#  Extremely Low Molecular Gas Content in the Vicinity of a Red Nugget Galaxy
at $z=1.91$

T. Morishita  Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218, USA<EMAIL_ADDRESS>Q. D’Amato  INAF/IRA, Istituto
di Radioastronomia, Via Piero Gobetti 101, 40129, Bologna, Italy  Dipartimento
di Fisica e Astronomia dell’Università degli Studi di Bologna, via P. Gobetti
93/2, 40129 Bologna, Italy  L. E. Abramson  The Carnegie Observatories, 813
Santa Barbara Street, Pasadena, CA 91101, USA  Abdurro’uf  Institute of
Astronomy and Astrophysics, Academia Sinica, Taipei 10617, Taiwan  M.
Stiavelli  Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218, USA<EMAIL_ADDRESS>R. A. Lucas  Space Telescope
Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA;
<EMAIL_ADDRESS>
(Accepted December 30, 2020; Received October 19, 2020; Revised December 20,
2020)

###### Abstract

We present Atacama Large Millimeter/submillimeter Array (ALMA) Band 5
observations of a galaxy at $z=1.91$, GDS24569, in search of molecular gas in
its vicinity via the [C i] 3P1-3P0 line. GDS24569 is a massive ($\log
M_{*}/M_{\odot}=11$), passively evolving galaxy, and characterized by compact
morphology with an effective radius of $\sim 0.5$ kpc. We apply two blind
detection algorithms to the spectral data cubes, and find no promising
detection in or around GDS24569 out to projected distance of $\sim 320$ kpc,
while a narrow tentative line ($4.1\sigma$) is identified at $+1200$ km / s by
one of the algorithms. From the non-detection of [C i], we place a $3\sigma$
upper limit on molecular hydrogen mass, $\sim 7.1\times 10^{9}\,M_{\odot}$,
which converts to an extremely low gas-to-stellar mass fraction of $\,\hbox
to0.0pt{\lower 3.5pt\hbox{$\mathchar 0\relax\sim$}\hss}\raise
1.0pt\hbox{$<$}\,5\%$. We conduct a spectral energy distribution modeling by
including optical-to-far-infrared data, and find a considerably high ($\sim
0.1\%$) dust-to-stellar mass ratio, i.e. $\sim 10$-$100\times$ higher than
those of local early-type galaxies. In combination with a previous result of
an insufficient number of surrounding satellite galaxies, it is suggested that
GDS24569 is unlikely to experience significant size evolution via satellite
mergers. We discuss possible physical mechanisms that quenched GDS24569.

galaxies: evolution – galaxies: formation

††journal: ApJ††journal: ApJ

[0.5em]0em1em

##  1 Introduction

The origin of the most massive galaxies in the local universe has been a long-
standing subject of galaxy evolution. From analysis of stellar populations and
chemical abundances of local galaxies, it has been inferred that the most
massive galaxies in the local universe completed their formation at redshift
$z\,\hbox to0.0pt{\lower 3.5pt\hbox{$\mathchar 0\relax\sim$}\hss}\raise
1.0pt\hbox{$>$}\,2$ (Kauffmann et al., 2003; Thomas et al., 2003; Gallazzi et
al., 2005; Treu et al., 2005; McDermid et al., 2015). Recent near-infrared
(NIR) observations indeed found many distant galaxies to be already quenched,
showing consistency with the quenching timeline inferred from the local and
low-$z$ universe (Brammer et al., 2009; Marchesini et al., 2009; Muzzin et
al., 2013; Tomczak et al., 2014).

Interestingly, a large fraction of high-$z$ massive quenched galaxies are
characterized by compact morphology (Cimatti et al., 2004; Daddi et al., 2005;
Trujillo et al., 2007; Buitrago et al., 2008; Ichikawa et al., 2010; Cassata
et al., 2011). While the average size of galaxies is smaller at that high
redshift (Trujillo et al., 2006; Morishita et al., 2014; van der Wel et al.,
2014), high-resolution imaging by the Hubble Space Telescope (HST) and the
adaptive optics of ground-based facilities revealed that some of them have
even smaller radius compared to the local counterpart at a similar mass, by a
factor of $\sim 5$ (van Dokkum et al., 2008; Damjanov et al., 2009; Szomoru et
al., 2010). Given the absence of such a compact galaxy population in normal
fields in the local universe (Shen et al., 2003; Taylor et al., 2010, but see
Valentinuzzi et al. 2010 for their presence in dense fields), the transition
of galaxies in the size-mass plane implies that many high-$z$ compact galaxies
would have to experience significant size evolution.

