# Different influence of gas accretion on the evolution of star-forming and
non-star-forming galaxies

Min Bao School of Physics and Technology, Nanjing Normal University, Nanjing
210023, China  School of Astronomy and Space Science, Nanjing University,
Nanjing 210023, China  Wenlong Zhao  School of Physics and Technology, Nanjing
Normal University, Nanjing 210023, China  Qirong Yuan School of Physics and
Technology, Nanjing Normal University, Nanjing 210023, China Qirong Yuan
<EMAIL_ADDRESS>
###### Abstract

Using integral field spectroscopic data from the Mapping Nearby Galaxies at
Apache Point Observatory survey, we investigate the spatially resolved
properties and empirical relations of a star-forming galaxy and a non-star-
forming galaxy hosting counter-rotating stellar disks (CRDs). The DESI $g,r,z$
color images reveal no evidence of merger remnants in either galaxy,
suggesting that gas accretion fuels the formation of CRDs. Based on the
visible counter-rotation in the stellar velocity field, we can fit a spatial
boundary to distinguish the inner and outer regions dominated by two stellar
disks in each galaxy. In the inner region of the star-forming CRDs, stars are
co-rotating with ionized gas, and the stellar population is younger.
Comparison of the star-forming main sequence relations between the inner and
outer regions reveals enhanced star formation in the inner region. Given the
abundant pre-existing gas in the star-forming galaxy, collisions between pre-
existing and external gas efficiently consume angular momentum, triggering
star formation in the inner region. Conversely, in the outer region of the
non-star-forming CRDs, stars are co-rotating with ionized gas, and the stellar
population is younger. Comparison of the stellar mass-metallicity relations
between the inner and outer regions indicates enriched gas-phase metallicity
in the outer region. Considering the less abundant pre-existing gas in the
non-star-forming galaxy, external gas could preserve angular momentum, fueling
star formation in the outer region. Overall, gas accretion exhibits different
influence on the evolution of star-forming and non-star-forming galaxies.

galaxies: kinematics and dynamics — galaxies: evolution

##  1 Introduction

Gas accretion, known as a key process in baryon cycle, can provide material
for galaxy evolution (Husemann et al., 2011; Chen et al., 2013; Sánchez
Almeida et al., 2014). On one hand, metal-poor gas in the circumgalactic
medium (CGM) is accreted into galaxies, dilutes the gas-phase metallicity in
the interstellar medium (ISM), and fuels the star formation. On the other
hand, the metals produced by stars are released into the ISM through processes
including stellar winds or supernova explosions. Furthermore, the intensive
star formation in the galactic center can trigger outflows in galactic-scale,
which entrain the metals from the ISM (Veilleux et al., 2005), and generate
feedback on star formation in the ISM. The impacts of gas accretion on the
star formation and metallicity inside galaxies, as well as its influence on
galaxy evolution are still open questions.

Based on single-fiber observations, Andrews & Martini (2013) discovered a
negative correlation between gas-phase metallicity and star formation rate,
verifying the contribution of gas accretion to galaxy evolution. With the
development of long-slit spectroscopic and integral field spectroscopic
instruments, the existence of kinematically misaligned galaxies has been
revealed (Corsini, 2014), which are characterized by the misaligned rotations
between two components such as gas-gas, gas-star, or star-star. The misaligned
rotations are defined by $\Delta\phi\equiv|\phi_{1}-\phi_{2}|>30^{\circ}$,
where $\phi_{1}$ and $\phi_{2}$ represent the position angles of two
components. The position angle is defined by the counterclockwise angle
between the north and a line bisecting the velocity field on the receding
side. The previous studies indicated that these galaxies have undergone gas
acquisition events, including mergers and gas accretion, which deliever
reversed angular momentum from external. Numerical simulations suggested that
gas accretion from the cosmic web dominates the galaxy growth with
contribution $\sim$3 to 4 times more than mergers (Sánchez Almeida et al.,
2014). Therefore, the misaligned galaxies in the local Universe can serve as
valuable laboratories for investigating the influence of gas accretion on
galaxy evolution.

In previous studies, the detection rate of gas-star misalignment in the non-
star-forming galaxies has been reported to range from approximately 20% to 50%
(Sarzi et al., 2006; Davis et al., 2011; Barrera-Ballesteros et al., 2015),
while in the star-forming galaxies, it is notably lower at around 2% to 5%
(Jin et al., 2016; Bryant et al., 2019). Bevacqua et al. (2022) recently
analyzed data from the Mapping Nearby Galaxies at Apache Point Observatory
(MaNGA) survey, identifying 64 star-star counter-rotating galaxies, and
finding frequencies of less than 5% for the non-star-forming galaxies and less
than 1% for the star-forming galaxies. The counter-rotation is defined by
$\Delta\phi\equiv|\phi_{1}-\phi_{2}|>150^{\circ}$. Given the abundant gas
content in the star-forming galaxies, collisions between pre-existing and
external gas can efficiently consume the angular momentum. Meanwhile, the non-
star-forming galaxies have lower gas content, allowing external gas to retain
its angular momentum and to manifest as counter-rotation. These differences in
pre-existing gas content and efficiency of angular momentum consumption
suggest different formation scenarios for the misalignments (including
counter-rotations) in the star-forming and non-star-forming galaxies.

