# Stars, gas, and star formation of distant post-starburst galaxies

Po-Feng Wu (吳柏鋒)  Institute of Astrophysics, National Taiwan University,
Taipei 10617, Taiwan  Department of Physics and Center for Theoretical
Physics, National Taiwan University, Taipei 10617, Taiwan  Physics Division,
National Center for Theoretical Sciences, Taipei 10617, Taiwan  Rachel
Bezanson  Department of Physics and Astronomy and PITT PACC, University of
Pittsburgh, Pittsburgh, PA 15260, USA  Francesco D’Eugenio  Kavli Institute
for Cosmology, University of Cambridge, Madingley Road, Cambridge, CB3 0HA,
United Kingdom  Cavendish Laboratory - Astrophysics Group, University of
Cambridge, 19 JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom  Anna R.
Gallazzi  INAF-Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5,
50125 Firenze, Italy  Jenny E. Greene  Department of Astrophysical Sciences,
Princeton University, Princeton, NJ 08544, USA  Michael V. Maseda  Department
of Astronomy, University of Wisconsin-Madison, 475 N. Charter St., Madison, WI
53706, USA  Katherine A. Suess  Department of Astronomy and Astrophysics,
University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064,
USA  Kavli Institute for Particle Astrophysics and Cosmology and Department of
Physics, Stanford University, Stanford, CA 94305, USA  Arjen van der Wel
Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, B-9000
Gent, Belgium Po-Feng Wu<EMAIL_ADDRESS>
###### Abstract

We present a comprehensive multi-wavelength study of 5 poststarburst galaxies
with $M_{\ast}>10^{11}M_{\odot}$ at $z\sim 0.7$, examining their stars, gas,
and current and past star-formation activities. Using optical images from the
Subaru telescope and Hubble Space Telescope, we observe a high incidence of
companion galaxies and low surface brightness tidal features, indicating that
quenching is closely related to interactions between galaxies. From optical
spectra provided by the LEGA-C survey, we model the stellar continuum to
derive the star-formation histories and show that the stellar masses of
progenitors ranging from $2\times 10^{9}M_{\odot}$ to $10^{11}M_{\odot}$,
undergoing a burst of star formation several hundred million years prior to
observation, with a decay time scale of $\sim 100$ million years. Our ALMA
observations detect CO(2-1) emission in four galaxies, with the molecular gas
spreading over up to $>1"$, or $\sim 10$ kpc, with a mass of up to $\sim
2\times 10^{10}M_{\odot}$. However, star-forming regions are unresolved by
either the slit spectra or 3 GHz continuum observed by the Very Large Array.
Comparisons between the star-formation rates and gas masses, and the sizes of
CO emission and star-forming regions suggest a low star-forming efficiency. We
show that the star-formation rates derived from IR and radio luminosities with
commonly-used calibrations tend to overestimate the true values because of the
prodigious amount of radiation from old stars and the contribution from AGN,
as the optical spectra reveal weak AGN-driven outflows.

Post-starburst galaxies (2176) — Star formation (1569) — Active galactic
nuclei (16) — Galaxy quenching (2040) — Galaxy stellar content (621) — Galaxy
evolution (594) — Interstellar medium(847) — Galaxy kinematics(602)

††facilities: ALMA, HST (ACS), Sptizer, Subaru, VLA, VLT:Melipal
(VIMOS)††software: astropy (Astropy Collaboration et al., 2013; The Astropy
Collaboration et al., 2018), BAGPIPES (Carnall et al., 2018), pPXF (Cappellari
& Emsellem, 2004; Cappellari, 2017), Matplotlib (Hunter, 2007)

##  1 Introduction

Over the past few decades, extensive extragalactic surveys have unveiled the
existence of two main categories of galaxies: the star-forming galaxies, which
are actively undergoing in-situ star-formation, and the quiescent galaxies,
whose star-formation rates (SFRs) are much lower compared to their stellar
mass budgets (Strateva et al., 2001; Willmer et al., 2006; Franzetti et al.,
2007). Investigations into the early Universe have shown that the number
density and total stellar mass density of quiescent galaxies increase with
time since $z\sim 4$ (Bell et al., 2004; Faber et al., 2007; Ilbert et al.,
2013; Muzzin et al., 2013). Given the low levels of star formation in
quiescent galaxies, the growth in their mass budgets and number demands that a
portion of the star-forming galaxies must have ceased star formation and
joined the quiescent population at any given time.

Observations have characterized large samples of transitioning galaxies and
have found that galaxies can spend varying lengths of time moving from the
star-forming to the quiescent category, driven by multiple mechanisms (Marigo
& Girardi, 2007; Barro et al., 2013; Schawinski et al., 2014; Wu et al., 2018;
Belli et al., 2019). Some galaxies undergo rapid truncation of star formation,
known as quenching, which contributes a smaller fraction of the quiescent
population in the local Universe but is likely to be the dominant process at
$z\gtrsim 1$ (Gonçalves et al., 2012; Wild et al., 2016; Rowlands et al.,
2018). Immediately following the sudden halt of star formation, the spectral
energy distributions (SEDs) of galaxies are briefly dominated by A-type stars.
These galaxies are referred to as poststarburst galaxies (Dressler & Gunn,
1983) and offer valuable insights into the physical conditions near the time
of quenching.

The quest to understand the suppression of star formation in the early
Universe through the examination of high-z poststarburst galaxies is both
illuminating and challenging. This phase is expected to last for just a few
hundred million years, much shorter than the lifetimes of galaxies, hence
poststarburst galaxies are rare objects (Le Borgne et al., 2006; Snyder et
al., 2011). Their defining characteristic, a dominant A-type stellar
population, is difficult to identify without either multiwavelength photometry
from restframe UV to near IR or deep spectra covering key diagnostic spectral
lines (Balogh et al., 1999; Dressler et al., 1999; Kriek et al., 2011;
Whitaker et al., 2012; Wu et al., 2020), both of which are resource-intensive.
Furthermore, with low SFRs by definition, poststarburst galaxies are likely to
exhibit weak optical emission lines, far-infrared continuum emission, and low
cold gas contents, making the observation of these properties beyond the local
Universe a costly endeavor.

Despite the cost, the study of distant poststarburst galaxies has been
gradually accumulating knowledge. With the aid of sophisticated algorithms and
stellar population synthesis models, high signal-to-noise optical spectra can
not only identify poststarburst galaxies but also constrain critical
parameters of their formation histories such as the timing and intensity of
the preceding burst events prior to quenching (Wild et al., 2020; Suess et
al., 2022). Meanwhile, deep and high-resolution optical images reveal that
poststarburst galaxies tend to be more compact than the typical quiescent
galaxies, yet often display disturbed morphologies (Wild et al., 2009; Vergani
et al., 2010; Wu et al., 2014, 2018; Setton et al., 2022). This points towards
a formation scenario in which quenching in distant Universe is the result of
intense central starbursts brought on by gravitational interactions between
galaxies (Wu et al., 2020; Himoto & Kajisawa, 2023). However, despite such
findings, deep rest-frame optical spectroscopy that is resolved spatially does
not always find positive stellar age gradients, as one would expect if the
central starbursts had happened (D’Eugenio et al., 2020; Setton et al., 2020).

The complexity of the problem of poststarburst galaxy studies is compounded by
the presence of dust. It is well known that dust forms in tandem with the
intense starburst event, thus, the young stellar population may be obscured
and its light highly attenuated or even completely shielded (Poggianti & Wu,
2000; Baron et al., 2022; Smercina et al., 2022). This presents a challenge in
that the optical light may no longer accurately reflect the true nature of the
stellar population. The emission from dust is also problematic, as many
poststarburst galaxies selected at $z\sim 1$ by the absence of emission lines
exhibit a non-negligible amount of mid-IR emission (Kocevski et al., 2011; Wu
et al., 2014). This inconsistency between star-formation tracers has yet to be
resolved.

In terms of the raw material for star-formation, molecular gas, the Atacama
Large Millimeter/submillimeter Array (ALMA) has revealed that some distant
massive poststarburst galaxies contain molecular gas amounting to more than
$10\%$ of their stellar mass contents (Bezanson et al., 2022). This finding
raises questions about the mechanisms that must be in operation to account for
the lack of star formation despite the availability of fuel. Although Mg
II$\lambda 2796,2803$ outflows at velocities of $\sim 1000$ km s-1 have been
discovered in several cases (Tremonti et al., 2007; Maltby et al., 2018),
there is yet to be clear evidence of molecular outflow in distant
poststarburst galaxies. The hypothesis that active galactic nuclei (AGNs) play
a significant role in the quenching process has been suggested (Springel et
al., 2005; Somerville & Davé, 2015), but clear signs of AGN such as point-
source X-ray or radio continuum emission do not always present in distant
poststarburst galaxies (Vergani et al., 2010). Deep rest-frame optical spectra
have shown that the nebular emission lines in poststarburst galaxies are more
often driven by low-ionization nuclear emission-line regions (LINERs) rather
than AGNs (Lemaux et al., 2010, 2017).

Our knowledge of quenching processes beyond the local Universe has been
steadily growing through the accumulation of observations. Nevertheless, it
has been challenging to synthesize the findings due to the different galaxy
samples and selection criteria used by various studies. Each study is limited
by the available data and adopts different selection methods, picking up
intrinsically different samples in terms of stellar ages, AGN, and etc (Yesuf
et al., 2014; Wu et al., 2020; Bezanson et al., 2022). It is thus not
straightforward to assume the properties observed in one sample can apply to
another.

In this paper, we present a comprehensive analysis of 5 poststarburst galaxies
at $z\sim 0.7$. The dataset includes ultra-deep optical slit spectra ($S/N>20\
\AA^{-1}$), interferometric observations of CO(2-1) molecular line, optical
images from the Hubble Space Telescope (HST), as well as deep multi-wavelength
images from X-ray to radio. This extensive dataset enables us to examine the
physical properties of stars, gas, and star-formation activities from the same
set of galaxies, providing a self-consistent understanding of the quenching
process in the distant Universe.

We will explore various hypotheses surrounding the quenching process that
occurred approximately 7 billion years ago. These hypotheses include whether
galaxy-galaxy interactions triggered the quenching, whether a centrally-
concentrated starburst occurred prior to the quenching, and the role of AGN in
the gas content and quenching. Additionally, we will investigate the accuracy
of star-formation rate (SFR) tracers at different wavelengths, as this
information is crucial for determining the star-formation efficiency (SFE),
i.e., the ratio of SFR to gas mass.

We detail our galaxy sample, data, and methodology in Section 2. We present
the spatial distributions and kinematics of stars, gas, and star-formation in
Section 3 and Section 4. The SFRs, molecular gas contents, and their relations
are discussed in Section 5 and Section 6. The implications of these results
for quenching are discussed in Section 7. Finally, our summary and conclusions
can be found in Section 8.

