# Post-starburst galaxies in SDSS-IV MaNGA: Two broad categories of
evolutionary pathways

Zhuo Cheng  Department of Astronomy, Tsinghua University, Beijing 100084,
China  Cheng Li Department of Astronomy, Tsinghua University, Beijing 100084,
China  Niu Li Department of Astronomy, Tsinghua University, Beijing 100084,
China  Renbin Yan  Department of Physics, The Chinese University of Hong Kong,
Sha Tin, NT, Hong Kong, China  Houjun Mo  Department of Astronomy, University
of Massachusetts, Amherst MA 01003-9305, USA

###### Abstract

We study the size-mass relation (SMR) and recent star formation history (SFH)
of post-starburst (PSB) galaxies in the local Universe, using spatially
resolved spectroscopy from the final data release of MaNGA. Our sample
includes 489 PSB galaxies: 94 cPSB galaxies with central PSB regions, 85 rPSB
galaxies with ring-like PSB regions and 310 iPSB galaxies with irregular PSB
regions. When compared to control galaxies of similar SFR, redshift and mass,
a similar SMR is found for all types of PSB samples except the cPSB galaxies
which have smaller sizes at intermediate masses ($9.5\lesssim\log_{10}(\rm
M_{\ast}/M_{\odot})\lesssim 10.5$). The iPSB galaxies in the star-forming
sequence (iPSB-SF) show no/weak gradients in $\textrm{D}_{n}(4000)$,
$\textrm{EW}(\textrm{H}\delta_{A})$ and $\textrm{EW}(\textrm{H}\alpha)$,
consistent with the global star-forming status of this type of galaxies, while
the quiescent iPSB (iPSB-Q) sample shows negative gradients in
$\textrm{D}_{n}(4000)$ and positive gradients in
$\textrm{EW}(\textrm{H}\delta_{A})$, indicating older stellar populations in
the inner regions. Both cPSB and rPSB samples show positive gradients in
$\textrm{D}_{n}(4000)$ and negative gradients in
$\textrm{EW}(\textrm{H}\delta_{A})$, indicating younger stellar populations in
the inner regions. These results imply that the four types of PSB galaxies can
be broadly divided into two distinct categories in terms of evolutionary
pathway: (1) iPSB-SF and iPSB-Q which have SMRs and SFHs similar to control
galaxies, preferring an inside-out quenching process, (2) rPSB and cPSB which
appear to be different stages of the same event, likely to follow the outside-
in quenching process driven by disruption events such as mergers that result
in a more compact structure as quenching proceeds.

galaxy evolution — post-starburst — formation and quenching

##  1 Introduction

Post-starburst (PSB) galaxies, also known as “E+A” or “K+A” galaxies, are
identified by strong Balmer absorption lines but no/weak $\textrm{H}\alpha$ or
[O ii] emission lines in their optical spectrum (e.g. Dressler & Gunn, 1983;
Poggianti et al., 1999; Goto, 2005). The lack of strong [O ii] or
$\textrm{H}\alpha$ emission indicates no or weak ongoing star formation, while
strong Balmer absorption lines indicate a starburst within the past
$\sim$1Gyr. Thus the two spectral features combine to indicate a burst of star
formation followed by a rapid cessation process of the star formation with a
timescale of $<1$Gyr. The PSB galaxies account for only about 1% of the galaxy
population in the local Universe (e.g. Goto et al., 2008; Wong et al., 2012;
Meusinger et al., 2017; Pawlik et al., 2018). Many of them fall in the “green
valley” of color-mass diagrams (e.g. Wong et al., 2012), a relatively rare
population located in between the two major populations of galaxies: the star-
forming blue cloud and the quiescent red sequence (e.g. Strateva et al., 2001;
Kauffmann et al., 2003; Baldry et al., 2004; Bell et al., 2004; Bundy et al.,
2005; Arnouts et al., 2007; Faber et al., 2007). Therefore, PSB galaxies are
widely believed to be transitioning from the blue cloud to the red sequence,
thus playing an important role in galaxy evolution, although the exact
fraction of quiescent galaxies that have undergone a PSB phase remains elusive
(e.g. Tran et al., 2003, 2004; Yang et al., 2008; Wild et al., 2009; Vergani
et al., 2010; Swinbank et al., 2012; Whitaker et al., 2012; Wong et al., 2012;
Pawlik et al., 2016; Yesuf, 2022).

Despite a rich history of studies in the past four decades, the physical
origin of the fast quenching in PSB galaxies is still under debate. In early
studies, since these galaxies were preferentially found in galaxy clusters
(e.g. Dressler & Gunn, 1983; Poggianti et al., 1999; Tran et al., 2003),
mechanisms occurring in dense environments such as perturbations by the
cluster tidal field (Byrd & Valtonen, 1990) and repeated encounters with
companion galaxies known as “harassment” (Moore et al., 1996, 1998) were
considered. In more recent studies ram-pressure stripping of the cold
interstellar medium (Gunn & Gott, 1972) has also been considered (e.g.
Paccagnella et al., 2017; Vulcani et al., 2020; Wilkinson et al., 2021).
However, Yesuf (2022) found that the satellite-quenching mechanisms operating
in high-density environments cannot account for most of their PSB galaxies
selected from the Sloan Digital Sky Survey (SDSS; York et al., 2000).

Gas removal driven by active galactic nuclear (AGN) activity has been
suggested as an alternative mechanism to quickly shut down the star formation
during the PSB phase (e.g. Goto, 2006; Yan et al., 2006; Wild et al., 2007;
Sell et al., 2014; Yesuf et al., 2014). However, A recent study of Chandra
observations by Lanz et al. (2022) showed that PSB galaxies can contain only
low-luminosity AGN, which are unable to radiatively drive out the cold gas in
low$-z$ PSB galaxies, as detected by many studies (e.g. Chang et al., 2001;
Buyle et al., 2006; Zwaan et al., 2013; French et al., 2015; Yesuf et al.,
2017; Bezanson et al., 2022; French et al., 2022).

In fact, it has been well-established that PSB galaxies generally reside in
the field and loose groups rather than dense environments based on large
spectroscopic surveys, both at low redshift such as the Las Campanas Redshift
Survey (e.g. Zabludoff et al., 1996), the 2dF Galaxy Redshift Survey (e.g.
Blake et al., 2004) and the SDSS (e.g. Hogg et al., 2006; Goto, 2007; Pawlik
et al., 2018), and at $z\sim 1$ such as the DEEP2 Galaxy Redshift Survey (e.g.
Yan et al., 2009). In addition, imaging observations have revealed that a
significant fraction of PSB galaxies present morphological disturbance in
their optical images signifying an ongoing or past merger, although the merger
fractions of PSB galaxies in different studies span a wide range depending on
the merger identification method, PSB sample selection and imaging data depth
and resolution (e.g. Couch et al., 1994; Dressler et al., 1994; Zabludoff et
al., 1996; Caldwell & Rose, 1997; Oemler et al., 1997; Couch et al., 1998;
Tran et al., 2004; Goto, 2005; Yang et al., 2008; Pracy et al., 2009; Trouille
et al., 2013; Pawlik et al., 2018; Sazonova et al., 2021; Wilkinson et al.,
2022; Verrico et al., 2022).

Studies of galaxy structure have found that PSB galaxies at intermediate-to-
high redshifts ($0.5<z<2.5$) are more compact than both star-forming and
quiescent galaxies (e.g. Newman et al., 2012; Yano et al., 2016; Almaini et
al., 2017; Maltby et al., 2018; Wu et al., 2018; Suess et al., 2020; Setton et
al., 2022). For instance, Setton et al. (2022) found the PSB galaxies at
$z\sim 0.7$ systematically lie $\sim 0.1$dex below the size-mass relation of
quiescent galaxies. For local galaxies, Chen et al. (2022) have recently
examined the size-relation of the SDSS-based PSB galaxy sample, finding the
PSB galaxies to be smaller than quiescent galaxies of similar mass and star
formation rate (SFR), especially in the stellar mass range of $\rm
10^{9.5}M_{\odot}\sim 10^{10.5}M_{\odot}$. These results are consistent with
the picture of fast quenching as induced by major mergers. It has been
suggested that, mergers may drive gas inward and centralized star formation,
thus leading to a more compact light distribution and resulting in both
quenching and structural transformation (e.g. Wellons et al., 2015; Zheng et
al., 2020).

