# Stellar Populations of Spectroscopically Decomposed Bulge-Disk for S0
Galaxies from the CALIFA survey

Mina Pak  Korea Astronomy and Space Science Institute (KASI), 776 Daeduk-
daero, Yuseong-gu, Daejeon 34055, Republic of Korea  Joon Hyeop Lee  Korea
Astronomy and Space Science Institute (KASI), 776 Daeduk-daero, Yuseong-gu,
Daejeon 34055, Republic of Korea  Korea University of Science and Technology
(UST), 217 Gajeong-ro Yuseong-gu, Daejeon 34113, Republic of Korea  Sree Oh
Research School of Astronomy and Astrophysics, Australian National University,
Canberra, ACT 2611, Australia  ARC Centre of Excellence for All Sky
Astrophysics in 3 Dimensions (ASTRO 3D), Australia  Francesco D’Eugenio
Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, B-9000
Gent, Belgium  Matthew Colless  Research School of Astronomy and Astrophysics,
Australian National University, Canberra, ACT 2611, Australia  ARC Centre of
Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia
Hyunjin Jeong  Korea Astronomy and Space Science Institute (KASI), 776 Daeduk-
daero, Yuseong-gu, Daejeon 34055, Republic of Korea  Woong-Seob Jeong  Korea
Astronomy and Space Science Institute (KASI), 776 Daeduk-daero, Yuseong-gu,
Daejeon 34055, Republic of Korea  Korea University of Science and Technology
(UST), 217 Gajeong-ro Yuseong-gu, Daejeon 34113, Republic of Korea

###### Abstract

We investigate the stellar population properties of bulges and disks
separately for $34$ S0s using integral field spectroscopy from the Calar Alto
Legacy Integral Field Area survey. The spatially resolved stellar age and
metallicity of bulge and disk components have been simultaneously estimated
using the penalized pixel fitting method with photometrically defined weights
for the two components. We find a tight correlation between age and
metallicity for bulges, while the relation for disks has a larger scatter than
that of bulges. This implies that the star formation histories of the disks
are more complicated than those of the bulges. Bulges of the high-mass S0s are
mostly comparable in metallicity, while bulges appear to be systematically
more metal-rich than disks for the low-mass S0s. The ages of bulges and disks
in the high-mass S0s appear to increase with local density. The bulge ages of
the low-mass S0s also increases with local density, but such a trend is not
clear in the disk ages of low-mass S0s. In addition, the age difference
between bulge and disk components ($\Delta$Age) tends to increase with local
density, both for the high-mass and low-mass S0s. The high-mass S0s have
systematically higher $\Delta$Age than the low-mass S0s at given local
density. Our results indicate that the stellar mass significantly influences
the evolution of S0 galaxies, but the environment also plays an important role
in determining the evolution of bulges and disks at given stellar mass.

##  1 Introduction

Galaxies generally contain complex structural components such as bulges,
stellar and gaseous disks, spiral arms, bars, and shells. Decomposing these
structures is key to understanding the complex formation and evolution history
of galaxies (Kormendy 1977; Peng et al. 2002; Erwin 2015; Erwin et al. 2015;
Johnston et al. 2012; Johnston et al. 2014; Tabor et al. 2017; Oh et al. 2020;
Barsanti et al. 2021). Bulge or spheroidal components, whose surface
brightness profiles roughly follow a de Vaucouleurs law (de Vaucouleurs,
1948), generally contain an old stellar population with metallicities spanning
the range from very metal-poor to super metal-rich. They follow the same
fundamental plane as elliptical galaxies (Bender et al. 1992; Falcón-Barroso
et al. 2002; Dalla Bontà et al. 2018). On the other hand, disks generally have
exponential surface brightness profile (Freeman, 1970) have stars with high
metallicity and a wide range of ages, together with hydrogen gas, molecular
clouds, dust and hot gas, heated by star formation and supernovae. The bulge
component is dominantly supported by random motion with little net rotation,
while the disk component is supported (and flattened) by rotation, making a
flattened disk (Cappellari et al. 2007; Emsellem et al. 2007; Emsellem et al.
2011; van de Sande et al. 2017). Since the two main components in a galaxy
have obviously different properties, the detailed study of kinematics and
stellar populations in decomposed bulges and disks is important for
understanding the different processes that contributed to their formation.

Since colors can be a proxy for the stellar populations, bulge-disk
decomposition has been widely applied to multi-band photometry in the past by
fitting analytic functions to the galaxy light distribution in order to
reconstruct the images of the various components (e.g. Kormendy 1977; Simard
1998; Peng et al. 2002; Erwin 2015). The comparison of colors between bulge
and disk has shown that disks are bluer than bulges in both spirals and S0s
(Bothun & Gregg 1990; Peletier & Balcells 1996; Hudson et al. 2010; Head et
al. 2014). This implies that disky galaxies have more recent star-formation
activity in the outer disk (de Jong, 1996) or higher metallicities in their
centers (Beckman et al. 1996; Pompei & Natali 1997). However, it has also
revealed that some galaxies have negative color gradients within both the
bulges and disks of disk galaxies (Terndrup et al. 1994; Peletier & Balcells
1996; Michard & Poulain 2000; Kannappan et al. 2009; Head et al. 2014), which
implies the presence of older or more metal-rich stellar populations in the
outer regions of these galaxies.

However, broadband colors cannot resolve the degeneracy between age and
metallicity. In order to reliably measure the physical properties of a stellar
population, we need to study its spectrum. Decomposition can also be done
using spectroscopic data, by taking into account the different kinematic
properties of bulges and disks. This involves decomposing the line-of-sight
velocity distribution (LOSVD) of a galaxy into kinematic components (Rubin et
al. 1992; Kuijken & Merrifield 1993). Indeed, more recently, decomposing has
applied the observed spectrum into spectral components (Coccato et al. 2011;
Johnston et al. 2012; Tabor et al. 2017; Fraser-McKelvie et al. 2018a; Oh et
al. 2018; Méndez-Abreu et al. 2019a;Johnston et al. 2021; Barsanti et al.
2021). The spectroscopic decomposition of dynamically distinct bulge and disk
components is indispensable to study a detailed exploration of their
individual formation histories.