Various scenarios of significant size evolution for compact galaxies have been
proposed in the past decade, including dry/wet, major/minor mergers (Khochfar
& Silk, 2006; Naab et al., 2007; Hopkins et al., 2009; Naab et al., 2009;
Nipoti et al., 2009) and AGN feedback (Fan et al., 2008; Damjanov et al.,
2009) (see Conselice, 2014, for a thorough review). Among these scenarios, the
dry minor merger scenario has been popularly discussed and taken as the most
successful scenario in terms of its efficiency of size increase; surrounding
satellite galaxies accrete to the central compact galaxy, without disturbing
the central core, and in this way it can efficiently evolve effective radii
with a small increase of stellar mass (Naab et al., 2009; Hopkins et al.,
2009; Oser et al., 2010; Trujillo et al., 2011), while not all of them may
have to follow the same path (Nipoti et al., 2012; Newman et al., 2012). The
resulting stellar populations and mass profiles from this inside-out evolution
are in good agreement with findings at intermediate redshifts (van Dokkum et
al., 2010; Patel et al., 2013; Morishita et al., 2015; Papovich et al., 2015)
and for local massive galaxies (Belfiore et al., 2017; Ellison et al., 2018).

However, such an interpretation remains indirect, and the data still admit
other scenarios. For example, such compact galaxies may not have to be the
typical massive galaxy population at low redshift. In fact, there are a
significant number of compact galaxies but more preferably in cluster
environments (Valentinuzzi et al., 2010; Poggianti et al., 2013). It has also
been proposed that the observed trend of average galaxy sizes reflects
progenitor bias (e.g., Carollo et al., 2013; Fagioli et al., 2016), where
large radius galaxies may appear at later time and drive apparent size
evolution while high-$z$ compact galaxies remain as they are.

Toward more direct understanding of their following evolutionary path, Mármol-
Queraltó et al. (2012) studied satellite galaxies around massive galaxies to
calculate possible size increase that would likely happen through accreting
these satellite galaxies. Interestingly, their results indicated that the
extant satellite galaxies are not enough to account for significant size
evolution to the local relation. Furthermore, Morishita & Ichikawa (2016)
studied a compact galaxy at $z=1.91$, GDS24569, in deep HST images from the
extreme deep field (XDF) project (Illingworth et al., 2016), to search for
satellite galaxies around it down to $\log M_{*}/M_{\odot}\sim 7.2$. Their
conclusion is that the number of satellites is not enough either, and extra
mass increase by, e.g. additional star formation, is required for GDS24569 to
be on the local size-mass relation.

This poses the question whether additional in situ star formation is possible
in such compact quenched galaxies. One missing key component in these studies
is gas, in particular in the form of molecular hydrogen. While the stellar
component is not enough for the mass increase required to be on the local
relation, additional star formation caused by remaining or newly accreted gas
could change their sizes significantly (i.e. the scenario C in Morishita &
Ichikawa, 2016).

To answer the question, we here present new observations with the Atacama
Large Millimeter/submillimeter Array (ALMA) on GDS24569. Our configuration
allows wide field-of-view (FoV) coverage to the extent of its virial radius,
$r\sim 300$ kpc. Due to the spectral window available for the source redshift,
we target atomic carbon, [C i] 3P1-3P0 (rest-frame frequency 492 GHz,
hereafter [C i]), which is known as a good alternative tracer of molecular
hydrogen in extragalactic systems, originated from photodissociation regions
(e.g., Papadopoulos et al., 2004; Bell et al., 2007; Offner et al., 2014;
Salak et al., 2019). The line has an excitation temperature of $23.6$ K and a
critical density for collisions with hydrogen atoms of $\sim 1.2\times 10^{3}$
cm-3. While CO(4-3) is also available in the same spectral window, it is not
optimal to search for cool gas owing to its slightly higher excitation
temperature (55.3 K). Atomic carbon is found to well trace CO, at least in
low-density environments i.e. at the boundaries of molecular clouds (Glover et
al., 2015), at an almost constant ratio of
$N([\textrm{C}~{}\textsc{i}])/N({\rm CO})\sim 0.1-0.2$ in the local universe
(Keene et al., 1997; Ojha et al., 2001; Ikeda et al., 2002). Early studies
presented [C i] as an excellent gas tracer at high redshifts too (e.g., Weiß
et al., 2005; Walter et al., 2011; Valentino et al., 2018).

In this study, we exploit the exquisite sensitivity of ALMA and the ubiquity
of [C i] to search for previously unseen gas content in and around GDS24569,
aiming to infer the primary quenching mechanism and possible future
evolutionary path. The paper is structured as follows: In Section 2, we
describe our observations and data reduction. In Section 3, we present our
analysis method of a blind search for gas in the ALMA data, and results. While
the primary goal in this study is to search for surrounding gas, the dataset
also provides us an opportunity to investigate the cause of quenching in the
central galaxy from a panchromatic analysis over optical-to-far-infrared (FIR)
wavelengths (Section 3.4). In Section 4, we discuss our results and present
our interpretation. Throughout, magnitudes are quoted in the AB system
assuming $\Omega_{m}=0.3$, $\Omega_{\Lambda}=0.7$, $H_{0}=70\,{\rm
km~{}s^{-1}}\,{\rm Mpc}^{-1}$, and we assume the Salpeter (1955) initial mass
function.

