# Spatially resolved analysis of Stellar Populations in NGC 2992: Impact of
AGN feedback

Xiaoyu Xu (许啸宇) School of Astronomy and Space Science, Nanjing University,
Nanjing 210023, China  Key Laboratory of Modern Astronomy and Astrophysics,
Nanjing University, Nanjing 210023, China  Department of Astronomy, Xiamen
University, Xiamen, Fujian 361005, China  Junfeng Wang Department of
Astronomy, Xiamen University, Xiamen, Fujian 361005, China  Zhiyuan Li School
of Astronomy and Space Science, Nanjing University, Nanjing 210023, China  Key
Laboratory of Modern Astronomy and Astrophysics, Nanjing University, Nanjing
210023, China  Yanmei Chen  School of Astronomy and Space Science, Nanjing
University, Nanjing 210023, China  Key Laboratory of Modern Astronomy and
Astrophysics, Nanjing University, Nanjing 210023, China

###### Abstract

In NGC 2992, a galaxy-scale ionized gas outflow driven by AGN has long been
recognized, yet its impact on the host galaxy has remained elusive. In this
paper, we utilize data from the archival Very Large Telescope (VLT)/MUSE to
present a spatially resolved analysis of stellar populations in this galaxy.
Two different stellar population templates are employed to fit the stellar
continuum, allowing us to determine the light-weighted stellar age,
metallicity, the fraction of the young stellar population (age $<100$ Myr,
$P_{\rm Y}$), and the average age and metallicity of $P_{\rm Y}$. Our results
reveal the presence of a very young stellar population ($\leq 40$ Myr) within
the dust lane and nearly along the galaxy’s major axis. The light-weighted
stellar age and the fraction of $P_{\rm Y}$ show negative trends along the
major and minor axes. The average age and metallicity of $P_{\rm Y}$ present
positive trends with increasing distance, except along the northern direction
of the major axis. Within the circumnuclear region ($<1$ kpc), the
distribution of the young stellar population is spatially anti-correlated with
the AGN outflow cone. The highest fraction of $P_{\rm Y}$ is observed at the
outskirts of the nuclear radio bubble in the northern region near the nucleus.
Considering the coupling efficiency and timescales, we propose that the AGN
outflow in this galaxy may exert both negative and positive feedback on its
host. Additionally, the star formation and the AGN activities could be
attributed to the interaction between NGC 2992 and NGC 2993.

Seyfert galaxies (1447) — Galaxy winds (626) — Galaxy stellar content (621)

††facilities: VLT (MUSE)††software: astropy (Astropy Collaboration et al.,
2013, 2018), EsoReflex (Freudling et al., 2013), Vorbin (Cappellari & Copin,
2003), PPXF (Cappellari, 2023), DS9 (Joye & Mandel, 2003),

##  1 Introduction

It is widely anticipated that active galactic nuclei (AGNs) can exert a
significant influence on the surrounding environment and the evolution of
their host galaxies. This influence is manifested through the release of
energy in the form of radiation and the generation of powerful outflows (e.g.
Fabian, 2012). Observations have provided substantial evidence for the
presence of AGN outflows in both neutral (atomic and molecular) and ionized
phases (e.g., Veilleux et al., 2013; Harrison et al., 2014; Fluetsch et al.,
2019; Mingozzi et al., 2019).

In a negative feedback scenario, AGN outflows have the capability to heat
and/or expel cold gas, leading to a depletion of gas supplies that
subsequently suppresses star formation (SF) (e.g. Silk & Rees, 1998; Hopkins
et al., 2008; Silk & Mamon, 2012). Some studies have shown that AGN outflows
exhibit a spatial anti-correlation with star formation regions within the host
galaxies of some high-redshift AGNs, providing direct evidence of quasar-
driven outflows quenching star formation in galaxies (e.g. Cano-Díaz et al.,
2012; Cresci et al., 2015). However, these studies are based on the H$\alpha$
emission line, which may not be a good tracer of the obscured SF. Follow-up
studies based on the far-infrared (FIR) luminosity did not confirm the anti-
correlation (Scholtz et al., 2020, 2021). In many luminous AGNs, the molecular
gas depletion time caused by AGN outflows is shorter compared to star-forming
galaxies, indicating a significant impact of AGN outflows on both star
formation and the gas reservoir within the host galaxy (e.g. Fiore et al.,
2017; Fluetsch et al., 2019).

