates from an AGN-driven
outflow.

In order to see how the galaxy merger could affect the gas density from the
spatially-resolved view, we also estimate electron density ($n_{\rm e}$) of
ionized gas from the line flux ratio of [S ii]$\lambda\lambda$6716,6731 that
is known as a good tracer of $n_{\rm e}$ and widely used for
AGN141414Recently, some caveats of using [S ii] doublet for $n_{\rm e}$ have
been reported (Davies et al. (2020), and references therein). (e.g.,
Osterbrock & Ferland (2006); Kawasaki et al. (2017); Kawaguchi et al. (2018);
Joh et al. (2021)), which tells us how $n_{\rm e}$ could be different among
the inner and outer regions of our GOALS sample. Here, a conversion formula is
employed to estimate $n_{\rm e}$ from the [S ii] ratio (see e.g., Kakkad et
al. (2022), and reference therein). Albeit with a large uncertainty ($\sim$30
%), we find a spatial gradient of $n_{\rm e}$, i.e., high-density gas with
$n_{\rm e}\sim 10^{3}$ cm-3 is located in the central 0.5 kpc while low-
density gas with $n_{\rm e}<100$ cm-3 is distributed in the outer region.

###  3.4 Outflow properties as a function of merger stage

Finally, we investigate how $\sigma_{0}$ could be associated with the merger
stages as shown in Figure 8. We find that ionized gas outflow is more powerful
as a sequence of merger stages; the outflow strength in the late-stage (stage
D) mergers is about 1.5 times stronger than that in the early-state (stage B)
mergers. We also check the correlation between $\sigma_{0}$ and $D_{\rm 12}$
in which $D_{\rm 12}$ is the separation between the two nuclei in units of kpc
(see Yamada et al. (2021)). We confirm a negative correlation between two
quantities for samples with merger stages from B to D. We further find that
$n_{\rm e}$ estimated from the [S ii] doublet (see Section 3.3) seems larger
in the late-stage merger. Recently, Yamada et al. (2021) reported that the
outflow velocity of molecular gas of X-ray AGN in merger stage D correlates
with Eddington ratio151515Yamada et al. (2021) also reported a positive
correlation between outflow velocity of molecular gas and X-ray bolometric
correction that may be correlated with Eddington ratio (see e.g., Toba et al.
(2019)).. Molecular outflows are also correlated with ionized gas outflow
regarding the mass outflow rate (Fiore et al., 2017). These results suggest
that the galaxy merger could induce a dense ionized gas outflow driven by AGN,
particularly in the late-stage merger. At the same time, an important caveat
to be kept in mind is that those results are based only on nine objects. We
cannot rule out the possibility that the observed trends are affected by a
selection effect (see below). Further observations for the GOALS sample with a
wider range of redshift, brightness, and dynamical state are needed to
corroborate our conclusion.

Figure 8: The outflow strength ($\sigma_{0}$) as a function of the merger
stage. Since especially objects classified as stage A might be affected by the
selection effect or even classified as stage D, our conclusions are based
primarily on results from stage B to D (see the text for details).

We also note that $\sigma_{0}$ for merger stage A is comparably large to stage
D. One possible reason for this is that merger stage A is a too early phase
(i.e., two galaxies are too far from each other) to affect the strength of the
ionized gas outflow, and thus $\sigma_{0}$ could depend on the nature of the
individual object rather than the contribution of the merger process. Indeed,
NGC 6921, NGC 7674, and NGC 7679 (that are classified as merger stage A) are
all reported as strong AGNs with X-ray detections161616NGC 7674 and MGC 7679
are also reported [Ne v]$\lambda$14.32 $\mu$m detections (Inami et al., 2013).
(see Yamada et al. (2021), for details). In particular, NGC 7674 is expected
to harbor dual SMBHs (Kharb et al. (2017), but see also Breiding et al. (2022)
for counterargument), which could have a quite strong AGN outflow171717The
Eddington ratio of NGC 7674 is also larger than other AGN in our sample
(Yamada et al., 2021).. A full investigation of this object will be reported
(S.Yamada et al. in preparation). Another possibility is that those objects
are indeed at the very last stage of former merging events so that no tidal
features are visible (which means they are stage D). On the other hand, if the
trend in Figure 8 is robust without being affected by the selection effect,
this result could suggest that galaxy merger is not the only path to ignite
AGN as introduced in Section 1.

Arribas et al. (2014) reported that SF-driven outflow strength traced by
H$\alpha$ line in SFGs is correlated with dynamical phases (that corresponds
to the merger stage, see Rodríguez-Zaurín et al. (2011), for more detail)
along the merging process. Rich et al. (2015) also reported from an IFU
observation that the low-velocity shocks become increasingly prominent as a
merger progresses (see also Rich et al. (2011)). In addition, the outflow
strength ($\sigma_{0}$) seems to be correlated with the Eddington ratio (e.g.,
Bae & Woo (2014); Toba et al. (2017b)). Taking account of those findings into
account, our observations support that galaxy mergers enhance both SF and AGN
activity and play an important role in the co-evolution of galaxies and SMBHs.

##  4 Summary

In order to reveal how the galaxy merger could affect the strength of the
ionized gas outflow from a spatially-resolved point of view, we analyze 9
local U/LIRGs at $z<0.04$ through the IFU observations with KOOLS-IFU on
Seimei Telescope. The observed targets are selected from a 60 $\mu$m flux-
limited sample in the GOALS project, covering a wide range of merger states
from an early-stage (A) to late-stage (D). We successfully detect various
emission lines of H$\beta$, [O iii]$\lambda\lambda$4959,5007, H$\alpha$, [N
ii]$\lambda\lambda$6549,6583, and [S ii]$\lambda\lambda$6716,6731 over 70% of
fibers. This work mainly focuses on the strength of the ionized gas outflow
($\sigma_{0}$) by using a combination of velocity shift and dispersion of [O
iii]$\lambda$5007 line. With all the caveats discussed in Sections 3.3 and 3.4
in mind, we find $\sigma_{0}$ shows a negative correlation with the distance
from the galaxy center and a positive correlation with a sequence of merger
stages. This indicates that galaxy mergers may induce AGN-driven outflow and
maximize the late-stage merger, which is in good agreement with previous works
reporting that the Eddington ratio of AGN increases along with the merger
stage.

Since our follow-up observation campaign with KOOLS-IFU is ongoing, and about
130 GOALS samples are observable from the Seimei telescope, this work provides
a benchmark for revealing the spatially-resolved outflow properties from a
statical point of view in the future.

We gratefully thank the anonymous referee for a careful reading of the
manuscript and very helpful comments. We acknowledge Dr. Kyuseok Oh for
providing a finding chart for our observations in 2019. This work is supported
by JSPS KAKENHI Grant numbers 18J01050, 19K14759, and 22H01266 (YT), 19J22216
(SY), 20H01946 (YU), and 20K04027 (NO). SY is grateful for support from RIKEN
Special Postdoctoral Researcher Program.