Figure 1:  (Left): Pseudo RGB image (F160W+F814W+F435W of HST) of the observed
field. The two ALMA pointings are overlaid (Data1 and Data2; white circles).
The target, GDS24569, is centered in the image (red square). The position of
the tentative detection found in Data2 (Section 3.2.2) is also shown (green
circle), while no optical/IR counterpart is found at the position. (Right):
Dust continuum map, created by collapsing the entire frequency range of the
combined data cube. The coordinates of the objects in the left panel are
indicated with the same symbols. No continuum emission is detected near the
position of GDS24569. The beam size is shown at the bottom right (orange
ellipse).

##  2 Data and Analysis

###  2.1 Target galaxy

Our primary target, GDS24569, is a massive ($\log M_{*}/M_{\odot}\sim 11$)
galaxy at $z=1.91$, originally reported in Daddi et al. (2005), identified in
a spectroscopic campaign with HST, GRAPES (Pirzkal et al., 2004). The galaxy
is passively evolving, characterized by its spectral features, and has compact
morphology with effective light radius $\sim 0.5$ kpc (Szomoru et al., 2010),
which converts to stellar mass density of $\log\Sigma_{*}/M_{\odot}{\rm
kpc}^{-2}\sim 11$ (Figure 1). Morishita et al. (2019) analyzed its spectral
energy distribution (SED) by fitting photometric and spectroscopic data
points, and revealed that the galaxy experienced a very short period of star
formation $\sim 0.5$ Gyr prior to its observed redshift, characterizing it as
a quenched galaxy (see also Section 4).

On the size-mass plane, GDS24569 is located $\sim 2\sigma$ below the median
size of passive galaxies at that redshift and stellar mass (van der Wel et
al., 2014). To speculate its future evolutionary path, Morishita & Ichikawa
(2016) investigated surrounding sources photometrically selected in extremely
deep images from the XDF project (Illingworth et al., 2013), down to $\sim
10^{8}\,M_{\odot}$. There are insufficient satellite galaxies to move GDS24569
onto the local size mass relation when following a simple formula for a minor
merger scenario, $\Delta r\propto\Delta M^{2}$ (Naab et al., 2009). While
GDS24569 may end up as one of the compact population found in the local
universe, it is worth investigating any contribution from optically-dark
components, which may trigger star formation and size evolution, before we
conclude its fate.

###  2.2 ALMA Cycle 7 observation

Interferometric observations with Band 5 were executed in ALMA cycle 7 (PID.
2019.1.01127.S, PI T. Morishita). We designed the observations so they would
reveal gas components down to $\sim 10^{8}M_{\odot}$ within the virial radius
of GDS24569, $\sim 300$ kpc, via the [C i] emission line with an excitation
temperature of $\sim 30$ K. Since our purpose here is not to resolve each gas
clump, we optimize the antennas’ configuration for a large FoV, resulting in
the final beam size of $1.0\times\,0.8$ arcsec2. We set three 1.875 GHz-width
spectral windows, one of which was tuned to cover the [C i] frequency of the
target ($\sim 169$ GHz), while the other two spectral windows were centered on
168.5 GHz and 170.4 GHz for a continuum estimate.

Our observations, originally executed in November 2019 with on-source exposure
of 107 minutes, were accidentally off the central pointing for $\sim 12$
arcsec, while GDS24569 was still within the FoV (dubbed as Data2). The
observations were compensated in January 2020, with the target in the center
as it was originally planned (Data1). We therefore acquired two datasets with
the same setup for frequency and exposure time as described above (Figure 1),
which allow us an independent check on possible detection (Section 3). We ran
the tclean task of CASA on each of the datasets, with parameters of pixel
scale 0.16 arcsec and velocity resolution element $\sim 28$ km / s ($\sim
15.6$ MHz).

##  3 Method and Results

###  3.1 Dust Continuum Emission

In Figure 1, we show a continuum map created by collapsing the spectral data
cube over the entire velocity range, $-4000$-$3000$ km / s. No continuum
source is detected near the position of GDS24569. Root-mean-squares (RMSs) are
calculated by imstat of CASA; 27 $\mu$Jy / beam and 34 $\mu$Jy / beam for
Data1 and Data2, respectively, and 21 $\mu$Jy / beam for the combined data
cube at the target source position. This non-detection of dust emission is
consistent with the optical-to-NIR SED analysis of GDS24569, $A_{V}\sim 0.4$
mag (Morishita et al., 2019). We will use the upper limit derived here for a
panchromatic analysis in Section 4.

Figure 2:  (Top): Distribution of fluxes measured at 1000 random positions in
one of the data cubes. Fluxes are in units of mJy per beam per spectral
element. (Bottom): Radial distribution of RMSs estimated at each radius in the
three data sets — Data1 (cyan), Data2 (yellow), and combined (red) cubes.
Corresponding molecular hydrogen mass limits ($3\sigma$) for a line width of
$\Delta v=200$ km /s are shown in the right $y$-axis.