##  2 Data and Analysis

Poststarburst galaxies in this work are selected based on their spectra taken
by the Large Extragalactic Galaxy Astrophysics Census survey (LEGA-C, van der
Wel et al., 2016) and then follow-up by ALMA to measure the CO(2-1) emission.
All galaxies are in the COSMOS field (Scoville et al., 2007), and plenty of
ancillary multi-wavelength data are publicly available.

###  2.1 The LEGA-C survey and sample selection

Figure 1: The rest-frame U-V and V-J color-color diagram of poststarburst
galaxies in this study. Small dots are galaxies in the LEGA-C survey with
$0.6\leq z\leq 1.0$, color-coded by their $\mbox{EW(H}\delta\mbox{)}$. The
dotted lines separate quiescent galaxies at the upper left from star-forming
galaxies at the bottom right. Post-starburst galaxies, i.e., quiescent
galaxies with strong Balmer absorption, tend to, but not exclusively be with
the bluest V-J colors. Spectroscopy can pick up poststarburst galaxies that
would not be identified with photometries.

In recent years, a variety of methods have been proposed and adopted to
identify galaxies with recently rapidly declining SFRs. Each selection method
carries its own limitations and biases (e.g., see discussion in Yesuf et al.,
2014; Wu et al., 2020). The selection criteria should depend on the data
available and scientific goals. The LEGA-C survey obtains rest-frame optical
spectra of $\sim 3000$ galaxies at $0.6\leq z\leq 1.0$. The typical continuum
signal-to-noise ratio (S/N) is 20 Å-1 with a spectral resolution of $R\simeq
3500$ (Straatman et al., 2018; van der Wel et al., 2021), allowing us to use
spectral features to select the sample as in many early studies (e.g.
Zabludoff et al., 1996; Goto, 2005).

Poststarburst galaxies are often identified as those galaxies with strong
Balmer absorption and weak emission lines. We use the H$\delta$ absorption
line as the tracer for the star-formation activities in the recent past. For
the star-formation tracer, we choose H$\beta$ instead of the commonly-used [O
II]$\lambda 3727,3729$ doublet because the [O II] emission in galaxies with
low SFRs are likely dominated by AGN or old stars (Lemaux et al., 2010, 2017;
Maseda et al., 2021).

We define poststarburst galaxies as those with

$\displaystyle EW(H\beta)_{em}$ $\displaystyle\geq-1.5\mbox{\AA}$ (1)
$\displaystyle EW(H\delta)$ $\displaystyle\geq 4\mbox{\AA}.$

as measured from the 2nd data release (DR2, Straatman et al., 2018) of the
LEGA-C project. Wu et al. (2018) showed that $EW(H\beta)_{em}=-1\mbox{\AA}$
separates star-forming from quiescent galaxies well. Here we adopt a slightly
higher equivalent width cut to potentially include galaxies with
poststarburst-like SFHs but slightly higher SFRs. These looser definitions do
not lead to a contaminated sample, as we will show later in the paper.

To measure the line strengths, we employ a joint fitting of both the stellar
continuum and emission lines using the Penalized Pixel-Fitting method (pPFX;
Cappellari & Emsellem, 2004; Cappellari, 2017), as described in (Straatman et
al., 2018). We use the Lick H$\delta_{a}$ definition (Worthey, 1994) to
measure the equivalent width of H$\delta$ and determine it from the spectra
after subtracting the emission line models generated by pPFX. In DR2, the
emission-line fluxes are directly taken from the results of pPXF fit and EWs
were derived by dividing the line fluxes by the local continuum averaging over
a 200Å-wide region centered on the line.

For ALMA follow-ups, we select galaxies at redshifts $z<0.84$, as the CO(2-1)
line can be observed with ALMA Band 4 receivers. A lower mass limit of
$\log(M_{\ast}/M_{\odot})>10.8$ is also set. We further require galaxies to
have either position angles $P.A.<20\degree$ or axis ratios $b/a>0.7$ measured
from HST F814W images. As LEGA-C slits are oriented north-south, these
galaxies are easier to be spatially resolved in the slit spectra.

From 1550 primary targets in LEGA-C DR2, spectra of 678 galaxies cover both
$EW(H\beta)_{em}$ and $EW(H\delta)$. Thirty-seven galaxies fulfill the
equivalent width cut of Equation 1 and 6 of them also meet our criteria of
redshift, stellar mass, and shapes. All 6 of them are proposed for ALMA
observation and 5 are observed.

Table 1 lists the spectral features of the 5 galaxies. We use DR2 spectra for
sample selection but the analysis is done with the 3rd data release (DR3, van
der Wel et al., 2021). We thus list measurements from both sets. We also list
the widely-used spectral index $\mbox{D}_{n}\mbox{4000}$. The DR3 improves sky
subtraction and flux calibration, therefore, the overall shapes of spectra and
the line strengths may change between DR2 and DR3. Furthermore, the emission
line fluxes and equivalents widths are measured differently in DR3. The DR3
uses Platefit (Tremonti et al., 2004; Brinchmann et al., 2004) on spectra
after subtracting the best-fit continuum model to fit the emission lines. The
equivalent width of the emission line is calculated based on the measured line
flux and the continuum flux from the continuum model over the same wavelength
range (Maseda et al., 2021). The reason for not using pPXF for emission-line
fluxes is that pPXF does not measure faint lines well and Platefit is
customized for such a task.

Between DR3 and DR2, the scatters in $\mbox{D}_{n}\mbox{4000}$ and
$\mbox{EW(H}\delta\mbox{)}$ are 0.08 and 0.8Å, respectively. For
EW(H$\beta$)em, the DR3 has $\sim 20\%$ more detections above 3$\sigma$
uncertainties than DR2 and DR3 is on average $\sim 1.3$ times higher than DR2
with $\sim 1\AA$ scatter for galaxies with $EW(H\beta)_{em}\geq-5\mbox{\AA}$
in DR2. We only examine galaxies with weak emission because they are more
relevant to our study. The scatters are larger than the formal errors listed
in Table 1 because the uncertainties in the calibration and modeling of
spectra are not taken into account. Although a few galaxies may have fallen
out of the selection criteria in DR3, they still possess a
’poststarburst’-like star formation history and will be shown to be so later
in the paper.

Table 1: Poststarburst galaxy sample

ID | z | EW(H$\beta$)ema,da,dfootnotemark:  |  $\mbox{EW(H}\delta\mbox{)}$bbMeasured from emission-line-subtracted spectra. |  $\mbox{D}_{n}\mbox{4000}$bbMeasured from emission-line-subtracted spectra. | EW(H$\beta$)ema,da,dfootnotemark:  |  $\mbox{EW(H}\delta\mbox{)}$bbMeasured from emission-line-subtracted spectra. |  $\mbox{D}_{n}\mbox{4000}$bbMeasured from emission-line-subtracted spectra.
---|---|---|---|---|---|---|---
|  | (Å) | (Å) |  | (Å) | (Å) |
|  |  | DR2 |  |  | DR3 |
133501 | 0.72916 | $<0.45$ | 5.30$\pm$0.12 | 1.57$\pm$0.01 | $<0.17$ | 3.57$\pm$0.33 | 1.54$\pm$0.02
144377 | 0.69650 | $<0.17$ | 4.25$\pm$0.15 | –ccThe spectra does not cover the wavelength range. | -0.43$\pm$0.05 | 4.42$\pm$0.17 | –ccThe spectra does not cover the wavelength range.
209377 | 0.74703 | -1.41$\pm$0.13 | 4.67$\pm$0.09 | 1.45$\pm$0.01 | -1.96$\pm$0.07 | 5.34$\pm$0.10 | 1.39$\pm$0.01
210541 | 0.71477 | $<0.21$ | 7.02$\pm$0.17 | 1.39$\pm$0.01 | -1.53$\pm$0.07 | 7.07$\pm$0.15 | 1.32$\pm$0.01
260163 | 0.75285 | $<0.53$ | 7.51$\pm$0.26 | 1.34$\pm$0.01 | $<0.82$ | 8.26$\pm$0.29 | 1.35$\pm$0.02

ddfootnotetext: Upper limits are 3$\sigma$ limits.

Figure 1 shows our sample on the UVJ diagram, a widely used technique to
differentiate between quiescent and star-forming galaxies and identify
poststarburst galaxies when only multi-wavelength broadband photometry is
available. In this diagram, poststarburst galaxies are identified as quiescent
galaxies with the bluest V-J colors (e.g., Whitaker et al., 2012), which are
also likely to have high $\mbox{EW(H}\delta\mbox{)}$. However, not all
quiescent galaxies with high $\mbox{EW(H}\delta\mbox{)}$ have blue V-J colors.
Using spectral features, we can detect poststarburst galaxies that may be
missed by broadband photometry alone (Wu et al., 2020).

###  2.2 Extracting kinematics of stars and ionized gas

The deep LEGA-C spectra, taken with slits of north-south orientation and a
pixel scale of 0$\farcs$2, offers exquisite detail with generally $<1"$ seeing
(Straatman et al., 2018). For each row of the 2D spectra with median $S/N>2$
per pixel, we use pPXF to fit a model of the stellar continuum.

The stellar template is a non-negative, linear combination of (Vazdekis, 1999)
single stellar population (SSP) models, which are based on the Medium-
resolution INT Library of Empirical Spectra (MILES, Sánchez-Blázquez et al.,
2006) with Girardi et al. (2000) isochrones.

We mask out wavelength ranges where significant emission lines are present.
Major lines are [O II]$\lambda 3727,3729$, H$\delta$, H$\gamma$, H$\beta$, and
[O III]$\lambda 4959,5007$. The exact wavelength range is determined by visual
inspection. It will be shown later in the paper that the line emission in each
galaxy exhibits a variety of shapes and velocities. A common practice of
modeling emission lines with Gaussian is not applicable to these galaxies.
These fits yield spatially-resolved line-of-sight stellar velocity profiles
along the north-south direction. Subtracting the best-fit stellar templates
from the observed spectra gives us the line emission from the ionized gas
along the slit.

###  2.3 Deriving star-formation histories

In this paper, we use the code BAGPIPES (Carnall et al., 2018) to fit the
observed LEGA-C spectra and broadband spectral energy distribution (SED) from
UV to mid-IR to constrain the SFHs.