Jin et al. (2016) studied 66 gas-star misaligned galaxies from the MaNGA
survey, and found that the star-forming ones exhibit a positive radial
gradient in Dn4000, whereas the non-star-forming ones show a negative radial
gradient. They proposed that the misaligned gas in the star-forming galaxies
originates from gas-rich satellites or the cosmic web, where the consumption
of angular momentum drives gas inflow, subsequently triggering central star
formation. Meanwhile, the non-star-forming misaligned galaxies may form from
gas-poor progenitors by accreting misaligned gas. As a series, Xu et al.
(2022) compared the spatially resolved properties of 456 gas-star misaligned
galaxies with control galaxies, and found different trends in star-forming and
non-star-forming populations. In star-forming population, the misaligned
galaxies have enhanced central star formation compared to their control
galaxies, while the difference is small in non-star-forming population. These
phenomenons support the different formation scenarios for two populations
proposed by Jin et al. (2016). Furthermore, Zhou et al. (2022) compared the
global properties of these 456 gas-star misaligned galaxies with control
galaxies, suggesting that the star-forming misaligned galaxies form via gas
accretion, while the non-star-forming misaligned galaxies may either form
through gas accretion or evolve from star-forming misaligned galaxies.

Bevacqua et al. (2022) investigated the kinematics of 64 star-star counter-
rotating galaxies. They found that the ionized gas in half of these galaxies
is co-rotating with one of the stellar disks, which hosts younger stellar
population. Bao et al. (2022) collected 101 star-star counter-rotating
galaxies from the MaNGA survey, and categorized them into four types based on
the velocities of stars and ionized gas. These counter-rotating galaxies are
also classified into star-forming and non-star-forming populations. It turned
out that the formation scenarios for star-star counter-rotations are different
in two populations, which are governed by the efficiency of angular momentum
consumption. In the star-forming galaxies with more abundant pre-existing gas,
collisions between pre-existing and external gas efficiently consume the
angular momentum. As a result, the inflowing gas can trigger star formation in
the center, leading to the co-rotating gas with stars in the inner region.
Meanwhile, the consumption of angular momentum is less efficient in the non-
star-forming galaxies, so that external gas can fuel star formation on the
outskirts, leading to co-rotating gas with stars in the outer region.

In this study, we aim to investigate the influence of gas accretion on galaxy
evolution, including star formation and metal enrichment in different regions,
by comparing spatially resolved properties and empirical relations. We focus
on two galaxies, one star-forming (SDSS J090852.63+445556.1, named SDSS
J0908+4455) and one non-star-forming (SDSS J093053.94+352623.2, named SDSS
J0930+3526), selected from the sample of Bao et al. (2022) due to their
visible counter-rotations between inner and outer regions in the stellar
velocity fields. To make comparisons between these two regions, we fit a
spatial boundary in the stellar velocity field of each galaxy. The involved
data are presented in Section 2. In Section 3, we present the spatially
resolved properties and empirical relations. Finally, we discuss the gas
accretion fueling formation of counter-rotations and the influence of gas
accretion on star formation and metal enrichment in Section 4. Throughout this
paper, we adopt a set of cosmological parameters as follows: $H_{0}$ = 70 km
s-1, $\Omega_{\rm m}$ = 0.30, $\Omega_{\rm\Lambda}$ = 0.70.

##  2 The Data

The MaNGA survey is one of the three core programs in the fourth-generation
Sloan Digital Sky Survey (SDSS-IV) (Bundy et al., 2015; Law et al., 2016).
MaNGA utilized the Baryon Oscillation Spectroscopic Survey (BOSS)
spectrographs (Smee et al., 2013) on the 2.5-m Sloan Foundation Telescope
(Gunn et al., 2006). This survey conducted IFU observations on a
representative sample, which consists of approximately 10,010 unique galaxies
with a flat stellar mass distribution in $10^{9}-10^{11}\rm~{}M_{\odot}$ and a
redshift distribution in $0.01-0.15$ (Blanton et al., 2017). Two dual-channel
BOSS spectrographs (Smee et al., 2013) provide simultaneous wavelength
coverage from 3,600 to 10,000Å. The spectral resolution is $\sim$2,000, which
allows measurements of all strong emission line species from [O
ii]$\lambda$3726 to [S ii]$\lambda$6731.

We obtain the global properties including redshift ($z$), axial ratio
($q=b/a$) and photometric position angle ($\phi$) from NASA-Sloan Atlas (NSA,
Blanton et al. 2011). The global stellar mass and attenuation-corrected star
formation rate are obtained by MaNGA Data Reduction Pipeline (DRP, Law et al.
2016) and Data Analysis Pipeline (DAP, Westfall et al. 2019). The spatially
resolved properties, including emission line flux, stellar (or gas) velocity
and velocity dispersion, as well as 4000 Å break (Dn4000) indicating the light
weighted stellar population age, are extracted from the MaNGA DAP. The gas
kinematics is traced by ionized hydrogen (H$\alpha$), while all the emission
line centers are tied together in the velocity space in the MaNGA DAP. In
addition, we acquire the stellar mass ($M_{\star}$) in each spaxel from the
data cube of PIPE3D (Sánchez et al., 2016), which analyzed the physical
properties of stellar populations of a galaxy using the spectral fitting tool
FIT3D.

We use H$\alpha$/H$\beta$ ratio to estimate the extinction corrected intensity
of emission lines under the Case B (Calzetti, 2001):

$F_{\lambda}=F_{\lambda,0}\times{10}^{-0.4k(\lambda)E(B-V)},$ (1)

where $k(\lambda)$ is the Galactic dust attenuation curve, and color excess
$E(B-V)=0.934\times{\rm ln}[(F_{H\alpha}/F_{H\beta})/2.86]$.

The star formation rate (SFR) quantifies the star formation activity within
106-7 years. Following the method from Kennicutt (1998), we utilize the
H$\alpha$ luminosity in each spaxel to estimate the spatially resolved SFR
with a Salpeter IMF (Salpeter, 1955):

$SFR(M_{\odot}\ yr^{-1})=7.9\times 10^{-42}L_{H\alpha}(1-f_{AGN}),$ (2)

where we consider a correction factor $f_{\rm AGN}$ to mitigate contamination
from active galactic nuclei (AGN), as described in Section 3.1.