###  3.2 Clump Finding Algorithms

Our primary goal in this study is to search for gas clumps in the data cubes
via the [C i] emission line, both in the position of GDS24569 and its
neighboring regions out to $r\sim 300$ kpc, which is its approximate virial
radius. Despite a complicated aspect of blind detection in interferometric
data cubes, our advantage is that we have two independent data cubes, so that
any detection found in one data cube can be checked in the other. We start
with a fiducial detection algorithm, clumpdind (Williams et al., 1994), but
also apply a method introduced in D’Amato et al. (2020) to check the
consistency.

Figure 3:  Spectrum extracted in the position of GDS24569 in the combined data
cube, with an aperture of the beam size. No significant flux excess is seen.

####  3.2.1 Starlink Clumpfind Algorithm

To search for line detection across the data cubes, we apply an automated
detection algorithm. We first run the clumpfind algorithm, implemented in the
starlink package (Currie et al., 2014). One of the parameters for clumpfind is
the noise level of the data represented by RMSs. While imstat of CASA provides
a RMS value at each frequency value, the noise is correlated significantly for
our case with a relatively large beam size. Furthermore, the data show
differential noise structure along the radial direction from the center, where
larger noise structures frequently appear at a larger radius. To estimate a
more realistic noise level, we extract apertures of beam size in 1000 randomly
selected positions in each cube, to measure RMSs in annuli at every 10 pixels
from the center. As an example, the distribution of extracted fluxes is shown
in the top panel of Figure 2, where the distribution is well fitted with a
Gaussian. A radial distribution of derived RMSs ($=$ FWHM / 2.355 of Gaussian
fit) are shown in the bottom panel of Figure 2. The RMS varies from
$\sigma\sim 45$ $\mu$Jy / beam / spectral element at the innermost region to
130 $\mu$Jy / beam / spectral element at the outermost region.

We run the clumpfind algorithm on each of two data cubes with various RMSs
taken from the estimated range above. Other configuration parameters are also
determined through our initial tests (VELORES=5, MINPIX=50, and FWHMBEAM=3).
With the setup, the algorithm initially detects $\sim 100$ sources from the
entire FoV of each dataset for different RMS values. However, most of the
identified clumps are located at outer regions, $r\,\hbox to0.0pt{\lower
3.5pt\hbox{$\mathchar 0\relax\sim$}\hss}\raise 1.0pt\hbox{$>$}\,15$ arcsec.
Our visual inspection does not confirm any of these clumps as real sources.
Furthermore, none of these sources are commonly identified in both of the data
cubes. We thus conclude that all of the detected clumps are artifacts. To
confirm this, we also apply the same method to the data cubes but with signs
of fluxes inverted. We find a similar number of detections with a similar
spatial distribution as for the real cubes.

The spectrum extracted from the position of GDS24569 in the combined cubes is
shown in Figure 3. No obvious line is detected beyond the noise limit
associated with each spectral element.

####  3.2.2 D’Amato et al. (2020)’s method

To double-check the non-detection in Section 3.2.1, we also apply a blind
detection method introduced in D’Amato et al. (2020), that relies on spectral,
spatial and reliability criteria.

We perform the detection on the signal-to-noise-ratio- (S/N-) cube. In order
to produce it, we firstly generate a noise-cube, where the pixels have the
value of the RMS in a box centered in them. We choose a box with an area equal
to that of 10 beams, since we find that this size allows us to trace the local
variation of the noise in each channel, still having enough statistics per
box. The RMS is recursively calculated to convergence masking all pixels above
$3\times$ RMS at each iteration. The S/N-cube is then obtained as the ratio
between the original data-cube and the noise cube.

In order to perform the detection, we firstly scan each spaxel searching for a
given amount of contiguous channels ($\mathrm{N_{ch}}$) above a given S/N
threshold. We search for $\mathrm{N_{ch}}$=2, 3, 4, 5 (corresponding to $\sim$
60, 90, 120, 150 km / s, respectively) above a S/N threshold of 1.5, 2, 2.5
and 3. Then, among the candidate detections, we reject all those with a number
of contiguous pixels lower than a given amount $\mathrm{N_{ch}}$. For each
combination of $\mathrm{N_{ch}}$ and S/N threshold, we try
$\mathrm{N_{px}}=2,3,4$.

Finally, in order to estimate the incidence of spurious detections, we perform
the same algorithm on the “negative” S/N-cube, where the pixels have the same
value and inverted sign of the original (“positive”) S/N-cube. Then, for any
combination of $\mathrm{N_{ch}}$, S/N threshold and $\mathrm{N_{px}}$ we
reject all the candidate detections obtained from the positive S/N-cube that
have a peak S/N lower than the maximum peak S/N of the detections obtained
from the negative S/N-cube using the same parameter combination. Finally, we
crop the detection area to the half-primary-beam-width.