## References

  * Abdurro’uf et al. (2022) Abdurro’uf, et al., 2022, ApJS, 259, 35
  * Alonso-Herrero et al. (2000) Alonso-Herrero, A., Rieke, G. H., Rieke, M. J., & Scoville, N. Z. 2000, ApJ, 532, 845
  * Alonso-Herrero et al. (2009) Alonso-Herrero, A., García-Marín, M., Monreal-Ibero, A., Colina, L., Arribas, S., Alfonso-Garzón, J., & Labiano, A. 2009, A&A, 506, 1541
  * Armus et al. (2009) Armus, L., et al. 2009, PASP, 121, 559
  * Armus et al. (2020) Armus L., Charmandaris V.,& Soifer B. T., 2020, Nat. Astron., 4, 467
  * Arribas et al. (2008) Arribas, S., Colina, L., Monreal-Ibero, A., Alfonso, J., García-Marín, M., & Alonso-Herrero, A. 2008, A&A, 479, 687
  * Arribas et al. (2014) Arribas, S., Colina, L., Bellocchi, E., Maiolino, R., & Villar-Martín, M. 2014, A&A, 568, A14,
  * Bae & Woo (2014) Bae, H.-J., & Woo, J.-H. 2014, ApJ, 795, 30
  * Bae & Woo (2016) Bae, H.-J., & Woo, J.-H. 2016, ApJ, 828, 97
  * Bae et al. (2017) Bae, H.-J., Woo, J.-H., Karouzos, M., Gallo, E., Flohic, H., Shen, Y., & Yoon, S.-J. 2017, ApJ, 837, 91
  * Baldwin et al. (1981) Baldwin J. A., Phillips M. M., Terlevich R., 1981, PASP, 93, 5
  * Barcos-Muñoz et al. (2017) Barcos-Muñoz, L., et al. 2017, ApJ, 843, 117
  * Barden et al. (1994) Barden, S. C., Armandroff, T., Muller, G., Rudeen, A. C., Lewis, J., & Groves, L. 1994, Proc. SPIE, 2198, 87
  * Barden & Armandroff (1995) Barden, S. C., & Armandroff, T. 1995, Proc. SPIE, 2476, 56
  * Bellocchi et al. (2013) Bellocchi, E., Arribas, S., Colina, L., & Miralles-Caballero, D. 2013, A&A, 557, A59
  * Bischetti et al. (2017) Bischetti, M., et al. 2017, A&A, 598, A122
  * Blecha et al. (2018) Blecha, L., Snyder, G. F., Satyapal, S., & Ellison, S. L. 2018, MNRAS, 478, 3056
  * Breiding et al. (2022) Breiding, P., Burke-Spolaor, S., An, T., Bansal, K., Mohan, P., Taylor, B. G., & Zhang, Y. 2022, ApJ, 933, 143
  * Bryant et al. (2015) Bryant, J. J., et al. 2015, MNRAS, 447, 2857
  * Bundy et al. (2015) Bundy, K., et al. 2015, ApJ, 798, 7
  * Calderone et al. (2017) Calderone, G., Nicastro, L., Ghisellini, G., Dotti, M., Sbarrato, T., Shankar, F., & Colpi, M., 2017, MNRAS, 472, 4051
  * Casey (2012) Casey, C. M. 2012, MNRAS, 425, 3094
  * Cazzoli et al. (2016) Cazzoli, S., Arribas, S., Maiolino, R., & Colina, L., 2016, A&A, 590, A125
  * Chambers et al. (2016) Chambers, K. C., et al. 2016, arXiv:1612.05560
  * Chary & Elbaz (2001) Chary, R., & Elbaz, D. 2001, ApJ, 556, 562
  * Chen et al. (2019) Chen, X., et al. 2019, PASJ, 71, 29
  * Chu et al. (2017) Chu, Jason K., et al. 2017, ApJS, 229, 25,
  * Condon et al. (2021) Condon, J. J., Cotton, W. D., Jarrett, T., Marchetti, L., Matthews, A. M., Mauch, T., & Moloko, M. E. 2021, ApJS, 257, 35
  * Conselice (2014) Conselice, C. J. 2014, ARA&A, 52, 291
  * Croom et al. (2021) Croom, S. M., et al. 2021, MNRAS, 505, 991
  * Davies et al. (2020) Davies R. et al., 2020, MNRAS, 498, 4150
  * de Zeeuw et al. (2002) de Zeeuw, P. T., et al. 2002, MNRAS, 329, 513
  * Díaz-Santos et al. (2017) Díaz-Santos, T., et al. 2017, ApJ, 846, 32
  * Dietrich et al. (2002) Dietrich M., Appenzeller I., Vestergaard M., & Wagner S. J., 2002, ApJ, 564, 581
  * Draper & Ballantyne (2012) Draper, A. R., & Ballantyne, D. R. 2012, ApJ, 751, 72
  * Finnerty et al. (2020) Finnerty, L., et al. 2020, ApJ, 905, 16
  * Fiore et al. (2017) Fiore, F., et al. 2017, A&A, 601, A143
  * Fluetsch et al. (2021) Fluetsch, A., et al. 2021, MNRAS, 505, 5753
  * García-Marín et al. (2006) García-Marín, M., Colina, L., Arribas, S., Alonso-Herrero, A., & Mediavilla, E. 2006, ApJ, 650, 850
  * García-Marín et al. (2009) García-Marín, M., Colina, L., Arribas, S., & Monreal-Ibero, A. 2009, A&A, 505, 1319
  * Grandi (1982) Grandi S. A., 1982, ApJ, 255, 25
  * Haan et al. (2011) Haan, S., et al. 2011, ApJS, 197, 27
  * Harrison et al. (2018) Harrison, C. M., Costa, T., Tadhunter, C. N., Flütsch, A., Kakkad, D., Perna, M. & Vietri, G. 2018, Nature Astron., 2, 198
  * Herrero-Illana et al. (2019) Herrero-Illana, R., et al. 2019, A&A, 628, A71
  * Hickox & Alexander (2018) Hickox, R. C., & Alexander, D. M. 2018, ARA&A, 56, 625
  * Howell et al. (2010) Howell, J. H., et al. 2010, ApJ, 715, 572
  * Imanishi et al. (2007) Imanishi, M., Dudley, C. C., Maiolino, R., Maloney, P. R., Nakagawa, T., & Risaliti, G. 2007, ApJS, 171, 72
  * Imanishi (2009) Imanishi, M. 2009, ApJ, 694, 751
  * Inami et al. (2013) Inami, H., et al. 2013, ApJ, 777, 156
  * Inami et al. (2018) Inami, H., et al. 2018, A&A, 617, A130
  * Iwasawa et al. (2011) Iwasawa, K., et al. 2011, A&A, 529, A106
  * Jin et al. (2019) Jin, J-J., Zhu, Y.-N., Wu, H., Lei, F.-J., Cao, C., Meng, X.-M., Zhou, Z.-M., & Lam, M. I. 2019, ApJS, 244, 33
  * Jogee al. (1998) Jogee, S., Kenney, J. D. P., & Smith, B. J. 1998, ApJ, 494, 185
  * Joh et al. (2021) Joh, K,, Nagao, T., Wada, K., Terao, K., & Yamashita, T. 2021, PASJ, 73, 1152
  * Jun et al. (2020) Jun, H. D., et al. 2020, ApJ, 888, 110
  * Kakkad et al. (2022) Kakkad, D., et al. 2022, MNRAS, 511, 2105
  * Kauffmann et al. (2003) Kauffmann, G., et al. 2003, MNRAS, 346, 1055
  * Kawaguchi et al. (2018) Kawaguchi, T., et al. 2018, PASJ, 70, 93
  * Kawasaki et al. (2017) Kawasaki, K., Nagao, T., Toba, Y., Terao, K., & Matsuoka, K. 2017, ApJ, 842, 44
  * Kelly (2007) Kelly B. C., 2007, ApJ, 665, 1489
  * Kewley et al. (2006) Kewley, L. J., Groves, B., Kauffmann, G., & Heckman, T. 2006, MNRAS, 372, 961
  * Kharb et al. (2017) Kharb, P., Lal, D. V., & Merritt, D. 2017, Nat. Astron., 1, 727
  * Kim et al. (2013) Kim, D.-C., et al. 2013, ApJ, 768, 102
  * Kurita et al. (2020) Kurita, M., et al. 2020, PASJ, 72, 48
  * Larson et al. (2020) Larson, K. L., et al. 2020, ApJ, 888, 92
  * Leon et al. (2007) Leon, S., et al. 2007, A&A, 473, 747
  * Linden et al. (2017) Linden, S. T., et al. 2017, ApJ, 843, 91
  * Linden et al. (2019) Linden, S. T., et al. 2019, ApJ, 881, 70
  * Markwardt (2009) Markwardt, C. B. 2009, ASP Conf. Ser., 411, 251
  * Matsubayashi et al. (2019) Matsubayashi, K., et al. 2019, PASJ, 71, 102
  * Narayanan et al. (2010) Narayanan, D., et al. 2010, MNRAS, 407, 1701
  * Osterbrock & Ferland (2006) Osterbrock, D. E., & Ferland, G. J. 2006, Astrophysics of Gaseous Nebulae and Active Galactic Nuclei, 2nd ed. (Sausalito, CA: University Science Books)
  * Pan et al. (2019) Pan, H.-A., et al. 2019, ApJ, 881, 119
  * Perna et al. (2021) Perna, M., et al. 2021, A&A, 646, A101
  * Perna et al. (2022) Perna, M., et al. 2022, A&A, 662, A94
  * Petty et al. (2014) Petty, S. M., et al. 2014, AJ, 148, 111
  * Piqueras López, et al. (2012) Piqueras López, J., Colina, L., Arribas, S., Alonso-Herrero, A., & Bedregal, A. G. 2012, A&A, 546, A64
  * Polletta et al. (2007) Polletta, M., et al. 2007, ApJ, 663, 81
  * Privon et al. (2015) Privon, G. C., et al. 2015, ApJ, 814, 39
  * Rakshit & Woo (2018) Rakshit, S., & Woo, J.-H. 2018, ApJ, 865, 5
  * Ricci et al. (2017) Ricci, C., et al. 2017, MNRAS, 468, 1273
  * Ricci et al. (2021) Ricci, C., et al. 2021, MNRAS, 506, 5935
  * Rich et al. (2011) Rich, J. A., Kewley, L. J., & Dopita, M. A. 2011, ApJ, 734, 87
  * Rich et al. (2012) Rich, J. A., Torrey, P., Kewley, L. J., Dopita, M. A., & Rupke, D. S. N. 2012, ApJ, 753, 5
  * Rich et al. (2015) Rich, J. A., Kewley, L. J., & Dopita, M. A. 2015, ApJS, 221, 28
  * Rodríguez-Zaurín et al. (2011) Rodríguez-Zaurín, J., Arribas, S., Monreal-Ibero, A., Colina, L., Alonso-Herrero, A., & Alfonso-Garzón, J. 2011, A&A, 527, A60
  * Sánchez et al. (2012) Sánchez, S. F., et al. 2012, A&A, 538, A8
  * Sánchez et al. (2016) Sánchez, S. F., et al. 2016, A&A, 594, A36
  * Sanders & Mirabel (1996) Sanders, D. B., & Mirabel, I. F. 1996, ARA&A, 34, 749
  * Sanders et al. (1988) Sanders D. B., Soifer B. T., Elias J. H., Madore B. F., Matthews K., Neugebauer G., & Scoville N. Z., 1988, ApJ, 325, 74
  * Sanders et al. (2003) Sanders, D. B., Mazzarella, J. M., Kim, D., Surace, J. A., & Soifer, B. T. 2003, AJ, 126, 1607
  * Schawinski et al. (2011) Schawinski, K., Treister, E., Urry, C. M., Cardamone, C. N., Simmons, B., & Yi, S. K. 2011, ApJ, 727, L31
  * Schlafly & Finkbeiner (2011) Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103
  * Schneider et al. (2020) Schneider, E. E., Ostriker, E. C., Robertson, B. E., & Thompson, T. A. 2020, ApJ, 895, 43
  * Science Software Branch at STScI (2012) Science Software Branch at STScI 2012, Astrophysics Source Code Library, ascl:1207.011
  * Sharma et al. (2021) Sharma, R. S., et al. 2021, (arXiv:2101.01729)
  * Shin et al. (2019) Shin J., Woo J.-H., Chung A., Baek J., Cho K., Kang D., & Bae H.-J., 2019, ApJ, 881, 147
  * Stierwalt et al. (2013) Stierwalt, S., et al. 2013, ApJS, 206, 1
  * Stierwalt et al. (2014) Stierwalt, S., et al. 2014, ApJ, 790, 124
  * Toba et al. (2013) Toba, Y., et al. 2013, PASJ, 65, 113
  * Toba et al. (2014) Toba, Y., et al. 2014, ApJ, 788, 45
  * Toba et al. (2015) Toba, Y., et al. 2015, PASJ, 67, 86
  * Toba & Nagao (2016) Toba, Y., & Nagao, T. 2016, ApJ, 820, 46
  * Toba et al. (2017a) Toba, Y., et al. 2017a, ApJ, 840, 21
  * Toba et al. (2017b) Toba, Y., Bae, H.-J., Nagao, T., Woo, J.-H., Wang, W.-H., Wagner, A. Y., Sun, A.-L., & Chang, Y.-Y. 2017b, ApJ, 850, 140
  * Toba et al. (2017c) Toba, Y., Komugi, S., Nagao, T., Yamashita, T., Wang, W.-H., Imanishi, M., & Sun, A.-L. 2017c, ApJ, 851, 98
  * Toba et al. (2019) Toba, Y, Ueda, Y., Matsuoka, K., Shidatsu, M., Nagao, T., Terashima, Y., Wang, W.-H., & Chang, Y.-Y. 2019, MNRAS, 484, 196
  * Toba et al. (2021a) Toba, Y., et al. 2021a, ApJ, 912, 91
  * Toba et al. (2021b) Toba, Y., et al. 2021b, A&A, 649, L11
  * Tody (1986) Tody, D. 1986, Proc. SPIE, 627, 733
  * Tody (1993) Tody, D. 1993, in ASP Conf. Ser. 52, Astronomical Data Analysis Software and Systems II, ed. R. J. Hanisch, R. J. V. Brissenden, & J. Barnes (San Francisco, CA: ASP), 173
  * Torres-Albà et al. (2018) Torres-Albà, N., et al. 2018, A&A, 620, A140
  * U et al. (2012) U, V., et al. 2012, ApJS, 203, 9
  * U et al. (2019) U, V., et al. 2019, ApJ, 871, 166
  * Veilleux et al. (2002) Veilleux, S., Kim, D.-C., & Sanders, D. B. 2002, ApJS, 143, 315
  * Véron-Cetty et al. (2004) Véron-Cetty, M.-P., Joly M., & Véron P., 2004, A&A, 417, 515
  * Vestergaard & Wilkes (2001) Vestergaard, M., & Wilkes B. J., 2001, ApJS, 134, 1
  * Woo et al. (2016) Woo, J.-H., Bae, H.-J., Son, D., & Karouzos, M. 2016, ApJ, 817, 108
  * Yamada et al. (2019) Yamada S., Ueda Y., Tanimoto A., Kawamuro T., Imanishi M., & Toba Y., 2019, ApJ, 876, 96
  * Yamada et al. (2020) Yamada S., Ueda Y., Tanimoto A., Oda S., Imanishi M., Toba Y., & Ricci C., 2020, ApJ, 897, 107
  * Yamada et al. (2021) Yamada S., Ueda Y., Tanimoto A., Imanishi M., Toba Y., Ricci C., & Privon G. C., 2021, ApJS, 257, 61
  * Yamashita et al. (2017) Yamashita, T., et al. 2017, ApJ, 844, 96
  * York et al. (2000) York, D. G., et al. 2000, AJ, 120, 1579
  * Yoshida (2005) Yoshida, M. 2005, J. Korean Astron. Soc., 38, 117
  * Zakamska et al. (2016) Zakamska, N. L., et al. 2016, MNRAS, 459, 3144