A spectroscopic bulge-disk decomposition technique was introduced in Johnston
et al. (2012) and Johnston et al. (2014). They decomposed the bulge and disk
components using long-slit spectra along the major axes of S0s. They fitted
the one-dimensional light profiles as a function of wavelength, and then
integrated these profiles to obtain the global bulge and disk spectra for each
S0 galaxy. These studies found that the bulge of S0s contains systematically
younger and more metal-rich stellar populations. However, they also note that
using only their long-slit spectra it is impossible to determine whether these
young stellar populations are genuinely associated with the bulge, or if they
represent instead contamination by the central disk population.

Johnston et al. (2017) applied a new bulge-disk decomposition method to the
Mapping Nearby Galaxies at Apache Point Observatory (MaNGA; Bundy et al. 2015)
integral field spectroscopy (IFS) data. They obtained image slices at each
wavelength and then constructed bulge and disk spectra from the weighted flux
at each wavelength, from which they measured the stellar populations of the
two components using the Lick system. Méndez-Abreu et al. (2019b) also carried
out a spectro-photometric decomposition for three galaxies from the Calar Alto
Legacy Integral Field Area survey (CALIFA; Sánchez et al. 2012). Tabor et al.
(2017) introduced simultaneous spectral fitting of the two components using
the Python version of the penalized pixel fitting code (pPXF; Cappellari &
Emsellem 2004; Cappellari 2017) and applied this to three S0s from the CALIFA
survey and to 302 early-type galaxies from the MaNGA survey; the populations
and kinematics of the bulge and disk components have been presented in Tabor
et al. (2019). Barsanti et al. (2021) also investigated the stellar
populations separately in the bulges and the disks of S0s in dense
environments using the Sydney-AAO Multi-object Integral field (SAMI) Galaxy
Survey. These studies have found interesting constraints on S0 formation, but
the consistent and systematic comparison of spectroscopically decomposed bulge
and disk components between different environments has rarely been conducted,
as yet.

Johnston et al. (2014) found that $13$ S0s in the Virgo cluster have younger
and more metal-rich stellar populations in their bulges than in their disks by
analyzing the Lick indices of decomposed bulges and disks from long-slit
spectroscopic data. They inferred that a normal spiral galaxy hosting an old
bulge and a young star-forming disk may undergo star formation quenching in
its disk by gas stripping in the cluster and, simultaneously, the remaining
gas may have fallen into the central bulge, triggering star formation in the
bulge for the last time before the galaxy finally fades to a present-day S0.
S0s in the clusters could have been through this process in their life.

Fraser-McKelvie et al. (2018a) focused on the different formation pathways as
a function of stellar mass for S0s by investigating the stellar populations of
$279$ S0s in the MaNGA survey from Lick indices separately measured in bulges
and disks. They found that massive galaxies (M⋆ $>10^{10}$ M⊙) tend to have
older bulges and younger disks, while less massive galaxies (M⋆ $<10^{10}$ M⊙)
tend to have younger bulges and older disks. They argued that the role of
environment is negligible. Tabor et al. (2019) performed spectroscopic
decomposition of 302 early-type galaxies from the MaNGA survey. In their
results, bulges and disks have similar ages, but bulges have systematically
higher metallicities. The disks appear to have a wide range of both age and
metallicity, indicating more complicated star formation histories compared to
the bulges. Barsanti et al. (2021) found that bulges are relatively redder and
more metal-rich than their surrounding disks, while they did not find any
notable trend with age. Their results indicate that the redder color in bulges
is mainly due to the higher metallicity of the bulge stellar populations.
These previous results together indicate possible differences in the bulge and
disk formation of S0s between high- and low-density environments, but more
consistent and systematic comparisons are necessary to clarify the situation.

Up to now two main formation pathways for S0s have been proposed: the fading
of spirals to S0s (e.g. Moran et al. 2007; Laurikainen et al. 2010; Cappellari
et al. 2011; Kormendy & Bender 2012; Johnston et al. 2014) and mergers or
gravitational interactions (Bekki 1998; Tapia et al. 2017; Diaz et al. 2018;
Rizzo et al. 2018). In the scenario of spirals fading to S0s, gas within
spiral arms is stripped through environmental mechanisms such as ram pressure
stripping (Gunn & Gott, 1972), harassment (Moore et al., 1999), thermal
evaporation (Cowie & Songaila, 1977), and strangulation (Larson et al., 1980),
which results in star formation quenching. Secular evolution driven by a bar
is also a possible mechanism involved in quenching of spiral galaxies, perhaps
inducing a transient starburst by funnelling gas towards the centre and
growing the bulge (Combes & Sanders 1981; Kormendy & Kennicutt 2004;
Athanassoula 2013). Bars are common structures in disk galaxies in the local
universe: the bar fraction has been reported to be up to $\sim 50\%$ in
optical bands (Marinova & Jogee 2007; Reese et al. 2007; Barazza et al. 2008)
and rises to $\sim 70\%$ in near-infrared studies (Knapen et al. 2000;
Menéndez-Delmestre et al. 2007). Passive spiral galaxies may be evidence for
the fading of spirals to S0s. The numerical simulations from Bekki et al.
(2002) show how cluster environmental quenching processes can transform
spirals into S0s, passing through an intermediate passive spiral phase. The
spiral arm structures fade over several Gyrs after the gas is stripped.
Recently, however, several observational studies found that passive spirals
can be found anywhere from galaxies in isolation to the centers of clusters,
and hence no single mechanism can completely explain their origin (Fraser-
McKelvie et al. 2016; Fraser-McKelvie et al. 2018b; Pak et al. 2019; Pak et
al. 2021; Deeley et al. 2020).