Although many studies have provided strong evidence for a merger origin of PSB
galaxies, the fact that a considerable fraction of PSB galaxies show regular
morphologies appear to require other mechanisms in addition to mergers in
order to fully explain the PSB galaxy population. As pointed out in Sazonova
et al. (2021) and Wilkinson et al. (2022), however, features of morphology
disturbance fade on timescales of $\sim 200$Myr according to hydrodynamic
simulations, and so a possible merger origin for all the PSB galaxies cannot
be simply ruled out based on the merger fractions estimated from galaxy
images.

Previous studies mostly used either single-fiber or slitless spectroscopy
which probes only a small region in the galactic center of low-$z$ galaxies
(e.g. the central 1-2 kpc in SDSS galaxies). Integral field spectroscopy
available in recent years has allowed the PSB features to be detected in off-
center regions of many galaxies (e.g. Chen et al., 2019; Zheng et al., 2020;
Greene et al., 2021; Wu, 2021; Otter et al., 2022; Werle et al., 2022). Using
an early sample of the Mapping Nearby Galaxies at Apache Point Observatory
(MaNGA Bundy et al., 2015) survey, Chen et al. (2019) identified 360 PSB
galaxies, of which only 31 galaxies present the PSB feature in their center
(hereafter central PSB galaxies, or cPSB galaxies in short). In their sample,
37 galaxies show a ring-like PSB region (hereafter rPSB galaxies), and the PSB
regions of the remaining 292 galaxies have irregular shapes and locations.
Both cPSB and rPSB galaxies in their sample presented positive gradients in
$\textrm{D}_{n}(4000)$ (the spectral break at around 4000Å) indicative of
younger stellar populations in the inner regions. This result implied that the
star formation in PSB galaxies get shut down from outside in, opposite to the
“inside-out” quenching process as found for massive galaxies in the general
population (e.g. Li et al., 2015; Wang et al., 2018). The outside-in quenching
was also seen by Wu (2021) in a small sample of MaNGA-based PSB galaxies, and
by Werle et al. (2022) in the PSB galaxies at the centers of eight clusters
from $z\sim 0.3$ to $z\sim 0.4$ as observed with the Multi Unit Spectroscopic
Explorer (MUSE).

In this work, we make full use of the final data release of the MaNGA survey,
which provides integral field spectroscopy for $\sim$10,000 nearby galaxies,
to study both the size-mass relation and the recent star formation history
(SFH) of PSB galaxies in the local Universe. We consider not only the cPSB and
rPSB types of PSB galaxies as in previous MaNGA-based studies, but also those
with irregular PSB regions (hereafter iPSB galaxies), which dominate the PSB
galaxy population. We use three spectral indices to indicate the recent SFH of
the PSB regions: the equivalent width (EW) of the $\textrm{H}\alpha$ emission
line ($\textrm{EW}(\textrm{H}\alpha)$, indicator of ongoing star formation),
the EW of the H$\delta$ absorption line ($\textrm{EW}(\textrm{H}\delta_{A})$,
sensitive to young population formed in the past 0.1-1 Gyr; Bruzual & Charlot
2003), and $\textrm{D}_{n}(4000)$ (a good proxy for the luminosity-weighted
stellar age; Kauffmann et al. 2003). We make comparisons between each of the
PSB samples and a carefully-selected control sample, closely matched in
redshift, stellar mass and star formation rate. As we will show, the different
PSB samples behave differently in both the size-mass relation and the SFH
diagnostic parameters, indicating different evolutionary pathways for
different types of PSB galaxies.

This paper is organized as follows. In section 2, we describe the MaNGA data
and the identification of the PSB galaxies. In section 3, we present the
analysis of the size-mass relation and recent SFH. We discuss our results in
section 4 and summarize in section 5. Throughout the paper, we assume a
$\Lambda$CDM cosmology with $\Omega_{m}=0.3$ and $\Omega_{\Lambda}=0.7$, and a
Hubble constant of $\rm H_{0}=$70 km $\rm s^{-2}$ $\rm Mpc^{-1}$.

##  2 Data

###  2.1 MaNGA

MaNGA is one of the three major projects of the fourth-generation Sloan
Digital Sky Survey (SDSS-IV; Blanton et al., 2017). During its six-year
operation from July 2014 through August 2020, MaNGA has successfully obtained
high-quality integral field spectroscopy (IFS) for 10,010 galaxies with
redshift $0.01<z<0.15$ and stellar mass $5\times
10^{8}\textrm{M}_{\odot}\leq\textrm{M}_{\ast}\leq 3\times
10^{11}\textrm{M}_{\odot}$ (Bundy et al., 2015; Abdurro’uf et al., 2021).
MaNGA target galaxies are selected from the SDSS spectroscopic galaxy sample
and are included in three samples (Yan et al., 2016a; Wake et al., 2017):
Primary, Secondary and Color-Ehanced samples. Targets in the Primary and
Secondary samples are each observed out to 1.5 or 2.5 times effective radius
($R_{e}$), and the two samples together have a flat distribution of the
$K$-corrected $i-$band absolute magnitude ($M_{i}$). The Color-Enhanced sample
further selects low-mass red galaxies and high-mass blue galaxies on the plane
of NUV$-i$ color index versus $M_{i}$, which are not well sampled by the
Primary/Secondary samples (Wake et al., 2017).

The IFS data of MaNGA are obtained using 17 pluggable Integral Field Units
(IFUs) with a field of view ranging from $12^{\prime\prime}$ to
$32^{\prime\prime}$, and each IFU is a hexagonal-formatted fiber bundle made
from $2^{\prime\prime}$-core-diameter fibers with a $0.5^{\prime\prime}$ gap
between adjacent fibers, thus producing datacubes with an effective spatial
resolution of $\sim 2.5^{\prime\prime}$ (Drory et al., 2015; Law et al.,
2015). The fibers are fed to two dual-channel BOSS spectrographs (Smee et al.,
2013) at the 2.5-meter Sloan Telescope (Gunn et al., 2006), producing spectra
with a spectral resolution of $R\sim$2000 in the wavelength range from 3622 to
10354Å. A typical exposure time of 3 hours ensures a $r$-band continuum S/N of
4$\sim$8 (per-fiber per pixel) at 1$\sim$2 $R_{e}$ (Drory et al., 2015). MaNGA
raw data are reduced with the Data Reduction Pipeline (DRP; Law et al., 2016)
to produce sky-subtracted and spectrophotometrically-calibrated spectra for
scientific studies. Details of the flux calibration, MaNGA survey strategy,
and data quality tests can be found in Yan et al. (2016a, b). All the MaNGA
data products are released as part of the final data release of SDSS-IV
(Abdurro’uf et al., 2021).

Figure 1: Four examples of PSB galaxy. From left to right, the first
column:SDSS image of the galaxy with the magenta hexagonal field of view of
MaNGA; the second column: $\textrm{EW}(\textrm{H}\delta_{A})$ map of this
galaxy; the third column: $\textrm{EW}(\textrm{H}\alpha)$ map of this galaxy;
the forth column: $\textrm{D}_{n}(4000)$ map of this galaxy. Black boundaries
of PSB regions are over-plotted in all panels.

###  2.2 Identification of post-starburst galaxies

PSB galaxies are commonly identified by two spectral features jointly: strong
equivalent width (EW) of high-order Balmer absorption lines produced by
massive young stars, and weak/no H$\alpha$ emission indicative of weak/no
ongoing star formation. We identify our PSB galaxies by searching for
continuous regions in MaNGA datacubes that present both features. This is done
in two successive steps: we first select “H$\delta$-strong regions” in each
galaxy that have strong H$\delta$ absorption, from which we then identify PSB
regions by examining both H$\alpha$ emission and H$\delta$ absorption lines in
the stacked spectrum of each region. This procedure is similar to the
procedure of identifying Wolf-Rayet galaxies in Liang et al. (2020) where the
authors firstly search for Hii regions in the MaNGA datacubes and then examine
the stacked spectra of those regions to further identify Wolf-Rayet regions.
The reason to use stacked spectra rather than original spaxels is two-fold. On
the one hand, as shown in Liang et al. (2020), by stacking the spectra of all
the original spaxels in a region, we can significantly increase the spectral
S/N, thus ensuring robust identification for regions with relatively weak
spectral features. On the other hand, the limited spatial resolution of MaNGA
($\sim 2.5^{\prime\prime}$, or $\sim 1.5$kpc at the median redshift
$\left<z\right>\sim 0.03$ of MaNGA) means that our data cannot resolve
individual PSB regions, which are smaller than $\sim 100$pc if assumed to have
sizes comparable to Hii regions. Therefore, following Liang et al. (2020), we
adopt a maximum radius for our PSB regions to be
$r_{p}^{\textrm{max}}=\textrm{max}\\{1.5^{\prime\prime},500\textrm{pc}\\}$,
which is comparable to half of the MaNGA resolution, and is a trade-off
between higher S/Ns from stacking more spectra and stronger dilution to PSB
features.