Alternatively, some works have suggested that AGN outflows can also trigger or
enhance SF processes, known as positive feedback (e.g. Silk, 2013; Zubovas &
Bourne, 2017). In some luminous AGNs, regions of active star formation can be
found surrounding the AGN outflows, indicating that the outflows compress the
gas and trigger star formation at the edge of the outflow (e.g. Cresci et al.,
2015; Venturi et al., 2023). Using near-infrared adaptive optics integral
field spectrograph (IFS) data, Davies et al. (2007) found some evidence of a
young stellar population (10-300 Myr) in the central region ($<1$ kpc) of
several nearby Seyfert galaxies. In some of these Seyfert galaxies (e.g. Mkr
231, Circinus, NGC 7469), AGN-driven outflows in the central region have been
detected (e.g. Feruglio et al., 2010; Mingozzi et al., 2019; Robleto-Orús et
al., 2021; Kakkad et al., 2023). Lipari et al. (2009) identified a very young
stellar population ($<15$ Myr) in the nuclear region ($\sim 200$ pc) of Mrk
231, where a powerful cold gas outflow was observed (Feruglio et al., 2010,
2015). These observational findings might suggest the presence of an AGN
positive feedback scenario. Recently, Venturi et al. (2023) discovered a young
stellar population ($<$100–150 Myr) co-located with the ionized gas loop in
the Teacup galaxy, with the star formation timescale aligning with the
expansion time of the loop, indicating a positive AGN feedback in this galaxy.

NGC 2992 is a member of an interacting system Arp 245. Figure 1 shows a V band
image of the interacting system Arp 245 observed using the du Pont telescope
(from NED111https://ned.ipac.caltech.edu), which includes NGC 2992, a star-
forming galaxy NGC 2993, and a tidal dwarf galaxy Arp 245N. Notably, there is
a prominent dust lane along the major axis of NGC 2992 and a diffuse bridge
connecting NGC 2992 and NGC 2993 (e.g., Duc et al., 2000). According to Duc et
al. (2000), this system is in an early stage of interaction, approximately 100
Myr after perigalacticon.

NGC 2992 is a nearly edge-on spiral galaxy situated at $z=0.00771$ (Keel,
1996) which corresponds to a distance of 32.5 Mpc ($1\arcsec\sim 150$ pc).
Within this galaxy resides an AGN renowned for its remarkable variability.
Notably, the 2-10 keV flux of NGC 2992 exhibits fluctuations of a factor of
$\sim 30$ over periods of weeks to months (e.g. Marinucci et al., 2018; Middei
et al., 2022). Additionally, the optical classification of this AGN varies
between Seyfert 1.5 and 1.9 (Trippe et al., 2008).

NGC 2992 features two prominent figure-eight-shaped radio bubbles that extend
to the northwest and southeast in the circumnuclear region ($<1$ kpc). These
radio bubbles, approximately $8\arcsec$ in size, exhibit an axis misalignment
of about $26^{\circ}$ from the galaxy’s major axis (Ulvestad & Wilson, 1984;
Zanchettin et al., 2023). The figure-eight-shaped radio bubbles are likely
expanding bubbles driven by AGN as suggested by García-Lorenzo et al. (2001)
and Colbert et al. (2005). Recently, Xu & Wang (2022) suggested that the
majority of the circumnuclear extended soft X-ray emission ($r\sim
750\rm\,pc$) originates from AGN-driven outflows. On the galactic scale, Irwin
et al. (2017) reported C-band (5–7 GHz) observations of NGC 2992, presenting
compelling evidence of a bipolar radio outflow detected in linearly polarized
emission.

In the optical band, the detection of a biconical AGN outflow aligned with the
minor axis of the NGC 2992 galactic disk has been reported in various studies
(e.g. Veilleux et al., 2001; Mingozzi et al., 2019; López-Cobá et al., 2020;
Kakkad et al., 2022; Zanchettin et al., 2023). This outflow extends over
approximately $7\rm\,kpc$ (Zanchettin et al., 2023). Based on the spatially
resolved Baldwin, Phillips, and Telervich (BPT, Baldwin et al., 1981; Veilleux
& Osterbrock, 1987) diagnostic diagrams, the primary ionization source of the
outflow was confirmed to be the AGN (Mingozzi et al., 2019; López-Cobá et al.,
2020; Guolo-Pereira et al., 2021; Kakkad et al., 2022).