Mergers, accretion or gravitational interactions can also form S0s. The
hierarchical models of galaxy formation assume that the bulges of S0s formed
by a major merger of disk galaxies or by a sequence of minor merger events
(Somerville & Primack 1999). More recent studies in Hopkins et al. (2009) show
that disks can survive even $1:1$ mergers depending on the initial gas
content. This scenario seems consistent with the fact that most S0s reside in
groups and with observations reporting merging relics in many S0s (Kuntschner
et al. 2002; Eliche-Moral et al. 2012; Borlaff et al. 2014). Diaz et al.
(2018) introduced a new pathway in lower density environments, where an
isolated, high-redshift compact elliptical (cE) galaxy experiences a merger
with a smaller gas-rich disk galaxy. The merger remnant effectively transforms
into a smooth disk without spiral structure around the cE, which ultimately
evolves into an S0.

The goal of this paper is to better understand the evolution of S0s by
separately relating bulge and disk stellar populations of CALIFA galaxies to
local environment. While previous studies have focused either on clusters
(Virgo) or field (MaNGA), this is the first study to use a range of
environment consistently. Compared to MaNGA (Husemann et al. 2013), CALIFA
(Sánchez et al. 2012) offers better spatial resolution ($2.4^{\arcsec}$ in
median; García-Benito et al. 2015), hence better accuracy in the photometric
decomposition. In addition, bulge-disk decomposition suffers from
degeneracies, therefore we use the algorithm of Oh et al. (2020) to overcome
this issue. We use a new subroutine of pPXF for dealing with degeneracy in the
solutions obtained by both photometrically and kinematically decomposing the
bulge and disk components, as recently proposed by Oh et al. (2020). In
particular, we focus on the systematic comparison of bulge and disk
populations along a wide range of local density, which has been rarely
conducted in the previous studies.

This paper is organized as follows. Section 2 describes the galaxy samples
adopted from the CALIFA survey. The analysis of data is in Section 3. We
present our results in Section 4. Finally, our discussion and conclusions are
given in Sections 5 and 6. Throughout the paper we adopt a standard
$\Lambda$CDM cosmology with $\Omega_{m}=0.3$, $\Omega_{\Lambda}=0.7$, and
$H_{0}=70$ km s-1 Mpc-1.

##  2 DATA and Sample Selection

Figure 1: The DECaLS and the SDSS images ($200\arcsec\times 200\arcsec$) of
the 34 lenticular galaxies. The galaxies are ordered from high to low stellar
mass from NASA-Sloan Atlas (NSA, Blanton et al. 2011) catalog. The name of the
galaxies is shown in the top corner of each galaxy. In case the images from
SDSS, we label the ‘SDSS’ in the bottom right corner of each image. North is
at the top and east is to the left.

The CALIFA survey (Sánchez et al. 2012; Husemann et al. 2013) was carried out
using the 3.5-m telescope of the Calar Alto observatory with the PMAS/PPAK
spectrograph (Roth et al. 2005; Kelz et al. 2006). The field of view of PPAK
is $74\arcsec\times 64\arcsec$, which is filled with $382$ fibers of
$2.7\arcsec$ diameter each (Kelz et al., 2006). The galaxies were observed
with two spectroscopic setups, using the gratings V500 with a nominal
resolution ($\lambda$/$\Delta\lambda$) of $850$ at $5000$ Å (FWHM $\sim 6$ Å)
and a wavelength range from $3745$ to $7500$ Å, and V1200 with a better
spectral resolution of $1650$ at $4500$ Å (FWHM $\sim 2.7$ Å) and ranging from
$3650$ to $4840$ Å. More detailed information about the CALIFA sample, and the
observational strategy, is available in the papers of the CALIFA team (Walcher
et al. 2014; Sánchez et al. 2012; Husemann et al. 2013; García-Benito et al.
2015; and Sánchez et al. 2016). We here analyzed galaxies using only the V500
data cube.

We visually select S0 galaxies from the CALIFA survey. Using composite color
images from the Dark Energy Camera Legacy Survey (DECaLS; Dey et al. 2016) and
the 14 data release of the Sloan Digital Sky Survey (SDSS DR14; Abolfathi et
al. 2018), we selected $87$ S0 galaxies showing a prominent spheroidal
component in the center together with a disk-like structure similar to
spirals, but without spiral arms. Then, we reject $25$ galaxies with heavily
distorted morphology as well as paired and interacting galaxies, since
galaxies with distorted features cannot be successfully constructed in the
structural model from GALFIT (Peng et al., 2002). We also remove two galaxies
closely neighbored by bright stars, which significantly contaminate galaxy
light. Finally, significantly inclined (edge-on) $26$ galaxies are also
removed from the sample, because structural components in such galaxies cannot
be well decomposed in our method. This process was performed with visual
inspections of individual galaxies since we found that a typical disk axis
ratio cut does not work for early-type edge-on galaxies with spherical stellar
haloes. The final sample contains $34$ S0 galaxies (see Figure 1). Our S0s
have stellar masses of $9.0\leq$ log (M$\star$/M$\odot$) $<11.5$, based on
stellar masses from the NASA-Sloan Atlas (NSA, Blanton et al. 2011) catalog.
For comparison, we additionally use the nine passive spiral galaxies as
described in Pak et al. (2019).

##  3 Analysis

###  3.1 Photometric decomposition

We have performed a photometric bulge-disk decomposition to obtain the light
fraction of both components at each resolved point in the galaxy. Firstly, the
data cube has been collapsed across the whole wavelength range to produce a
fair single image of the galaxy at the appropriate spatial resolution. Since
the galaxies in our sample are nearby and therefore S/N of CALIFA data is
fairly high, we apply GALFIT (Peng et al., 2002) to this collapsed image
directly to fit a Sérsic bulge and an exponential disk, adopting Sérsic index,
magnitudes, position angles, flattenings, and scale radii as free parameters,
with initial estimates from Méndez-Abreu et al. (2017). The parameters are not
available for three passive spirals in Méndez-Abreu et al. (2017). In these
cases, we use the resulting values from double Sérsic fits in one-dimension as
initial estimates. We also leave the position angles and flattenings of each
component as free parameters. GALFIT produces flux models of the bulge and
disk components, convolved with the point spread function of the CALIFA data.
Finally, we estimate the bulge-to-total (B/T) light ratio for each spaxel as
the bulge model flux/(bulge model flux + disk model flux), which is used as a
relative flux constraint in the spectral bulge-disk decomposition.