The gas-phase metallicity 12 + $\log$(O/H) serves as a reliable indicator of
the star formation history. We use $\rm R_{23}$ indicator from Tremonti et al.
(2004) to estimate the gas-phase metallicity in each spaxel:

$12+log(O/H)=9.185-0.313x-0.264x^{2}-0.321x^{3},$ (3)

where $\rm x\equiv\log\\{({\hbox{[O\,{\sc ii}]}}\lambda\lambda
3726,3729+{\hbox{[O\,{\sc iii}]}}\lambda\lambda
4959,5007)/{\hbox{H$\beta$}}\\}$.

SDSS J0908+4455 and SDSS J0930+3526 have been identified as galaxies hosting
counter-rotating stellar disks (CRDs) by Bao et al. (2022), characterized by
visible counter-rotations between the inner and outer regions in stellar
velocity fields. Bao et al. (2022) found that the external gas, which is
counter-rotating with the pre-existing gas, provides material for the
formation of CRDs, while the formation scenarios for the star-forming and non-
star-forming galaxies are different. The global $M_{\star}$ and SFR indicate
that SDSS J0908+4455 is a star-forming galaxy located in the blue-cloud, while
SDSS J0930+3526 is a non-star-forming galaxy located in the green-valley,
approaching the red-sequence. The comparisons on spatially resolved properties
and empirical relations between these two galaxies can help verifying the
formation scenarios proposed by Bao et al. (2022), and investigating the
contributions of different scenarios to galaxy evolution.

##  3 Results

###  3.1 Spatially resolved properties

Figure 1(a) displays the SDSS $g,r,i$ color image of SDSS J0908+4455. Figure
1(b) displays the stellar velocity field for the spaxels with spectral signal-
to-noise ratio (S/N) higher than 3, and the same criterion is used in the
following maps of stellar properties. Stars in the inner region are counter-
rotating with that in the outer region, indicating the existence of two CRDs
in this galaxy. Given that MaNGA DAP employed the PPXF single kinematic
component fit in the stellar continuum spectra, one of the stellar disks with
stronger absorption dominates the stellar velocity. Therefore, the stellar
velocity in the inner region is dominated by one stellar disk (named inner
disk), while the stellar velocity in the outer region is dominated by another
stellar disk (named outer disk).

Figure 1: Spatially resolved properties of SDSS J0908+4455. (a) SDSS $g,r,i$
color image. (b) The stellar velocity field for spaxels with spectral S/N
higher than 3. The black dashed ellipse shows the rotation track where the
directions of stellar rotation reverse, and keeps same in panel (e). (c) The
gas velocity field for spaxels with H$\alpha$ emission line S/N higher than 3.
(d) The differences in position angles between the stars and gas as functions
of radii. (e) The stellar velocity dispersion field for spaxels with spectral
S/N higher than 3. The black dashed line shows the major axis, and keeps the
same in the following maps of SDSS J0908+4455. (f) The D${}_{n}4000$ map for
spaxels with spectral S/N higher than 3.

Figure 1(c) displays the gas velocity field for the spaxels with H$\alpha$
emission line S/N higher than 3. Comparing the stellar and gas velocity
fields, we find that the inner disk is co-rotating with the gas disk, while
the outer disk is counter-rotating with the gas disk. We employ KINEMETRY
package (Krajnović et al., 2011) to fit the stellar and gas velocity fields in
each 0.5′′ (i.e. pixel size) rotation track, and obtain the position angles.
We then compute the differences in position angles between stars and gas,
$\Delta\phi=|\phi_{\star}-\phi_{\rm gas}|$, as a function of radii, displayed
in Figure 1(d). The differences reverse from $\Delta\phi\sim$0∘ to
$\Delta\phi\sim$180∘ at a radius of $R\sim 3^{\prime\prime}$. We take this
radius as a spatial boundary for the regions dominated by inner and outer
disks. A rotation track with $R\sim 3^{\prime\prime}$ is over-plotted onto the
stellar velocity field as a black dashed ellipse in Figure 1(b).

Figure 1(e) displays the stellar velocity dispersion field. The black dashed
line in Figure 1(e) represents the photometric major axis (hereafter major
axis) of SDSS J0908+4455, and the black dashed ellipse is the same as Figure
1(b). The stellar velocity dispersion is high in two centrosymmetric regions
(i.e. 2$\sigma$ regions) along the major axis, coinciding with the boundary
between the inner and outer regions. The absorption strengths of two stellar
disks are comparable at this boundary, leading to broadened absorption lines
and resulting in high velocity dispersions. Figure 1(f) displays the Dn4000
map, which describes the star formation intensity in Gyr-timescale. Along the
major axis (black dashed line), Dn4000 exhibits a low value of $\sim$1.3 in
the galactic disk, including the 2$\sigma$ regions.

Figure 2: Spatially resolved properties of SDSS J0930+3526. (a) SDSS $g,r,i$
color image. (b) The stellar velocity field for spaxels with spectral S/N
higher than 3. The black dashed ellipse shows the rotation track where the
directions of stellar rotation reverse, and keeps same in panel (e). (c) The
gas velocity field for spaxels with H$\alpha$ emission line S/N higher than 3.
(d) The differences in position angles between the stars and gas as functions
of radii. (e) The stellar velocity dispersion field for spaxels with spectral
S/N higher than 3. The black dashed line shows the major axis, and keeps the
same in the following maps of SDSS J0930+3526. (f) The D${}_{n}4000$ map for
spaxels with spectral S/N higher than 3.