####  2.3.1 Spectral-photometric fitting

Table 2: Priors for the SFH fitting Component | parameter | Symbol / Unit | range | prior | Hyperparameters
---|---|---|---|---|---
SFH | Stellar mass formed | $M_{\ast}/M_{\odot}$ | ($10^{10.5}$, $10^{12.5})$ | logarithmic |  |
| Stellar metallicity | $Z/Z_{\odot}$ | (0.1, 2.5) | logarithmic |  |
| decay timescale |  $\tau$ / Gyr | (0.05, 4) | logarithmic |  |
| look-back time of formation |  $t_{form}$ / Gyr | (4, $t_{Hubble}$) | uniform |  |
| look-back time of burst |  $t_{burst}$ / Gyr | (0, 2) | uniform |  |
| burst fraction | $f_{burst}$ | (0, 1) | uniform |  |
Dust | Dust attenuation at 5500Å |  $A_{v}$ / mag | (0, 8) | uniform |  |
| Power-law slope | n | (0.1, 2) | Gaussian | $\mu=0.7$ | $\sigma=0.5$
| Birth-cloud-to-diffuse attenuation | $\eta$ | (1, 5) | uniform |  |
Calibration | 0th order |  | (0.5, 1.5) | Guassian | $\mu=1$ | $\sigma=0.25$
| 1st order |  | (-0.5, 0.5) | Guassian | $\mu=0$ | $\sigma=0.25$
| 2nd order |  | (-0.5, 0.5) | Guassian | $\mu=0$ | $\sigma=0.25$
Noise model | White noise scaling |  | (0.1, 10) | logarithmic |  |
Table 3: The star-formation histories of poststarburst galaxies ID | $\log(M_{\ast}/M_{\odot})$ | $\tau$ | $t_{form}$ | $t_{burst}$ | $f_{burst}$ | $A_{v}$ | $n$ | $\eta$ | $t_{q}$
---|---|---|---|---|---|---|---|---|---
|  | (Gyr) | (Gyr) | (Gyr) |  | (mag) |  |  | (Gyr)
133501 | $10.99^{+0.03}_{-0.03}$ | $0.07^{+0.03}_{-0.02}$ | $6.45^{+0.40}_{-0.83}$ | $1.13^{+0.04}_{-0.04}$ | $0.42^{+0.09}_{-0.06}$ | $0.18^{+0.05}_{-0.04}$ | $0.86^{+0.23}_{-0.17}$ | $2.92^{+1.34}_{-1.23}$ | $0.57^{+0.03}_{-0.03}$
144377 | $11.07^{+0.02}_{-0.02}$ | $0.30^{+0.02}_{-0.02}$ | $5.57^{+1.08}_{-1.04}$ | $1.12^{+0.02}_{-0.02}$ | $0.98^{+0.01}_{-0.03}$ | $0.43^{+0.04}_{-0.05}$ | $1.03^{+0.07}_{-0.06}$ | $1.81^{+0.24}_{-0.19}$ | –
209377 | $11.14^{+0.02}_{-0.02}$ | $0.16^{+0.02}_{-0.02}$ | $4.74^{+1.01}_{-0.50}$ | $0.69^{+0.12}_{-0.10}$ | $0.15^{+0.08}_{-0.05}$ | $0.11^{+0.02}_{-0.02}$ | $1.31^{+0.15}_{-0.15}$ | $2.67^{+1.69}_{-1.40}$ | $0.23^{+0.04}_{-0.03}$
210541 | $11.25^{+0.04}_{-0.05}$ | $0.10^{+0.02}_{-0.01}$ | $4.56^{+0.80}_{-0.42}$ | $0.53^{+0.05}_{-0.05}$ | $0.23^{+0.03}_{-0.03}$ | $1.31^{+0.10}_{-0.11}$ | $0.50^{+0.07}_{-0.05}$ | $1.44^{+0.42}_{-0.30}$ | $0.05^{+0.01}_{-0.01}$
260163 | $10.94^{+0.04}_{-0.04}$ | $0.15^{+0.02}_{-0.03}$ | $5.35^{+1.00}_{-0.90}$ | $0.68^{+0.09}_{-0.09}$ | $0.48^{+0.17}_{-0.11}$ | $1.00^{+0.09}_{-0.08}$ | $1.15^{+0.08}_{-0.08}$ | $4.34^{+0.47}_{-0.67}$ | $0.15^{+0.02}_{-0.02}$
Figure 2: The observed spectrum and photometry of LEGA-C 210541 and the best-
fit model spectrum. Wavelength regions that may contain line emission (grey
areas) are not fitted. The spectrum is multiplied by the factor shown in the
middle panel to account for the mismatch to the broadband SED (see Section
2.3.1). The uncertainties of photometric measurements are smaller than the
sizes of the squares in the bottom panel and thus not shown. The bottom right
panel is the SFH posteriors. The line is the median and the shaded area shows
the 16th and 84th percentiles of the posteriors. The fits of other galaxies
are in the Appendix.  Figure 2: Continue. Figure 2: Continue. Figure 2:
Continue. Figure 2: Continue. Figure 3: The correlations between spectral
indices and SFH parameters. The spectrum of LEGA-C 144377 does not cover the
$\mbox{D}_{n}\mbox{4000}$ region. $\mbox{D}_{n}\mbox{4000}$ serves as a good
qualitative proxy to the look-back time of the burst and the time that a
galaxy became quiescent. On the other hand, there is no clear correlation
between the burst strength and either $\mbox{D}_{n}\mbox{4000}$ or
$\mbox{EW(H}\delta\mbox{)}$. LEGA-C 144377 has not become quiescent (see main
text), we manually put it at $t_{q}=-0.1$.

Poststarburst galaxies, by the selection, are supposed to have rapidly falling
recent SFRs. We assume that a poststarburst galaxy forms stars in two phases;
a constant rate then followed by an exponentially-decay burst as described by
the following parametric form:

$SFR(t)\propto\left\\{\begin{array}[]{cr}\quad c,&t_{burst}\leq t\leq
t_{form}\ ;\\\ e^{[-(t_{burst}-t)/\tau]},&\ t<t_{burst},\end{array}\right.$
(2)

where $c$ is a constant, $t$ is the look-back time, $\tau$ is the timescale of
the exponential decay, $t_{form}$ and $t_{burst}$ are the look-back times that
the constant phase, and exponential phase starts, respectively. To ensure that
the burst is represented by the exponential form rather than a short period of
intensive constant star formation, we impose a minimum constant phase of 2 Gy,
i.e., $t_{form}-t_{burst}\geq 2$ Gyr. Our tests indicate that extending the
minimum length of the constant phase has no significant impact on our results.
The relative SFRs in these two phases are controlled by the parameter
$f_{burst}$:

$\frac{\int_{0}^{t_{burst}}e^{[-(t_{burst}-t)/\tau]}dt}{c\times(t_{form}-t_{burst})}=\frac{f_{burst}}{1-f_{burst}}.$
(3)

$f_{burst}$ is the fractional stellar masses ever formed in the exponential
phase thus between 0 and 1.

We employ the (Charlot & Fall, 2000) form of attenuation curve, characterized
by $A_{\lambda}\propto\lambda^{-n}$, where the parameter $n$ is allowed to
vary. We also allow the attenuation of stars in the birth cloud ($t<10^{7}$
yr) to be different from that of older stars with $A_{bc}=\eta\times A_{old}$.
The dust emission models are taken from Draine & Li (2007). The stellar
continuum templates are generated with the updated Bruzual & Charlot (2003)
stellar population synthesis model (Chevallard & Charlot, 2016) using the
MILES stellar spectral library (Falcón-Barroso et al., 2011). We assume all
stars have the same metal content with a scaled-Solar abundance. The redshift
and velocity dispersion values are fixed as in LEGA-C DR3 (van der Wel et al.,
2021).

The spectra are binned every 5 pixels before fitting using SpectRes (Carnall,
2017). The binning reduces processing time while preserving the constraining
power because LEGA-C spectra have a pixel scale of $0.6/(1+z)\
\mbox{pixel}^{-1}$ at the restframe, and the MILES templates have a resolution
of 2.5Å. We then visually inspect the spectra and mask out wavelengths with
line emission. We will show in Section 4.1 that the emission lines in our
poststarburst galaxies are highly asymmetric and at least partially driven by
AGN, rendering the use of Gaussians implemented in BAGPIPES inadequate.

We include GALEX NUV, CFHT $u^{*}$, Subaru/HSC g, r, i, and z, VISTA/VIRCAM Y,
J, H, and $K_{s}$, Spitzer/IRAC ch1 and ch2 from the COSMOS2020 Classic
catalog (Weaver et al., 2022) and Spitzer/MIPS 24$\mu$m from a matched IR
source catalog of Jin et al. (2018) in our fitting111Part of the photometry is
acquired by the COSMOS program, which can be accessed via 10.17909/T9XW2Q
(catalog 10.17909/T9XW2Q). We set a floor uncertainty of 5% for each
photometric measurement. We add a second-order Chebyshev polynomial
perturbation and a white noise model to the spectroscopic data to handle
possible mismatch of the overall shape between the spectrum and the SED, as
well as a possible underestimate of the uncertainties of the spectra. BAGPIPES
takes a Bayesian approach to evaluate the most probable parameter sets. The
priors are listed in Table 2. Figure 2 shows an example of the fitting. We
refer readers to Carnall et al. (2019b) for the details of the implementation.

####  2.3.2 Star-formation histories of poststarburst galaxies

The best-fit SFHs suggest that all poststarburst galaxies actually had a
‘burst’, i.e., an increase of SFR in the past (Table 3 and Figure 3). In most
cases, the starburst began 0.5-1 Gyr ago, produced 15-50% of the stellar mass
ever formed, and with exponentially decaying timescales of approximately 100
Myrs. Our poststarburst galaxies are at the very late stage of the starburst
events, $>4\tau$-decaying times after the burst. LEGA-C 133501 is even at
$\sim 10\tau$-decaying times after the onset of the burst.

LEGA-C 144377 is a unique case among the sample galaxies. Essentially all its
stellar masses formed in a prolonged burst with an e-folding time of 300 Myrs.
To verify this result, various settings were modified in the fitting
procedure, including the adoption of a different dust extinction law,
exclusion of certain photometric bands or spectra in specific wavelength
ranges, substitutions of the parametric SFH with a double power law, and use a
non-parametric SFH. Despite these changes, all tests produced similar results,
indicating that $\sim 90\%$ of stars formed around 0.5-1 Gyr ago. We note that
such a strong burst in poststarburst galaxies at similar redshifts has been
presented before (Wild et al., 2020; Suess et al., 2022), indicating the
diversity of poststarburst galaxies.

From the SFHs, we calculate $t_{q}$, the look-back time at which the star
formation rate dropped below $10^{-10}$ yr-1, a fiducial value to
differentiate between star-forming and quiescent galaxies. The oldest
poststarburst galaxies became quiescent less than 600 million years ago, while
the majority have $t_{q}<250$ Myr. Notably, LEGA-C 144377 is situated above
this fiducial cut-off.

The correlations between SFH parameters and spectral indices are shown in
Figure 3. It is not surprising that $\mbox{D}_{n}\mbox{4000}$ is strongly
correlated with the onset of the burst and the time of quenching. However,
neither $\mbox{D}_{n}\mbox{4000}$ nor $\mbox{EW(H}\delta\mbox{)}$ is a
reliable indicator of burst strength. Deriving this parameter requires
spectral modeling.

We note that the assumed parametric form and priors do not enforce a higher
peak SFR of the exponential component than the constant part. We have applied
the poststarburst parametric SFH to fit a set of randomly selected quiescent
galaxies with $\mbox{EW(H}\delta\mbox{)}<2\AA$. The peak SFRs of the
exponential components are either lower than the constant component or exceed
the constant component for less than 10% in the most prominent case,
indicating a lack of a ‘burst’ event in the recent past. The significant
increase of SFRs of poststarburst galaxies in the fitting is necessary to
match the observed data.