From this analysis, we find one tentative detection ($4.1\,\sigma$) at $+1200$
km / s at projected distance $\sim 14$ kpc away from GDS24569 in Data2 (top
panel of Figure 4), while no optical counterpart is identified in the XDF
dataset (Figure 1). The RMS at the position is $87\,\mu$Jy / beam. The line is
narrow, and fitted with a gaussian of FWHM $=84$ km / s ($\sim 3$ spectral
elements). The total flux from the integral of the gaussian fit is
$S_{[\textrm{C}~{}\textsc{i}]}\Delta v\sim 7.5$ mJy km / s. The line is not
identified at the same spectral position in Data1, with only 1 positive pixel
of S / N $\sim 1$ (bottom panel of Figure 4). This may be attributed to lower
sensitivity at the position in Data1, which is $\sim 10.5$ arcsec away from
the center, while the RMS value is $\sim 120\,\mu$Jy / beam and the line
should still be detectable at S / N $\sim 3$. We thus leave this detection as
tentative, while including this emission would not change our analysis and
main conclusion in Section 4.

Figure 4:  (Top): Tentative line detection at $V\sim 1200$ km / s in Data2 is
shown (left panel; red circle) in the velocity integrated map (centered on its
pointing). The position of GDS24569 is also shown (black cross). The beam size
is shown at bottom-right (white ellipse). The Gaussian fit to the tentative
line is overlaid in the extracted spectrum (right panel; red dashed line).
(Bottom): Same as above but for Data1. No significant flux excess is seen at
the velocity (red dashed line).

###  3.3 Upper limits in molecular gas mass

In this subsection, we attempt to place an upper limit on molecular hydrogen
mass from the estimated RMSs in Section 3.2.1. Following a recipe by
Papadopoulos et al. (2004, also ), molecular hydrogen gas mass is inferred by:

$\displaystyle M_{\rm
H_{2}}=1375.8{D_{l}^{2}\over{(1+z)}}({X[\textrm{C}~{}\textsc{i}]\over{10^{-5}}})^{-1}$
$\displaystyle\times({A_{10}\over{10^{-7}{\rm
s^{-1}}}})^{-1}Q_{10}^{-1}{S_{{[\textrm{C}~{}\textsc{i}]}}\Delta v\over{\rm
Jy\ km\ s^{-1}}}M_{\odot}.$ (1)

The equation consists of two steps: conversion from observed [C i] intensity
to atomic carbon mass, and then to molecular hydrogen mass. The conversion
involves a couple of parameters. We adopt the excitation factor $Q_{10}=0.5$
as a fiducial value, assuming local thermodynamic equilibrium (i.e. optically
thin). $Q_{10}$ ranges from 0 to 1, depending on the temperature, density and
radiation field, though none of these values can be constrained without line
ratios to other excitation levels. We adopt a molecular [C i]-to-${\rm H_{2}}$
conversion factor $X{[\textrm{C}~{}\textsc{i}]}=1.5\times 10^{-5}$ taken from
(Jiao et al., 2019). The value is the lower limit measured in nearby galaxies,
and gives us a conservative upper limit in molecular hydrogen mass, whereas
the conversion factor can be as high as $X{[\textrm{C}~{}\textsc{i}]}=5\times
10^{-5}$ (e.g., Frerking et al., 1989; Weiß et al., 2003, 2005). The
conversion to molecular hydrogen mass includes the mass in Helium by a
correction factor of 1.36 (Solomon & Vanden Bout, 2005). $A_{10}=7.93\times
10^{-8}$ s-1 is the Einstein A-coefficient, and $D_{l}$ is the luminosity
distance to the source redshift, $z=1.91$.

Since our input for the equation above is the upper limit for flux density, we
need to assume the line width to obtain a velocity-integrated line intensity,
$S_{[\textrm{C}~{}\textsc{i}]}\Delta v$. We set $\Delta v=300$ km / s based on
stellar velocity dispersion measurements in massive compact quiescent galaxies
(e.g., van de Sande et al., 2013; Belli et al., 2017), while narrower line
width has been seen in massive rotating disks ($\sim 200$ km / s; Weiß et al.,
2005; Man et al., 2019). With this we obtain
$S_{[\textrm{C}~{}\textsc{i}]}\Delta v\sim 42$ mJy km / s / beam as a
$3\sigma$ upper limit in the position of GDS24569.

By substituting these numbers in the equation above, we obtain a conservative
$3\sigma$ upper limit on molecular hydrogen mass of $\sim 7.1\times
10^{9}\,M_{\odot}$, characterizing a significantly low gas mass fraction
$f_{\rm gas}\,\hbox to0.0pt{\lower 3.5pt\hbox{$\mathchar
0\relax\sim$}\hss}\raise 1.0pt\hbox{$<$}\,5\%$.

Figure 5:  (Top): Spectral energy distribution of GDS24569. Broadband
photometric data points used for the fit are shown (red points for detection
and arrows for upper limits). The zoom-in region (green rectangle) is shown in
the right panel to highlight the NIR grism spectra of WFC3/G141 and G102 (red
and blue lines, respectively). Flux contribution from stellar and dust (blue
and red dashed lines) components, as well as the best-fit total flux (black
solid line with uncertainty shaded in gray). (Bottom): Star formation (left),
mass accumulation (middle), and metallicity evolution (right) histories of
GDS24569. The star formation rate of the star-forming main sequence for a
given stellar mass at each lookback time (Speagle et al., 2014) is shown in
the left panel (dashed line with blue hatch).