Some evidence of interaction between AGN outflows and the ISM had been found
in NGC 2992 (e.g. Irwin et al., 2017; Xu & Wang, 2022; Zanchettin et al.,
2023), suggesting that AGN outflows may impact star formation in the host
galaxy. The ongoing interaction between NGC 2992 and NGC 2993 could lead to
gas inflow and trigger star formation in these galaxies. However, due to AGN
ionization contamination, classical emission-line star formation rate (SFR)
probes (e.g., H$\alpha$ emission) are not suitable for use in active galaxies.
Utilizing stellar population synthesis through full spectral fitting can
provide insights into the young star formation in AGN host galaxies. Comparing
the distribution of young stellar populations with AGN outflows in NGC 2992
could aid in exploring the relationship between AGN outflows and star
formation. Furthermore, the distribution of young stellar populations may also
indicate the impact of the galaxy interaction.

In this study, we present a spatially resolved analysis of NGC 2992 using the
deep VLT/MUSE data. Although this archival data has been analyzed in previous
studies (e.g., Mingozzi et al., 2019; López-Cobá et al., 2020; Kakkad et al.,
2022; Zanchettin et al., 2023), our analysis focuses on the spatially resolved
properties of the stellar populations and a potential connection between the
AGN outflows and the stellar populations. In Sec. 2, we describe the
observations and reduction of the data. The spatially resolved properties of
stellar populations and the radial profiles are shown in Sec. 3. In Sec. 4,
discussions about the impacts of the AGN and galaxy merger are presented.
Lastly, a summary is provided in Sec. 5.

Figure 1: An optical (V band) image of the interacting system Arp 245 (from
NED). The black box denotes the FoV of the VLT/MUSE data.

##  2 Observations and Data Reduction

Table 1: SSPs used in the stellar population synthesis.  Model | BC03 | FSPS
---|---|---
Evolution track | Padova (1994) | MIST
Spectral library | STELIB | MILES
Metallicity ($\rm Z_{\odot}$) | 0.02, 0.2, 0.4, 1, 2.5 | 0.018, 0.18, 0.56, 1, 1.8
| 0.001, 0.003, 0.005, 0.01, 0.03, 0.055 | 0.001, 0.003, 0.005, 0.01, 0.03, 0.06
Age (Gyr) | 0.064, 0.081, 0.1, 0.29, 0.57, 0.90 | 0.08, 0.1, 0.31, 0.63, 0.79
| 3.0, 5.0, 11, 15, 20 | 3.2, 5.0, 12.6, 15.8
Figure 2: Top panel: An example of spectra (shown in blue) with the continuum
(orange line) from a spaxel at $\Delta$RA $=\rm-4.\arcsec 0$ and $\Delta$Dec
$=\rm 2.\arcsec 6$ from the nucleus. The shaded regions show the masked bands
when fitting the continuum. The lower left panel shows the spectrum zoomed in
on [O iii] emission lines, and the lower right panel H$\alpha$ and [N ii].
Sky-blue lines and red lines denote narrow and broad emission lines,
respectively. For better visualization, the residual (shown in pink) is
arbitrarily shifted below zero.

###  2.1 MUSE data

NGC 2992 was observed in the wide field mode (WFM) by MUSE (Bacon et al.,
2010, 2014) in 2015, with a total exposure time of $\sim 10\rm\,ks$, under
program 094.B-0321(A) (PI: Marconi). A field of view (FoV) of $\sim 1$ arcmin2
with spatial sampling of $\rm 0.\arcsec 2$ pixel-1 is provided, while the
spatial resolution of these data was limited by seeing ($\sim 1\arcsec$). The
wavelength coverage is $\rm 4650-9300\,\AA$ with a mean resolution of R $\sim$
3000\. We downloaded data from ESO archive222$\rm
http://archive.eso.org/eso/eso\\_archive\\_main.html$ and used EsoReflex
(Freudling et al., 2013) with MUSE workflow v2.8.5 (Weilbacher et al., 2020)
to reduce the data. The final data cube was corrected for Milky Way
extinction, using $A_{\rm V}=0.166$ (Schlafly & Finkbeiner, 2011) and the
extinction law of Fitzpatrick (1999).