Figure 2(a) displays the SDSS $g,r,i$ color image of SDSS J0930+3526. Figures
2(b) and 2(e) display the stellar velocity and velocity dispersion fields. On
one hand, the stellar kinematics is similar to SDSS J0908+4455 in: (1)
counter-rotating inner and outer disks shown in the stellar velocity field
(Figure 2b); (2) high stellar velocity dispersion at the boundary of two disks
(Figure 2e). On the other hand, the difference from SDSS J0908+4455 is that
the inner disk is counter-rotating with the gas disk (Figure 2c), while the
outer disk is co-rotating with the gas disk. We applied the same method to fit
the stellar and gas rotations in SDSS J0930+3526. The differences in position
angles between stars and gas in Figure 2(d) reverses from $\Delta\phi\sim$180∘
to $\Delta\phi\sim$0∘ at a radius of $R\sim 3^{\prime\prime}$. Rotation tracks
with $R\sim 3^{\prime\prime}$ are over-plotted onto the stellar kinematic
fields in Figures 2(b) and 2(e). Figure 2(f) displays the Dn4000 map. Along
the major axis (black dashed line), Dn4000 presents the highest value of
$\sim$1.7 in the central region, while it has a lower value of $\sim$1.4 in
the galactic disk, including the 2$\sigma$ regions.

Figure 3: BPT diagnostic and spatially resolved maps of SDSS J0908+4455 and
SDSS J0930+3526, for the spaxels with H$\beta$, [O iii]$\lambda$5007,
H$\alpha$, and [N ii]$\lambda$6583 emission line S/Ns higher than 3. (a) The
BPT diagnostic map of SDSS J0908+4455. The black solid curve shows the
demarcation between the star-forming and composite regions defined by Kewley
et al. (2001), and the black dashed curve shows the demarcation between the
composite and AGN regions defined by Kauffmann et al. (2003). The blue and
green dots mark the spaxels in star-forming and composite regions that are
color-coded by the distance to the black solid curve. (b) The spatially
resolved BPT map of J0908. The color-codes are the same as the panel (a). (c)
The BPT diagnostic map of SDSS J0930+3526. The color- and symbol-codes are the
same as panel (a), except for the red dots mark the spaxels in AGN region. (d)
The spatially resolved BPT map of SDSS J0930+3526. The color-codes are the
same as panel (c).

Mapping diagnostic emission line ratios can provide information on the
mechanisms of gas ionization. Figure 3(a) displays the [N ii] BPT diagnostic
map of SDSS J0908+4455 for spaxels with H$\beta$, [O iii]$\lambda$5007,
H$\alpha$ and [N ii]$\lambda$6583 emission line S/Ns higher than 3, and the
same criteria are used in the following BPT maps. The black solid curve shows
the demarcation between the star-forming and composite regions defined by
Kewley et al. (2001), and the black dashed curve shows the demarcation between
the composite and AGN regions defined by Kauffmann et al. (2003). Each dot
represents the line ratios measured in corresponding spaxel, with color coded
by the distance to the black solid curve. Figure 3(b) displays the spatially
resolved BPT map of SDSS J0908+4455, with the black dashed line representing
the major axis and the color-codes being the same as Figure 3(a). The spaxels
along the major axis are characterized by star formation, while the spaxels
perpendicular to the major axis locate in the composite region. Figures 3(c)
and 3(d) display the [N ii] BPT diagnostic map and spatially resolved BPT map
of SDSS J0930+3526. The black solid and dashed curves in Figure 3(c), as well
as the color-codes in Figures 3(c) and 3(d) are the same as Figure 3(a). In
Figure 3(d), the spaxels along the major axis (black dashed line) are
basically characterized by star formation, with a few areas belonging to the
composite region.

Figure 4: AGN fractions of SDSS J0908+4455 and SDSS J0930+3526, for the
spaxels with H$\beta$, [O iii]$\lambda$5007, H$\alpha$, and [N
ii]$\lambda$6583 emission line S/Ns higher than 3. (a) The BPT diagnostic map
of SDSS J0908+4455. The spaxels are color-coded by AGN fraction. The brown
dashed curve is the best-fit linear correlation between [N ii]/H$\alpha$ and
[O iii]/H$\beta$ in the linear space. The black diamond on the left marks the
endpoint on the brown dashed curve, where the AGN fraction is set as 0. The
black diamond on the right marks the other endpoint, where the AGN fraction is
set as 1. (b) The AGN fraction map of SDSS J0908+4455. The color-codes are the
same as panel (a). (c) The BPT diagnostic map of SDSS J0930+3526. The color-
and symbol-codes are the same as panel(a). (d) The AGN fraction map of SDSS
J0908+4455. The color-codes are the same as panel(c).

The spatially resolved empirical relations, including star-forming main
sequence relation (MSR) and stellar mass-metallicity relation (MZR) can offer
insights into the star formation history of a galaxy. However, these relations
can be contaminated by AGN. To exclude the contamination, we adopt the methods
from Davies et al. (2016) and Shin et al. (2019) to quantify the contribution
of AGN in each spaxel. Figures 4(a) and 4(c) display the same [N ii] BPT
diagnostic maps as Figures 3(a) and 3(c). We fit a linear correlation between
[N ii]/H$\alpha$ and [O iii]/H$\beta$ in the linear space for two galaxies,
respectively. The red dashed curves in Figures 4(a) and 4(c) show the best-fit
results for two galaxies. The black diamonds in Figure 4(c) mark the
endpoints, obtained by projecting the dots with the minimum (P0) and maximum
(P1) [N ii]/H$\alpha$ values onto the curve. Since the distribution of SDSS
J0908+4455 in the [N ii] BPT diagnostic map (Figure 4a) is less extended than
SDSS J0930+3526 (Figure 4c), we extract the minimum and maximum values from
Figure 4(c), and project them onto the curve in Figure 4(a) (black diamonds).
The AGN fraction is defined by $f_{\rm AGN}=L_{\rm P0,N}/L_{\rm P0,P1}$, where
LP0,N represents the projected distance along the curve between P0 and the Nth
dot, and LP0,P1 represents the projected distance along the curve between P0
and P1. The color of each spaxel in Figures 4(a) and 4(c) is coded by the AGN
fraction. Figures 4(b) and 4(d) display the spatially resolved maps of AGN
fraction, where the color-codes are the same as Figures 4(a) and 4(c).