###  3.4 Panchromatic analysis of GDS24569

Morishita et al. (2019) investigated the star formation history of GDS24569
from a combined dataset of NIR spectrum and optical-to-NIR broadband
photometry. We re-fit the dataset with a SED fitting code, gsf
(ver.1.4111https://github.com/mtakahiro/gsf/tree/version1.4). From Morishita
et al. (2019), we retrieve broadband photometry of HST and Spitzer up to IRAC
CH4, originally published by the 3D-HST team (Skelton et al., 2014). Deep
spectra of WFC3-IR G102 and G141 originally taken in 3D-HST, FIGS (Pirzkal et
al., 2017), and CLEAR (Estrada-Carpenter et al., 2019), which were reduced and
presented in Morishita et al. (2019), are also included, to constrain its
stellar populations and star formation history.

Specifically, in this redshift range, the deep grism spectra capture the
Balmer break and absorption features at rest-frame $\sim 4000$ Å, while the
broadband coverage extending to rest-frame $K$-band is sensitive to variation
in metallicity and dust attenuation. This comprehensive coverage enables to
break the well-known age-dust-metallicity degeneracy, and enables robust
characterization of star formation histories too. Interested readers are
referred to Morishita et al. (2018, 2019), that presented intensive tests with
simulated datasets, for more details.

We include the upper limit on the continuum obtained from our ALMA
observations (Section 3.1). We also include Spitzer MIPS $24\mu$m flux from
Whitaker et al. (2014), and upper limits on MIPS $70\mu$m, Herschel PACS $100$
and $160\,\mu$m from the GOODS Herschel program (Elbaz et al., 2011). The
broadband photometric data points used here are summarized in Table 1.

Following Morishita et al. (2019), we simultaneously fit these
photometric+spectroscopic data points by using synthetic spectral templates.
We generate the fitting templates by using fsps (Conroy et al., 2009), with a
setup of the MILES spectral library with the Salpeter (1955) initial mass
function, age pixels of [0.01,0.03,0.1,0.3,0.5,0.7,1.0,1.5,2.0,3.0] / Gyr, and
metallicity in a range of $\log Z_{\odot}\in[-0.8,0.6]$ with a step size of
0.05, and the Calzetti et al. (2000) dust attenuation model. We calculate FIR
dust emission templates based on the recipe provided by Draine & Li (2007).
Due to the limited number of FIR data points, we limit the calculation to
their LMC model with $q_{\rm PAH}=2.37\%$.

In Figure 5, we show the best-fit SED and star formation history of GDS24569.
The result indicates that GDS24569 had the last primary star formation
activity $\sim 0.5$ Gyr ago, and then rapidly declined its star formation rate
$\sim 100$ Myr before the observed redshift. Such a star formation history is
in fact speculated from the absence of significant flux at rest-frame UV
wavelength, as well as deep 4000 Å break and Balmer absorption lines seen in
the deep grism spectra, characterizing GDS24569 as a post-starburst galaxy
(Dressler & Gunn, 1983). Such rapid decrease in star formation activity is
also seen in other massive galaxies (Belli et al., 2019; Morishita et al.,
2019), while their primary quenching process remains unclear. The low gas
fraction and the inferred dust mass of the system found in this study
potentially add further constraints on the primary quenching mechanism
(Section 4).

It is worth noting that the derived metallicity of GDS24569, $\log
Z_{*}/Z_{\odot}\sim-0.2$ dex, is $\sim 0.4$ dex below the mean relation of
massive, non-compact quenched galaxies at $z\sim 2$ (Morishita et al., 2019).
While the statistical significance is still small due to the scatter around
the mean relation ($\Delta\sim 0.2$ dex), this may further provide us a hint
to its following evolution; if GDS24569 is representative of the compact
galaxy population at this redshift, then a similarly low metallicity trend may
be seen in local compact galaxies. Such a low metallicity implies that
GDS24569 presumably experienced star formation of a short timescale in a
relatively pristine gas environment (e.g., Kriek et al., 2016, see also
below).

The best-fit result returns dust mass $\log M_{\rm
dust}/M_{\odot}=8.3\pm{0.6}$. Despite the non-detection in ALMA Band 5, its
strong upper limit constrains the FIR component sufficiently well within our
providing templates, in combination with the MIPS $24\mu$m data point that
constrains the polycyclic aromatic hydrocarbon (PAH) feature. The best-fit
dust mass derives dust-to-stellar mass fraction $M_{\rm dust}/M_{*}\sim
1.4\times 10^{-3}$ and $3\,\sigma$ upper limit on gas-to-dust ratio of
$\,\hbox to0.0pt{\lower 3.5pt\hbox{$\mathchar 0\relax\sim$}\hss}\raise
1.0pt\hbox{$<$}\,30$. The inferred dust-to-stellar mass fraction is much
higher than those of local early-type galaxies, ranging from $M_{\rm
dust}/M_{*}\sim 10^{-6}$ to $10^{-5}$ (Smith et al., 2012; Lianou et al.,
2016), while a similar value was found from the stacking analysis of massive
galaxies at $z\sim 1.8$ in Gobat et al. (2018). Such a significant amount of
dust may play a critical role in suppressing star-formation activity, by
preventing formation of hydrogen molecules (e.g., Kajisawa et al., 2015;
Conroy et al., 2015). Our finding of the low molecular gas mass fraction
derived above is consistent with this scenario.