###  2.4 Star-formation rates

The SFRs is a crucial piece of information on poststarburst galaxies,
nevertheless, hard to estimate. The peculiar SFHs question the applicability
of conventional conversions from light to SFRs. The high incidence of AGN in
poststarburst galaxies adds another source of uncertainties as AGN could
contribute to almost all wavelengths used for estimating the SFRs. Here we
calculate 4 SFRs based on data at different wavelengths which trace various
physical processes, following conventional calibrations and methodologies.
Considering the potential contribution from AGN, the values reported here
should be considered as upper limits.

Firstly, we derive the SFRs by averaging the reconstructed SFHs over the last
100 Myrs. With a timescale of $\sim 100$Myrs for the $\tau$-decay (Table 3),
the instantaneous SFRs are roughly half of the listed values. Next, we
calculate the SFRs based on dust-corrected H$\beta$ emission, using the
calibration by Kennicutt & Evans (2012) and the Chabrier (2003) IMF, with an
assumption of an intrinsic flux ratio of $H\alpha/H\beta=2.86$. We use the
best-fit $A_{V}$, $n$, and $\eta$ to calculate the attenuation of stars with
$<10$ Myr at the wavelength of H$\beta$ and use the value as the attenuation
of the H$\beta$ emission line.

Additionally, we determine the SFRs from the restframe 2800 Å UV and 8-1000
$\mu$m IR luminosities of the best-fit SED models, using the prescription by
Bell et al. (2005) and a Chabrier (2003) IMF. The SFRs are computed as
$\Psi[M_{\odot}\ \mbox{yr}^{-1}]=1.09\times
10^{-10}(L_{IR}+2.2L_{UV})[L_{\odot}]$. We will demonstrate in Sec. 5 that the
old stars in poststarburst galaxies can contribute a large fraction of energy
that heats the dust. This common calibration can be an overestimate.

Unlike the UV luminosity, which is relatively well-constrained by the NUV and
$u^{*}$ bands, the total IR luminosities are only sampled by a single Spitzer
MIPS 24$\mu$m measurement. To verify the result, we identify LEGA-C 201541 and
LEGA-C 260163 in the far-IR source catalog of Jin et al. (2018) that are
detected at 100 $\mu$m with an S/N$>4$. We re-fit with the addition of 100
$\mu$m photometry and find that the SFRs change by less than a factor of 2,
which does not affect our conclusions.

Finally, we cross-match the poststarburst galaxies with the COSMOS VLA 3 GHz
source catalog (Smolčić et al., 2017), with a maximum matching radius of
0$\farcs$7 (Barišić et al., 2017). We convert the radio continuum fluxes to
SFRs using the Bell (2003) calibration of the radio-FIR correlation and report
the values in Table 4. We note that the contribution of AGN to the 3 GHz
luminosity cannot be ignored. In particular, the inferred $SFR_{3GHz}$ for
LEGA-C 209377, which exceeds $2000\ \mbox{M}_{\odot}\ \mbox{yr}^{-1}$, is
almost for sure contaminated by AGN. This galaxy has a 3 GHz luminosity of
$8.6\times 10^{24}\ \mbox{W}\ \mbox{Hz}^{-1}$ (Barišić et al., 2017), which is
significantly higher than the commonly-used threshold for identifying radio-
loud AGN ($10^{23}\ \mbox{W}\ \mbox{Hz}^{-1}$, Best et al., 2005). The 3 GHz
luminosities of all other galaxies in our sample are all lower than $10^{23}\
\mbox{W}\ \mbox{Hz}^{-1}$.

Table 4 reveals an intriguing disagreement among the SFRs derived by different
methods. Notably, the SFRs estimated using the UV+IR and 3 GHz continuum
emission appear to be consistently higher, potentially resulting in the
misclassification of some poststarburst galaxies as part of the star-forming
main sequence. We will discuss this discrepancy in Section5.

Table 4: Star Formation Rates

ID | SED | $H\beta$ | UV+IR | 3 GHz
---|---|---|---|---
133501 | $0.0^{+0.1}_{-0.0}$ | (0.2) | $2.9^{+0.7}_{-0.6}$ | $17\pm 3$
144377 | $17.8^{+1.8}_{-1.8}$ | $1.0\pm 0.1$ | $24^{+2}_{-3}$ | $31\pm 3$
209377 | $4.4^{+0.9}_{-0.6}$ | $2.7\pm 0.1$ | $7.7^{+0.9}_{-0.7}$ | $2733\pm 142$
210541 | $6.0^{+2.3}_{-1.5}$ | $3.8\pm 0.2$ | $40^{+4}_{-5}$ | $42\pm 3$
260163 | $8.0^{+1.9}_{-2.0}$ | (12.1) | $19^{+3}_{-2}$ | (27)

  * •

SFRs in $M_{\odot}$ yr-1. Values for the ‘SED’ and ‘UV+IR’ are based on the
16th, 50th, and 84th percentiles of the spectrophotometric fitting. Values for
‘H$\beta$’ and ‘3 GHz’ are derived from the fluxes and their uncertainties,
respectively. Here we do not attempt to quantify the fluxes contributed by
AGN. Numbers in parentheses are 3-$\sigma$ upper limits.

###  2.5 ALMA observations

Table 5: ALMA observation ID | z | $T_{int}$ | beam size | beam P.A. | $S_{CO(2-1)\Delta v}$ | $L_{CO}$ |  $\log(M_{H2}/M_{\odot})$aaMeasured from continuum-subtracted spectra. | $M_{H2}/M_{\ast}$
---|---|---|---|---|---|---|---|---
|  | (min) |  |  ($\degree$) |  (Jy km s-1) |  ($10^{9}$ K km s-1 pc2) |  |
133501 | 0.72916 | 146 | $2\farcs 2\times 1\farcs 7$ | 83 | $<0.125$ | $<0.89$ |  $<$9.68 | $<0.05$
144377 | 0.69650 | 106 | $2\farcs 2\times 1\farcs 5$ | $-87$ |  0.414$\pm$0.040 |  2.68$\pm$0.26 |  10.17$\pm$0.04 | 0.13
209377 | 0.74703 | 126 | $1\farcs 4\times 1\farcs 2$ | 76 |  0.077$\pm$0.021 |  0.57$\pm$0.16 |  9.50$\pm$0.12 | 0.02
210541 | 0.71477 | 86 | $2\farcs 2\times 1\farcs 8$ | 75 |  0.375$\pm$0.026 |  2.56$\pm$0.18 |  10.15$\pm$0.03 | 0.08
260163 | 0.75285 | 115 | $1\farcs 4\times 1\farcs 2$ | 71 |  0.491$\pm$0.056 |  3.72$\pm$0.42 |  10.31$\pm$0.05 | 0.23

Figure 4: The moment 0 maps of CO(2-1) and best-fit Gaussian models. Contours
increase every 3$\sigma$, starting from 3$\sigma$, where $\sigma$ is measured
from the central 3” of the residual maps. The beam sizes are plotted at the
lower left corners. All 3 CO(2-1) emissions can be modeled by a single
Gaussian component, with no clear sign of disturbed morphology or outflow
under the current resolution.

The ALMA observations were carried out in program 2019.1.00702.S (PI: P. Wu)
in January and February 2019 using the ALMA Band 4 receivers (Asayama et al.,
2014). The total on-source integration time for each target is 1.5-2.5 hours.
The data are reduced and imaged using the standard ALMA pipeline. The spatial
resolutions range from 1$\farcs$2-2$\farcs$2 (9-16 kpc) with a robust
parameter of 0.5 (Table 5).

The CO(2-1) emission is clearly detected in three galaxies, LEGA-C 144377,
210541, and 260163, around their optical centers at an 8-15$\sigma$ level. Our
visual inspection suggests that the CO emission is marginally resolved and we
model the emission as a 2D elliptical Gaussian using the CASA task IMFIT,
which measures the apparent sizes and then performs deconvolution to constrain
the intrinsic sizes of sources. For LEGA-C 144377 IMFIT fails to obtain an
intrinsic size because the measured image size is similar to the beam size.
The other two galaxies both have major axes of $\sim 1"$ after deconvolution
(Table 6). All three galaxies are well represented by the Gaussian model
(Figure 4). We also fit the sources either assuming a disk model or in the
visibility space, the results are consistent within the uncertainties.

Table 6: Deconvolved sizes of ALMA sources

|  |  | 144377 |  |  | 210541 |  |  | 260163 |
---|---|---|---|---|---|---|---|---|---|---
|  | FluxaaAssuming $r_{21}=0.8$ and $\alpha_{CO}=4.0$ | SizebbThe sources sizes and P.A. are deconvolved sizes derived with CASA task IMFIT. Sources that are smaller than the beam have no deconvolved values.  | P.A. | FluxaaThe unit for VLA 3 GHz flux density is $\mu$Jy. The unit for ALMA CO(2-1) flux is mJy km s-1.  | SizebbThe sources sizes and P.A. are deconvolved sizes derived with CASA task IMFIT. Sources that are smaller than the beam have no deconvolved values.  | P.A. | FluxaaThe unit for VLA 3 GHz flux density is $\mu$Jy. The unit for ALMA CO(2-1) flux is mJy km s-1.  | SizebbThe sources sizes and P.A. are deconvolved sizes derived with CASA task IMFIT. Sources that are smaller than the beam have no deconvolved values.  | P.A.
|  |  | (”) | (∘) |  | (”) | (∘) |  | (”) | (∘)
ALMA CO(2-1) | beam |  | $2.20\times 1.49$ | -87 |  | $2.23\times 1.75$ | 75 |  | $1.38\times 1.16$ | 71
robust=0.5 | source | 420(39) | - | - | 375(26) | $1.26(0.13)\times 0.60(0.42)$ | 57(26) | 494(57) | $1.06(0.30)\times 0.85(0.33)$ | 90(74)
ALMA CO(2-1) | beam |  | $2.60\times 2.04$ | -88 |  | $2.66\times 2.18$ | 74 |  | $1.80\times 1.50$ | 61
Natural | source | 405(31) | - | - | 386(17) | $1.38(0.18)\times 0.92(0.18)$ | 64(22) | 576(48) | $1.70(0.25)\times 0.92(0.18)$ | 81(36)
ALMA CO(2-1) | beam |  | $1.64\times 0.83$ | -88 |  | $1.49\times 1.23$ | 70 |  | $1.13\times 0.93$ | -89
Uniform | source | 350(93) | - | - | 279(28) | - | - | 402(76) | - | -
VLA 3 GHz | beam |  | $0.75\times 0.75$ |  |  | $0.75\times 0.75$ |  |  | $0.75\times 0.75$ |
| source | 32.7(4.9) | $0.59(0.17)\times 0.07(0.25)$ | 29(14) | 42.9(4.1) | - | - | 0.7(5.9) | - | -

Note. — Numbers in the parentheses are uncertainties.