# A Lower Bound on the Mass of Compact Objects from Dissipative Dark Matter

James Gurian  Institute for Gravitation and the Cosmos, The Pennsylvania State
University, University Park, PA 16802, USA  Department of Astronomy and
Astrophysics, The Pennsylvania State University, University Park, PA, 16802,
USA,  Michael Ryan  Institute for Gravitation and the Cosmos, The Pennsylvania
State University, University Park, PA 16802, USA  Department of Physics, The
Pennsylvania State University, University Park, PA, 16802, USA  Sarah Schon
Institute for Gravitation and the Cosmos, The Pennsylvania State University,
University Park, PA 16802, USA  Department of Physics, The Pennsylvania State
University, University Park, PA, 16802, USA  Donghui Jeong  Institute for
Gravitation and the Cosmos, The Pennsylvania State University, University
Park, PA 16802, USA  Department of Astronomy and Astrophysics, The
Pennsylvania State University, University Park, PA, 16802, USA,  School of
Physics, Korea Institute for Advanced Study (KIAS), 85 Hoegiro, Dongdaemun-gu,
Seoul, 02455, Republic of Korea  Sarah Shandera  Institute for Gravitation and
the Cosmos, The Pennsylvania State University, University Park, PA 16802, USA
Department of Physics, The Pennsylvania State University, University Park, PA,
16802, USA<EMAIL_ADDRESS>
###### Abstract