###  3.2 Spectroscopic decomposition

Figure 2: An example of two-dimensional maps of flux, kinematics, and stellar
population (UGC 1271). In the first row, the SDSS r-band image, B/T map, bulge
S/N, (S/N)bulge = $\sqrt{B/T}\times$ (S/N)continuum, and disk S/N,
(S/N)${}_{disk}=\sqrt{(1-B/T)}\times$ (S/N)continuum are presented. In the
middle and bottom rows, we show $V$, $\sigma$, luminosity-weighted age, and
metallicity in the bulge, and the disk components, respectively, whose
(S/N)bulge greater than $30$ and (S/N)disk greater than $20$. The ellipses
show the 1$R_{e}$ and 2Re flux contours and their position angles.

We spatially bin the CALIFA data by means of the centroidal Voronoi
tessellation algorithm of Cappellari & Copin (2003) using the PINGSoft
(Rosales-Ortega, 2012) software. The minimum signal-to-noise ratio (S/N) per
bin for each galaxy is set to be between 5 and 10, which are marginal values
for measuring kinematics. The small S/N criterion minimizes the loss of
spatial resolution in the binning result, although we may lose many spaxels
when we estimate the stellar populations with stricter S/N cuts. However,
because our purpose is the bulge-disk decomposition, we decided to secure
spatial resolution as fine as possible rather than to bundle up low-S/N
spaxels over large spatial areas, which possibly brings a negative effect on
the accuracy in the decomposition. In the analysis, we used the age and
metallicity averaged over the high-S/N bins for each component, which may
guarantee the minimum reliability of the results.

We estimate the luminosity-weighted age and metallicity from the CALIFA data
using the single stellar population model templates from Vazdekis et al.
(2010), covering a range in ages from $0.06$ to $15.8$ Gyr and metallicities
from $-1.71$ to $0.22$ (a total of $150$ templates). The templates are
broadened to match the spectral resolution of the CALIFA data using the code
log_rebin provided with the pPXF package. As recommended by van de Sande et
al. (2017), we first run pPXF for each bin to obtain a precise noise estimate
from the residual of the fit and then a second time to clip outliers using the
CLEAN keyword in pPXF. In a third iteration, we extract the velocity and
velocity dispersion using a 12th-order additive polynomial. Finally, with the
extracted velocity and velocity dispersion fixed, the mean age and metallicity
are estimated by using a 10th-order multiplicative (instead of additive)
polynomial. We do not apply the regularization in our analysis.

We fit bulge and disk components, weighted by their relative contributions
provided by the photometric decomposition at each spatial coordinate of the
data cube. We use the PYTHON version of the pPXF code (Cappellari & Emsellem,
2004), updated as described in Cappellari (2017), which allows multiple
components with different populations and kinematics to be fitted to spectra
simultaneously (Coccato et al. 2011; Johnston et al. 2014; Tabor et al. 2017).
The FRACTION keyword of pPXF allows simultaneous estimation of two components
(i.e. a bulge and a disk) with a constraint on the relative weights of the two
components:

$f_{bulge}=\frac{\Sigma w_{bulge}}{\Sigma w_{bulge}+\Sigma w_{disk}},$ (1)

where $w_{bulge}$ and $w_{disk}$ are the weights assigned to the set of
spectral templates for fitting the bulge and disk, respectively. The linear
least-squares sub-problem with an exact linear equality constraint (equation
1) can be simplified by adding the following extra constraint requiring only
minimal changes to the pPXF algorithm:

$(f_{bulge}-1)\Sigma w_{bulge}+f_{bulge}\Sigma w_{disk}\leq\Delta,$ (2)

where $\Delta$ regulates the precision required to satisfy inequality (2) and
is set to a small number (we use the single precision limit $\Delta=10^{-9}$).
Both the spectral templates and the galaxy spectrum have been normalized to
have a mean flux of order unity to satisfy the equality constraint to
sufficient numerical accuracy.

The pPXF method can result in unphysical solutions, which is a known issue of
simultaneously fitting multiple components. For example, the fit may give a
bulge rotation velocity larger than the disk rotation velocity and a bulge
velocity dispersion smaller than the disk velocity dispersion. Such cases are
obviously unrealistic given our understanding of galaxy structure and we
therefore adopt the method introduced in Oh et al. (2020) to deal with them,
using a ‘swapping’ subroutine to overcome the degeneracy resulting from two
similar local $\chi^{2}$ minima. This solution is activated when
$\sigma_{bulge}+\sigma_{error}<\sigma_{disk}$, where $\sigma_{error}$ is the
error in $\sigma$ from fitting a single component. Further details of the
method are described in Oh et al. (2020). An example of the two-dimensional
maps obtained for the kinematics and stellar populations of the bulge and disk
components is shown in Figure 2.

The mean age and metallicity of bulge and disk components are summarized in
Table 1. The mean values are calculated from bins with bulge S/N,
(S/N)${}_{bulge}>30$ and disk S/N, (S/N)${}_{disk}>20$, which are defined by
(S/N)bulge = $\sqrt{B/T}\times$ (S/N)continuum, and
(S/N)${}_{disk}=\sqrt{(1-B/T)}\times$ (S/N)continuum.