In practice, for a given galaxy we first perform full spectral fitting to the
MaNGA spectrum of every spaxel in the datacube using the spectral fitting code
described in detail in Li et al. (2020). The code uses stellar templates
constructed by a Principle Component Analysis of the single stellar population
(SSP) models of Bruzual & Charlot (2003) and assumes a Chabrier initial mass
function (Chabrier, 2003). We measure the EW of H$\delta$ absorption line
$\textrm{EW}(\textrm{H}\delta_{A})$ from the best-fit model spectrum of the
stellar component, and the EW of H$\alpha$ emission line
$\textrm{EW}(\textrm{H}\alpha)$ from the starlight-subtracted spectrum. We
then search for H$\delta$-strong regions on the two-dimensional map of
$\textrm{EW}(\textrm{H}\delta_{A})$. For this purpose, we have modified
HIIEXPLORER, a pipeline developed by Sánchez et al. (2012) for the
identification of Hii regions on maps of H$\alpha$ surface density. The
modified code starts by picking up the spaxel with the highest
$\textrm{EW}(\textrm{H}\delta_{A})$ ($>3$Å) over the map as the center of a
potential “H$\delta$-strong region”. Adjacent spaxels in the vicinity of the
central spaxel are appended to the region if their distances from the central
spaxel are less than $r_{p}^{\textrm{max}}$. The region is removed from the
map and the above procedure is repeatedly applied to the remaining map until
every spaxel is assigned to a region, or rejected.

For each of the H$\delta$-strong regions, we stack the spectra of its spaxels
in the same way as in Liang et al. (2020). In short, the spaxel spectra are
corrected to the rest frame using both the galaxy redshift and the stellar
velocity of each spaxel relative to the galaxy, and are weighted by the
inverse variance of flux errors provided by the MaNGA DRP (Law et al., 2016)
to produce a stacked spectrum of the region. Flux errors of the stacked
spectrum are firstly calculated by the standard formula in weighted mean
statistics, and then corrected for the effect of covariance following the
formula in Law et al. (2016, see their Figure 16). We ignore regions with the
stacked spectrum of S/N$<10$ in what follows. The code of Li et al. (2020) is
used again to fit each of the stacked spectra (with S/N$>10$), from which we
measure all emission line parameters and stellar indices that may be used in
our work. We identify PSB regions from the H$\delta$-strong regions, following
the same selection criteria as in Chen et al. (2019, see their §2.3): (i)
EW(H$\delta_{A}$)$>$ 3Å, (ii) EW(H$\alpha$) $<$ 10Å, and (iii)
$\log_{10}$[EW(H$\alpha$)]$<$ 0.23 $\times$ EW(H$\delta_{A}$) $-0.46$. We note
that we have adopted selection criteria from other studies (e.g. Goto et al.,
2008; Chen et al., 2022) and repeated the whole analysis, finding our
scientific conclusions to be robust to the different selection criteria.

A galaxy is identified to be a PSB galaxy if it contains one or more PSB
regions. In total, we have identified 3204 PSB regions, distributed in 489 PSB
galaxies. Following Chen et al. (2019), we visually examine the maps of
EW(H$\delta_{A}$) and EW(H$\alpha$) and classify our PSB galaxies into three
types according to the location of their PSB regions: (i) cPSB with the PSB
regions located at the galactic center, (ii) rPSB with a ring-like
distribution of multiple PSB regions, and (iii) iPSB with the PSB regions
distributed in an irregular manner. The numbers of the three types of galaxies
are 310 (iPSB), 85 (rPSB) and 94 (cPSB). Thus the majority of PSB galaxies are
iPSB, which have been rarely studied, however. In Figure 1 we show four
example PSB galaxies in our sample: two iPSB galaxies in the top two rows (one
star-forming galaxy and one quiescent galaxy according to their global star
formation rate), followed by a rPSB galaxy and a cPSB galaxy. The four panels
(from left to right) show the SDSS $gri$ composite image and maps of
$\textrm{D}_{n}(4000)$(the narrow version of the spectral break at around
4000Å, as originally defined in Balogh et al. 1999),
$\textrm{EW}(\textrm{H}\delta_{A})$ and $\textrm{EW}(\textrm{H}\alpha)$. The
latter three parameters are sensitive to young stellar populations of
different ages, thus can be used as good diagnostics for the recent star
formation history (SFH) of given region (e.g. Li et al., 2015; Wang et al.,
2018). The different types of PSB galaxies differ from each other in these
diagnostic parameters, indicating diverse SFHs in PSB galaxies. We will study
the recent SFHs of our PSB galaxies in the next section.

##  3 Results

###  3.1 Global properties of PSB galaxies

Figure 2: $Left$ $panel$: cPSB(blue dots), rPSB(green circles) and iPSB(yellow
crossed) are plotted on the stellar mass versus SFR diagram. The black contour
represents the MaNGA parent sample. The sample selection effects has been
corrected with $1/V_{max}$ weighting method. More details can be found in Wake
et al. (2017). The red solid line is the empirical divided line of SFG and QG.
$Middle$ $panel$: Same as left panel, but showing stellar mass versus NUV-r
color. The two horizontal dashed lines indicate NUV-r = 4 and 5. $Right$
$panel$: Same as left panel, but showing stellar mass versus $r$-band
effective radius.

Figure 2 examines the global properties of our PSB galaxy sample by displaying
all the PSB galaxies in three diagrams: the SFR-mass diagram (left), the
color-mass diagram (middle) and the size-mass relation (right), with different
colors/symbols for the three PSB types. For comparison, the distribution of
the parent MaNGA sample is plotted as black contours, for which we have
corrected the effect of sample incompleteness using the
$1/V_{\textrm{max}}$-weighting scheme following Wake et al. (2017). Stellar
masses ($M_{\ast}$) and star formation rates (SFR) of our galaxies are taken
from the GSWLC catalog111https://salims.pages.iu.edu/gswlc/ (Salim et al.,
2016), and effective radii ($R_{e}$) are provided in the NSA, measured through
two-dimensional Sersic profile fits to SDSS $r$-band images (Blanton et al.,
2011). The NUV$-r$ color indices, from NSA catalog, are based on the NUV image
from GALEX and the $r$-band image from SDSS. The red solid line in the SFR-
mass diagram is the empirical divider from Woo et al. (2013),
$\log_{10}$SFR($\rm M_{\odot}$ ${\rm yr}^{-1}$) = 0.64 $\times$ log $\rm
M_{*}(M_{\odot})-7.22$, which separates star-forming (SF) galaxies from
quiescent (Q) galaxies. The two horizontal dashed lines in the color-mass
diagram represent the commonly-used cuts of NUV$-r$=4 and NUV$-r$=5 which
divide the galaxies into red, green and blue populations. The dashed lines in
blue and red in the right panel are linear fits to the
$R_{e}$-$\rm\log_{10}M_{\ast}$ relation of star-forming galaxies and quiescent
galaxies, as selected from the parent MaNGA sample on the SFR-mass diagram.

Overall, to our surprise, the PSB galaxies in our sample are rarely red or
quenched. Rather, they are mostly blue or green with NUV$-r<5$ in the color-
mass diagram, and are mostly located in the star-forming sequence or the
transition region above the quiescent sequence in the SFR-mass diagram. This
is in contrast to the traditional view of PSB galaxies which have long been
assumed to be quenched after having experienced a recent starburst. When
divided into the three types, the PSB galaxies present different distributions
in these diagrams. First, the majority of the cPSB galaxies are found in the
transition region between red/blue or SF/Q populations, thus consistent with
the traditional expectation. Quantitatively, out of the 94 cPSB galaxies in
our sample, 48 (51.1%) fall in the green valley with $4<$NUV$-r<5$, and 27
(28.7%) are located just below the star-forming sequence with only a few
scattering to the sequence of quiescent galaxies. This result is similar to
previous findings from SDSS-based studies where the PSB galaxies were
identified based on spectroscopy of the central 1-2 kpc (e.g. Wong et al.,
2012; Chen et al., 2022), and it is broadly consistent with the standard
conjecture that PSB galaxies are in the transition phase between star-forming
and quenched galaxies. On the other hand, however, the spatially resolved
spectroscopy from MaNGA reveals that more than two third of the cPSB galaxies
are still globally star-forming and blue, although the star formation in their
central region has recently shutdown. Obviously, even when limited to galactic
centers, a significant fraction of PSB galaxies are not fully quenched.