###  3.2 Star-forming main sequence relation

Figure 5 displays the MSR of the spaxels in SDSS J0908+4455, with spectral S/N
and [O ii]$\lambda\lambda$3726,3729, H$\beta$, [O
iii]$\lambda\lambda$4959,5007, H$\alpha$, and [N ii]$\lambda$6583 emission
line S/Ns higher than 3, and the same criteria are used in the following MSRs
and MZRs. The SFR in each spaxel is estimated following Equation 2, which
excludes the contamination from AGN. In Figure 5(a), each dot represents the
location of corresponding spaxel in the main sequence plane, color-coded by
radius. The spaxels in SDSS J0908+4455 follow a tight MSR, characterized by a
linear correlation between $M_{\star}$ and SFR. Both $M_{\star}$ and SFR are
highest in the center, and monotonously decrease with increasing radius. The
dots in Figure 5(b) share the same positions with Figure 5(a), while are
color-coded by the light weighted stellar population age (Dn4000). It turns
out that the young stellar population locates in the inner region with high
$M_{\star}$ and SFR, indicating recent star formation in this region.

Figure 5: Star-forming main sequence of SDSS J0908+4455. (a) The dots show the
distributions of spaxels with spectral S/N and [O
ii]$\lambda\lambda$3726,3729, H$\beta$, [O iii]$\lambda\lambda$4959,5007,
H$\alpha$, and [N ii]$\lambda$6583 emission line S/Ns higher than 3 in the
main sequence plane. The colors are coded by the radii normalized to the
effective radius. (b) The distributions are the same as panel (a), while the
colors are coded by the D${}_{n}4000$ indices. (c) The distributions are the
same as panel (a). The light orange dots represent the spaxels that locate in
the inner region, while the light green dots represent the spaxels that locate
in the outer region. The orange square shows the median $M_{\star}$ and SFR
for each $M_{\star}$ bin in the inner region, while the green square marks the
median $M_{\star}$ and SFR for each $M_{\star}$ bin in the outer region. The
corresponding error bar shows the 25$\%$ to 75$\%$ SFR error in each bin.

In Figure 5(c), we take the spatial boundary (black dashed ellipse) from
Figure 1(b) to distinguish the spaxels dominated by the inner and outer disks.
The light-orange dots represent the spaxels in the inner region dominated by
the inner disk, and the light-green dots represent the spaxels in the outer
region dominated by the outer disk. We equally divide the spaxels in the inner
or outer regions into five $M_{\star}$ bins. For each bin in the inner region,
the orange square shows the median SFR, with the orange bar showing the 25% to
75% SFR error. Similarly, the green square shows the median SFR for each bin
in the outer region, with the green bar showing the SFR error. Overall, the
$M_{\star}$ and SFR in the inner region (light-orange dots) are higher than
that in the outer region (light-green dots). Furthermore, the SFR of the bin
with $M_{\star}\sim 10^{7.5}\rm M_{\odot}$ in the inner region (leftmost
orange square) exceeds that in the outer region. Given that the spaxels in the
inner and outer regions with $M_{\star}\sim 10^{7.5}\rm M_{\odot}$ have
continuous radii, presented as unified colors in this bin in Figure 5(a). The
difference in SFR between the inner and outer regions indicates a gap in the
star formation intensity between the inner and outer disks, implying the
enhanced star formation in the inner disk.

Figure 6: Star-forming main sequence of SDSS J0930+3526. (a) The dots show the
distributions of spaxels with spectral S/N and [O
ii]$\lambda\lambda$3726,3729, H$\beta$, [O iii]$\lambda\lambda$4959,5007,
H$\alpha$, and [N ii]$\lambda$6583 emission line S/Ns higher than 3 in the
main sequence plane. The colors are coded by the radii normalized to the
effective radius. (b) The distributions are the same as panel (a), while the
colors are coded by the D${}_{n}4000$ indices. (c) The distributions are the
same as panel (a). The light orange dots represent the spaxels that locate in
the inner region, while the light green dots represent the spaxels that locate
in the outer region. The orange square shows the median $M_{\star}$ and SFR
for each $M_{\star}$ bin in the inner region, while the green square marks the
median $M_{\star}$ and SFR for each $M_{\star}$ bin in the outer region. The
corresponding error bar shows the 25$\%$ to 75$\%$ SFR error in each bin.

Figure 6 displays the MSR of the spaxels in SDSS J0930+3526, with the SFR
estimated following Equation 2. In Figures 6(a) and 6(b), the dots represent
the locations of spaxels in the main sequence plane, color-coded by radii and
Dn4000, respectively. Similar to SDSS J0908+4455 (Figure 5a), the $M_{\star}$
and SFR decrease with increasing radius in Figure 6(a). However, the young
stellar population locates in the outer region with low $M_{\star}$ and SFR,
suggesting that additional star formation could occur recently in this region.
The S$\acute{\rm e}$rsic index of SDSS J0930+3526 equals $\sim$2.41,
indicating the existence of a bulge component in this galaxy, which can also
be found in the center of SDSS $g,r,i$ color image in Figure 2(a). The old
stellar population in the bulge dominates the age in the center. In Figure
6(c), the light-orange and light-green dots representing spaxels in the inner
and outer regions, are separated by the spatial boundary (black dashed
ellipse) from Figure 2(b), and are equally divided into five $M_{\star}$ bins.
The orange or green square shows the median SFR in each bin, and implies that
the $M_{\star}$ and SFR of inner and outer regions follow a consistent MSR.