Our estimate of dust mass is robust to different assumptions in the SED
modeling. We also fit our photometric data points with another SED fitting
code, piXedfit (Abdurro’uf et al.,
2021)222https://github.com/aabdurrouf/piXedfit, which adopts broader parameter
ranges for the dust component. The code returns $\log M_{\rm
dust}/M_{\odot}=8.2_{-0.6}^{+0.4}$, in good agreement with the dust mass
estimated by gsf.

No X-ray counterpart is found in the Chandra 7M sec catalog (Luo et al., 2017)
at the positions of GDS24569 or the tentative line in Sec 3.2.2. The non-
detection is reasonable given its passively evolving nature inferred from the
SED and undisturbed morphology.

##  4 Discussion and Summary

In this study, we investigated the vicinity of a massive compact galaxy,
GDS24569, for molecular gas that can induce star formation and lead to strong
size evolution to the local size-mass relation. Our two independent algorithms
on the unique data cubes did not confidently detect any gas clumps or
continuum emission, placing a conservative upper limit on molecular hydrogen
mass. We use this upper limit to further advance the argument presented in
Morishita & Ichikawa (2016), where they consider possible size evolution of
GDS24569 through accretion of photometrically identified 34 satellite
galaxies. We here assume that each of the satellites 1. has the smaller of
$f_{\rm gas}\times M_{*}$ and $7\times 10^{9}\,M_{\odot}$, 2. converts gas to
stars at $100\,\%$ efficiency, 3. accretes to the central galaxy. The total
mass contribution under this extreme assumption would be $\log
M_{*}/M_{\odot}\sim 9.5$, which still remains negligible compared to the
observed mass of GDS24569 and the total stellar mass of the satellites ($\log
M_{*}/M_{\odot}\sim 10.8$). The result secures the conclusion of Morishita &
Ichikawa (2016) that GDS24569 is unlikely to be on the size relation of the
early-type galaxies, at least via minor mergers, ending up $\sim 2\sigma$
below the local size-mass relation of early-type galaxies at $z\sim 0$ (e.g.,
Shen et al., 2003; Taylor et al., 2010; Poggianti et al., 2013) at most. Since
most of their satellite galaxies are not spectroscopically confirmed, this
extrapolation is rather optimistic and the actual size evolution can be even
less significant.

In the local universe, on the other hand, there are a portion of compact,
passively evolving galaxies in high-density regions i.e. in galaxy clusters
(e.g., Valentinuzzi et al., 2010). These local compact galaxies, characterized
by a similar light profile as for high-$z$ compact galaxies, dominate a
significant fraction of cluster member galaxies at $>3\times
10^{10}M_{\odot}$, $\sim 22\%$ (Valentinuzzi et al., 2010), whereas only $\sim
4.4\%$ in general fields (Poggianti et al., 2013). These findings imply
insignificant size evolution of (at least) some of compact galaxies at high
redshift, as is found in simulations (e.g., Wellons et al., 2016). Poggianti
et al. (2013) also found that compact galaxies in dense environments consist
of older stellar populations than those in general fields.

From these findings above, it is implied systematically earlier evolution of
compact galaxies in dense fields, which is suggested by Morishita et al.
(2017) and Abramson & Morishita (2018) from their structural analysis on
cluster and field galaxies, as well as by direct comparison of stellar age of
massive galaxies at $z\sim 2$ (Wu et al., 2018; Estrada-Carpenter et al.,
2020). In fact, the stellar metallicity of GDS24569 implied from our SED
fitting analysis is $\sim 0.4$ dex below the average trend of non-compact
galaxies at the same redshift. Assuming that GDS24569 is representative of the
progenitor population of local compact galaxies, then we may see systematical
differences in their metallicity and chemical composition from those of other
non-compact galaxies. While Taylor et al. (2010) found no significant
metallicity offset of compact galaxies in general fields, currently such
systematic comparison of local compact galaxies in dense environments has not
been established.