Next, different from cPSB galaxies, the rPSB galaxies are mostly located in
the SF sequence and the blue cloud, with only 3.5% (3/85) falling below the SF
sequence and 25.9% (22/85) having NUV$-r>4$. In an earlier MaNGA-based study
by Chen et al. (2019), cPSB galaxies are found in the transition region in the
plane of $\textrm{D}_{n}(4000)$ versus $\rm\log_{10}M_{\ast}$, and rPSB
galaxies fall slightly below the cPSB population but above the sequence of the
young galaxy population (see the bottom-left panel of their Figure 5). Our
result is not inconsistent with theirs, considering that the
$\textrm{D}_{n}(4000)$ examined in their work, the SFR we used and NUV$-r$
examined here are sensitive to stellar populations formed at different times.
We will examine the $\textrm{D}_{n}(4000)$ of our galaxies in subsection 3.3.
Finally, different from both cPSB and rPSB galaxies which are limited to
narrow ranges of SFR and NUV$-r$, the iPSB galaxies cover a wide range in both
parameters, though with a relatively large fraction falling in the star-
forming sequence ($269/310=86.8\%$) and the blue cloud with NUV$-r<4$
($235/310=75.8\%$).

As estimated by applying the SED fitting technique to multiband photometry,
the SFRs from GSWLC are averaged over the past 30-100 Myr and so they may be
higher than the current SFRs for PSB galaxies for which the SFRs are expected
to have rapidly declined. We have attempted to estimate the global SFRs for
our galaxies using the total H$\alpha$ luminosity within 1.5$Re$ from the
MaNGA data and compared the measurements with those from GSWLC. This
comparison has to be limited to a fraction of the MaNGA galaxies that have
substantially high SNR in most of the spaxels. Basically, we found consistent
SFR measurements with the GSWLC with no systematics over the full SFR range,
though with a median offset of 0.11 dex in $\log_{10}{\rm SFR}$ due to the
limited spatial coverage of the MaNGA datacubes. More importantly, the PSB
galaxies show similiar results to the parent MaNGA sample in this comparison,
demonstrating that the different timescales for SFR between SEDs and H$\alpha$
luminosities make little difference in our analyses of the PSB galaxies. This
can be understood from the fact that, PSB regions happen only in parts of the
host galaxies, thus contributing only to a fraction of the global SFR.

In the size-mass diagram as shown in the rightmost panel of Figure 2, the
parent sample shows a broad distribution, and at fixed mass the populations
with larger and smaller sizes roughly correspond to the star-forming and
quiescent galaxy populations. This result echoes early studies of the size-
mass relation of local galaxies (e.g. Shen et al., 2003), where galaxies with
early-type and late-type morphologies showed distinct size-mass relations. As
one can see, the PSB galaxies in our sample cover the full area of the parent
MaNGA sample except the regime of smallest $R_{e}$ at fixed stellar mass,
which are dominated by quiescent galaxies with smaller-than-average sizes.
This is consistent with the left two diagrams where the PSB sample as a whole
lacks the most quiescent or the reddest galaxies. When divided into different
types, cPSB galaxies with intermediate masses
($9.5\lesssim$$\log_{10}(\textrm{M}_{\ast}/\textrm{M}_{\odot})$$\lesssim
10.5$) appear to be smaller than other types of PSB galaxies which follow more
closely the parent sample. At lower masses, all types of PSB galaxies show
similar distributions to the parent sample. We will further study the size-
mass relation for the different types of PSB galaxies in the following
subsection.

Figure 3: Size-mass relation for PSB galaxies and control samples. Panels from
left to right are four PSB subsamples:iPSB-Q(purple), iPSB-SF(orange),
rPSB(brown) and cPSB(black). Panels from top to bottom show $R_{e}$
measurements based on SDSS $g$-band, $r-$band and $i-$band image. The dot
symbols show the distribution of individual PSB galaxies. The median values in
different stellar mass bins are plotted. Error bar indicates the Poisson
error. The median values of control SFR samples are also presented in each
panel. The shadow regions denote the Poisson errors. The dashed line is the
best fit for the size–mass relation of MaNGA galaxies in formula of log
$R_{e}$(kpc) = k $\times$ log $\rm M_{*}$($\rm M_{\odot}$) + b.  Figure 4: The
distributions of log $R_{e}$(kpc) in different stellar mass bins for
MaNGA(dashed line) and NSA volume-limited sample(solid line). Error bars are
Poisson counting errors. Sample selection effects with the $1/V_{max}$
weighting method have been considered during our calculation for the MaNGA
sample.

###  3.2 The size-mass relation

In Figure 3 we show the size-mass relation again, but for the different types
of PSB galaxies separately (panels from left to right) and for sizes measured
in three different photometric bands (panels from top to bottom). As we have
seen from Figure 2, the size-mass relation strongly depends on the global star
formation rate. Considering the wide coverage of the iPSB galaxies in the SFR-
mass diagram, we divide them into two subsets according to their location in
the diagram. This division results in 269 “iPSB-SF” galaxies located above the
dividing line (solid red line in the left panel of Figure 2) and 41 “iPSB-Q”
galaxies located below that line. For cPSB and rPSB samples we don’t attempt
to further select subsamples considering both the limited sample sizes and the
fact that they occupy relatively narrow ranges in SFR and color at fixed
stellar mass. To take into account the dependence on mass and SFR and to make
fair comparisons with normal galaxies, for each of the PSB samples we follow
Chen et al. (2022) to select a “control” sample of galaxies from the MaNGA
sample that is closely matched with the PSB galaxies in redshift, $M_{\ast}$
and SFR. In practice, we require the control sample to contain at most three
nearest-matched galaxies for each PSB galaxy, with matching tolerances of
$|\Delta z|<0.005$, $|\Delta\rm\log_{10}M_{\ast}|<0.05$ and
$|\Delta\rm\log_{10}SFR|<0.05$. This gives rise to sufficient matches for 80%
of the PSB galaxies in our sample. For the remaining 20% galaxies, we relax
the tolerances to be  $|\Delta z|<0.01$, $|\Delta\rm\log_{10}M_{\ast}|<0.2$
and $|\Delta\rm\log_{10}SFR|<0.2$ in order to have at least one match for each
PSB galaxy.

In Figure 3, panels from left to right compare the size-mass relation for PSB
galaxies of type iPSB-SF, iPSB-Q, rPSB and cPSB with that of the corresponding
control samples. Panels from top to bottom show the results for $R_{e}$
measured in SDSS $g$, $r$ and $i$ band. For PSB samples, we show both
individual galaxies in each sample (as the colored dots) and the median and
$1\sigma$ scatter (as the big crosses), while for the control samples we only
show the median and scatter for clarity (as the cyan band). The dashed lines
in blue and red present the result for the star-forming and quiescent galaxies
in the parent sample, and are repeated in every panel for reference. We find
that, when divided by the PSB type, the PSB galaxies in our sample show
different size-mass relations. The iPSB-SF and iPSB-Q types respectively
follow the relations of the star-forming population (the blue dashed line in
each panel) and the quiescent population (the red dashed line in each panel),
while the rPSB type appears to fall in between. The cPSB galaxies follow the
star-forming population at both high and low masses, but have relatively
smaller sizes at intermediate masses
($9.5\lesssim$$\log_{10}(\textrm{M}_{\ast}/\textrm{M}_{\odot})$$\lesssim
10.5$) which are comparable to the sizes of the quiescent population. When
compared to control galaxies selected from the parent MaNGA sample, the iPSB-
SF, iPSB-Q and rPSB samples closely follow the relations of their control
samples, while the cPSB galaxies with intermediate masses have a median size
that is systematically smaller than that of the control sample. This result of
the cPSB sample is well consistent with Chen et al. (2022, see their Figure
4)222We notice that the stellar masses and SFRs used in Chen et al. (2022)
were from the MPA-JHU SDSS catalog. We have repeated our analysis using the
same catalog and find similar results., where the SDSS-based PSB galaxies
(thus similar to our cPSB galaxies in definition) are found to be smaller than
control galaxies, also at
$9.5<$$\log_{10}(\textrm{M}_{\ast}/\textrm{M}_{\odot})$$<10.5$.