###  3.3 Stellar mass-metallicity relation

Figure 7 displays the MZR of spaxels in SDSS J0908+4455. The gas-phase
metallicity is estimated following Equation 3. In Figures 7(a) and 7(b), the
colors of dots represent radii and Dn4000, respectively. A tight correlation
between $M_{\star}$ and metallicity is observed for spaxels with
$M_{\star}>10^{7}~{}\rm M_{\odot}$, while it becomes scattered for spaxels
with $M_{\star}<10^{7}~{}\rm M_{\odot}$. The $M_{\star}$ and metallicity are
highest in the center, and decrease with increasing radius. Given the young
stellar population in the inner region (Figure 7b), the gas-phase metallicity
can be enriched by the recent star formation in this region. Figure 7(c)
displays the MZRs in the inner and outer regions, represented by light-orange
and light-green dots. Following the $M_{\star}$ bins in Figures 5(c), the
orange and green squares show the median metallicity in each $M_{\star}$ bin
with 25% - 75% metallicity error. Different from the gap observed in SFR
(Figure 5c), the gas-phase metallicity of the inner and outer regions are
consistent at the boundary, i.e. the inner and outer regions of SDSS
J0908+4455 follow a consistent MZR.

Figure 7: Stellar mass-metallicity relation of SDSS J0908+4455. (a) The dots
show the distributions of spaxels with spectral S/N and [O
ii]$\lambda\lambda$3726,3729, H$\beta$, [O iii]$\lambda\lambda$4959,5007,
H$\alpha$, and [N ii]$\lambda$6583 emission line S/Ns higher than 3 in the
stellar mass-metallicity plane. The colors are coded by the radii normalized
to the effective radius. (b) The distributions are the same as panel (a),
while the colors are coded by the D${}_{n}4000$ indices. (c) The distributions
are the same as panel (a). The light orange dots represent the spaxels that
locate in the inner region, while the light green dots represent the spaxels
that locate in the outer region. The orange square shows the median
$M_{\star}$ and $12+\log(\rm O/H)$ for each $M_{\star}$ bin in the inner
region, while the green square marks the median $M_{\star}$ and $12+\log(\rm
O/H)$ for each $M_{\star}$ bin in the outer region. The corresponding error
bar shows the 25$\%$ to 75$\%$ $12+\log(\rm O/H)$ error in each bin.

Figure 8 displays the MZR of spaxels in SDSS J0930+3526. The gas-phase
metallicity is estimated following Equation 3. In Figures 8(a) and 8(b), the
colors of dots represent radii and Dn4000\. In Figure 8(c), the $M_{\star}$
bins and color-codes are the same as Figures 6(c). The $M_{\star}$ of inner
region is higher than that of outer region in Figure 8(c), while the gas-phase
metallicity of two regions are comparable. Previous studies have demonstrated
positive correlations between $M_{\star}$ and metallicity both in global and
spatially resolved analyses (Tremonti et al., 2004; Kewley & Ellison, 2008;
Barrera-Ballesteros et al., 2016; Li et al., 2024). Combining the young
stellar population in the outer region (Figure 8b) of SDSS J0930+3526, the
additional star formation in this region could also contribute to the metal
enrichment.

Figure 8: Stellar mass-metallicity relation of SDSS J0930+3526. (a) The dots
show the distributions of spaxels with spectral S/N and [O
ii]$\lambda\lambda$3726,3729, H$\beta$, [O iii]$\lambda\lambda$4959,5007,
H$\alpha$, and [N ii]$\lambda$6583 emission line S/Ns higher than 3 in the
stellar mass-metallicity plane. The colors are coded by the radii normalized
to the effective radius. (b) The distributions are the same as panel (a),
while the colors are coded by the D${}_{n}4000$ indices. (c) The distributions
are the same as panel (a). The light orange dots represent the spaxels that
locate in the inner region, while the light green dots represent the spaxels
that locate in the outer region. The orange square shows the median
$M_{\star}$ and $12+\log(\rm O/H)$ for each $M_{\star}$ bin in the inner
region, while the green square marks the median $M_{\star}$ and $12+\log(\rm
O/H)$ for each $M_{\star}$ bin in the outer region. The corresponding error
bar shows the 25$\%$ to 75$\%$ $12+\log(\rm O/H)$ error in each bin.

##  4 Discussion

The evolution of a galaxy, known as a complex system, is regulated by both
internal and external processes. External processes, including galaxy mergers
and gas accretion, can deliever gas with misaligned angular momentum. Once the
external gas becomes more abundant than the pre-existing gas in progenitor, it
can fuel the formation of misaligned structures, including counter-rotations.
In observations, agreement still hasn’t been reached on whether mergers or gas
accretion dominate the formation of CRDs. Previous studies have proposed the
formation scenarios for CRDs as major merger (Crocker et al., 2009) or minor
merger (Pizzella et al., 2014; Fabricius et al., 2014; Katkov et al., 2024),
gas accretion from satellite (Coccato et al., 2011, 2013) or enviroment
(Coccato et al., 2013; Pizzella et al., 2014; Fabricius et al., 2014; Pizzella
et al., 2018), as well as merger with consequent slow gas accretion (Katkov et
al., 2016).