Lastly, we revisit possible quenching mechanisms that could occur in GDS24569.
Our observations found an extremely low gas mass fraction in the system,
$f_{\rm gas}\,\hbox to0.0pt{\lower 3.5pt\hbox{$\mathchar
0\relax\sim$}\hss}\raise 1.0pt\hbox{$<$}\,5\%$, whereas the fraction ranges
from $\sim 50\%$ to $\sim 100\%$ for the main sequence star-forming galaxies
at similar redshifts (Daddi et al., 2010; Tacconi et al., 2018; Hayashi et
al., 2018). Such a low gas mass fraction of passive galaxies is not a
surprise. For example, Sargent et al. (2015) reported a $3\,\sigma$ upper
limit of $f_{\rm gas}\,\hbox to0.0pt{\lower 3.5pt\hbox{$\mathchar
0\relax\sim$}\hss}\raise 1.0pt\hbox{$<$}\,5.8\%$ in a passively evolving
galaxy at $z=1.43$. Bezanson et al. (2019) reported a $3\,\sigma$ upper limit
$f_{\rm gas}\,\hbox to0.0pt{\lower 3.5pt\hbox{$\mathchar
0\relax\sim$}\hss}\raise 1.0pt\hbox{$<$}\,7\%$ in a galaxy at $z=1.522$.
Furthermore, the extremely low gas fraction of GDS24569 is worth comparing
with those of compact galaxies at an earlier phase, or blue nuggets (Barro et
al., 2013; Williams et al., 2014; van Dokkum et al., 2015). Barro et al.
(2017) reported a short depletion time ($\sim 27$ Myr) of a star-forming
compact galaxy at $z=2.3$ from their CO observations with ALMA. The galaxy is
intensively forming stars at $\sim 500\,M_{\odot}$ / yr, which is somewhat
comparable to the peak star formation rate of GDS24569 (Figure 5).333Our SFR
estimates are time-averaged at each pixel, and actual values could be higher
if star formation activity is more instantaneous. From this perspective, gas
depletion by the past intense star formation activity can reasonable be
considered as the primary cause of quenching for GDS24569.

We did not find gas clumps, disturbed gas structure, or dust emission in and
around GDS24569. Given that the last primary star forming activity occurred
relatively recently ($\sim 0.5$ Gyr), this suggests that the past star
formation activity was at least not caused by a galaxy-galaxy scale merger,
and that gas was consumed inside the system rather than being ejected. This is
consistent with a scenario derived from the local galaxies using stellar
metallicity as an indicator (Peng et al., 2015). It is yet unclear what caused
such intense star formation from our study. For example, Talia et al. (2018)
observed an AGN-hosting compact star forming galaxy, and concluded that the
star formation is likely caused by positive feedback from the AGN activity.
This positive feedback scenario seems possible given a higher fraction of
compact star forming galaxies host AGN than the overall star-forming
population (e.g., Kocevski et al., 2017; Wisnioski et al., 2018). On the other
hand, such high efficiency in star formation can also be induced without AGN
activity (Dekel & Burkert, 2014; Semenov et al., 2018), leaving the conclusion
still pending.

Given that the scenarios above are derived from one galaxy, we are still far
from getting a general consensus on primary quenching mechanisms in compact
massive galaxies. Nonetheless, in this study we showed that even non-detection
of molecular gas and dust emission, in combination with a wide wavelength data
coverage, sheds light on the nature of high-$z$ passive galaxies. Application
of this new approach to archival data will immediately improve statistical
arguments.

Table 1: Photometric fluxes of GDS24569, in units of $\mu$Jy.

F125W | F140W | F160W | F225W | F275W | F336W | F435W | F606W | F775W | F814W | F850LP
---|---|---|---|---|---|---|---|---|---|---
$K_{S}$ | IRAC CH1 | IRAC CH2 | IRAC CH3 | IRAC CH4 | MIPS $24\mu$m | MIPS $70\mu$m | PACS $100\mu$m | PACS $160\mu$m | ALMA Band 5 |
$3.26\pm 0.02$ | $4.49\pm 0.03$ | $5.30\pm 0.03$ | $<0.14$ | $<0.05$ | $<0.03$ | $<0.01$ | $0.11\pm 0.01$ | $0.26\pm 0.01$ | $0.35\pm 0.01$ | $0.62\pm 0.02$
$7.99\pm 0.09$ | $11.18\pm 0.07$ | $11.98\pm 0.06$ | $10.65\pm 0.42$ | $6.09\pm 0.44$ | $9.84\pm 2.72$ | $<8538.11$ | $<2203.38$ | $<6610.15$ | $<21.40$ |

Note. — $1\sigma$ errors are quoted for those with $S/N>1$, and $1\sigma$
upper limits for the rest of the data points.

## Acknowledgements

We thank the anonymous referee for providing constructive comments. This paper
makes use of the following ALMA data: ADS/JAO.ALMA#2019.1.01127.S. ALMA is a
partnership of ESO (representing its member states), NSF (USA) and NINS
(Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI
(Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA
Observatory is operated by ESO, AUI/NRAO and NAOJ. T.M. is grateful to Kate
Rowlands and Takuya Hashimoto for helpful discussion and advice on ALMA data
reduction. Support for this work was provided by NASA through grant numbers
HST-GO-15702.002, HST-GO-15702.002, and HST-AR-15804.002-A from the Space
Telescope Science Institute, which is operated by AURA, Inc., under NASA
contract NAS 5-26555.

Software: Astropy (Astropy Collaboration et al., 2013, 2018), numpy (Oliphant,
2006; Van Der Walt et al., 2011), python-fsps (Foreman-Mackey et al., 2014),
EMCEE (Foreman-Mackey et al., 2013).

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