To further examine the robustness of the size measurements, we make the images
using both natural weighting and uniform weighting and repeat the modeling
with elliptical Gaussian (Table 6). With uniform weighting, which yields
better angular resolutions but lower signal-to-noise ratios, LEGA-C 210541 and
260163 have $\sim 20\%$ lower model fluxes than those measured with robust=0.5
and become apparently unresolved despite the better angular resolutions. We
have examined the residual images to confirm that the Gaussian models
represent the sources well, as done in Figure 4. These results suggest the
existence of faint and extended emission that is missed in the uniform-
weighted maps with lower signal-to-noise ratios. In addition, with the more
sensitive but lower angular resolution images with natural weighting, the flux
and intrinsic size of LEGA-C 260163 become marginally larger, again implying
faint and diffuse emission.

To compromise between sensitivity and angular resolution, we choose to use the
robust=0.5 map for this paper. We then measure the fluxes by integrating the
data cubes over a 3” radius from the optical centers, then used either one or
two Gaussian components to fit the integrated spectra. We used the best-fit
Gaussian models and their uncertainties as the fluxes of the CO(2-1) emission,
as reported in Table 5. The results are in agreement with modeling the images
(Table 6). Additionally, we calculated the direct sum over the velocity range
where the line emission existed based on visual inspection, and the fluxes
from this method are consistent with the Gaussian fits.

The fourth galaxy, LEGA-C 209377, exhibits weak CO(2-1) emission 1” northwest
of the optical center. We follow a similar method for measuring its flux,
integrating over a 2” x 2” region centered at the peak of the emission, and
fitting a Gaussian to the spectrum. LEGA-C 133501 had no detectable CO(2-1)
emission. We estimated the upper limit of the flux using a single $\pm 400$km
s-1 channel.

To calculate H2 masses, we assumed $r_{21}=0.8$ and a Milky-Way-like CO–H2
conversion factor of $\alpha_{CO}=4.0$, as per Bolatto et al. (2013). The
molecular gas masses range from $2\times 10^{9}M_{\odot}$ to $3\times
10^{10}M_{\odot}$. The one undetected source, LEGA-C 133501, has a 3$\sigma$
upper limit of $4.8\times 10^{9}M_{\odot}$. The ratio between the masses of
molecular gas and stars, $f_{H2}\equiv M_{H2}/M_{\ast}$, range between 2% to
26% and are comparable to the values found in previous studies (Suess et al.,
2017; Bezanson et al., 2022; Zanella et al., 2023)

##  3 Spatial distribution of stars, molecular gas, and star-formation

Figure 5: The distributions of star, gas, and star formation of poststarburst
galaxies. First column: HSC $i$-band light. The contour levels are 31, 29, and
27 mag/”. Galaxies with similar redshifts to poststarburst galaxies are
labeled. Most poststarburst galaxies have clear tidal features or a companion
in the field of view. Second column: HST/F814W (gray scale image) and CO(2-1)
(contours) maps. The morphologies of the main stellar bodies of poststarburst
galaxies are vastly different. Contour levels are -3, 3, 6, 12, and 18
$\sigma$. Hashed ellipses are the primary beams. Third column: The VLA 3 GHz
maps. Radio emissions are unresolved. Fourth column: Spitzer MIPS 24$\mu$m
maps. Galaxies with CO(2-1) detections are also detect in 24$\mu$m. Hashed
circles in the 3rd and 4th columns are the nominal angular resolutions.

Figure 5 presents an overview of the spatial distribution of stars, gas, and
star formation in post-starburst galaxies through multiwavelength images
including Subaru HyperSuprimCam (HSC) $i$, HST/F814W, ALMA CO(2-1), VLA 3 GHz,
and Spitzer/MIPS 24$\mu$m maps of our sample. This figure provides a
comprehensive look at the distribution of these different components across
poststarburst galaxies and can be used to gain insights into the processes
that led to the cessation of star formation in these galaxies.

###  3.1 Stars

High-resolution images from the HST reveal a diverse array of morphologies
among poststarburst galaxies, including disk, elliptical, and tidal features.
LEGA-C 210541, for instance, is oriented face-on and displays two distinct
tidal arms. LEGA-C 209377 presents a low surface brightness fan-shaped
structure connecting a fainter stellar body located approximately 3″northwest.
LEGA-C 260163 has a small companion galaxy located around 3″southwest. These 3
galaxies are those showing more recent bursts. Conversely, the HST images of
LEGA-C 133501 and 144377 do not exhibit any clear tidal features. These
galaxies have older bursts that occurred more than 1 Gyr ago.

Deeper images from the HSC reveal even more low surface brightness features
that are not visible in the HST images, extending as far as 40 kpc from the
galaxy centers. For example, the two prominent tidal arms of LEGA-C 210541 are
only visible out to about $\sim 2\arcsec$ from the galaxy center in the HST
image but continue to about $\sim 5\arcsec$ (or approximately 37 kpc) in the
HSC image. Similarly, LEGA-C 209377 shows a fan-shaped feature at its
northwest in the HST images, but the HSC image reveals a wider, lower surface
brightness, and asymmetric light distribution toward the northeast. LEGA-C
144377 appears to be a normal spheroid galaxy in the HST image, but the HSC
image again reveals an asymmetric low-surface-brightness feature at the
southeast of the galaxy.

When viewed from a wider field of view, it is common to find nearby
companions. Four of the poststarburst galaxies have close neighbors at a
similar cosmological distance, estimated from either photometric or
spectroscopic redshifts. The $K_{s}$ band flux ratios range from 1:2 to 1:5
and the separations are between 50 kpc and 130 kpc. We investigate 1251
galaxies with similar stellar masses ($M_{\ast}>10^{11}M_{\odot}$) and
photometric redshifts ($0.6<z_{phot}<0.8$) in the COSMOS2020 catalog and find
that only 199 (or 16%) have a companion within 130 kpc, with a $\Delta
z_{phot}<0.02$, and a $K_{s}$ flux ratio exceeding 1/5. The probability that
our poststarburst galaxy was randomly selected from the larger sample is just
a mere 0.3%. This suggests that the interactions with nearby galaxies may have
played a role in the formation of poststarburst galaxies, although a larger
sample with dense spectroscopic redshifts will be needed to further verify
this result.

###  3.2 Star formation and molecular gas

The third and fourth columns of Figure 5 are two commonly used tracers of star
formation: VLA 3 GHz and Spitzer/MIPS 24$\mu$m. The Spitzer/MIPS24$\mu$m has a
low resolution of $\sim 6\arcsec$. Three galaxies (LEGA-C 210541, 144377, and
260163) have clear 24$\mu$m sources that coincide with the optical centers.
LEGA-C 209377 has a weak ($\sim 4.5\sigma$) detection at $\sim 1\arcsec$
northwest of the optical center, which also matches the weak CO(2-1)
detection.

Four poststarburst galaxies have 3 GHz emission at their optical centers.
LEGA-C 209377 is clearly a radio-loud AGN given its high luminosity. For other
sources, we model their emission as 2D elliptical Gaussian and constrain their
intrinsic sizes using IMFIT, assuming a circular beam of $0\farcs 75\times
0\farcs 75$ (Smolčić et al., 2017). LEGA-C 144377 has an elongated shape with
an intrinsic major axis of $\sim 0\farcs 6$ and the other two sources (LEGA-C
133501 and 210541) are point-source-like If the radio emission is powered by
star formation activities, this compactness implies that the star formation
concentrates within a small region, rather than being spread out over a large
area. Sub-kpc scale residual star formation has been shown to be prevalent at
the center of local poststarburst galaxies Wu (2021).

In addition to 3 GHz and 24$\mu$m emission, later in Section 4.1, we will show
from the H$\beta$ emission that LEGA-C 210541 has a central star-forming
region with an apparent angular size of $\sim 0\farcs 8$, which is comparable
to the seeing of our spectroscopic observation. Therefore, the 3 different
tracers all suggest that the star formation activities in poststarburst
galaxies, if exist, concentrate at galaxy centers.

Closely related to star formation is the raw material that fuels it: molecular
gas. The distributions of the CO(2-1) emission are plotted in contours in
Figure 5. The velocity ranges used to integrate the CO(2-1) emission are
listed in each panel.

LEGA-C 209377 exhibits a weak CO(2-1) detection of $3.5\sigma$ significance,
located at a distance of $\sim 1\arcsec$ northwest of its optical center.
Interestingly, this detection coincides with a fan-shaped stellar stream
connecting a small companion galaxy located $\sim 3\arcsec$ away.
Additionally, there is a tentative source of $\sim 4\sigma$ significance at
24$\mu$m at the same location. These observations suggest that this galaxy has
recently experienced gravitational disturbance, which may have triggered off-
center star formation and possibly led to quenching.

The CO(2-1) emission in LEGA-C 210541, 144377, and 260163 is well-detected
around the optical centers. LEGA-C 210541 and LEGA-C 260163 have intrinsic
sizes of $1\farcs 1$ ($\sim 8$ kpc) and $1\farcs 3$ ($\sim 10$ kpc),
respective. The CO emission observed in these 2 galaxies exhibits a spatial
distribution that extends beyond the confines of the spatially-unresolved
star-formation activities. This observation suggests that the molecular gas
present in these galaxies may not be linked to star formation.

The centers of the CO(2-1) emission in LEGA-C 144377 and LEGA-C 210541 align
closely with their respective optical centers, with an offset of approximately
$\sim 0\farcs 2$. Conversely, the center of the CO emission in LEGA-C 260163
is located $0\farcs 36\pm 0\farcs 08$ ($\sim 2.7\pm 0.6$ kpc) southwest of its
optical center. Given the reasonable detection ($S/N\simeq 9$), the offset is
small compared to the synthesized beam size of 1$\farcs$4 and yet still
significant. This offset suggests that the molecular gas is recently disturbed
and not yet dynamically settled.

##  4 Kinematics

With the ALMA observation and the ultra-deep optical slit spectra, these
galaxies provide us a rare opportunity to look into the kinematics of stars,
ionized gas, and molecular gas simultaneously.

###  4.1 Kinematics of ionized gas

Figure 6: The continuum-subtracted spectra of poststarburst galaxies. The
thick magenta lines are the best-fit multiple Gaussian models to the H$\beta$
and [O III]$\lambda$5007 lines. Thin orange, green, and gray lines are
individual Gaussian components. The [O III]$\lambda$5007 lines show asymmetric
broad components. Table 7: Properties of emission lines

LEGA-C ID | component | $f_{O3}$ | $f_{H\beta}$ | $f_{O2}$ | Velocity | FWHM | $\log(O3/Hb)$
---|---|---|---|---|---|---|---
|  | ($10^{-19}$ erg s-1 cm-2) | (km s-1) |
144377 | A | $370\pm 36$ | $187\pm 11$ | — | $186\pm 7$ | $469\pm 26$ | 0.42
| B | $477\pm 35$ | $132\pm 16$ | — | $-218\pm 54$ | $955\pm 63$ | 0.68
| total | $823\pm 12$ | $303\pm 9$ | — | — | — | 0.55
209377 | A | $777\pm 416$ | $84\pm 54$ | — | $-230\pm 51$ | $221\pm 34$ | 1.09
| B | $633\pm 55$ | $111\pm 56$ | — | $-123\pm 15$ | $182\pm 39$ | 0.88
| C | $359\pm 135$ | $6\pm 25$ | — | $15\pm 37$ | $202\pm 28$ | 1.90
| total | $1787\pm 13$ | $212\pm 9$ | $1412\pm 8$ | — | — | 1.07
210541 | A | $53\pm 6$ | $97\pm 4$ | — | $-24\pm 3$ | $151\pm 8$ | -0.14
| B | $193\pm 11$ | $7\pm 9$ | — | $-275\pm 31$ | $755\pm 77$ | 1.59
| total | $228\pm 10$ | $96\pm 5$ | — | — | — | 0.50
260163 | total | — | — | $124\pm 8$ | — | — | —

  * •

The flux of each component is derived from multiple Gaussian fits. Total
fluxes are calculated from summing the spectra over the wavelength range used
for fitting (Figure 6) for [O III]$\lambda$5007 and H$\beta$ and $\pm 800$ km
s-1 for [O II].