###  2.2 Stellar populations synthesis

We employed the Voronoi binning method (Cappellari & Copin, 2003) to spatially
rebin the data cube, aiming to achieve a mean signal-to-noise ratio (S/N)
threshold of 40 over the continuum emission in the wavelength range of $\rm
4800-7000\,\AA$. The Penalized Pixel-Fitting method (PPXF; Cappellari, 2023)
was used to fit the spectrum of every Voronoi bin within the same wavelength
range. The stellar population models used in this study include the Bruzual &
Charlot (2003, hereafter BC03) model and Flexible Stellar Population Synthesis
(FSPS; Conroy et al., 2009; Conroy & Gunn, 2010) model. BC03 model use the
Padova evolution track (Bressan et al., 1993) and the STELIB spectral library
(Le Borgne et al., 2003), while FSPS model employs the MESA Isochrones &
Stellar Tracks (MIST Dotter, 2016; Choi et al., 2016; Paxton et al., 2019) and
the MILES spectral libraby (Sánchez-Blázquez et al., 2006) (Table 1). Both
models adopted the same Chabrier (2003) initial mass function (IMF). We
employed a set of 85 representative single stellar populations (SSPs) with 17
ages ranging from 1 Myr to 20 Gyr and 5 metallicities ranging from 0.02 $\rm
Z_{\odot}$ to 2.5 $\rm Z_{\odot}$ provided from BC03 model. For FSPS
templates, we selected a set of SSPs with age and metallicity coverage as
similar as possible to the SSPs from the BC03 model. Increasing the number of
SSPs did not yield a significant improvement in the results. The complete list
of SSPs is shown in Table 1. Even though the Voronoi binning method was used,
the stellar continuum fitting is bad at the edge of FoV due to contamination
from sky lines. Hence, we exclude the binned spaxels with a continuum level
below $4\times 10^{-19}\rm\ erg\ cm^{-2}\ s^{-1}\AA^{-1}$ at $5100\rm\ \AA$
from the results of stellar population synthesis.

We obtained the stellar kinematics and properties of the stellar populations
by masking the gas emission lines (with a masking width of 1000 km/s) and
fitting the spectrum in each bin. The extinction curve from Calzetti et al.
(2000) was used to fit the stellar reddening. To obtain uncertainties of the
stellar population parameters, we employed the bootstrapping method (e.g.
Davidson & Flachaire, 2008). Firstly, the spectrum was fitted using PPXF.
Secondly, a new spectrum was generated by randomly adding $\pm$residual to the
best-fit model at each wavelength channel. This new spectrum was then fitted
using PPXF. The bootstrapping process was repeated 20 times, and one standard
deviation of every resulting stellar population parameter (e.g. age,
metallicity, light weights) from these 20 sets was used as the error.

For convenience, we used two simplified stellar populations with light-
weighted age ranges: $t\leq 100\,\rm Myr$ ($P_{\rm Y}$) and $100\,{\rm
Myr}\leq t$ ($P_{\rm O}$). In this work, we will focus on the young stellar
population ($P_{\rm Y}$), because the timescale of this population is
comparable to the dynamical timescale of the ionized outflow (see Sec. 4.1.2).
$f_{\rm Y}$ denotes the fraction of $P_{\rm Y}$, calculated by summing the
light weights of $P_{\rm Y}$ within each spaxel.

###  2.3 Emission lines

Previous studies have examined the optical emission lines in NGC 2992 using
the identical MUSE data (Mingozzi et al., 2019; López-Cobá et al., 2020;
Kakkad et al., 2022; Zanchettin et al., 2023).

After subtracting the stellar continuum, two Gaussian components were used to
fit the main gas emission lines: H$\beta$, [O iii]$\lambda\lambda$4959,5007,
H$\alpha$, [N ii]$\lambda\lambda$6548,6583, and [S
ii]$\lambda\lambda$6716,6731. For the same component, the velocity $v$ and the
velocity dispersion $\sigma$ of all emission lines share the same value. The
$\sigma$ range of the first component was limited to 50-200 km/s, while the
$\sigma$ of the second component was set to be at least 50 km/s larger than
that of the first component. Only components with S/N$\geq 3$ are retained.
Figure 2 illustrates an example of spectral fitting extracted from a spaxel in
the outflow cone (the red solid circle in Figure 5(a)). The morphology of the
first and the second components are very similar to the disk and the outflow
component defined by Mingozzi et al. (2019) and Kakkad et al. (2022). Hence,
the first and the second components are referred to as the disk and the
outflow component, respectively.