Table 1: The measurements of luminosity-weighted mean age and metallicity for
bulge and disk components for all our sample

Name | Stellar mass | Local density | AgeBulge | [M/H]Bulge | AgeDisk | [M/H]Disk
---|---|---|---|---|---|---
| log(M⋆/M⊙) | log$\rho_{M,1Mpc}$ | (Gyr) |  | (Gyr) |
Lenticular galaxies |  |  |  |  |  |
MCG-02-02-086 | 11.45 | 10.43 | 13.24 | $-0.15$ | 10.81 | $-0.15$
NGC1060 | 11.40 | 10.00 | 15.53 | $-0.02$ | 13.69 | $-0.04$
UGC10693 | 11.17 |  9.88 | 11.83 | $-0.56$ |  9.93 | $-0.57$
NGC0507 | 11.16 | 10.47 | 14.58 | $-0.32$ | 12.72 | $-0.35$
UGC10905 | 11.07 |  8.97 |  9.04 | $-0.61$ |  8.98 | $-0.54$
NGC5513 | 10.89 |  9.48 | 11.71 | $-0.69$ |  9.96 | $-0.67$
UGC02099 | 10.86 |  8.65 | 4.99 | $-1.12$ |  6.96 | $-1.10$
NGC0499 | 10.78 | 10.42 | 15.39 | $-0.03$ | 12.59 | $-0.04$
NGC7671 | 10.68 |  9.30 | 14.13 | $-0.12$ | 14.49 | $-0.23$
NGC0364 | 10.65 | 10.56 | 12.68 | $-0.40$ | 12.60 | $-0.46$
PGC11179 | 10.64 | $-$ | 14.63 | $-0.13$ | 15.27 | $-0.21$
NGC0528 | 10.62 | 10.19 | 14.62 | $-0.24$ | 13.66 | $-0.40$
NGC0472 | 10.61 |  9.93 |  8.77 | $-0.80$ |  7.73 | $-0.81$
NGC7683 | 10.59 |  9.90 | 11.76 | $-0.31$ | 12.59 | $-0.31$
NGC0515 | 10.58 | 10.68 | 13.53 | $-0.43$ | 14.39 | $-0.41$
NGC2476 | 10.58 |  9.95 | 12.59 | $-0.96$ | 12.28 | $-0.73$
NGC0426 | 10.56 | 10.32 | 13.06 | $-0.24$ | 13.66 | $-0.25$
NGC1665 | 10.51 |  8.85 |  7.30 | $-0.59$ |  6.64 | $-0.64$
NGC0842 | 10.50 | 10.08 | 11.62 | $-0.92$ | 12.59 | $-0.92$
IC2341 | 10.47 |  9.64 | 11.15 | $-1.01$ | $\;\;\;\,6.62^{\ast}$ |  $-0.85^{\ast}$
NGC7623 | 10.44 | 10.80 | 12.63 | $-0.38$ |  15.51∗ |  $-0.25^{\ast}$
NGC7611 | 10.43 | 10.68 | 12.03 | $-0.41$ |  8.77 | $-0.43$
NGC0517 | 10.42 | 10.38 | 10.45 | $-0.62$ |  9.06 | $-0.84$
NGC2767 | 10.41 | 10.38 | 14.40 | $-0.03$ | 12.82 | $-0.18$
NGC6945 | 10.40 |  9.77 |  10.66∗ |  $-0.54^{\ast}$ | $\;\;\;\,8.84^{\ast}$ |  $-0.58^{\ast}$
NGC6278 | 10.39 |  9.80 | 12.90 | $-0.26$ | 15.78 | $-0.39$
NGC1281 | 10.37 | $-$ | 15.33 |  $0.00$ | 11.93 | $-0.08$
NGC5473 | 10.35 |  9.99 | 11.21 | $-0.37$ |  9.43 | $-0.45$
NGC6427 | 10.31 |  9.82 |  8.38 | $-0.57$ | 11.80 | $-0.70$
NGC2880 | 10.18 |  9.55 |  8.44 | $-0.27$ |  6.44 | $-0.53$
NGC5602 | 10.13 |  9.40 |  5.90 | $-0.60$ |  6.45 | $-0.67$
MCG-01-52-012 | 10.02 |  9.53 |  3.22 | $-1.25$ |  4.05 | $-1.18$
IC3586 |  9.21 |  9.76 | $\quad 3.47^{\ast}$ |  $-1.09^{\ast}$ | $\;\;\;\,0.95^{\ast}$ |  $-1.33^{\ast}$
IC3065 |  9.00 |  9.75 | $\quad 0.75^{\ast}$ |  $-1.20^{\ast}$ |  2.84 | $-0.83$
Passive spiral galaxies |  |  |  |  |  |
UGC02018 | 10.73 |  9.02 |  9.84 | $-0.97$ |  8.01 | $-1.05$
UGC01271 | 10.54 | 10.38 | 12.59 | $-0.55$ | 12.39 | $-0.71$
NGC7563 | 10.52 | 10.25 | 14.27 | $-0.20$ |  14.45∗ |  $-0.17^{\ast}$
NGC2553 | 10.49 | 10.15 | 11.53 | $-0.58$ | 11.66 | $-0.69$
NGC3300 | 10.40 |  9.30 | 12.09 | $-0.35$ | 12.14 | $-0.50$
NGC0495 | 10.38 | 10.51 | 12.19 | $-0.41$ | 14.10 | $-0.46$
NGC5794 | 10.31 | 10.11 | 11.57 | $-0.60$ |  15.85∗ |  $-0.57^{\ast}$
NGC5876 | 10.31 |  9.78 | 11.53 | $-0.31$ |  9.03 | $-0.40$
NGC1666 | 10.23 |  9.65 |  9.69 | $-0.51$ |  8.05 | $-0.71$

Note. — Column 1: the name of 34 lenticulars and nine passive spirals. Column
2: the stellar mass from NSA catalog. Column 3: Local density described in
section 4.2. Column 4 and 5: the age and metallicity of bulge. Column 6 and 7:
the age and metallicity of disk. The symbol of ‘$\ast$’ denotes the galaxies
having insufficient bins ($<50$) in the bulge and the disk.