Although the MaNGA target galaxies are selected only by redshift and $i$-band
luminosity, the limited IFU sizes and the requirement for the galaxies to be
covered by the IFUs out to a fixed radius (1.5$R_{e}$ or 2.5$R_{e}$) may have
introduced size-related biases in the MaNGA sample. In Figure 4 we check this
out by comparing the distribution of $R_{e}$ of the MaNGA galaxies in narrow
bins of $\rm M_{\ast}$ with the distribution of galaxies in a volume-limited
sample, which is selected from NSA to have $0.01<z<0.08$ and $\rm
M_{\ast}>10^{9}M_{\odot}$. For MaNGA galaxies, the distributions are corrected
for sample incompleteness with the $1/V_{\textrm{max}}$-weighting method as
mentioned above. At all masses, we see no significant differences in the size
distributions, indicating that the MaNGA sample is unbiased in terms of galaxy
size, and so our results on the size-mass relations presented above should be
statistically robust and reliable. In addition, we have constructed another
control sample from the NSA using the same tolerances, and we show the size-
mass relations of this sample in Figure 3 as grey-shaded region. As can be
seen, the two control samples agree well with each other, indicating again
that the MaNGA sample provides unbiased results. Finally, size measurements
from different bands lead to very similar size-mass relations for any given
sample as can be seen in Figure 3, demonstrating that our results are robust
to the adopted photometric band.

Figure 5: $Top$ $row$: galaxies are plotted on the plane of central
$\textrm{D}_{n}(4000)$ versus the $\textrm{D}_{n}(4000)$ at $R_{e}$. Panels
from left to right are four PSB subsamples and corresponding control samples.
The colors of symbols are similar to Figure 3. iPSB-Q(cPSB) galaxies in
different $f_{q}$ ranges are highlighted by solid dots. The black solid line
in each panel represents the 1:1 relation. $Middle$ $row$: same as the top
row, but showing the $\textrm{EW}(\textrm{H}\delta_{A})$ result. $Bottom$
$row$: same as the top row, but showing the log10EW(H$\alpha$) result. Figure
6: Distributions in the plane of slope index versus stellar mass. Panels from
left to right are different diagnostics of recent SFH: $\textrm{D}_{n}(4000)$,
$\textrm{EW}(\textrm{H}\delta_{A})$, and $\textrm{EW}(\textrm{H}\alpha)$.
Panels from top to bottom are different PSB subsamples and corresponding
control SFR samples. The colors of symbols are similar to Figure 5. On the
left side of each panel, we also show the cumulative distribution of the slope
index.

###  3.3 Recent star formation histories

Following Li et al. (2015) and Wang et al. (2018), we use
$\textrm{D}_{n}(4000)$, $\textrm{EW}(\textrm{H}\delta_{A})$ and
$\textrm{EW}(\textrm{H}\alpha)$ to indicate the recent star formation history
(SFH) of the PSB galaxies and the control galaxies. It is well known that
$\textrm{D}_{n}(4000)$ and $\textrm{EW}(\textrm{H}\delta_{A})$ are sensitive
to young stellar populations formed in the past 1-2 Gyr and 0.1-1 Gyr,
respectively, and that $\textrm{EW}(\textrm{H}\alpha)$ indicates the ongoing
star formation. Therefore, the three parameters combine to provide a powerful
diagnostic of the recent SFH. By comparing the three parameters in the center
and outskirt of MaNGA galaxies, Li et al. (2015) and Wang et al. (2018) found
massive galaxies with $\rm M_{\ast}\gtrsim 10^{10}M_{\odot}$ to present
significant gradients in these parameters, indicative of an “inside-out”
process for the star formation cessation, while less massive galaxies show
weak or no gradients. In Figure 5, we compare the three parameters as measured
at $R_{e}$ and in the central region for the four types of PSB galaxies.
Panels from left to right correspond to samples of iPSB-SF, iPSB-Q, rPSB and
cPSB, and panels from top to bottom are the results for
$\textrm{D}_{n}(4000)$, $\textrm{EW}(\textrm{H}\delta_{A})$ and
$\textrm{EW}(\textrm{H}\alpha)$. The corresponding control galaxies are also
shown in each panel for comparison.

Overall, the different types of PSB galaxies behave differently. Most of the
iPSB-SF galaxies present no or weak gradients in all the three parameters,
with the central and outer regions showing similar values in all three
parameters, which are consistent with the global star-forming status of the
galaxies. Differently, most of the iPSB-Q galaxies present significant
gradients in $\textrm{D}_{n}(4000)$ and $\textrm{EW}(\textrm{H}\delta_{A})$,
with larger $\textrm{D}_{n}(4000)$ and smaller
$\textrm{EW}(\textrm{H}\delta_{A})$ (thus older stellar populations) in their
center than in the outskirt, and their $\textrm{EW}(\textrm{H}\alpha)$ are
comparably low ($<10$Å) in both central and outer regions. This result is
consistent with the global quiescence of the iPSB-Q galaxies, and also
consistent with the inside-out quenching picture as found previously for the
general population of massive galaxies, in which the star formation cessation
occurs first in the galactic center before extending to larger radii. We note
that a small fraction of the iPSB-SF galaxies with relatively large
$\textrm{D}_{n}(4000)$ and relatively small
$\textrm{EW}(\textrm{H}\delta_{A})$ appear to deviate from the 1:1 relations,
with the central region showing larger $\textrm{D}_{n}(4000)$ and smaller
$\textrm{EW}(\textrm{H}\delta_{A})$ than the outskirt. Although still forming
stars globally, these galaxies are likely to have just started the star
formation cessation process, expected to further deviate from the 1:1 relation
and follow up the iPSB-Q galaxies in the future. Eventually, both iPSB-SF and
iPSB-Q galaxies will be fully quiescent, moving back to the 1:1 relation but
with largest $\textrm{D}_{n}(4000)$ and smallest
$\textrm{EW}(\textrm{H}\delta_{A})$ and $\textrm{EW}(\textrm{H}\alpha)$. This
result implies that the two types of iPSB galaxies follow a similar
evolutionary pathway (i.e. the inside-out quenching process), but they are
currently at different stages.

The rPSB and cPSB types appear to follow an evolutionary pathway different
from the iPSB galaxies. In most cases, rPSB galaxies have small
$\textrm{D}_{n}(4000)$ ($\lesssim 1.6$) and large
$\textrm{EW}(\textrm{H}\delta_{A})$ ($\gtrsim 3$Å) in both central and outer
regions, as well as large $\textrm{EW}(\textrm{H}\alpha)$ ($\gtrsim 10$Å) in
the central region. This is consistent with the fact that this type of PSB
galaxies mostly fall in the star-forming sequence in the SFR-mass diagram (see
Figure 2). It is interesting that rPSB galaxies show smaller
$\textrm{D}_{n}(4000)$ and larger $\textrm{EW}(\textrm{H}\alpha)$ in the
center than in the outskirt, an effect that is opposite to any other type of
galaxies. This indicates older populations and weaker star formation in the
outskirt, and thus implies an “outside-in” quenching mode, if we assume these
galaxies are starting to cease star formation as indicated by the presence of
PSB regions in their outskirt. cPSB galaxies have small $\textrm{D}_{n}(4000)$
($\lesssim 1.6$) and small $\textrm{EW}(\textrm{H}\alpha)$ ($\lesssim 10$Å) in
both central and outer regions, implying that these galaxies have ceased star
formation in the recent past (within 1-2 Gyr). Their central regions have
larger $\textrm{EW}(\textrm{H}\delta_{A})$ ($\gtrsim 3$Å) than the outer
regions, implying that the star formation cessation occurs later in the
central region than in the outskirt. These behaviors are also consistent with
the “outside-in” quenching picture. Given the global star-forming status of
the rPSB galaxies and the quiescent status of the cPSB galaxies, it is natural
to conclude that the two types of PSB galaxies follow the outside-in mode of
quenching, but are currently at different stages.

The distribution of the control galaxies varies from panel to panel, which can
be understood by the dependence on stellar mass as found in Wang et al.
(2018). When compared to the control samples, both iPSB-SF and iPSB-Q galaxies
are similar to (though not exactly the same as) the corresponding control
galaxies, while rPSB and cPSB galaxies are quite different from their control
samples. This is more clearly seen in Figure 6, where we plot the gradient of
the three diagnostic parameters as a function of
$\log_{10}(\textrm{M}_{\ast}/\textrm{M}_{\odot})$ for both the PSB samples and
the control samples. The gradient of a parameter is defined as the difference
of its value at $R_{e}$ from that in the center. In the additional panel at
the right hand, we also show the cumulative distributions of the diagnostic
parameters. As can be seen, for a given parameter all the control samples show
similar trends between the parameter gradient and the stellar mass, with a
weak dependence on the type of the PSB galaxies. Consistent with Wang et al.
(2018), control galaxies at $\textrm{M}_{\ast}$$\gtrsim 10^{10}M_{\odot}$
present significant gradients in $\textrm{D}_{n}(4000)$ and
$\textrm{EW}(\textrm{H}\delta_{A})$, and no/weak gradients at lower masses.
Compared to the control samples, both iPSB-SF and iPSB-Q galaxies show high
similarities. In contrast, both rPSB and cPSB galaxies show different
gradients in all parameters except $\textrm{EW}(\textrm{H}\alpha)$ in case of
the cPSB sample. These results suggest again that the PSB galaxies in our
sample can be divided into two broad categories according to their
evolutionary pathway: (i) iPSB-SF and iPSB-Q to follow the inside-out
quenching mode as found for the majority of the general population galaxies,
and (ii) rPSB and cPSB to follow the outside-in quenching mode.