##  3 Results

###  3.1 Stellar extinction and kinematics

Figure 3: Left: The extinction in V band $A_{\rm V}$ derived from stellar
continuum fitting using FSPS templates. Black contours represent $A_{\rm
V}=1.0,\ 2.0,\ 3.0$, respectively. The nuclear region (with a radius
$r<1.2\arcsec$) is masked. The black star denotes the peak of [O iii] disk
component. Binned spaxels with stellar continuum below $4\times 10^{-19}\rm\
erg\ cm^{-2}\ s^{-1}\AA^{-1}$ at $5100\rm\ \AA$ are excluded. Right: HST/WFPC2
V-band image using the F606W filter (Malkan et al., 1998) superposed with the
contours of $A_{\rm V}$ in the left panel.  Figure 4: Stellar kinematics map
derived from stellar continuum fitting using FSPS templates. The black star
denotes the peak of [O iii] disk component. Binned spaxels with stellar
continuum below $4\times 10^{-19}\rm\ erg\ cm^{-2}\ s^{-1}\AA^{-1}$ at
$5100\rm\ \AA$ are excluded.

In the Hubble Space Telescope (HST) V-band image (right panel of Figure 3)
from Malkan et al. (1998), a prominent dust lane is observed nearly along the
major axis of NGC 2992. The extinction in V band $A_{\rm V}$ obtained from the
stellar continuum fitting aligns spatially with the morphology of this dust
lane (left panel of Figure 3). Mingozzi et al. (2019) and Zanchettin et al.
(2023) also calculated $A_{\rm V}$ from the Balmer decrement ($\rm
H\alpha/H\beta$), which is higher than the $A_{\rm V}$ obtained in this study.
Additionally, Zanchettin et al. (2023) identified a molecular gas disk with an
inclination angle of 80 degrees using ALMA CO(2-1) data, which coincides with
the major axis of NGC 2992. The dust lane also exhibits rough consistency with
the molecular disk discovered by Zanchettin et al. (2023).

Figure 4 displays the stellar kinematics derived from continuum fitting,
revealing a rotational stellar disk. For stars located at a distance of
$2\rm\,kpc$ from the nucleus, the rotation timescale $t_{\rm rot}$ is
estimated to be $\sim 60\rm\,Myr$. This suggests that the distribution of
stellar populations in the stellar disk, except for very young stars, will be
smoothed or disrupted due to rotation. The $A_{\rm V}$ and stellar kinematics
maps derived from BC03 synthesis are consistent with the Figure 3 and Figure
4.

###  3.2 Spatially resolved properties of stellar populations

Figure 5: Properties of stellar populations obtained from FSPS synthesis. (a):
Light-weighted mean logarithmic stellar age. Two overlaid blue regions are
used to derive radial profiles along the major and minor axes. The red solid
circle represents the location of the spectrum in Figure 2. (b): Light-
weighted mean metallicity in a unit of $Z_{\odot}$. (c): Fraction map of
$P_{\rm Y}$ (stellar populations with age $\rm<100\,Myr$). (d): Light-weighted
mean age of $P_{\rm Y}$. (e): Light-weighted mean metallicity of $P_{\rm Y}$.
All maps have black contours representing the dust extinction ($A_{\rm
V}=1.0,\ 2.0,\ 3.0$). The nuclear region (radius $r<1.2\arcsec$) is masked.
The black star denotes the peak of [O iii] disk component.  Figure 6: Same as
Figure 5 but derived from the BC03 synthesis.

In Figure 5, maps of the light-weighted average stellar age, light-weighted
mean metallicity $<Z>$, the fraction of young stellar population $f_{\rm Y}$,
and the mean age and metallicity ($<Z>_{\rm Y}$) of the young stellar
population derived from the FSPS synthesis are shown. In the average stellar
age map (Figure 5(a)), the stellar ages are lower within the dust lane. Along
the minor axis, the average age decreases as the distance from the nucleus
increases. In Figure 5(b), $<Z>$ derived from FSPS synthesis shows an
asymmetry pattern: sub-solar $<Z>$ in the northern, eastern, and western
regions, while solar $<Z>$ in the southern region. Compared to Figure 5(c) and
(e), the sub-solar $<Z>$ in the northern region is attributed to the very
young stellar population. In the eastern and western regions along the minor
axis, the sub-solar $<Z>$ is mainly contributed by the old stellar
populations. In the $f_{\rm Y}$ map (Figure 5(c)), high $f_{\rm Y}$ is
presented along the dust lane and at the edge of the stellar disk. Some
spectra in the edge of the disk have been checked and the continuum fitting is
reliable. However, $f_{\rm Y}$ is very low in the vicinity of the nuclear
region, except for the west region, despite the presence of dust and
substantial molecular gas (Zanchettin et al., 2023). Figure 5(d) shows that in
most regions of the stellar disk, the young stellar population is very young
($<40\rm\ Myr$). A super-solar metallicity of this young stellar population is
presented across the stellar disk except for the northern region (Figure
5(e)).