We study the fragmentation scale of dark gas formed in dissipative dark-matter
halos and show that the simple atomic-dark-matter model consistent with all
current observations can create low-mass fragments that can evolve into
compact objects forbidden by stellar astrophysics. We model the collapse of
the dark halo’s dense core by tracing the thermo-chemical evolution of a
uniform-density volume element under two extreme assumptions for density
evolution: hydrostatic equilibrium and pressure-free collapse. We then compute
the opacity-limited minimum fragment mass from the minimum temperature
achieved in these calculations. The results indicate that much of the
parameter space is highly unstable to small-scale fragmentation.

KIAS-P22051

##  1 Introduction

If dark matter is more similar than not to baryonic matter, the dark sector
may host a variety of new, interacting particles that give rise to phenomena
as rich and diverse as the astrophysical structures of luminous matter. In
particular, if the dark matter can efficiently dissipate its kinetic energy,
then dark matter itself can collapse to form compact objects such as dark
black holes (DBH) (D’Amico et al., 2018; Shandera et al., 2018; Chang et al.,
2019; Choquette et al., 2019; Latif et al., 2019), dark white dwarfs (Ryan &
Radice, 2022), or dark neutron stars (Hippert et al., 2021).

The mass spectrum of such compact objects is directly related to dark-matter
physics. Most strikingly, black holes below the baryonic Chandrasekhar limit
of about a solar mass cannot form through standard stellar evolution. But, the
Chandrasekhar limit $M_{\rm Chandra}\propto m_{\rm Planck}^{3}/m_{\rm
proton}^{2}$ is determined by the mass of the proton and so the analogous
limit could be much smaller for dark-matter fermions heavier than 1 GeV.
Constraints on compact object mergers can therefore constrain the microphysics
of dark matter (Singh et al., 2020).

Inferring the dark-matter microphysics from the observed mass spectrum,
however, requires an accurate forward model of the DBH formation process. To
make progress, we consider the scenario known as “atomic dark matter” (aDM)
(Goldberg & Hall, 1986; Ackerman et al., 2009; Feng et al., 2009; Kaplan et
al., 2010, 2011; Cyr-Racine & Sigurdson, 2013; Cyr-Racine et al., 2014; Fan et
al., 2013; Cline et al., 2014; Boddy et al., 2016; Foot & Vagnozzi, 2015,
2016; Randall & Scholtz, 2015; Agrawal et al., 2017a; Ghalsasi & McQuinn,
2018), in which the dark matter consists of two fundamental fermions (one
heavy and one light) oppositely charged under a dark electromagnetism. This
model provides a realistic yet tractable venue in which to explore the
consequences of dissipative dark matter. In this Letter, we present the
fragmentation mass scale for atomic-dark-matter halos by solving the evolution
of the thermo-chemical network, including both dark atomic and molecular
cooling processes.

In the aDM model, dark molecular hydrogen provides the dominant cooling
mechanism at temperatures below the dark-atomic-cooling limit. This parallels
the formation process of the first, or Population III, stars which formed in
pristine, low-metallicity gas clouds. There, the minimum temperature of the
gas imprints a characteristic mass scale which determines the mass of the
first stars (Bromm et al., 2002). Previous work has used a simple criterion
comparing cooling time from atomic processes to free-fall time to determine if
a halo could cool (Buckley & DiFranzo, 2018), and estimated the DBH mass as a
function of the dark-matter parameters by re-scaling results from the Pop. III
literature (Shandera et al., 2018). In that estimate, the energy of the lowest
allowed molecular transition was assumed to determine the coldest temperature
reached by the gas. However, our recent work (Ryan et al., 2021, 2022;
darkrec) which derives the relevant molecular processes now allows a direct
calculation of the cooling efficiency of the dark matter over a range of model
parameters. These parameters are as follows: the mass of the heavy fermion,
$M$; the mass of the light fermion, $m$; the fine structure constant,
$\alpha_{D}$; the dark photon temperature, $T_{D}$. We refer also to these
parameters by the ratios to their baryonic counterparts: $r_{M}=M/m_{p}$,
$r_{m}=m/m_{e}$, $r_{\alpha}=\alpha_{D}/\alpha$, $\xi=T_{D}/T_{\rm CMB}$.
Here, $p$, $e$ and ${\rm CMB}$ stand for proton, electron, and the cosmic
background photon.

If $\xi\sim 0.5$, at most $5\%$ of the dark matter can be atomic while
satisfying the constraint from the lack of dark acoustic oscillations in the
galaxy two-point correlation function (Cyr-Racine et al., 2014). Such a high
value of $\xi$ can be realized for dark matter thermally coupled to the
Standard Model particles at an early time if there are no additional
relativistic degrees of freedom in either the Standard Model or the dark
sector Agrawal et al. (2017b). Relaxing those assumptions allows smaller $\xi$
and opens up a parameter space where the dark matter can be entirely atomic.
We do not know of a fundamental lower bound on $\xi$, but for $\xi\lesssim
10^{-3}$ the calculation of the thermal and chemical evolution of the
primordial universe is complicated by the high dark particle to dark photon
ratio, $\eta_{D}$ (Gurian et al., 2022). A larger value of $\xi$ on the other
hand increases the primordial free electron fraction, which initially promotes
atomic cooling and molecule formation. However, evading the aforementioned
constraints from large scale structure with a higher value of $\xi$ requires
either a rather heavy dark electron $r_{m}\gtrsim 10$ or a large coupling
constant $r_{\alpha}>1$. Here we take $\xi=5\times 10^{-3}$ for which the dark
matter can be entirely atomic over a wide range of $r_{m}$ while $\eta_{D}$ is
tractably small. We further simplify the parameter space by choosing
$r_{\alpha}=1$. The radiative cooling rates have strong dependencies on
$r_{\alpha}$, so efficient cooling requires that $r_{\alpha}$ not be too much
smaller than one. On the other hand, constraints on the dark matter self-
scattering cross-section, which generally take the form of the upper bounds on
$\sigma/M$, tend to prefer some combination $r_{\alpha}<1$ or $r_{M}>1$. For a
more detailed discussion of the constraints on the dark matter cooling curve
at a range of scales, see Singh et al. (2020). With these two parameters
fixed, we study the fragment mass for a range of $r_{m}$ and $r_{M}$.

The full dynamical evolution of a collapsing gas cloud requires three-
dimensional simulations accounting for gravity and hydrodynamics. We instead
compute the chemical and thermal evolution of a homogeneous (uniform density)
parcel of gas. It turns out that these simple calculations have a clear
correspondence with the results of full three-dimensional simulations (Yoshida
et al., 2006). As suggested by Glover (2005) (Section 2.4) and Glover & Abel
(2008) (Eqs. 53-57), we bracket the likely range of results that full
simulations may find by considering two extremes for the density evolution:
adiabatic evolution corresponding to unrestricted gravitational runaway
(pressure-free collapse) and pressure-supported hydrostatic evolution where
the number density is held constant. For the latter, we assume a halo that
cools efficiently with a constant density can collapse the core because the
cooling will eventually eliminate the pressure support. Because the molecule
formation rates and cooling rates both increase with density, the hydrostatic
case represents the highest plausible minimum temperature. On the other hand,
the adiabatic case allows the molecular fraction and cooling rates to attain
their maxima.