##  4 Results

###  4.1 The age-metallicity relation of bulge and disk components

Figure 3: Stellar ages vs. metallicities of the bulge (left panel) and disk
(right panel) components for S0s (red circles) and passive spirals (dark blue
circles). The size of a symbol is proportional to the stellar mass. The error
bar indicates the standard deviation of the mean among the bins in each bulge
or disk. The galaxies are divided into a high-mass subsample (log
M⋆/M${}_{\odot}>10.75$; enclosed red open circles) and a low-mass subsample
(log M⋆/M${}_{\odot}\leq 10.75$). The fainter symbols indicate galaxies having
insufficient bins in the bulge or the disk ($<50$). The dashed line in both
panels is the linear fit for the bulges with more than $50$ bins and the
shaded area shows the dispersion about this fit. The Spearman correlation
coefficient and the significance of the null hypothesis are indicated in the
bottom left of each panel. Figure 4: The bulge-disk age difference
$\Delta$Age(Bulge-Disk) vs. the bulge-disk metallicity difference
$\Delta$[M/H](Bulge-Disk) for individual galaxies. Symbols are the same as
Figure 3. Figure 5: The stellar ages (left panels) and metallicities (right
panels) of bulges (top panels), disks (middle panels), and the difference
between bulge and disk (bottom panels), all as functions of stellar mass.

Figure 3 presents the luminosity-weighted ages and metallicities of the bulge
and disk components. We calculated the mean of total bulge and disk ages and
metallicities only when the number of bins with sufficient S/N ($>30$ for
bulges and $>20$ for disks) are $50$ or more. The bulges show a tight
correlation, with a Spearman correlation coefficient ($\rho$) of $\sim 0.80$.
The disks show a larger scatter than bulges, with $\rho\sim 0.66$, and are
clearly offset from the robust least-squares linear fit to the bulges. We
divide our S0s into a high-mass subsample (log M⋆/M${}_{\odot}>10.75$; $8$
S0s) and a low-mass subsample (log M⋆/M${}_{\odot}\leq 10.75$; $26$ S0s,
including two dS0); all passive spirals belong to the low-mass subsample. The
bulges for low-mass S0s with low metallicity tend to be largely deviated from
the fit. The disks of high-mass S0s are systematically offset from the robust
least-squares linear fit to the bulges. The bulges of the passive spirals
mostly lie well near the fit to the bulges. The disks of low-mass S0s and
passive spirals widely scattered; unlike the disks of high-mass galaxies, the
disks of some low-mass galaxies are as old as bulges. Although its faintness
makes the signals low, the bulge and disk of two dwarf S0 (dS0) galaxy
commonly have young ages.

As seen in Figure 4 and Figure 5, most bulges are older ($\sim 61\%$) and more
metal-rich ($\sim 83\%$) than their associated disks. The metallicities of the
bulges and disks are comparable for the high-mass S0s with standard deviation
of $0.03$. The standard deviation of metallicity difference for the low-mass
S0s is $0.14$. We can more clearly see this in comparing $\Delta$Age(Bulge-
Disk) and $\Delta$[M/H](Bulge-Disk) as a function of stellar mass in Figure 5.
Despite the large scatter, the age and metallicity of bulge and disk
components appear to be correlated with their global stellar mass. In
addition, galaxies with higher stellar masses have preferentially a larger
$\Delta$Age(Bulge-Disk), and the deviation of $\Delta$Age(Bulge-Disk) is
larger for galaxies with lower stellar masses. While $\Delta$[M/H](Bulge-Disk)
shows a negative correlations with stellar mass and is almost zero in the
higher-mass galaxies. The passive spirals are also widely dispersed in
$\Delta$Age(Bulge-Disk), and $\Delta$[M/H](Bulge-Disk) is mostly positive. The
results of Spearman’s rank coefficient ($\rho$) and the significance of
deviation (P0) are summarized in Table 2.

Table 2: Summary of the Spearman correlation coefficient ($\rho$) and
significance of deviation (P0) for age and metallicity as a function of
stellar mass and density

Y-axis | X-axis | total S0 | low-mass S0 | high-mass S0
---|---|---|---|---
|  |  $\rho$ (P0) |  $\rho$ (P0) |  $\rho$ (P0)
AgeBulge | log(M⋆/M⊙) | 0.41 (0.02) | 0.51 (0.01) | 0.33 (0.42)
| log$\rho_{M,1Mpc}$ | 0.62 (0.0003) | 0.52 (0.02) | 0.79 (0.02)
AgeDisk | log(M⋆/M⊙) | 0.37 (0.05) | 0.65 (0.00) | 0.36 (0.39)
| log$\rho_{M,1Mpc}$ | 0.45 (0.02) | 0.38 (0.10) | 0.81 (0.01)
$\Delta$Age(Bulge-Disk) | log(M⋆/M⊙) | 0.46 (0.01) | 0.21 (0.35) | 0.05 (0.91)
| log$\rho_{M,1Mpc}$ | 0.39 (0.05) | 0.24 (0.33) | 0.79 (0.02)
$[$M/H]Bulge | log(M⋆/M⊙) | 0.15 (0.41) | 0.18 (0.42) | 0.43 (0.30)
| log$\rho_{M,1Mpc}$ | 0.39 (0.04) | 0.16 (0.47) | 0.74 (0.04)
$[$M/H]Disk | log(M⋆/M⊙) | 0.35 (0.06) | 0.37 (0.09) | 0.38 (0.35)
| log$\rho_{M,1Mpc}$ | 0.43 (0.02) | 0.19 (0.42) | 0.69 (0.06)
$\Delta$[M/H](Bulge-Disk) | log(M⋆/M⊙) | -0.42 (0.02) | -0.19 (0.40) | 0.14 (0.74)
| log$\rho_{M,1Mpc}$ | 0.10 (0.64) | -0.10 (0.68) | 0.83 (0.01)

Note. — The Spearman correlation coefficient ($\rho$) will be between a value
of $-1$ and $+1$. $\rho=-1$ indicates a perfect negative correlation and
$\rho=+1$ indicates a perfect positive correlation.

###  4.2 Environment

Figure 6: The stellar ages (left panels) and metallicities (right panels) of
bulges (top panels), disks (middle panels), and the differences between bulge
and disk (bottom panels), as a function of local density; symbols are the same
as Figure 3. The Spearman correlation coefficient and significance for all
galaxies are shown at the bottom-right of the panels.