The spatially resolved properties of stellar populations obtained from BC03
synthesis are presented in Figure 6. The map of the mean stellar age (Figure
6(a)) is similar to the result obtained from FSPS synthesis (Figure 5(a)). The
$<Z>$ map (Figure 6(b)) shows super-solar metallicity throughout the galaxy,
except for the western region. In the $f_{\rm Y}$ map (Figure 6(c)),
relatively high $f_{\rm Y}$ is presented along the dust lane and at the edge
of the stellar disk. Figure 6(d) and (e) show that in most regions of the
stellar disk, the young stellar population is very young ($<40\rm\ Myr$) and
metal-poor.

Compared to the result from FSPS synthesis, $f_{\rm Y}$ obtained from BC03
synthesis is 0.1–0.2 lower in the dust lane and the edge of the stellar disk.
Additionally, the age of $P_{\rm Y}$ derived from BC03 synthesis is younger
than that obtained from FSPS synthesis in the dust lane. The $<Z>$ map
obtained from FSPS synthesis (Figure 5(b)) reveals sub-solar metallicity
throughout the galaxy, except for the southern region. However, $<Z>$ derived
from BC03 synthesis is different. In Figure 6(b), only in the western region
of NGC 2992 shows solar or sub-solar $<Z>$, likely originating from older
stellar populations compared to Figure 6(e). However, considering the galactic
rotation, the distribution of the old stellar populations should be smoothed,
casting doubt on the reliability of the pattern depicted in Figure 6(b). The
$<Z>_{\rm Y}$ maps derived from FSPS (Figure 5(e)) and BC03 (Figure 6(e))
synthesis exhibit significant differences. The former shows super-solar
$<Z>_{\rm Y}$ across the stellar disk except for the northern region, while
the latter presents sub-solar $<Z>_{\rm Y}$ throughout the disk. The disparity
in metallicity derived from BC03 and FSPS stellar templates suggests that the
metallicity measurements may not be reliable.

The consistent findings about the distribution and the mean age of $P_{\rm Y}$
from both FSPS and BC03 stellar templates indicate the presence of a very
young stellar population ($<40$ Myr) within the dust lane. Guolo-Pereira et
al. (2021) analyzed the stellar populations in the nuclear region ($\leq
3\arcsec$) in NGC 2992 using Gemini Multi-Object Spectrograph (GMOS) data.
They found a young ($<$100 Myr) stellar population with a relatively high
light-weighted fraction ($10\%\leq f_{\rm Y}\leq 30\%$) in the nuclear region.
Although the innermost region ($<1.2\arcsec$) is excluded in our work, the
findings of Guolo-Pereira et al. (2021) are broadly consistent with our
result. Friedrich et al. (2010) also found evidence for a short burst of star
formation (40-−50 Myr ago) in the nuclear region ($\sim 3\arcsec\times
3\arcsec$) using data from the near-infrared integral field spectrograph
SINFONI on the VLT. Furthermore, Mingozzi et al. (2019) presented the BPT
diagrams of NGC 2992 based on the same MUSE data. Their [S ii] BPT diagram
reveals some star formation regions within the dust lane, which is also
consistent with our results.

###  3.3 Radial profiles along the major and minor axes

Figure 7: Radial profiles of results derived from FSPS synthesis. (a): Light-
weighted mean logarithmic stellar age. (b): Light-weighted mean metallicity in
a unit of $Z_{\odot}$. (c): $f_{\rm Y}$. (d): Light-weighted mean age of
$P_{\rm Y}$. (e): Light-weighted mean age of $P_{\rm Y}$. Major-N and Major-S
refer to the radial profiles along the major axis towards the north and south
directions, respectively. Similarly, Minor-E and Minor-W indicate the radial
profile along the minor axis towards the east and west directions,
respectively. Note that the radial distance along the major and the minor axes
are presented in the bottom and top horizontal axes, respectively.  Figure 8:
Same as Figure 7, but for radial profiles obtained from BC03 synthesis.