The adiabatic collapse calculation is carried out using DarkKROME (Ryan et
al., 2022), while the hydrostatic calculation is implemented independently,
closely following Tegmark et al. (1997). The true thermo-chemical evolution of
a three-dimensional self-gravitating gas cloud must lie somewhere between what
we calculate under these extreme assumptions. Both calculations produce a
minimum temperature for the collapsing gas, which is associated with the final
mass of any compact object formed. We calculate a lower bound on this mass
using the opacity limit argument of Low & Lynden-Bell (1976) and Rees (1976).

##  2 Thermo-chemical evolution

Figure 1: The minimum temperature of a $10^{8}\,\rm M_{\odot}$ atomic dark
matter halo at $z=10$ with $r_{\alpha}=1$ and $\xi=5\times 10^{-3}$, under
constant-density evolution (left) and adiabatic collapse (right). The region
which does not cool substantially is shaded in dark gray. Light blue/gray
corresponds to cooling to the atomic limit, while dark blue indicates
molecular cooling. Molecular cooling is more efficient under adiabatic
collapse because the compressional heating and increasing density promote
molecule formation. Contours of equal suppression of the halo mass function
compared to CDM are shown (dashed): to the left of these contours CDM-like
virialized halos are very rare.

Using DarkKROME (Ryan et al., 2022), we trace the evolution of the adiabatic
collapse of a uniform-density element for a range of dark parameters. For a
halo of mass $M_{\rm Halo}$ at redshift $z$, the calculation is initialized at
the virial density $\rho_{V}=178\bar{\rho}_{m}(z)$ and virial temperature

$T_{V}=\left(\frac{4\pi}{3}\rho_{V}\right)^{1/3}\frac{Gr_{M}m_{H}}{5k_{B}}M_{\rm
Halo}^{2/3},$ (2.1)

with $G$ the gravitational constant, $m_{H}$ the mass of Standard Model
hydrogen, $k_{B}$ the Boltzmann constant and $M_{\rm Halo}$ the halo mass.
Note that the halo mass enters our calculation only by determining the initial
temperature of the gas parcel. The density evolves as

$\frac{d\rho}{dt}=\frac{\rho}{t_{ff}},$ (2.2)

with the free-fall time $t_{ff}=\sqrt{(3\pi)/(32G\rho)}$, and the temperature
evolves according to the energy balance equation:

$\frac{dT}{dt}=(\gamma-1)\frac{\Gamma(T,\\{n_{i}\\})-\Lambda(T,\\{n_{i}\\})}{k_{B}\sum_{i}n_{i}},\,$
(2.3)

where $\gamma$ is the adiabatic index, $\Gamma$ the heating rate, $\Lambda$
the cooling function, and $n_{i}$ the number density of each dark matter
species. We denote the set of all $n_{i}$ by $\\{n_{i}\\}$. The heating rate
is dominated by compressional heating with
$\Gamma_{c}=\sum_{i}n_{i}k_{B}T/t_{ff}$. The cooling rate $\Lambda$ includes
both atomic and molecular processes, as discussed in Ryan et al. (2021, 2022).
We initialize the chemical abundances by the background abundances computed
using the method described in darkrec. We then simultaneously solve the
chemical-reaction network of Ryan et al. (2021) and the thermal equation
Eq.(2.3). Assuming secluded dark matter, we only compute for a dark-matter-
only cloud, not including baryons. The calculation is halted either when the
halo exceeds the virial temperature at the current density by a factor of 5
(indicating that ignoring pressure support is grossly inappropriate) or at the
density threshold above which the collapsing cloud is opaque to molecular
lines (Appendix A).

Independent of DarkKROME, we solve the same chemical-reaction network in
hydrostatic equilibrium with a constant density, fixed at $\rho=\rho_{V}$,
inspired by Tegmark et al. (1997). The temperature is again evolved according
to Eq. (2.3). This implementation uses simpler molecular cooling rates, re-
scaled from Hollenbach & McKee (1979), and neglects heating and cooling due to
the formation and destruction of molecules (endo- and exo-ergic processes). At
constant density, the compressional heating vanishes, and we evolve the
network for a free-fall time at the virial density. We have checked that our
analysis reproduces the results of Tegmark et al. (1997), who tracked the
density evolution through spherical collapse, and that the result agrees with
the DarkKROME in the appropriate low-density limit.

Collapse and fragmentation first occur within the dark-matter halos exceeding
the Jeans mass. In the baryonic sector, such halos form at $z\approx 20$ with
mass $M\sim 10^{6}\,\rm M_{\odot}$ (Glover, 2012; Stiavelli, 2009). Atomic
dark matter introduces modifications to the linear matter power spectrum
through dark acoustic oscillations (DAO) and diffusion damping (Cyr-Racine &
Sigurdson, 2013; darkrec), both of which suppress the abundance of dark-matter
halos with low mass. We therefore focus on somewhat heavier $10^{8}\,\rm
M_{\odot}$ halos that form later, around $z=10$. A suppression scale of the
linear power spectrum around or below halo mass of $10^{8}\rm M_{\odot}$ is
consistent with the suppression scale of the allowed $\sim\rm keV$ warm dark
matter (Smith & Markovic, 2011). For both aDM and WDM bound structures which
do not resemble virialized cold dark matter (CDM) halos may persist below this
scale (Angulo et al., 2013; Stücker et al., 2021). Their role in the formation
of compact objects requires further study.

In Fig. 1, we show the minimum temperature obtained in our calculations for
$10^{8}\rm M_{\odot}$ halos at redshift 10 (when $10^{8}\,M_{\odot}$ halos are
common). The color bar shows the ratio of temperature to the atomic-limit
temperature $T_{a}=10^{4}r_{m}r_{\alpha}^{2}\,\rm K$. In the hydrostatic case
(left panel), this minimum temperature is simply the temperature after one
free-fall time since there is no heating. We have also shaded in gray the
region which fails to cool by at least a factor of four from its initial
temperature. This region fails to radiate its thermal energy within a free-
fall time and likely does not undergo runaway gravitational collapse. Because
$T_{v}\propto r_{M}^{2/3}$, in the bottom right portion of the figure cooling
is actually prohibited by the low initial $T/T_{a}$. Although this region is
“cold”, it will remain near the initial, virial equilibrium rather than
collapsing. In the adiabatic case (right panel), the minimum temperature is
the lowest temperature achieved before the density cutoff due to high opacity
(See Appendix A). Typically, the gas begins to heat or evolve quasi-
isothermally well before the end of the run. Those halos which fail to ever
cool significantly below the initial temperature are unlikely to fragment down
to small scales—these too are shaded out in gray.

Cooling below the atomic-limit temperature (blue area) requires the active
participation of molecules. The formation of molecular hydrogen requires free
electrons, which are cosmologically scarce for $\xi=5\times 10^{-3}\ll 1$,
that we have adopted. Therefore, molecular cooling requires either a)
achieving a temperature high enough to increase the ionization fraction
followed by atomic cooling, or b) a large enough primordial molecular fraction
and molecular cooling rate that the primordial molecules alone can cool the
halo. In case a) the primordial molecules are dissociated and the problem
becomes largely insensitive to the primordial abundances (and hence the value
of $\xi$). The $r_{M}$ and $r_{m}$ dependence of the molecular cooling rate
decreases the cooling efficiency in the high $r_{M}$, low $r_{m}$ regime. In
the adiabatic case, compressional heating can raise an initially low gas
temperature sufficiently to ionize the gas. Moreover, the increasing density
also boosts both the molecular cooling and formation rates, leading to
molecular cooling in a larger part of the parameter space. In particular, the
critical transition point between low density limit cooling (where every
collisional excitation leads to a radiative decay, rate $\propto n^{2}$) and
local thermal equilibrium cooling (where collisional de-excitation
contributes, rate $\propto n$) exhibits a strong direct dependence on $r_{m}$.
For vibrational cooling, $n_{\rm crit}\propto r_{m}^{19/4}$, so that molecular
cooling remains efficient at high densities for large $r_{m}$.