Figure 7: The [O III]$\lambda$5007/H$\beta$ flux ratios and stellar masses of
each emission component of poststarburst galaxies. For LEGA-C 209377, the sum
of components are also plotted. The shapes of markers represent different
galaxies and the open, filled, and hashed symbols are different kinematic
components in a galaxy. The stellar masses of LEGA-C 209377 are shifted by
hand for the presentation. Black lines separate galaxies dominated by star-
forming regions (bottom) from AGN (top), as well as the mixed region in
between (Juneau et al., 2014). Small dots are other LEGA-C galaxies where the
flux ratios can be measured. Blue and red represent star-forming and quiescent
galaxies, respectively. All kinematic components in poststarburst galaxies
except LEGA-C 210541 A have among the highest [O III]$\lambda$5007/H$\beta$
for galaxies of similar stellar masses, suggesting that the AGN is the source
of the ionization.

To unveil the subtle emission lines present in poststarburst galaxies, we
subtract best-fit stellar continuum models from the 1D spectra, as
demonstrated in Figure 6. Despite their weak H$\beta$ emission, our
poststarburst galaxies exhibit well-detected lines in a few instances due to
the high signal-to-noise ratios. Along with H$\beta$, we detect the presence
of [O II]$\lambda$3727,3729 and [O III]$\lambda$4959,5007 in the majority of
our sample galaxies. Additionally, LEGA-C 209377 exhibits [Ne III]3869 and
LEGA-C 210541 shows a tentative detection. The shapes of these emission lines,
particularly that of [O III]$\lambda$5007, show clear asymmetry and hint at
the presence of multiple kinematic components, including broad, blue-shifted
emission.

Figure 8: The position-velocity diagrams of the [O III]$\lambda$5007 emission.
The systematic velocity is set by the stellar velocity at the central pixel.
The black solid lines are the stellar velocities. The kinematics of the [O
III]$\lambda$5007 gas is detached from the stars. The velocities of the wind
can be up to a few hundred km s-1. In LEGA-C 144377 and LEGA-C 210541, the gas
is concentrated at galaxy centers.

In Figure 8, we present the [O III]$\lambda 5007$ position-velocity (PV)
diagrams along the slits of LEGA-C 144377, 209377, and 210541. By fitting
stellar population synthesis models to each row of the 2D spectra, we subtract
out the stellar continua similar to Figure 6. Only pixels with $S/N\geq 2$ are
presented, and for comparison, the stellar velocities are also plotted.

The [O III] emission of LEGA-C 144377 and LEGA-C 210541 appear to be spatially
unresolved, with flux distributions that can be modeled as Gaussian
distributions, centered on the galaxy centers, and with FWHM of approximately
$\sim 0\farcs 8$. In contrast, LEGA-C 209377 exhibits multiple kinematic
components on its PV diagram.

We employ a multi-Gaussian approach to model the 1D spectra, fitting [O
III]$\lambda$5007 and H$\beta$ simultaneously while assuming that the two
lines are produced by the same kinematic components, sharing the same velocity
and FWHM. To mitigate potential issues caused by imperfect continuum
subtraction, we exclude the weaker [O III]$\lambda$4959 from the fitting
process. The wavelength ranges for fitting are carefully selected based on
visual inspection of the line emission. In the case of LEGA-C 144377 and
LEGA-C 210541, we find that 2 kinematic components are sufficient, while
LEGA-C 209377 requires 3 components, as determined by visual inspection of the
fitting results and the PV diagram. The sums and individual Gaussians are
displayed in Figure 6. LEGA-C 260163 exhibits clear [O II] emission but no
H$\beta$ emission. We attempt to model the [O II] doublet with Gaussians,
however, the uncertainties are too large to yield a convincing model.
Similarly, we are unable to obtain a satisfactory model for the [O II] of
LEGA-C 209377 either, likely due to its complex velocity structure as shown by
H$\beta$ and [O III]$\lambda$5007\. The central velocities and FWHM as well as
fluxes of each kinematic component are listed in Table 7. For the [O II]
emission that cannot fit well, we determined its flux by summing over $\pm
800$ km s-1. We also calculate the total fluxes from the direct sum of
H$\beta$ and [O III]$\lambda$5007 of all galaxies and the results are
consistent with Gaussian models.

We find that the line-of-sight velocities of many kinematic components are
$\sim 200$ km s-1 different from those of the stellar bodies. Some of them
have line widths of $\gtrsim 500$ km s-1. The line emission is thus unlikely
powered by star-formation activities. Meanwhiles, the [O
III]$\lambda$5007/H$\beta$ flux ratios of most kinematic components rank among
the highest in the LEGA-C sample (Figure 7). For LEGA-C 209377, although the
fluxes of individual components may be uncertain, the total fluxes determined
through direct sum are reliable measurements (Tabel 7). Based on their [O
III]$\lambda$5007/H$\beta$ flux ratios and stellar masses, all components
except LEGA-C 210541 A would be classified as AGN-driven (Juneau et al.,
2014).

LEGA-C 210541 B and the integrate fluxes of LEGA-C 209377 have [O
III]$\lambda$5007/H$\beta$ ratios $\gtrsim 10$, which cannot be produced by
shock-ionization ($\lesssim 2.5$, see, e.g., Rich et al., 2011) or be
attributed to low-ionization nuclear emission-line regions (LINERs) (Kewley et
al., 2006). The emission in LEGA-C 144377 has line widths of $\sim 500-1000$
km s-1, which is also unlikely powered by old stars or shocks (Ho et al.,
2014). Therefore, AGN is likely the main driver of line emission in these
galaxies. However, no X-ray counterparts are found in public X-ray source
catalogs (Cappelluti et al., 2009; Civano et al., 2016; Marchesi et al., 2016)
and their Spitzer IRAC mid-IR colors (Stern et al., 2012) do not classify them
as AGN either (S. Velvalcke, private communication).

###  4.2 Kinematics of CO

Figure 9: Kinematics of CO, ionized gas, and stars. First column: The spectra
of CO(2-1) (gray), H$\beta$ (blue), [O III] (green), and [O II] (brown) of
poststarburst galaxies. The CO spectra are extracted in a $4”\times 4”$
squared region located at the optical centers of galaxies. The spectra of
LEGA-C 144377, 210541, and 260163 are binned to $\sim 25$km s-1. The rest two
are binned to $\sim 50$km s-1 for presentation. The kinematics of CO(2-1) and
ionized gas are decoupled. Middle column: The spatial distributions of red-
and blue-shifted CO emission overplotted on the HST F814W images. Contours are
every 3$\sigma$. The centroids of blue- and redshifted CO emission show small
displacements. Right column: Comparison of the stellar (gray circles) and CO
(colored squares) velocities. The positions of CO are the centroids measured
from Gaussian fits (see main text) projected in the N-S direction. The
velocity gradients of CO is in the same direction as the stars but stronger.

The first column of Figure 9 presents the CO spectra, integrated over an area
of 2” from the centers of and binned in velocity for clarity. These spectra
exhibit double-horn profiles for LEGA-C 144377 and LEGA-C 260163, while LEGA-C
210541 shows a centrally-peaked profile. The tentative detection of LEGA-C
209377 is observed at $\sim 0$km s-1. Such double-horn and singly-peaked
profiles have been previously noted in poststarburst galaxies at similar
redshifts (Suess et al., 2017; Bezanson et al., 2022).

Furthermore, the overplotted ionized emission line profiles reveal that for
LEGA-C 144377, 209377, and 260163, the velocity distribution of the CO does
not align with those of H$\beta$, [O III], or [O II]. Similarly, LEGA-C 210541
presents a broad blueshift ionized gas component that lacks a corresponding CO
counterpart. The CO has a similar central velocity to that of the narrow
component LEGA-C 210541 A but with a smaller FWHM ($\sim 100$ km s-1 compared
to $\sim 150$ km s-1). LEGA-C 210541 A is also the only component with the [O
III]$\lambda$5007/H$\beta$ flux ratio consistent with being powered by star-
formation activities.

The second column of Figure 9 presents maps of red- and blue-shifted CO
emission, with the velocity ranges for integration chosen by visual
inspection. We detect slight offsets between the red and blue components and
determine their centroids through fitting with either Gaussian or point source
models in both image and visibility spaces. The separations between the red
and blue components ranging from $0\farcs 25$ to $0\farcs 5$ and all methods
yield consistent results.

In the third column of Figure 9, we compare the velocity gradients of CO and
stars along the N-S direction, acknowledging the vastly different angular
resolutions and measurement types of the optical and sub-mm data. We observe
that the velocity gradients of stars and CO in LEGA-C 144377 and LEGA-C 260163
are in the same direction, but the CO appears to have stronger gradients.
Given the worse angular resolution of the ALMA data, thus the more serious
beam smearing effect, the higher CO velocity gradients are likely real. For
the flat galaxy LEGA-C 260163, the CO velocity gradient is clearly along the
photometric major axis of the stellar light, potentially indicating compact
disks co-rotating with the stars at the central $\lesssim 0\farcs 5$.

##  5 Star-formation rate

By definition, poststarburst galaxies are galaxies with low SFRs. Star-
formation tracers from poststarburst galaxies thus should be faint by nature.
The 5 poststarburst galaxies are rare cases where multiple SFR indicators are
available together. We see that different SFR indicators can disagree with
each other by an order of magnitude or more (Table 4). Overall, $SFR_{UV+IR}$
and $SFR_{3GHz}$ are higher than $SFR_{SED}$ and $SFR_{H\beta}$.

All the SFRs have their own shortcomings. First of all, the fiducial
calibration of the FIR-based SFR assumes a constant SFR in the past $\sim$100
Myrs. Based on our models, this assumption clearly cannot apply to
poststarburst galaxies. Hayward et al. (2014) post-processed hydrodynamical
simulations with dust radiative transfer and calculated the SED of galaxies
during the galaxy merging processes. They found that the FIR luminosity can
overestimate the SFR by more than 10 times in the poststarburst phase because
the dust is mainly heated by the prodigious amount of radiation from stars
with ages of hundreds of Myr.