###  3.4 The fraction of PSB regions

Figure 7: Normalized distributions of $f_{\rm PSB}(1.5R_{e})$ for the four
types of PSB samples. The 1/$V_{max}$-weighting scheme is performed to correct
for sample incompleteness. The red vertical dashed line indicates $f_{\rm
PSB}(1.5R_{e})=0.5$.

In this subsection, we further consider the potential dependence of the size-
mass relation and recent SFH on the fraction of PSB regions in our galaxies.
The fraction of PSB regions, $f_{\rm PSB}(R)$, is defined by the mass-weighted
fraction of spaxels that belong to the PSB regions within a given galactic
radius $R$,

$f_{\rm PSB}(R)=\frac{\sum_{r<R}m_{*,i}\times f_{i}}{\sum_{r<R}m_{*,i}}$ (1)

Here $m_{*,i}$ is the stellar mass of the $i$th spaxel, $f_{i}=1$ or $0$
depending on whether the $i$th spaxel belongs to any PSB region, and
$R=1.5R_{e}$. Figure 7 shows the histograms of $f_{\rm PSB}(1.5R_{e})$ for the
different PSB samples. We see that both iPSB and rPSB galaxies exclusively
have relatively small fractions of PSB regions with $f_{\rm
PSB}(1.5R_{e})<0.5$, while the cPSB galaxies span a full range of $f_{\rm
PSB}(1.5R_{e})$. We find 23.3% of the cPSB sample to have $f_{\rm
PSB}(1.5R_{e})>0.5$, after the $1/V_{\rm max}$-weighting scheme is applied to
correct for sample incompleteness.

Figure 8: Size-mass relation for cPSB galaxies with $f_{\rm
PSB}(1.5R_{e})<0.5$ (left panel) and those with $f_{\rm PSB}(1.5R_{e})>0.5$
(right panel), as well as the corresponding control samples. Figure 9: Same as
Figure 6, but for cPSB galaxies with $f_{\rm PSB}(1.5R_{e})<0.5$ (upper
panels) and those with $f_{\rm PSB}(1.5R_{e})>0.5$ (lower panel), separately.

We divide the cPSB sample into two subsamples at $f_{\rm PSB}(1.5R_{e})=0.5$,
and for each subsample we repeat the analysis of the size-mass relation and
recent SFH in the same way as above. Figure 8 shows the size-mass relations,
and Figure 9 shows the slope indices of the three SFH diagnostics as a
function of stellar mass. Overall, the size-mass relations and recent SFHs of
the two subsamples are similar to what we found above for the cPSB galaxies as
a whole, implying that our main results are not dependent on the PSB fraction
of the galaxies. It is interesting to note that the cPSB galaxies with $f_{\rm
PSB}(1.5R_{e})>0.5$ have higher masses as well as smaller sizes at fixed mass
when compared to those with $f_{\rm PSB}(1.5R_{e})<0.5$.

##  4 Discussion

###  4.1 Implications of the size-mass relation

A number of previous studies have investigated the structure and/or the size-
mass relation of PSB galaxies at different redshifts, and consistently
concluded that the PSB galaxies are more compact relative to coeval star-
forming and quiescent galaxies (e.g. Whitaker et al., 2012; Yano et al., 2016;
Wu et al., 2018, 2020; Chen et al., 2022; Setton et al., 2022). For instance,
using the NEWFIRM Medium-Band Survey (NMBS), Whitaker et al. (2012) found a
large population of PSB galaxies at $1<z<2$, which had smaller sizes than
older galaxies at those redshifts. With the same survey, Yano et al. (2016)
examined the structure of galaxies at $0.5<z<2$ with different spectral types
as classified using the UV-to-NIR spectral energy distributions (SEDs), and
found the PSB galaxies at $z>1.5$ to be significantly smaller than any other
types of galaxies at the same redshift. Wu et al. (2018) analyzed the
spectroscopically selected PSB galaxies at $z\sim 0.7$ from the LEGA-C survey,
and found these galaxies are much smaller than expected from the global
relation of normal quiescent galaxies. A similar result has been recently
obtained by Setton et al. (2022) for the PSB galaxies from the SQuIGGLE
sample, also at $z\sim 0.7$, which lie $\sim$0.1dex below the size-mass
relation of quiescent galaxies. For the local universe, Chen et al. (2022)
have recently studied the size-mass relation of the PSB galaxies in the SDSS,
which are similar to the cPSB galaxies in our sample in the sense that the PSB
feature is limited to the central 1-2 kpc of these galaxies. Consistent with
their result, our cPSB galaxies at intermediate masses
($9.5\lesssim$$\log_{10}(\textrm{M}_{\ast}/\textrm{M}_{\odot})$$\lesssim
10.5$) present smaller half-light radii than control galaxies of similar mass
and SFR. The smaller size of the PSB galaxies at fixed mass as consistently
found in previous studies and for different redshifts have been usually
attributed to mergers or other violent events, which can drive gas inward and
trigger or enhance the star formation in the inner region of galaxies.
Obviously, this is consistent with galaxy mergers as the origin of PSB
galaxies, as discussed in section 1.

Thanks to the spatially resolved spectroscopy from MaNGA, our sample
additionally includes other types of PSB galaxies in which the PSB regions are
located beyond the galactic center. We find the different types of PSB
galaxies to show different size-mass relations. In particular, the smaller
size at fixed mass as previously found for intermediate-mass galaxies holds
only for cPSB galaxies in our sample. Differently, the iPSB and rPSB closely
follow the size-mass relation of the control galaxies. Our result of the size-
mass relation further complicates the evolution picture of PSB galaxies, which
cannot be purely attributed to galaxy mergers. Rather, PSB galaxies as a whole
must follow diverse evolutionary pathways, depending on both stellar mass and
the location of the PSB regions.

###  4.2 Two broad categories of evolution pathways

PSB galaxies are widely thought to be in a transition phase between star-
forming galaxies and quiescent galaxies. The paucity of both the “green-
valley” galaxies and the PSB galaxies imply that the time-scale of the
transition phase must be very short. However, the importance of the PSB phase
in galaxy evolution has been questioned by some observational studies. For
instance, the large reservoirs of cold gas detected in many low-$z$ PSB
galaxies (e.g. Chang et al., 2001; Buyle et al., 2006; Zwaan et al., 2013;
French et al., 2015) are in conflict with the gas-poor nature of quenched
galaxies, and the low incidence of PSB galaxies in some galaxy clusters at
intermediate redshifts is insufficient to explain the quiescent galaxy
population in those clusters (e.g. De Lucia et al., 2009; Dressler et al.,
2013). Dressler et al. (2013) suggested that the PSB galaxies in both clusters
and the field are already quiescent, but passing through a brief PSB phase of
the evolutionary cycle within the quiescent sequence, which could be triggered
by tidal interactions or mergers with low-mass gas-rich companions. More
recently, in a comprehensive study of the PSB galaxies in the SDSS, Pawlik et
al. (2018) found evidence for three different pathways of galaxies that can
lead to a PSB phase, all triggered by violent events such as galaxy mergers:
(1) gas-rich major mergers causing the transformation of blue-cloud galaxies
(via the PSB phase) to the red sequence, accounting for 60-70% of the PSB
galaxies in their sample, (2) less violent events causing the cyclic evolution
of low-mass star-forming galaxies within the blue cloud (the blue-PSB-blue
cycle), and (3) less violent events causing the cyclic evolution of massive
quiescent galaxies within the red sequence (the red-PSB-red cycle). The three
different pathways of PSB galaxies and their merger origin are nicely
illustrated by Pawlik et al. (2019) based on the Evolution and Assembly of
GaLaxies and their Environments (EAGLE) cosmological simulation. It is
interesting that the same simulation additionally presents a fourth pathway of
a PSB phase, in which the rapid decline in the star formation of a galaxy is
caused by environmental effects such as ram-pressure stripping, without
leading to morphological transformation (Pawlik et al., 2019).