Fig. 1 also shows the contours of increasing levels of suppression in the aDM
halo mass function relative to the CDM case: to the right of these contours,
aDM halos are about as common as in CDM. A higher value of $\xi$ would push
these contours to the right (narrowing the interesting parameter space) while
a smaller value would move the contours to the left. We use the Press-
Schechter formalism for this calculation as done in darkrec, where the halo
mass is defined from the linear density field smoothed with a sharp-k filter.
This mass assignment is $M_{sk}=\frac{4\pi}{3}\bar{\rho}[cR_{sk}]^{3}$, where
$R_{sk}$ is the filter radius and $c=2.7$ is a calibration factor from
simulations. For $\xi\ll 1$, the effect which controls the suppression scale
is dark diffusion damping. The diffusion scale $k_{D}$ is given by
(Zaldarriaga & Harari, 1995)

$\frac{1}{k_{D}^{2}}=\int_{0}^{a_{\rm
dec}}\frac{da}{a^{2}H(a)}\frac{1}{6(1+R)n_{{\rm e}_{\rm D}}\sigma_{\rm
T,D}a}\left[\frac{16}{15}+\frac{R^{2}}{1+R}\right],$ (2.4)

with $a$ the scale factor, $\sigma_{\rm T,D}$ the dark Thomson cross section
and $R(a)=\frac{3\bar{\rho}_{DM}}{4\bar{\rho}_{\gamma,D}}$. For large $R$,
this scale is very close to the horizon size at dark-photon decoupling, which
is controlled by the temperature ratio $\xi$ and the dark atomic binding
energy $E_{{\rm H}_{\rm D}}=r_{m}r_{\alpha}^{2}E_{{\rm H}}$ (where $E_{{\rm
H}}$ is the Standard Model binding energy). Diffusion damping imposes a
Gaussian cutoff in the linear power spectrum $P(k)\rightarrow
P(k)e^{-(k/k_{D})^{2}}$. In the Press-Schechter treatment (Press & Schechter,
1974; darkrec), this strongly suppresses the halo mass function below the
cutoff scale.

Figure 2: The halo mass function for two representative choices of parameters
(see Fig. 1). The bottom color band of each curve indicates the minimum
temperature of those halos which collapse under hydrostatic evolution, while
the top band illustrates the adiabatic density case. The black region fails to
cool.

The dependence of these results on redshift and halo mass is shown in Fig. 2
by plotting the Press-Schechter halo mass function, with the range of halo
masses that experience significant cooling (according to the virial
temperature associated with the specified aDM parameters, redshift, and halo
mass by Eq. (2.1)) colored by their minimum temperature. As the density and
virial temperature at fixed halo mass drop at low redshift, only increasingly
hot (heavy) halos can cool. The halo mass function drops sharply below the
cutoff scale. We emphasize again that the Press-Schechter formalism fails to
capture any possible sheets and filaments below the cutoff scale (Angulo et
al., 2013; Stücker et al., 2021).

##  3 Minimum Mass

Figure 3: The opacity-limited minimum fragment mass for a $10^{8}\,\rm
M_{\odot}$ atomic dark matter halo at $z=10$ with $r_{\alpha}=1$ and
$\xi=5\times 10^{-3}$ (as Fig. 1), under constant-density evolution (left) and
adiabatic collapse (right). The region which fails to cool significantly
(gray) and the halo-mass-suppression iso-contours (dashed) are again shown.
The result is plotted as a fraction of the Chandrasekhar mass, $M_{C}$. The
value of $M_{C}$ is shown on right-hand vertical axes.

We can heuristically relate the minimum temperature to the mass of any compact
objects based on the scaling of the Chandreskhar limit $M_{\rm C}\propto
r_{M}^{-2}$ and the Jeans mass at fixed density $M_{\rm J}\propto
T^{3/2}r_{M}^{-3/2}$, both of which imply that a large value of $r_{M}$ allows
the formation of low-mass compact objects. A somewhat heavier dark proton,
$r_{M}>1$, is generally preferred by constraints on the dark-matter momentum
transfer, which provide upper bounds on $\sigma/M$ for the elastic scattering
of neutral dark atoms (Tulin & Yu, 2018). Of course, the temperature of the
collapsing gas also depends on the dark matter parameters via the cooling
rates. We can use the minimum temperature achieved in our calculations to
compute a lower bound on the mass of any fragments in these halos using the
opacity limit argument of Low & Lynden-Bell (1976) and Rees (1976). In order
for fragmentation to continue the fragment must be able to radiate ${\cal
O}(1)$ of its gravitational binding energy within a free-fall time, while the
radiation rate is bounded above by that of a black sphere. Equating these
rates gives

$\displaystyle M_{f}$ $\displaystyle\approx\left(\frac{\hbar
c}{G}\right)^{3/2}\left(m_{p}r_{M}\right)^{-2}\left(\frac{k_{B}T}{r_{M}m_{p}c^{2}}\right)^{1/4}$
$\displaystyle\approx M_{\rm
Chandra}r_{M}^{-2}\left(\frac{k_{B}T}{r_{M}m_{p}c^{2}}\right)^{1/4}\equiv
M_{C}\left(\frac{k_{B}T}{r_{M}m_{p}c^{2}}\right)^{1/4},$ (3.1)

where $M_{C}\equiv M_{\rm Chandra}r_{M}^{-2}$ is the Chandrasekhar mass of the
dark matter (Shandera et al., 2018). For baryons, $M_{f}\sim
0.045f^{-1/2}(T/3000\,{\rm K})^{1/4}\,M_{\odot}$ with $f<1$ being the
radiation efficiency (Becerra et al., 2018). We bound the analogous fragment
mass in the aDM by inserting the minimum temperatures obtained above in this
expression. We show the result $M_{f}/M_{C}$ in Fig. 3, where we have
calculated the Chandrasekhar mass as $M_{C}\approx\left(\frac{\hbar
c}{G}\right)^{3/2}\left(m_{p}r_{M}\right)^{-2}$. Note that for all realistic
halos, $k_{B}T\ll r_{M}m_{p}c^{2}$: the temperature is much smaller than the
proton mass and the fragment mass is much smaller than the Chandrasekhar mass.

As a lower bound, this result is quite robust. However, caution is warranted
in correlating this lower bound with the true mass of compact objects in the
halo. If accretion is inefficient, these fragments may remain below the
Chandrasekhar limit (where fermionic degeneracy pressure can halt collapse).
On the other hand, for Pop. III stars, the eventual stellar mass (after
accretion) exceeds the opacity limit by a factor of $\sim 10^{4}-10^{5}$. For
atomic dark matter fragments, such growth would imply the eventual formation
of black holes, which could still be easily sub-solar-mass. Of course, this
growth factor depends on the detailed evolution of the collapsing gas cloud
and subsequent star-forming disk (Hirano et al., 2014). As such, our result
cannot be directly translated to a final (post-accretion) mass for the compact
objects. Instead, Fig. 3 should be taken as a qualitative measure of the
instability of the halo to small-scale fragmentation. In this light, our
calculations indicate that a substantial portion of the parameter space is
dramatically more prone to forming low-mass fragments as compared to baryonic
matter.

##  4 Summary and conclusion

We have modeled the thermo-chemical evolution of atomic dark matter halos by
following the evolution of an infinitesimal volume element, including both
atomic and molecular processes. The density evolution is independently
specified, and we study the results in two extreme cases: adiabatic collapse
($\dot{\rho}=\rho/t_{ff}$) and hydrostatic equilibrium (constant density), to
study the range of possibilities. We also illustrate the dependence of these
results on halo mass and redshift. The mass scale of the seed dark-matter
fragments forming in the halos is determined by the minimum temperature the
fragmenting gas reaches during its collapse. As an early exploration of the
dependence of this mass scale on the model parameters, we have calculated the
opacity-limited minimum fragment mass at this minimum temperature. We show
that there is a substantial parameter space where these halos can fragment on
scales far below one solar mass. Moreover, the Chandrasekhar mass of the dark
matter is ${\mathcal{O}(1\,\rm M_{\odot})}/r_{M}^{2}$, which can clearly also
be much less than one solar mass. Unless accretion is dramatically enhanced
compared to the baryonic case, these halos may host compact objects that, at
formation time, are orders of magnitude smaller than allowed by astrophysical
processes in baryonic matter. We leave the final size of the compact objects,
which requires modeling of accretion physics, as an object of future work.