Based on the model SFH and dust attenuation (Section 2.3.1), we calculate how
much the radiation is attenuated by dust for stars of different ages. This
quantity can be interpreted as the contribution to dust heating from different
ages of stars under the common energy balance assumption, which is adopted in
our fitting scheme. Figure 10a shows the normalized cumulative distributions
of attenuated stellar radiation as a function of stellar ages. The curves also
inform us of the main stellar population that heats up the dust.

We show a model star-forming galaxy with $SFR(t)\propto\exp(-t/10\ Gyr)$,
$Z_{\odot}=1$, $A_{v}=1.5$, $n=0.8$, and $\eta=2$ for comparison. For the
model star-forming galaxy, stars younger than 100 Myrs contribute to $\sim
67\%$ of the dust heating. On the other hand, for poststarburst galaxies which
have significantly larger $SFR_{UV+IR}$ than $SFR_{SED}$ (LEGA-C 133501,
210541, and 260163), the majority ($\sim 60\%$) of the dust heating is
provided by stars with ages between 100 Myrs and 1 Gyrs. Stars younger than
100 Myrs only contribute $\lesssim 30\%$, even $0\%$, of the energy. Adopting
the fiducial FIR-based SFR calibration can potentially overestimate the SFR by
more than an order of magnitude if the SFR was rapidly declining in the recent
past. Similarily, the large number of old stars also contributes significantly
to the UV radiation (Figure 10a).

With the SFHs, we can attempt to quantify how much the $SFR_{UV+IR}$ is
overestimated for poststarburst galaxies. We have computed the $SFR_{UV+IR}$
as $\Psi[M_{\odot}\ \mbox{yr}^{-1}]=1.09\times
10^{-10}(L_{IR}+2.2L_{UV})[L_{\odot}]$. Taking the model star-forming galaxy
in Figure 10 as the baseline, $67\%$ and $70\%$ of the total IR and UV
radiation is contributed by stars younger than 100 Myrs, respectively.
Therefore, if we use only the contribution from young stars to estimate the
SFR, we can rewrite the equation for the model star-forming galaxy as
$\Psi[M_{\odot}\ \mbox{yr}^{-1}]=(1.63\times
10^{-10}L_{IR_{<100Myr}}+3.46\times 10^{-10}L_{UV_{<100Myr}})[L_{\odot}]$,
where $L_{IR_{<100Myr}}$ and $L_{UV_{<100Myr}}$ are the luminosities from
stars younger than 100 Myrs. We then apply this new ‘calibration’ to
poststarburst galaxies, plug in $L_{UV_{<100Myr}}$ and $L_{IR_{<100Myr}}$
based on the best-fit models. We find the new $SFR_{UV+IR_{<100Myr}}$ is
consistent with $SFR_{SED}$ (Figure 10b). This result illustrates that the
commonly-used calibration can overestimate the SFRs of poststarburst galaxies
due to their peculiar SFHs.

In addition, as AGN is present from the optical emission lines (Figure 7), we
should not ignore the potential contributions to SFR tracers. Not only
H$\beta$ emission is powered by AGN, but also IR and radio continua.
Therefore, $SFR_{H\beta}$, $SFR_{UV+IR}$, and $SFR_{3GHz}$ may all
overestimate the true SFR due to the contribution from AGN. The compact 3 GHz
emission is morphologically consistent with being powered by AGN. On the other
hand, the SPS models fit the optical spectra well (Figure 2). There is no need
to include a featureless continuum component. Therefore, we consider the SFRs
from fitting the spectra are not contaminated by AGN and adopt $SFR_{SED}$ as
our fiducial $SFR$.

Nevertheless, $SFR_{SED}$ should also be used with caution. Firstly, the
posterior SFHs can be biased by the choice of priors (Carnall et al., 2019a;
Leja et al., 2019; Suess et al., 2022). Moreover, if poststarburst galaxies
are indeed the descendant of dusty, compact central starbursts, then the
youngest stars in poststarburst galaxies may still be deeply embedded in dust
clouds (Poggianti & Wu, 2000; Kocevski et al., 2011). The attenuation at the
optical wavelength in some poststarburst regions in a few local galaxies is
argued to be up to thousands of magnitudes (Smercina et al., 2022), therefore,
optical and NIR light would not probe deep in the dust clouds and
underestimates the true attenuation and SFRs. Smercina et al. (2018) proposed
to use MIR nebular neon emission lines, [Ne II] at 12.8$\mu$m and [Ne III] at
15.6$\mu$m, to avoid the issue of high attenuation (Ho & Keto, 2007). With the
MIR nebular emission lines, the problem on SFRs may be solvable with JWST up
to $z\sim 0.8$. Given that SFRs are dominated by systematic uncertainties,
there is still much work to be done to verify their low SFEs.

Figure 10: (a) The cumulative distribution of attenuated stellar radiation and
UV luminosities as a function of stellar ages of poststarburst galaxies. The
curves are calculated based on the best-fit SFHs and dust attenuation. The
attenuated light then re-emitted in the IR. About 70% of the $L_{TIR}$ of a
star-forming galaxy (light blue) is heated by stars younger than 100 Myrs. The
contribution from stars of $<100$ Myr can be much lower in poststarburst
galaxies. Similarly, a larger fraction of the UV radiation of poststarburst
galaxies is contributed by older stars compared to star-forming galaxies. The
radiation from old stars results in overestimates of SFRs based on FIR and UV
luminosities. (b) The contamination from old stars to the $SFR_{UV+IR}$. The
filled symbols show the $SFR_{UV+IR}$ after excluding the contribution from
stars older than 100 Myrs (see main text). The new $SFR$ are much lower than
original $SFR_{UV+IR}$ and more consistent with $SFR_{SED}$.

##  6 Molecular gas content and star formation

Figure 11: The correlations between molecular gas fraction and
$\mbox{D}_{n}\mbox{4000}$, $\mbox{EW(H}\delta\mbox{)}$, look-back time of the
onset of the burst, and the look-back time when galaxies became quiescent.
Poststarburst galaxies at similar redshifts with CO measurements in Bezanson
et al. (2022) ($z\sim 0.6$) and Zanella et al. (2023) ($z\sim 1.2$) are also
plotted. Figure 12: The $M_{H2}/M_{\odot}$ and SFRs of poststarburst galaxies.
Each panel shows the SFR measured by different methods. Poststarburst galaxies
with SFRs beyond the displayed ranges are placed at the edges of the panels.
Pink circles are quiescent galaxies in Spilker et al. (2018), with SFRs
measured by the same methods. Blue crosses and circles are star-forming
galaxies at $z\sim 1.2$ from the PHIBSS (Tacconi et al., 2013) and $z\sim 0$
from the xCOLDGASS (Saintonge et al., 2011), for which the SFRs and $M_{H2}$
are taken from the papers and adopting an $\alpha_{CO}=4$. The solid line is
the scaling relation between SFR and $M_{H2}$ fitted with the PHIBSSS and
xCOLDGASS data and the shaded area shows a 0.2 dex scatter. SFRs of
poststarburst galaxies from different methods can differ by an order of
magnitude. Adopting the more reliable $SFR_{SED}$, poststarburst galaxies have
lower SFEs than typical star-forming galaxies.

Figure 11 shows the correlation between $f_{H_{2}}$ and age-related parameters
of our poststarburst galaxies. Samples at similar redshifts (Bezanson et al.,
2022; Zanella et al., 2023) are also plotted. Although caution must be taken
in drawing any definitive conclusions from such a small sample size.
Nevertheless, there appears to be a tentative trend indicating that
poststarburst that became quiescent earlier exhibit lower $f_{H_{2}}$. The
three galaxies with a clear detection of CO(2-1) also have lower $t_{q}$,
indicating a more recent quiescent state (LEGA-C 144377, 201541, and 260163).
This trend is consistent with the findings of Bezanson et al. (2022), who
recently measured the molecular gas and SFH of massive poststarburst galaxies
at similar redshifts, and found that while poststarburst galaxies can
initially contain molecular gas, it depletes rapidly within $\sim 100$ Myr.
The age-sensitive $\mbox{D}_{n}\mbox{4000}$ reveal a consistent picture in
such that there are no poststarburst galaxy with CO detection and with
$D_{n}4000\gtrsim 1.4$ (Figure 11).

We compare the molecular gas masses and SFRs of poststarburst galaxies (from
Table 4) to those of normal star-forming galaxies (Figure 12). As a point of
reference, we include star-forming galaxies at redshifts $z=1-1.3$ from the
PHIBSS survey (blue crosses, Tacconi et al., 2013) and local massive star-
forming galaxies from the xCOLDGASS sample (blue circles, Saintonge et al.,
2011). We also show the measurements of 8 massive quiescent galaxies from
Spilker et al. (2018) for comparison. The molecular gas masses have been
adjusted to $\alpha_{CO}=4.0$ for consistency, and the SFRs are extracted from
the papers.

We adopt $SFR_{SED}$ as our primary measurement of star formation rate, but we
present the other $SFRs$ for completeness. We find that poststarburst galaxies
exhibit similar or even higher molecular gas fractions than normal star-
forming galaxies. Furthermore, when we adopt $SFR_{H\beta}$, we observe a
larger deviation from the scaling relation. Due to the contamination of AGN,
we anticipate that the true deviation is even larger.

These deviations suggest that poststarburst galaxies may have several times
lower SFEs than normal star-forming galaxies. While they still possess a
considerable amount of molecular gas, there should be some physical processes
that suppress star formation, preventing the gas from converting to stars.

Interestingly, poststarburst galaxies fall roughly on the scaling relation in
the 3rd and 4th panels. Had we relied on $SFR_{UV+IR}$ or $SFR_{3GHz}$ as
proxies for SFR, our conclusion would have been vastly different. Nonetheless,
we have established that $SFR_{UV+IR}$ tends to overestimate SFRs (Section 5).
The same trend of overestimation has been observed in quiescent galaxies,
where $SFR_{UV+IR}$ exceeds $SFR_{SED}$ and $SFR_{H\beta}$ systematically.
This trend can be attributed to the fact that most of the light that heats up
dust in these galaxies emanates from old stars. For $SFR_{3GHz}$, if the 3 GHz
continuum traces the star formation activities, we should expect that the 3
GHz continuum and the CO(2-1) emission have similar sizes. LEGA-C 210541 gives
a strong piece of counter-evidence in such that its CO(2-1) emission extends
over $\sim 1\farcs 3$ ($\sim 10$ kpc) while the 3 GHz emission is unresolved
under a $0\farcs 75$ beam. Assuming a typical SFE and $SFR=SFR_{SED}$, the
expected 3 GHz flux is below the current detection limit, in line with the
fact that no 3 GHz source of $\sim 1"$ is detected. The 3rd and 4th panels
hence highlight the non-trivial task of accurately determining SFRs in
poststarburst galaxies - a crucial aspect of understanding quenching.