We investigate the environmental effects on the stellar populations of bulge
and disk components. We calculate projected stellar mass density applying
spline kernels (see Appendix A2 in Lee et al. 2010) by using the galaxies from
the NASA-Sloan Atlas (Blanton et al., 2011) within the velocity slice of $\pm
500$ km s-1 and distance scale of $1$ Mpc for each target galaxy. For
completeness, we use the subsample of galaxies with mass $>10^{9.5}$ M⊙, but
the mass of each target galaxy itself is not considered in calculating the
mass density.

Figure 6 presents the age and metallicity of each bulge and disk as a function
of local density. It seems that both the stellar mass and environment do play
a key role in the stellar populations of each bulge and disk. The ages of
bulges and disks of high-mass S0s appear to increase with local density
($\rho=0.79$ for bulges and $\rho=0.81$ for disks). For low-mass S0s, the
bulge ages also increase with local density ($\rho=0.52$), but such a trend is
unclear in the disk ages ($\rho=0.38$). In addition, the $\Delta$Age(Bulge-
Disk) tends to be constant with local density, both for the high-mass and low-
mass S0s. The high-mass S0s have systematically higher $\Delta$Age(Bulge-Disk)
than the low-mass S0s at given local density.

The metallicity of bulges and disks of high-mass S0s increases with local
density ($\rho=0.74$ for bulges and $\rho=0.69$ for disks), but low-mass S0s
show no clear trend ($\rho=0.16$ for bulges and $\rho=0.19$ for disks). For
the high-mass S0s, the metallicity in high-density environments appears to be
larger than that in low-density environments both for bulges and disks, and
$\Delta$[M/H](Bulge-Disk) is zero on average, regardless of local density. The
results of Spearman’s rank coefficient ($\rho$) and the significance of
deviation (P0) are also summarized in Table 2.

##  5 discussion

Today, it is widely believed that there are two main pathways for the
formation of S0s: (1) fading of spirals to S0s and (2) merger(s) and/or
accretion. From a kinematical perspective, it is quite clear that slow-
rotating S0s (stellar $v/\sigma<0.5$) appear to be found preferentially in
low-density environments, in accordance with the scenario that they are the
descendants of mergers/accretion, while fast-rotating S0s dominate in denser
environments, consistent with the spiral-fading scenario through the rapid
consumption or removal of gas (Deeley et al. 2020; Coccato et al. 2020).

However, the detailed analysis of the decomposed stellar populations implies
more complex stories than those revealed by kinematics only. From our results,
bulges tend to be older in more massive host galaxies ($\rho=0.41$), while the
ages of the disks depend less on host galaxy mass ($\rho=0.37$). This implies
that a more massive galaxy forms its bulge earlier, whereas disk formation is
barely dependent on the mass of the host galaxy and more extended in time.
However, even at a fixed stellar mass, there is a large dispersion in stellar
population properties, suggesting that either stochasticity or another
physical factor other than stellar mass also influences a galaxy star-
formation history.

Recently, the stellar populations in each component were analyzed through both
line strength measurements and full spectral fitting to obtain estimates of
the luminosity- and mass-weighted properties. Johnston et al. (2021), where
their sample of four S0s in the Centaurus Cluster and four isolated S0s
observed with MUSE, revealed that the bulges are more metal-rich than the
disks. They interpreted that the majority of the mass in these galaxies was
built up early in the lifetime of the galaxy, with the bulges and disks
forming from the same material through dissipational processes at high
redshift. The younger stellar populations and asymmetric features seen in the
field S0s may indicate that these galaxies have been affected more by minor
mergers than the cluster galaxies. Using MaNGA sample, Tabor et al. (2019)
showed bulges of S0s tend to be consistently more metal-rich than their disk
counterparts, and while the ages of both bulge and disk are comparable, there
is an interesting tail of younger and more metal-poor disks (see figure 2 of
Tabor et al. 2019). On the other hand, Méndez-Abreu et al. (2019a) concluded
that star formation only ever occurs in the disk of CALIFA S0s.

Since the luminosity-weighted age is sensitive to small fractions of recently
generated stars, our analysis is more representative of recent star-formation
histories than the mass-weighted age, which is representative of the average
epoch when the bulk of the stars in a galaxy formed. From the analysis of 279
S0s from the MaNGA sample, Fraser-McKelvie et al. (2018b) suggested that both
mass and environment are important in the formation of S0s, but mass plays a
more significant role than environment. However, although there is the caveat
of small number statistics, our results about environments are robust. Bulges
and disks tend to be older as the local density increases. The ages of disks
increase for high-mass S0s but show a weak trend for low-mass S0s with local
density. As a result, bulges are older than disks in high-density
environments. This is consistent with the widely-believed scenario that S0s in
dense environment were formed by major merger(s) or rapid collapse at an early
epoch before falling into a higher-mass halo. Star formation in the early-
formed bulges may have been quenched by some internal mechanisms, such as mass
quenching (Kauffmann et al. 2003; Wake et al. 2012) or AGN feedback (Fabian
2012 for a review; George et al. 2019). The bulge quenching may not be due to
environmental effects, because environmental effects must have also quenched
the star formation in the disks, but disks are slightly younger than bulges at
high density in our results. Thus, even after the bulge quenching, star
formation in disks must have continued for some time. Alternatively, the disks
may have re-formed for a time after the bulge was quenched. As time went on,
those S0s may have moved to higher-density environments hostile to star
formation in general. Eventually, star formation in the disks may have been
also quenched by environmental effects, which explains why disks in high-
density environments are older than those in low-density environments.

It is noted that high-mass S0s have slightly younger disks than bulges in
high-density environments, but [M/H] is almost the same between bulge and
disk. If the disks were created from surrounding matter ejected from early
violent mergers, this result seems reasonable. The bulge and disk in an S0 may
have similar metallicity because their sources are the same, and the later
star formation may have made the disk younger without much altering its
metallicity. Strangulation is a valid alternative explanation: the star-
forming gas is contained by the surrounding medium and this forces higher
recycling rates than possible in the field.