Figure 9: DESI $g,r,z$ color images, with the purple hexagon displaying the
field-of-view of MaNGA survey. (a) The image of SDSS J0908+4455. (b) The image
of SDSS J0930+3526.

Ji et al. (2014) simulated mergers with different mass ratios, incorporating
physical processes such as gas cooling, star formation, and supernova
feedback, and investigated the corresponding merger times. For a surface
brightness limit of 25 mag arcsec-2, the merger remnant features can be
observed in $\sim$2.57 Gyr for equal-mass mergers, while can be observed in
$\sim$5.19 Gyr for unequal-mass mergers. Figures 9(a) and 9(b) display the
DESI images of SDSS J0908+4455 and SDSS J0930+3526, which are much deeper than
25 mag arcsec-2 in $r$-band. Equal-mass mergers, known as disruptive events,
can destroy the present morphology of galaxies and tend to form elliptical
galaxies (Bournaud et al., 2005; Qu et al., 2011). However, disk structures
are present in both DESI images in Figures 9(a) and 9(b), which exclude the
possiblity of CRDs contributed by equal-mass mergers. Following the method
from Li et al. (2021), we collect the $g$\- and $r$-band images, convolve one
band having smaller seeing with a Gaussian function to match the point spread
function of the other band, and stack two images to improve S/N. By visual
inspection, we find no merger remnant features in these two galaxies,
indicating that SDSS J0908+4455 and SDSS J0930+3526 haven’t experienced merger
events at least within the past 5 Gyr.

Chen et al. (2016) investigated the gas-star misalignment in 9 star-forming
galaxies, and found that the stellar population is younger and star formation
is more active in the center compared to the outskirts. Jin et al. (2016)
enlarged the sample to 10 star-forming, 26 green-valley, and 30 quiescent gas-
star misaligned galaxies. They also observed a positive radial gradient of
Dn4000 in the star-forming misaligned galaxies, while the Dn4000 follows a
negative radial gradient in the non-star-forming ones. Xu et al. (2022)
further enlarged the sample to 72 star-forming, 142 green-valley and 242
quiescent gas-star misaligned galaxies. They found enhanced star formation in
the center of the star-forming misaligned galaxies, manifested as positive a
radial gradient of Dn4000 and a negative radial gradient of star formation
rate surface density. All these phenomenons support a scenario that accreted
gas with misaligned angular momentum is more abundant than the pre-existing
gas in the progenitors, resulting in kinematic misalignment between gas and
stars. Additionally, the pre-existing gas in the star-forming galaxies is
abundant, so that gas collisions can efficiently consume angular momentum,
trigger gas inflow and star formation in the center.

Figure 10: The star-forming main sequence relation along the major axis of
SDSS J0908+4455. (a) The stellar velocity field of SDSS J0908+4455 with
spectral S/N higher than 3. The black dashed ellipse is the boundary same as
Figure 1(b). The rectangles are centered on the major axis and extend $\pm$0.5
arcsec along the direction of minor axis, with orange, green, black colors
corresponding to the inner region, outer region, boundary between them. (b)
The star-forming main sequence relation inside the rectangles with spectral
S/N and [O ii]$\lambda\lambda$3726,3729, H$\beta$, [O
iii]$\lambda\lambda$4959,5007, H$\alpha$, and [N ii]$\lambda$6583 emission
line S/Ns higher than 3. The green, black, orange dots show the distributions
of the spaxels in rectangles with corresponding colors. The green and orange
solid lines are the best-fit linear correlations for the green and orange
dots.

The younger stellar population (Figure 5b) and enhanced star formation (Figure
5c) in the inner region of SDSS J0908+4455 support this scenario. To make a
clear comparison between the inner and outer regions, we exclude spaxels at
the boundary in the main sequence plane. Figure 10 displays the stellar
velocity field of SDSS J0908+4455. The black dashed ellipse represents the
spatial boundary, the same as Figure 1(b). Rectangles are centered on the
major axis and extends $\pm$0.5 arcsec along the direction of minor axis. The
orange and green rectangles mark the areas dominated by the inner and outer
disks, while the black rectangles mark the boundary areas. Figure 10(b)
displays the MSRs in different areas. Dots represent spaxels extracted from
different rectangles in Figure 10(a), with the yellow, green and black colors
corresponding to inner region, outer region and boundary. The orange and green
lines show the best-fit linear correlations for the inner and outer regions,
which have comparable slopes equaling 1.07 and 0.87, respectively. Meanwhile,
an obvious gap of $\sim$0.5 dex exists in SFR between two regions in Figure
10(b), quantitatively demonstrating the star formation enhancement in the
inner disk.

Figure 11: The stellar properties of the inner and outer regions of SDSS
J0908+4455 and SDSS J0930+3526. The marks show the H$\beta$ indices as
functions of [MgFe]′ indices, with the model-grid showing the prediction from
single stellar population models (Thomas et al., 2011). The blue star and
circle show the average indices of the inner and outer regions of SDSS
J0908+4455, and the red star and circle show the average indices of the inner
and outer regions of SDSS J0930+3526.