##  7 Discussion

The diverse high-quality data provide us a rare opportunity to look
simultaneously into the stars, gas, and star-formation of distant
poststarburst galaxies. In this section, we discuss the implication of
quenching from the multi-wavelength data.

We note that galaxies in this study do not reside in massive clusters. Galaxy
clusters also play a role in triggering starburst and quenching at similar
redshifts, through mechanisms that only operate in cluster environments
(Muzzin et al., 2012; Wu et al., 2014; Matharu et al., 2021) but investigating
these cluster-specific mechanisms is beyond the scope of this paper.

###  7.1 Implication to the quenching process

The poststarburst galaxies may be a remnant of the collision or merging of
gas-rich galaxies that induced gas inflows, triggered intense star formation
and AGN, and also fueled outflows that brought negative feedback (Barnes &
Hernquist, 1996; Hopkins et al., 2006). According to simulations, the
poststarburst phase may last from a few hundred million years to nearly a
billion years after the merging event (Bekki et al., 2005; Snyder et al.,
2011). The disturbed stellar morphologies may be visible for a similar time
frame of about half a billion years (Lotz et al., 2008, 2010a, 2010b).

Our modeling suggests that these poststarburst galaxies experienced a
starburst event several hundred million years ago and then underwent rapid
quenching. Out of the five galaxies we observed, four exhibit disturbed
morphologies as seen through either HST or HSC imaging. The high incident rate
of disturbed features is consistent with the observation from $\sim 100$
massive poststarburst galaxies at similar redshift by Verrico et al. (2022).
The residual star formation, if present, appears to be centralized around the
galaxy cores (Figure 5). Molecular gas is also centrally concentrated in most
cases. The multi-wavelength data point towards strong galaxy interaction as
the primary cause.

From the SFHs and current gas mass, we can estimate the stellar and gas masses
of the progenitors. The stellar mass of the progenitor is the current stellar
mass minus the mass formed in the burst, taking into account the mass returned
into the interstellar medium (ISM) towards the end of the stellar evolution.
The gas mass of the progenitor is the sum of the current gas mass and the
stellar mass formed in the burst. Using the values derived in Section 2.3.1
and Section 2.5, we find a wide range of initial stellar masses and gas
fractions of progenitors. Despite the present-day stellar masses are all
$1-2\times 10^{11}M_{\odot}$, the stellar masses before bursts range from
$\sim 2\times 10^{9}M_{\odot}$ to $\sim 10^{11}M_{\odot}$ in our sample.
Moreover, the molecular gas fraction $M_{H_{2}}/M_{\ast}$ ranges from $\sim
0.3$ for the high-mass progenitors to $\sim 50$ for the lowest-mass
progenitor. In this calculation, we have neglected the possible contribution
of atomic hydrogen. For local poststarburst galaxies with
$M_{\ast}>10^{10}M_{\odot}$, Zwaan et al. (2013) shows that $M_{HI}/M_{\odot}$
is generally a few percent. Since there is no information for larger
distances, we apply the local value. Also, we have not accounted for potential
mass loss caused by tidal disruption or outflows during the process, as
observational constraints are lacking. However, the off-center detection of CO
in LEGA-C 209377 and a case study by Spilker et al. (2022) show that gas
stripping occurs. Therefore, the gas fraction we derive may be considered as a
lower limit.

Our observations suggest that galaxies with $M_{\ast}\sim 10^{11}M_{\odot}$
and $M_{H_{2}}/M_{\ast}\sim 0.3$ could be progenitors of poststarburst
galaxies. Such a molecular gas fraction is fairly typical for star-forming
galaxies at $z\sim 1$ (Tacconi et al., 2013; Wang et al., 2022). This result
indicates that rapid elevation and then truncation of SFR could happen in
normal star-forming galaxies and may not require a particularly gas-rich
progenitor. For the other extreme, there are currently fewer measurements of
molecular gas contents for lower-mass galaxies with $M_{\ast}\sim
10^{9}M_{\odot}$ but galaxies with $M_{H_{2}}/M_{\ast}>10$ have been found
however very rare at $z\sim 1$ (Liu et al., 2019). These extremely gas-rich
systems may become the most extreme poststarburst galaxies at later times.

It will be intriguing to see whether hydrodynamical simulations are able to
reproduce these observations; from the inferred wide ranges of initial stellar
and gas masses, produce starbursts with such rapid and extreme bursts with 100
Myr e-folding times, forming several $10^{10}M_{\odot}$ stars, and match the
morphologies at the similar time after the burst as constrained by the data.
Answering these questions with accuracy could shed light on the mechanisms
driving poststarburst galaxies and the role of galaxy interactions and
feedback in quenching their star formation.

###  7.2 The role of AGN

In the quenching process, the role of AGN is considered to be crucial due to
its energy and momentum output. Despite being frequently associated with the
quenching of star formation in poststarburst galaxies, many poststarburst
galaxies do not exhibit bright radio and X-ray emission or distinct mid-IR
colors (Nielsen et al., 2012; Meusinger et al., 2017). Only one poststarburst
galaxy in this study shows luminous radio continuum emission, none is detected
in X-ray, and none is classified as AGN based on the mid-IR color selection of
Stern et al. (2012). The low radio AGN fraction is consistent with the
previous study of Greene et al. (2020), who demonstrated that only 5% of $\sim
1000$ massive poststarburst galaxies at $z\sim 0.7$ exhibit $L_{3GHz}\gtrsim
10^{24}$ W Hz-1. Notably, the radio and X-ray surveys conducted in the COSMOS
field are among the deepest blind surveys to date. Thus, the lack of radio and
X-ray detections unequivocally indicates the low emission levels of
poststarburst galaxies at these wavelengths.

In contrast, when [O III]$\lambda$5007 falls within the spectral range, three
out of 4 poststarburst galaxies exhibit [O III]$\lambda$5007 gas flows powered
by AGN (Tabel 7 and Figure 7). This high incidence rate of AGN-driven [O
III]$\lambda$5007 emission stands in contrast to the $\sim 5\%$ incidence rate
reported by Greene et al. (2020). Our high incidence rate is likely
attributable to the ultra-deep LEGA-C spectra, which allowed us to precisely
model the stellar continua and discern weak emission lines. Our results
suggest that AGN may be more prevalent than previously assumed.

Nevertheless, the impact of the AGN-driven wind on CO gas is unclear. Evidence
of outflowing CO gas has been reported (Spilker et al., 2022), but in our
sample, there are no indications of disturbed morphology or high-velocity
components at our current angular resolution and sensitivity, despite the
detection of AGN-driven ionized gas. While it is possible that AGN activity
plays a role in quenching star formation, our observations suggest that any
significant impact on the molecular gas likely occurs prior to the phase
identified in our study. Furthermore, it is possible that the AGN has not
fully cleared or destroyed the gas reservoir thus residual star formation is
allowed. This conclusion is consistent with local integral field unit (IFU)
observations of poststarburst galaxies, showing residual star formation at
sub-kpc scales in their centers (Wu, 2021). In addition, a higher incidence
rate of AGN in poststarburst galaxies with younger stellar ages, as found by
Greene et al. (2020), suggests that the peak AGN activity may occur during an
earlier phase of the quenching process.

##  8 Summary and Future Work

We present a comprehensive study of 5 massive poststarburst galaxies with
$M_{\odot}\gtrsim 10^{11}M_{\odot}$ at $z\sim 0.7$, utilizing multi-wavelength
observations to trace the stars, gas, and current and past star formation
activities.

The ultra-deep spectra from the LEGA-C survey give us good constraints on the
SFHs. We find that these galaxies underwent bursts of star formation several
hundred Myr ago, with a decay time scale of approximately 100 Myr. Prior to
the burst, these massive poststarburst galaxies were heterogeneous, with
stellar masses ranging from $2\times 10^{9}M_{\odot}$ to $>10^{11}M_{\odot}$,
and with gas masses up to 50 times the stellar mass for the lowest-mass
progenitor to $\sim 30\%$ of the stellar mass for the high-mass progenitors.
Our deep spectra also reveal that weak AGN-driven [O III] outflows are common
in poststarburst galaxies.

Examining high-resolution images from HST and deep images from HSC, we find in
our sample of 5 galaxies, 4 of them have low surface brightness tidal features
that extend over tens of kpc. In addition, 4 of them have a companion galaxy
within $\sim 100$ kpc, with $K_{s}$-band flux greater than 20% of the
poststarburst galaxy, and at a similar redshift.

Some poststarburst galaxies possess CO gas of $\sim 10^{10}M_{\odot}$ at the
galaxy centers, with intrinsic sizes of $>1\arcsec$, or $\sim 10$ kpc. In
contrast, neither the 3 GHz continuum image from VLA nor the H$\beta$ emission
from LEGA-C slit spectra suggest extended star-forming regions. Both of these
observations have angular resolutions of $\sim 0\farcs 8$. Our results suggest
that the star-forming regions are more compact than the CO gas, and the star-
formation activities are suppressed. Comparing the SFRs derived from SED
fitting and the molecular contents leads us to the same conclusion;
poststarburst galaxies have lower SFEs than star-forming galaxies.

Meanwhiles, we find that the SFRs obtained through UV and IR continuum and 3
GHz continuum tend to overestimate the SFR of poststarburst galaxies. This is
due to the fact that, unlike normal star-forming galaxies, stars older than
100 Myr are the primary source of dust heating and UV radiation in
poststarburst galaxies, rendering IR and UV continua inadequate indicators for
star formation. Moreover, both IR and 3 GHz continuum flux may reflect not
only star formation but also AGN activity. Despite that the AGN-driven ionized
outflows are prevalent, we do not find CO outflow at current angular
resolutions and sensitivities. While AGN may contribute to quenching as
indicated by many studies, they do not entirely clear out or destroy the cold
gas reservoir.

The multi-wavelength observations of the 5 galaxies in our study provide
compelling evidence that quenching is linked to interactions between galaxies,
which can trigger centrally-concentrated starbursts followed by a rapid
truncation of star formation. AGN is common in this phase. This process is not
restricted to gas-rich, low-stellar-mass galaxies, but can also occur in high-
stellar-mass galaxies where the gas mass is only a small fraction of the
stellar mass like typical massive star-forming galaxies at $z\sim 1$. When
combined with the SFHs derived from deep optical spectra, our findings, offer
valuable insights into the changes that take place in galaxy properties during
the quenching process and can be used to refine simulations of galaxy
formation and evolution. This work is a step forward to understanding the
mechanisms that shut down star formation in distant galaxies.

PFW thanks Dr. Chen Chien-Chou and Dr. Sharon Meidt for fruitful discussions.
PFW acknowledges funding through the National Science and Technology Council
grant 111-2112-M-002-048-MY2 and National Taiwan University grant NTU 112L7318
and NTU 112L7439. FDE acknowledges funding through the ERC Advanced grant
695671 “QUENCH” and support by the Science and Technology Facilities Council
(STFC). AG acknowledges support from INAF-Minigrant-2022 ”LEGA-C”
1.05.12.04.01. This paper makes use of the following ALMA data:
ADS/JAO.ALMA#2019.1.00702.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.

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