Since the PSB galaxies in Pawlik et al. (2018) were selected with the SDSS
single-fiber spectroscopy, the PSB feature is limited to the central 1-2 kpc
of their galaxies, similar to the case of cPSB galaxies in our work.
Therefore, the three evolutionary pathways suggested by those authors should
be relevant only to the cPSB type. Although the situation becomes more complex
when the other types are included, our results indicate that the PSB galaxies
as a whole can be divided into two broad categories according to their recent
SFH. The first category consists of the iPSB-SF and iPSB-Q types, which
present high similarities to the corresponding control samples in all the
three SFH diagnostic parameters, likely to follow an inside-out quenching
process as previously found for the general galaxy population. The other
category consists of the cPSB and rPSB types of galaxies, which present
younger stellar populations in the center than in the outskirt, thus likely to
follow an outside-in quenching process. The three evolutionary pathways
suggested by Pawlik et al. (2018) should be applied only to the cPSB type, and
so they all belong to the second category. The limited size of our sample
doesn’t allow us to distinguish the three pathways of the cPSB type as done in
Pawlik et al. (2018), but one can well expect so if a sufficiently large
sample becomes available considering the (almost) same selection criteria of
our cPSB galaxies and the SDSS-based PSB galaxies.

We note that, when discussing the quenching pathways we haven’t considered the
quenching of an already quenched but recently “rejuvenated” galaxy (e.g.
caused by a merger-induced central starburst), which is not the same as the
original quenching prior to rejuvenation. For a given spaxel, to distinguish
these two quenching processes would need careful stellar population synthesis
modeling. For a galaxy in which the onset of quenching varies radially as
indicated by radial gradients of the recent SFH in relatively massive galaxies
(e.g. Wang et al., 2018), the original quenching and the quenching after
rejuvenation can be distinguished according to the radial variation of the
three SFH diagnostic parameters. For instance, we can certainly rule out the
case of quenching after a central starburst for most of our galaxies. In this
case, one would expect small $\textrm{D}_{n}(4000)$ in the central region due
to the recent starburst as well as large $\textrm{D}_{n}(4000)$ in the
originally quenched outerskirt. As can be seen from the first row of Figure 5,
however, we find almost no spaxels to be located in the upper-left corner of
the $\textrm{D}_{n}(4000)$ diagram for all the PSB types. All the galaxies are
found at either the lower-left corner with relatively low
$\textrm{D}_{n}(4000)$ or the upper-right corner (below the 1:1 relation) with
large $\textrm{D}_{n}(4000)$, in both the center and the outskirt. This fact
suggests the original quenching to be the dominant quenching process for the
galaxies in our sample. One exception may happen if the central starburst
occurs very recently. In this case, the $\textrm{D}_{n}(4000)$ in the central
region doesn’t have time to substantially decrease, and as a result the galaxy
would have similarly large $\textrm{D}_{n}(4000)$ at both the center and
outskirt and meanwhile have large central $\textrm{EW}(\textrm{H}\alpha)$ and
weak $\textrm{EW}(\textrm{H}\alpha)$ at the outerskirt. Such cases are not
observed in Figure 5, too. This imply that, it rarely happens that a fully-
quenched galaxy becomes rejuvenated and restarts quenching only in their
central region; rather, it is more likely that star formation rejuvenation
happens over a wide range of galactic radii (although the central region may
be more enhanced in star formation due to the merger-driven gas inflow), and
the consequent quenching happens earlier at larger radii and propagates inward
(thus still in an outside-in manner). In any case, the outside-in quenching
inferred from our data for the cPSB and rPSB galaxies cannot be a consequence
of a central starburst.

###  4.3 The evolutionary relation between rPSB and cPSB types

Figure 10: $Top$ $row$: radial gradients of the average lighted-weighted age
of PSB samples. The shadowed regions show the 30% to 70% percentile of the
distributions. From left to right, the spectral fitting codes are different.
The average results of cPSB types with different $f_{\rm PSB}$ are highlighted
by dashed and dotted lines. $Bottom$ $row$: same as the top row, but showing
the mass-weighted age result.

The rPSB and cPSB types are similar in $\textrm{D}_{n}(4000)$ and
$\textrm{EW}(\textrm{H}\delta_{A})$, but different in
$\textrm{EW}(\textrm{H}\alpha)$, with the rPSB galaxies showing larger
$\textrm{EW}(\textrm{H}\alpha)$ in their centers. As a result, the rPSB
galaxies mostly fall in the star-forming sequence and the blue cloud, while
the cPSB galaxies mostly fall below the star-forming sequence and in the green
valley. These similarities and differences appear to suggest that the rPSB and
cPSB may have the same origin (e.g. mergers or environmental effects) but at
different evolutionary stages. In the outside-in quenching process as inferred
for both types, the cessation of the star formation in a galaxy in this
category will first happen in its outskirt, and then extends to smaller radii.
During this process, the galaxy will be observed as a rPSB galaxy at an early
stage, and then a cPSB galaxy later on.

The two types also differ in the size-mass relation. The rPSB type follows the
same relation as the control sample and the average relation of star-forming
galaxies, while the cPSB galaxies have smaller half-light radii at
intermediate-to-low masses. This result is also consistent with the rPSB
galaxies being progenitors of cPSB galaxies. In a recent study of PSB galaxies
at $z\sim 0.7$, Setton et al. (2022) studied the evolution of the PSB galaxy
properties as a function of the time since the star formation was quenched.
The sizes of PSB galaxies were found to show a negative or no correlation with
the time since quenching. If the outside-in process is taken into account, one
would expect a PSB galaxy to become smaller or similarly sized when it evolves
to a later stage as a cPSB galaxy. This conjecture can be tested using current
hydrodynamic simulations of galaxy formation.

We note that, in an earlier study of the MaNGA-based PSB galaxy sample, Chen
et al. (2019) found the rPSB and cPSB galaxies are quite different in the
radial gradient in mass-weighted stellar age, based on data products produced
by the spectral fitting code Pipe3D (Sánchez et al., 2016). This result
indicated that cPSB and rPSB are not simply different evolutionary stages of
the same event. Instead of using stellar population properties derived from
the technique of stellar population synthesis such as Pipe3D, in our work we
opt for the three SFH indicators which are directly measured from the stacked
spectrum of each region and thus are model-independent. In fact, the spectral
fitting code used in this work also provides measurements of stellar
population properties. In Figure 10, we compare the radial gradients in both
light-weighted (upper panels) and mass-weighted (lower panels) age for the
four types of PSB samples, as obtained by applying our code (the left panels)
and the Pipe3D (version 2.4.3; the middle panels) which is the same version as
used in Chen et al. (2019). In addition, in the rightmost panels, we show the
results based on the new version of Pipe3D (version 3.1.1) which has replaced
the stellar library of MILES by the recently available library of MaStar (Yan
et al., 2019). As can be seen, the different codes produce similar results for
light-weighted age, but the mass-weighted profiles are quite different,
particularly for the rPSB sample (the blue lines) and the iPSB-SF sample (the
yellow lines). The strong (negative) gradients in mass-weighted age for the
rPSB type and the flat profile for the cPSB as reported in Chen et al. (2019)
are also seen in our figure (the middle lower panel). However, the gradient in
the rPSB galaxies becomes rather weak when the new version of Pipe3D is
applied, a result which is close to (though not exactly the same as) the
result of our code where we see little difference between the cPSB and rPSB
samples. The discrepancies between the different codes reflect the known issue
of stellar population modeling which suffers from strong degeneracies between
model parameters such as age, metallicity, dust attenuation, etc.

In the left-hand panels of Figure 10, we also show the stellar age profiles
for the two subsamples of cPSB galaxies, with $f_{\rm PSB}<0.5$ and $f_{\rm
PSB}>0.5$ as analyzed in subsection 3.4. It is seen that the two subsamples
show very similar profiles, implying that the cPSB galaxies of different
$f_{\rm PSB}$ fall in the same category as mentioned above. The broad range of
$f_{\rm PSB}$ found for the cPSB galaxies may reflect the galaxy-to-galaxy
variation of the relative timescales between the PSB phase and the overall
quenching procedure of the host galaxy. If so, the quenching timescale must be
somehow dependent on the stellar mass of galaxies, as indicated by the
correlation of $f_{\rm PSB}$ with $\textrm{M}_{\ast}$ (see subsection 3.4).