In low-density environments, even if high-mass S0s formed in the same way at
an early epoch, they may be more easily rejuvenated by interactions with gas-
rich neighboring galaxies (Sanders et al. 1999; Sancisi et al. 2008), a
process known to be more frequent in low-density environments with relatively
low velocity dispersions (Toomre & Toomre 1972; Lavery & Henry 1988; Byrd &
Valtonen 1990). Subsequent new star formation may influence both age and
metallicity in the host galaxies; whereas age always becomes younger in such
interactions and subsequent star formation, the change in metallicity may
largely depend on the properties of the interacting neighbors. In low-density
environments, both bulges and disks seem to be influenced by gas accretion.
Since gas stripping is not strong in low-density environments, they can keep
forming stars using accreted gas and consequently contain relatively younger
stars. In this scenario, therefore, $\Delta$Age and $\Delta$[M/H] are almost
zero on average, regardless of mass.

For low-mass S0s, both $\Delta$Age and $\Delta$[M/H] is almost constant with
local density. At fixed local density, $\Delta$Age for low-mass S0s is
systematically smaller than that for high-mass S0s; however, low-mass S0s at
the highest density have larger $\Delta$Age than high-mass S0s at the lowest
density. This result indicates that the impact on S0 formation of environment
is more significant than that of stellar mass. The bulges and disks of low-
mass S0s are preferentially fast rotators (Figure 7). The relatively small age
difference between bulge and disk and their fast rotation support the faded-
spiral scenario (gas consumption by steady star formation) for the low-mass
S0s, at least in low-density environments. On the other hand, the S0 galaxies
with bulges much older than disks, found mostly in high-density environments,
may have experienced environmental quenching (e.g. gas stripping) rather than
steady fading. Unlike the bulges, the ages of the disks do not show a clear
dependence on stellar mass. This may be because disks are more vulnerable to
external influence than bulges. The large scatter in the age-metallicity
relation of disks shows how complex their star formation histories are,
compared to those of bulges.

Although it is not majority in our sample, there are $8$ out of $34$ S0s with
younger age and more metal-rich than the corresponding disks, which are
similar to the $13$ S0s of the Virgo cluster by decomposing long-slit
spectroscopic data (Johnston et al., 2014). They are preferentially in lower-
density environment in our sample, and most of them are low-mass S0s: 7 low-
mass and one high-mass sample. The $13$ S0s from Johnston et al. (2014) are
preferentially in lower-density region or outskirt of the cluster with similar
projected luminosity density to our sample, even though they are in the Virgo
cluster. Their stellar masses (log M⋆/M⊙) taken from NSA catalog also span a
range of $9.2-10.6$ which is the same as our low-mass sample. Johnston et al.
(2014) interpreted their results as evidence of late bulge starbursts
activated by in-fallen gas, and our sample may share the same formation
history with those S0s in the Virgo cluster. Since the Virgo cluster is an
irregular and dynamically young cluster, further comparative studies with S0s
in more regular and dynamically old clusters would be helpful to fully
understand the evolution of S0s in various cluster environments.

Figure 7: The $\lambda_{R}-\epsilon$ diagram for bulges and disks; symbols are
the same as Figure 3. We have measured $\lambda_{R}$ for bulges and disks
following the equation (6) from Emsellem et al. (2007). For bulges,
$\lambda_{R}$ is measured at R $<$ Re.

##  6 Conclusion

We have analyzed the stellar populations of decomposed bulge and disk
components for $34$ S0s using data from the CALIFA survey. The decomposed
spectra of bulges and disks give several important constraints on the
formation histories of S0 galaxies relating to their stellar mass and
environment. In general, the stellar age-metallicity relation of bulges
appears to be tight, whereas that of disks shows a negative offset from the
bulge relation and has larger scatter. This implies that the star-formation
history of the disks may be much more complex than that of the bulges. We
found that age has more influence on the offset in the age-metallicity
relation between bulge and disk than does metallicity. Most bulges are older
than disks, while there is no systematic difference in metallicity.

Our results show that the formation histories of S0 galaxies depend on both
their stellar mass and their environment. A more massive S0 galaxy tends to
have a larger age difference between its bulge and disk. However, when stellar
mass is controlled, an S0 galaxy in a higher-density environment tends to have
a larger age difference. From these results, we suggest two scenarios of S0
formation depending on environment.

1\. In dense environments, S0s were formed by major merger(s) or rapid
collapse at an early epoch. The star formation in the early-formed bulges was
quenched by internal mechanisms. After the bulge quenching, the ambient
material ejected from the violent merger (re)formed disks, which continued
their star formation for a long time (up to 5 Gyr from our results). As the
S0s moved to higher-density environments over time, the star formation in
disks was eventually also quenched, mainly by environmental effects such as
gas-stripping.

2\. In low-density environments, bulges were formed at an early epoch in a
similar way to the bulges in high-density environments. However, unlike their
high-density counterparts, they have been more easily rejuvenated by
interactions with gas-rich neighbor galaxies. Both bulges and disks may have
been influenced by gas accretion, and so the bulges and disks in low-density
environment have very similar stellar populations. The major quenching
mechanism in low-density environments may be simple fading through gas
consumption by steady star formation.

In short, S0s in low-density environments may be faded spirals, while high-
mass S0s in dense environments may have formed via dissipative merger(s),
subsequent disk re-building, and finally environmental quenching. These
scenarios are consistent with our overall results, but remain somewhat
speculative and are too simple to explain all details. Thus, they need to be
more rigorously tested and elaborated in further investigations. Most
importantly, a much larger sample needs to be analyzed in a consistent method
to ensure high statistical reliability.

We gratefully thank the anonymous referee for constructive comments that have
significantly improved this manuscript. We are also grateful to Yujin Yang for
helpful discussions. This study uses data provided by the Calar Alto Legacy
Integral Field Area (CALIFA) survey (http://califa.caha.es/). Based on
observations collected at the Centro Astronómico Hispano Alemán (CAHA) at
Calar Alto, operated jointly by the Max-Planck-Institut für Astronomie and the
Instituto de Astrofísica de Andalucía (CSIC). Parts of this research were
conducted by the Australian Research Council Centre of Excellence for All Sky
Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013.
FDE acknowledges funding through the H2020 ERC Consolidator Grant 683184.

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