Gas-phase metallicity can provide insights into the origin of external gas.
Belfiore et al. (2017) studied the gas-phase metallicity in star-forming
regions across a representative sample of 550 MaNGA galaxies with
$M_{\star}\sim 10^{9}-10^{11.5}~{}\rm M_{\odot}$. They found the radial
metallicity gradient lying flat at $M_{\star}\sim 10^{9}~{}\rm M_{\odot}$,
while exhibiting slope as -0.14 dex $Re^{-1}$ at $M_{\star}\sim
10^{10.5}~{}\rm M_{\odot}$. The metallicity gradient approximately equals
-0.05 dex $Re^{-1}$ at $M_{\star}\sim 10^{9.5}-10^{9.75}~{}\rm M_{\odot}$
(Belfiore et al., 2017). For SDSS J0908+4455, the MaNGA DRP estimates its
global stellar mass to be $M_{\star}\sim 10^{9.6}~{}\rm M_{\odot}$.
Additionally, the effective radius of this galaxy is $\sim$3.0 arcsec,
coinciding with the radius of boundary between the inner and outer regions. In
other words, the inner disk happen to dominate the region inside the effective
radius. The MZR of inner region in Figure 7(c) implies a radial metallicity
gradient of $\sim$-0.1 dex $Re^{-1}$, steeper than the gradient of galaxies
with similar stellar mass, but comparable to that of more massive galaxies
(Belfiore et al., 2017). Gas accretion from the cosmic web can deliever metal-
poor gas into SDSS J0908+4455, which dilutes the gas-phase metallicity in the
disk. Meanwhile, the enhanced star formation in the inner disk can enrich the
gas-phase metallicity in the center, which steepens the radial metallicity
gradient.

To estimate the stellar properties of the inner and outer regions of two
galaxies, we collect the stellar indices from the MaNGA DRP, and calculate the
combined magnesium-iron index [MgFe]′ as $\sqrt{\rm Mgb\cdot(0.72\cdot
Fe5270+0.28\cdot Fe5335)}$, which is independent of $\alpha$-enhancement and
can be an effective indicator of the stellar metallicity (Thomas & Maraston,
2003). Figure 11 displays the H$\beta$ indices as functions of [MgFe]′
indices, with the model-grid showing the prediction from single stellar
population models (Thomas et al., 2011). The blue star and circle show the
average indices of the inner and outer regions of SDSS J0908+4455, and the red
star and circle show the average indices of the inner and outer regions of
SDSS J0930+3526. In SDSS J0908+4455, comparing the marks with the model-grid,
the stellar population ages of the inner and outer regions equal $\sim$1.53
Gyr and $\sim$2.64 Gyr, while the stellar metallicity (i.e. [Z/H]) of the
inner and outer regions are comparable, equaling $\sim$-0.14 and $\sim$-0.19.
The younger stellar population in the inner region supports the scenario that
the accreted gas triggers star formation in the inner region. In SDSS
J0930+3526, by similar comparisons, the stellar population ages of the inner
and outer regions equal $\sim$1.90 Gyr and $\sim$0.98 Gyr, while the stellar
metallicity of the inner and outer regions are comparable, equaling $\sim$0.24
and $\sim$0.19. Conversely, the younger stellar population in the outer region
supports the scenario that the accreted gas triggered star formation in the
outer region.

In Figure 6(c), the MSRs of inner region (orange squares) and outer region
(green squares) in SDSS J0930+3526 follow a consistent gradient. The pearson
coefficient ($r$), ranging from 0 to 1, is a parameter quantifying the
relativity between two parameters. A value closer to 1 indicates a strong
linear correlation between the two parameters. The r value between $M_{\star}$
and SFR (orange and green dots) in Figure 6(c) equals $\sim$0.93, indicating a
tight linear correlation. Thus, the inner and outer regions in SDSS J0930+3526
follow an unified MSR. In Figure 8(c), $M_{\star}$ of the inner region (green
dots) is generally higher than that of the outer region (orange dots).
However, the gas-phase metallicity of two regions turns out to be comparable.
The r value between $M_{\star}$ and metallicity equals $\sim$0.08, indicating
no linear correlation when considering the inner and outer regions as a whole.
Combining the younger stellar population in the outer region in Figure 11, we
propose that the external gas fueled the additional star formation in the
outer region of SDSS J0930+3526 and contributed to metal enrichment.

##  5 Summary

In this paper, we studied the spatially resolved physical properties and
empirical relations of two galaxies hosting CRDs, one star-forming galaxy and
one non-star-forming galaxy. The observational evidences support the formation
scenarios for CRDs proposed by Bao et al. (2022), and shed light on the
internal evolution processes along with the formation of CRDs.

SDSS J0908+4455 is a star-forming galaxy with more abundant pre-existing gas.
Efficient collisions between pre-existing and external gas can consume angular
momentum and trigger star formation in the inner region. The observational
evidences are as follows: (1) the stellar population in the inner region is
younger than that in the outer region; (2) the inner disk is co-rotating with
the gas disk; (3) the MSR of inner region has a comparable slope but $\sim$0.5
dex higher SFR compared to that of outer region, which indicates enhanced star
formation in the inner region; (4) the MZR of inner region implies a steep
radial gradient, which supports gas accretion from the cosmic web plus
enhanced star formation in the center.

SDSS J0930+3526 is a non-star-forming galaxy with less abundant pre-existing
gas. The angular momentum of external gas could be reserved. Consequently, the
external gas fueled star formation in the outer region, which enriched the
gas-phase metallicity in this region. The observational evidences are as
follows: (1) the stellar population in the outer region is younger than that
in the inner region; (2) the outer disk is co-rotating with the gas disk; (3)
the stellar mass of the inner region is generally higher than that of the
outer region, while the gas-phase metallicity of these two regions are
comparable, which indicates enriched gas-phase metallicity in the outer
region.

Acknowledgements: MB acknowledges support from the National Natural Science
Foundation of China, NSFC Grant No. 12303009. QY acknowledges support from the
National Natural Science Foundation of China, NSFC Grant Nos. 12273013,
12173020. 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 web site 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, the Chilean Participation
Group, the French Participation Group, Harvard-Smithsonian Center for
Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins
University, Kavli Institute for the Physics and Mathematics of the Universe
(IPMU) / University of Tokyo, 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
Observatory of China, New Mexico State University, New York University,
University of Notre Dame, Observatório 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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