Otter et al. (2022) have recently analyzed ALMA observations of the 12CO(0-1)
distribution in 13 cPSB and rPSB galaxies selected from the MaNGA survey.
Their results show stellar disturbances as well as centrally concentrated and
highly disturbed molecular gas in both cPSB and rPSB galaxies, indicating a
common merger origin. If the two types of galaxies have distinct origins and
are not sequential evolutionary phases, as pointed out by Otter et al. (2022),
a natural question would arise: why do some mergers lead to a cPSB phase
whereas others lead to a rPSB phase? The authors suggested that outflows could
be an alternative process primarily impacting cPSB galaxies, considering the
fact that this type of galaxies are more disturbed in both ionized and
molecular gas when compared to rPSB galaxies. Using integral-field
spectroscopy from the SAMI Galaxy Survey, Owers et al. (2019) found that the
PSB galaxies in galaxy clusters mostly present PSB regions in their outskirt,
and concluded that these galaxies follow an outside-in quenching driven by ram
pressure stripping.

In summary, the rPSB type of galaxies appear to have multiple origins
depending on environment. The majority of rPSB galaxies, which are located in
the field and loose groups with dynamical conditions more favorable for galaxy
interactions and mergers, are likely to have the same merger origin and
experience the same sequential evolutionary pathway as the cPSB type. For
those located in dense environments such as galaxy clusters, ram-pressure
stripping may play a more important role. Both mergers and ram-pressure
stripping lead to outside-in quenching.

###  4.4 The evolutionary relation between iPSB-SF and iPSB-Q types

The majority of the PSB galaxies in our sample are classified as iPSB, either
iPSB-SF or iPSB-Q according to their global SFR, and these two types behave
similarly in many aspects including the size-mass relation and the SFH
indicators. They differ mainly by the global SFR, by definition, with one in
the star-forming sequence and one in the quiescent sequence. Thus, it is
natural to speculate that they are different evolutionary stages of the same
evolutionary pathway, with the iPSB-SF type being progenitors of the iPSB-Q
type. However, we would like to caution that this conjecture may be true only
for a portion of the iPSB galaxies; for some galaxies, the iPSB-SF and iPSB-Q
types may be induced by distinct events. For instance, “rejuvenated” star
formation in the outskirt of an already quiescent galaxy due to recent gas
accretion can lead to an iPSB phase, after which the galaxy returns to the
quiescent sequence. This is similar to the red-PSB-red cycle as proposed in
previous studies (e.g. Dressler et al., 2013; Pawlik et al., 2018). More
detailed studies of the stellar populations and environment for these types of
galaxies, both observational and theoretical, would be needed in future when
larger samples and more reliable techniques of stellar population synthesis
become available.

##  5 Summary

In this work, we use the spatially resolved spectroscopy from the final data
release of the MaNGA survey to identify post-starburst galaxies (PSB) in the
local Universe. The PSB galaxies are identified in a two-step method. For each
galaxy from MaNGA, we first select regions with a size of $\sim$kpc and strong
H$\delta$ absorption, from which we then select PSB regions that have
relatively weak H$\alpha$ emission. For each region, we have stacked the
original spectra of its spaxels to obtain a spectrum of high S/N, and we
perform full spectral fitting to the stacked spectrum to measure emission line
parameters and stellar indices that are used for the identification and
scientific analysis in this work. Out of the 10,010 galaxies from MaNGA, we
have identified a sample of 489 PSB galaxies, each with at least one PSB
region. These galaxies are then classified into three different types
according to the location of their PSB regions: 94 cPSB galaxies in which the
PSB regions are found at the galactic center, 85 rPSB galaxies in which the
PSB regions are off-center and form a ring-like shape, and 310 iPSB galaxies
in which the PSB regions present irregular locations and shapes. Each of the
iPSB galaxies is further classified as either iPSB-SF if located in the star-
forming sequence in the diagram of star formation rate (SFR) versus stellar
mass, or iPSB-Q if located in the quiescent sequence in the same diagram.

We first compare the size-mass relation of the four types of PSB galaxies with
control samples of normal galaxies that are closely matched in redshift,
stellar mass and SFR. We then study the recent star formation history (SFH) of
the PSB samples and the corresponding control samples, using three spectral
indices to indicate the recent SFH: $\textrm{EW}(\textrm{H}\alpha)$
(equivalent width of the H$\alpha$ emission line),
$\textrm{EW}(\textrm{H}\delta_{A})$ (equivalent width of the H$\delta$
absorption line), and $\textrm{D}_{n}(4000)$ (depth of the break at 4000Å). In
addition, we examine the potential dependence on the fraction of PSB regions
in our galaxies.

Our conclusions can be summarized as follows.

  * •

Different types of PSB galaxies show different size-mass relations: iPSB-SF
galaxies closely follow the size-mass relation of normal star-forming
galaxies, iPSB-Q galaxies follow the relation of quiescent galaxies, rPSB
galaxies appear to fall in between, and cPSB galaxies follow the relation of
star-forming galaxies at both high and low masses and that of quiescent
galaxies at intermediate masses.

  * •

When compared to control galaxies of similar SFR, redshift, and mass, the cPSB
galaxies have smaller sizes at $9.5\lesssim\log_{10}(\rm
M_{\ast}/M_{\odot})\lesssim 10.5$, while the other types of PSB galaxies show
similar sizes to their control galaxies at a given mass.

  * •

The iPSB-SF sample shows no/weak gradients in $\textrm{D}_{n}(4000)$,
$\textrm{EW}(\textrm{H}\delta_{A})$ and $\textrm{EW}(\textrm{H}\alpha)$,
consistent with the global star-forming status of this type of galaxies.

  * •

The iPSB-Q sample shows negative gradients in $\textrm{D}_{n}(4000)$, positive
gradients in $\textrm{EW}(\textrm{H}\delta_{A})$, and no gradients in
$\textrm{EW}(\textrm{H}\alpha)$. This result indicates older stellar
populations in the inner regions, consistent with an “inside-out” quenching
process.

  * •

The cPSB sample shows positive gradients in $\textrm{D}_{n}(4000)$, negative
gradients in $\textrm{EW}(\textrm{H}\delta_{A})$, and no gradients in
$\textrm{EW}(\textrm{H}\alpha)$, indicating younger stellar populations in the
inner regions and an “outside-in” quenching process.

  * •

The rPSB sample is similar to the cPSB sample in the gradients in both
$\textrm{D}_{n}(4000)$ and $\textrm{EW}(\textrm{H}\delta_{A})$, but shows
negative gradients in $\textrm{EW}(\textrm{H}\alpha)$. This result implies
that rPSB and cPSB galaxies are different stages of the same evolutionary
pathway.

  * •

Both rPSB and iPSB galaxies have relatively small fractions of PSB regions,
with $f_{\rm PSB}<0.5$ within 1.5$R_{e}$, while cPSB galaxies spand a full
range in $f_{\rm PSB}$. The size-mass relation and recent SFHs of cPSB
galaxies show no dependence on $f_{\rm PSB}$.

  * •

The four types of PSB galaxies can be broadly divided into two categories in
terms of evolutionary pathway: (1) iPSB-SF and iPSB-Q in the first category
which have similar SFH to normal galaxies and appear to prefer an inside-out
quenching process, and (2) cPSB and rPSB in the other category which prefer an
outside-in quenching process, likely driven by disruption events such as
mergers which make the galaxies more compact than the average quiescent
galaxies.

## Acknowledgments

We’re grateful to the anonymous referee for the helpful comments on our paper.
This work is supported by the National Key R&D Program of China (grant No.
2022YFA1602902), and the National Natural Science Foundation of China (grant
Nos. 11821303, 11733002, 11973030, 11673015, 11733004, 11761131004,
11761141012).

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P.
Sloan Foundation, the U.S. Department of Energy Office of Science, and the
Participating Institutions.

SDSS-IV acknowledges support and resources from the Center for High
Performance Computing at the University of Utah. The SDSS website is
www.sdss.org.

SDSS-IV is managed by the Astrophysical Research Consortium for the
Participating Institutions of the SDSS Collaboration including the Brazilian
Participation Group, the Carnegie Institution for Science, Carnegie Mellon
University, Center for Astrophysics — Harvard & Smithsonian, the Chilean
Participation Group, the French Participation Group, Instituto de Astrofísica
de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and
Mathematics of the Universe (IPMU) / University of Tokyo, the Korean
Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut
für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA
Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-
Institut für Extraterrestrische Physik (MPE), National Astronomical
Observatories of China, New Mexico State University, New York University,
University of Notre Dame, Observatário Nacional / MCTI, The Ohio State
University, Pennsylvania State University, Shanghai Astronomical Observatory,
United Kingdom Participation Group, Universidad Nacional Autónoma de México,
University of Arizona, University of Colorado Boulder, University of Oxford,
University of Portsmouth, University of Utah, University of Virginia,
University of Washington, University of Wisconsin, Vanderbilt University, and
Yale University.

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