We thank Neal Dalal and Daniel Egana-Ugrinovic for discussions about the
eventual fate of gas fragments. Funding for this work was provided by the
Charles E. Kaufman Foundation of the Pittsburgh Foundation. This work was
supported at Pennsylvania State University by NASA ATP Program No.
80NSSC22K0819. DJ is also supported by KIAS Individual Grant PG088301 at Korea
Institute for Advanced Study.

## References

  * Ackerman et al. (2009) Ackerman, L., Buckley, M. R., Carroll, S. M., & Kamionkowski, M. 2009, Phys. Rev. D, 79, doi: 10.1103/physrevd.79.023519
  * Agrawal et al. (2017a) Agrawal, P., Cyr-Racine, F.-Y., Randall, L., & Scholtz, J. 2017a, J. Cosmology Astropart. Phys, 2017, 021, doi: 10.1088/1475-7516/2017/08/021
  * Agrawal et al. (2017b) —. 2017b, Journal of Cosmology and Astroparticle Physics, 2017, 021, doi: 10.1088/1475-7516/2017/08/021
  * Angulo et al. (2013) Angulo, R. E., Hahn, O., & Abel, T. 2013, Monthly Notices of the Royal Astronomical Society, 434, 3337–3347, doi: 10.1093/mnras/stt1246
  * Becerra et al. (2018) Becerra, F., Marinacci, F., Inayoshi, K., Bromm, V., & Hernquist, L. E. 2018, ApJ, 857, 138, doi: 10.3847/1538-4357/aab8f4
  * Boddy et al. (2016) Boddy, K. K., Kaplinghat, M., Kwa, A., & Peter, A. H. G. 2016, Physical Review D, 94, 123017, doi: 10.1103/PhysRevD.94.123017
  * Bromm et al. (2002) Bromm, V., Coppi, P. S., & Larson, R. B. 2002, The Astrophysical Journal, 564, 23–51, doi: 10.1086/323947
  * Buckley & DiFranzo (2018) Buckley, M. R., & DiFranzo, A. 2018, Physical Review Letters, 120, 051102, doi: 10.1103/PhysRevLett.120.051102
  * Chang et al. (2019) Chang, J. H., Egana-Ugrinovic, D., Essig, R., & Kouvaris, C. 2019, JCAP, 03, 036, doi: 10.1088/1475-7516/2019/03/036
  * Choquette et al. (2019) Choquette, J., Cline, J. M., & Cornell, J. M. 2019, J. Cosmology Astropart. Phys, 2019, 036, doi: 10.1088/1475-7516/2019/07/036
  * Cline et al. (2014) Cline, J. M., Liu, Z., Moore, G. D., & Xue, W. 2014, Phys. Rev. D, 90, 015023
  * Cyr-Racine et al. (2014) Cyr-Racine, F.-Y., de Putter, R., Raccanelli, A., & Sigurdson, K. 2014, Phys. Rev. D, 89, 063517, doi: 10.1103/PhysRevD.89.063517
  * Cyr-Racine et al. (2014) Cyr-Racine, F.-Y., de Putter, R., Raccanelli, A., & Sigurdson, K. 2014, Physical Review D, 89, 063517, doi: 10.1103/PhysRevD.89.063517
  * Cyr-Racine & Sigurdson (2013) Cyr-Racine, F.-Y., & Sigurdson, K. 2013, Physical Review D, 87, 103515, doi: 10.1103/PhysRevD.87.103515
  * D’Amico et al. (2018) D’Amico, G., Panci, P., Lupi, A., Bovino, S., & Silk, J. 2018, Monthly Notices of the Royal Astronomical Society, 473, 328, doi: 10.1093/mnras/stx2419
  * Fan et al. (2013) Fan, J., Katz, A., Randall, L., & Reece, M. 2013, Physics of Dark Universe, 2, 139, doi: 10.1016/j.dark.2013.07.001
  * Feng et al. (2009) Feng, J. L., Kaplinghat, M., Tu, H., & Yu, H.-B. 2009, J. Cosmology Astropart. Phys, 2009, 004, doi: 10.1088/1475-7516/2009/07/004
  * Foot & Vagnozzi (2015) Foot, R., & Vagnozzi, S. 2015, Phys. Rev. D, 91, 023512, doi: 10.1103/physrevd.91.023512
  * Foot & Vagnozzi (2016) —. 2016, J. Cosmology Astropart. Phys, 2016, 013, doi: 10.1088/1475-7516/2016/07/013
  * Ghalsasi & McQuinn (2018) Ghalsasi, A., & McQuinn, M. 2018, Phys. Rev. D, 97, 123018, doi: 10.1103/PhysRevD.97.123018
  * Glover (2005) Glover, S. 2005, Space Science Reviews, 117, 445–508, doi: 10.1007/s11214-005-5821-y
  * Glover (2012) —. 2012, in The First Galaxies (Springer Berlin Heidelberg), 103–174, doi: 10.1007/978-3-642-32362-1_3
  * Glover & Abel (2008) Glover, S. C. O., & Abel, T. 2008, Monthly Notices of the Royal Astronomical Society, 388, 1627–1651, doi: 10.1111/j.1365-2966.2008.13224.x
  * Goldberg & Hall (1986) Goldberg, H., & Hall, L. J. 1986, Physics Letters B, Volume 174, Issue 2, p. 151-155., 174, 151, doi: 10.1016/0370-2693(86)90731-8
  * Gurian et al. (2022) Gurian, J., Jeong, D., Ryan, M., & Shandera, S. 2022, The Astrophysical Journal, 934, 121, doi: 10.3847/1538-4357/ac75e4
  * Hippert et al. (2021) Hippert, M., Setford, J., Tan, H., et al. 2021, arXiv e-prints, arXiv:2103.01965.  https://arxiv.org/abs/2103.01965
  * Hirano et al. (2014) Hirano, S., Hosokawa, T., Yoshida, N., et al. 2014, ApJ, 781, 60, doi: 10.1088/0004-637X/781/2/60
  * Hollenbach & McKee (1979) Hollenbach, D., & McKee, C. F. 1979, ApJS, 41, 555, doi: 10.1086/190631
  * Kaplan et al. (2010) Kaplan, D. E., Krnjaic, G. Z., Rehermann, K. R., & Wells, C. M. 2010, Journal of Cosmology and Astroparticle Physics, 2010, 021, doi: 10.1088/1475-7516/2010/05/021
  * Kaplan et al. (2011) —. 2011, Journal of Cosmology and Astroparticle Physics, 2011, 011, doi: 10.1088/1475-7516/2011/10/011
  * Latif et al. (2019) Latif, M. A., Lupi, A., Schleicher, D. R. G., et al. 2019, Monthly Notices of the Royal Astronomical Society, 485, 3352, doi: 10.1093/mnras/stz608
  * Low & Lynden-Bell (1976) Low, C., & Lynden-Bell, D. 1976, MNRAS, 176, 367, doi: 10.1093/mnras/176.2.367
  * Press & Schechter (1974) Press, W. H., & Schechter, P. 1974, ApJ, 187, 425, doi: 10.1086/152650
  * Randall & Scholtz (2015) Randall, L., & Scholtz, J. 2015, J. Cosmology Astropart. Phys, 2015, 057, doi: 10.1088/1475-7516/2015/09/057
  * Rees (1976) Rees, M. J. 1976, MNRAS, 176, 483, doi: 10.1093/mnras/176.3.483
  * Ryan et al. (2021) Ryan, M., Gurian, J., Shandera, S., & Jeong, D. 2021, Molecular Chemistry for Dark Matter.  https://arxiv.org/abs/2106.13245
  * Ryan & Radice (2022) Ryan, M., & Radice, D. 2022, Exotic Compact Objects: The Dark White Dwarf.  https://arxiv.org/abs/2201.05626
  * Ryan et al. (2022) Ryan, M., Shandera, S., Gurian, J., & Jeong, D. 2022, ApJ, 934, 122, doi: 10.3847/1538-4357/ac75e5
  * Seager et al. (2000) Seager, S., Sasselov, D. D., & Scott, D. 2000, The Astrophysical Journal Supplement Series, 128, 407, doi: 10.1086/313388
  * Shandera et al. (2018) Shandera, S., Jeong, D., & Gebhardt, H. S. G. 2018, Physical Review Letters, 120, 241102, doi: 10.1103/PhysRevLett.120.241102
  * Singh et al. (2020) Singh, D., Ryan, M., Magee, R., et al. 2020, arXiv:2009.05209 [astro-ph].  http://arxiv.org/abs/2009.05209
  * Smith & Markovic (2011) Smith, R. E., & Markovic, K. 2011, Phys. Rev. D, 84, 063507, doi: 10.1103/PhysRevD.84.063507
  * Sobolev (1960) Sobolev, V. V. 1960, Moving envelopes of stars (Harvard University Press)
  * Stiavelli (2009) Stiavelli, M. 2009, The First Stars (John Wiley & Sons, Ltd), 5–38, doi: https://doi.org/10.1002/9783527627363.ch2
  * Stücker et al. (2021) Stücker, J., Angulo, R. E., Hahn, O., & White, S. D. M. 2021, Monthly Notices of the Royal Astronomical Society, 509, 1703, doi: 10.1093/mnras/stab3078
  * Tegmark et al. (1997) Tegmark, M., Silk, J., Rees, M. J., et al. 1997, The Astrophysical Journal, 474, 1, doi: 10.1086/303434
  * Tulin & Yu (2018) Tulin, S., & Yu, H.-B. 2018, Phys. Rep., 730, 1, doi: 10.1016/j.physrep.2017.11.004
  * Turner et al. (1977) Turner, J., Kirby-Docken, K., & Dalgarno, A. 1977, ApJS, 35, 281, doi: 10.1086/190481
  * Yoshida et al. (2006) Yoshida, N., Omukai, K., Hernquist, L., & Abel, T. 2006, The Astrophysical Journal, 652, 6–25, doi: 10.1086/507978
  * Zaldarriaga & Harari (1995) Zaldarriaga, M., & Harari, D. D. 1995, Phys. Rev. D, 52, 3276, doi: 10.1103/PhysRevD.52.3276

##  Appendix A Molecular Line Opacity

Throughout, we have assumed optically thin cooling, where every emitted photon
escapes the collapsing gas cloud. This assumption breaks down at higher
densities where cooling is inefficient due to the high opacity. Therefore, the
minimum temperature is achieved before opacity becomes significant, so we stop
the computation at the density where the opacity becomes large. Since the
atomic cooling is fairly insensitive to the stopping condition, we consider
only the molecular line opacity:

$\alpha_{\nu}=\frac{h\nu}{4\pi}\phi(\nu)(n_{u}B_{u\ell}-n_{\ell}B_{\ell u}),$
(A1)

where $\nu$ is the photon frequency, $\phi{(\nu)}$ is the line profile
function, $n_{u}$ is the number density in the upper state, $n_{\ell}$ is the
number density in the lower state, and $B_{u\ell}$ and $B_{\ell u}$ are the
Einstein coefficients. For this order-of-magnitude estimate, we can ignore the
second term that represents stimulated emission. The $B$ coefficient is
related to the $A$ coefficient as

$B_{u\ell}=\frac{c^{2}}{2h\nu_{0}^{3}}A_{u\ell},$ (A2)

with $\nu_{0}$ the line center. Then,

$\alpha_{\nu}=\frac{c^{2}\nu}{8\pi\nu_{0}^{3}}\phi(\nu)n_{u}A_{\ell u}.$ (A3)

To calculate the photon escape probability, we evaluate the Sobolev optical
depth (Sobolev, 1960; Yoshida et al., 2006; Seager et al., 2000):

$\tau=\frac{\alpha_{\nu_{0}}/\phi(\nu_{0})}{\Delta\nu}L.$ (A4)

where $\Delta\nu=\frac{\nu_{0}}{c}v_{\rm thermal}$ the thermally broadened
line width, and $L$ the Sobolev length, which is the distance at which the
velocity gradient in the collapsing cloud Doppler-shifts the photon out of the
line. This length scale is

$L=\frac{v_{\rm thermal}}{dV_{r}/dr}\approx v_{\rm thermal}t_{ff},$ (A5)

where is $V_{r}$ the radial velocity gradient and $t_{ff}$ the freefall time.
Then, inserting $t_{ff}$ and noting that $v_{\rm thermal}$ cancels,

$\tau=\frac{c^{3}n_{u}A_{\ell
u}}{8\pi\nu_{0}^{3}}\sqrt{\frac{3\pi}{32Gr_{M}m_{H}n_{\rm tot}}}.$ (A6)

If the excited states are in thermal equilibrium when opacity begins to
contribute and a few excited states are populated, (as is the case for Pop.
III stars) then $n_{u}$ for each populated state is a factor a few smaller
than $n_{\rm tot}$. We neglect this factor by equating $n_{\rm tot}$ and
$n_{u}$, $n_{u}=n_{tot}\equiv n$, for

$n=\frac{2048\pi\nu^{6}Gr_{M}m_{H}\tau^{2}}{3c^{6}A_{\ell u}^{2}}.$ (A7)

By considering the order of magnitude of the relevant Einstein coefficients in
Turner et al. (1977) and inserting the scaling of $\nu_{0}$ and $A_{u\ell}$
with the dark parameters from Ryan et al. (2021), we have

$\displaystyle n_{\rm rot}$
$\displaystyle\approx\left[r_{\alpha}^{-2}r_{M}^{5}\right]10^{8}\tau^{2}\,{\rm
cm^{-3}}$ (A8) $\displaystyle n_{\rm vib}$
$\displaystyle\approx\left[r_{\alpha}^{-2}r_{m}^{2}r_{M}^{3}\right]10^{6}\tau^{2}\,{\rm
cm^{-3}}.$ (A9)

For Pop. III stars, this opacity begins to contribute at densities around
$10^{10}\,\rm cm^{-3}$ and temperatures slightly less than $1000$ K, before
saturating around $10^{15}\,\rm cm^{-3}$. Noting that the Sobolev escape
fraction $(1-\exp(-\tau))/\tau$ for $\tau=1$ is 63% while for $\tau=10$ it is
10% and that at low temperatures the rotational transitions dominate the
cooling, taking $r_{m}=r_{M}=r_{\alpha}=1$ is roughly consistent with the
threshold $n\sim 10^{10}\,\rm cm^{-3}$ found in the literature.

Above this density threshold, an adiabatically collapsing gas cloud cooled by
molecular transitions will begin to heat. That is, the minimum temperature of
our adiabatic runs is achieved before $n_{\tau}\equiv n_{\rm rot}$. Similarly,
the transition at $n_{\rm crit}$ from low-density ($\propto n^{2}$) to high-
density/local-thermodynamic-equilibrium (LTE, $\propto n$) molecular cooling
will cause such a cloud to heat, as the LTE cooling is outcompeted by
adiabatic heating ($n^{3/2}$). Therefore, the simulations must run at least
until the particle density crosses the $\min(n_{crit},n_{\tau})$ threshold. In
contrast, we can only trust the computation up to $n_{\tau}$, since our
cooling rates are valid both in the LDL and in LTE but not in the optically
thick regime. Therefore, we stop the calculation at
$n_{f}=\min(n_{\tau},n_{\rm crit})$.