Figure 7 shows the radial profiles of the average stellar age, metallicity,
$f_{\rm Y}$, and the mean age and metallicity ($<Z>_{\rm Y}$) of the young
stellar population $P_{\rm Y}$ obtained from FSPS synthesis. The errors are
estimated from the standard deviation of the resulting stellar population
properties obtained from the bootstrapping method (see Sect 2.2). Note that
the innermost point in the west direction along the minor axis (Minor-W) falls
within the dust lane, where $f_{\rm Y}$ is high. This point is excluded when
analyzing trends along the minor axis. In Figure 7(a), negative trends of
stellar age are observed along both the major and minor axes, consistent with
an inside-out star formation scenario. In Figure 7(b), $<Z>$ shows positive
trends in all directions except for the north of the major axis. Regarding
$P_{\rm Y}$, $f_{\rm Y}$ exhibits a positive trend along both the major and
the minor axes (Figure 7(c)). Additionally, excluding the innermost and
outmost point of Minor-W, $f_{\rm Y}$ along the major axis is higher than that
along the minor axis. The average age of $P_{\rm Y}$ exhibits a positive trend
along both the major and minor axes. $<Z>_{\rm Y}$ derived from FSPS synthesis
exhibits weak positive trends along the minor axis and a positive trend along
the major axis in the south direction. However, in the north direction, a
significant negative trend is observed.

Figure 8 presents the radial profiles obtained from BC03 synthesis. The trends
of the stellar age (Figure 8(a)) and $f_{\rm Y}$ (Figure 8(c)) are similar to
the results obtained from FSPS synthesis. $<Z>$ is notably lower along the
west direction compared to other directions. The average age of $P_{\rm Y}$
presents a positive trend along the minor axis, while no significant trend is
observed along the major axis (Figure 8(d)). Along the minor axis, the average
age of $P_{\rm Y}$ is significantly higher than that along the major axis
(Figure 8(d)), in contrast to the findings of the FSPS synthesis (Figure
7(d)). When compared to the results in Figure 7(d) obtained from FSPS
synthesis, the average ages of $P_{\rm Y}$ derived from BC03 synthesis are
lower along the major axis and in the inner regions along the minor axis.
$<Z>_{\rm Y}$ shows a positive trend along the minor axis, while a weak
negative trend is observed along the north direction of the major axis (Figure
8(e)). Along the major axis, $<Z>_{\rm Y}$ is higher compared to that along
the minor axis. Compared to Figure 7(e) obtained from FSPS synthesis,
$<Z>_{\rm Y}$ derived from BC03 synthesis is lower along both the major and
minor axes, except in the north direction of the major axis.

When comparing the radial profiles derived from BC03 and FSPS synthesis,
although there exists some conflicting results, some main findings are
generally consistent. The trends of the stellar age and $f_{\rm Y}$ obtained
from these two syntheses are similar, with $f_{\rm Y}$ derived from FSPS
generally higher. The average age of $P_{\rm Y}$ shows positive trends along
the minor axis in both BC03 and FSPS synthesis, although the trend obtained
from FSPS is weaker. Positive trends of $<Z>_{\rm Y}$ along the minor axis and
a negative trend along the north direction of the major axis are observed in
both syntheses, while the positive trend from FSPS and the negative trend from
BC03 are relatively weaker. These consistent findings about $P_{\rm Y}$
suggest that the young stellar population in the inner regions is younger and
metal poorer than that in the outer regions, except for the north direction of
the major axis.

##  4 Discussion

###  4.1 Possible AGN feedback on the star formation in NGC 2992

Figure 9: Left: $f_{\rm Y}$ map derived from FSPS synthesis (Figure 5(c))
superposed with the contours of [O iii] outflow component. The [O iii]
contours corresponding to 1000 and 5000 $\times 10^{-20}\,\rm
erg\,s^{-1}\,cm^{-2}$. Middle: Central region of $f_{\rm Y}$ map superposed
with the contours of soft X-ray emission from Xu & Wang (2022). The lowest
X-ray contour level is $\rm 0.09\,counts/pixel$, and the contour values
increase by a factor of 2.9. Right: Same as the middle panel but superposed
with the figure-eight-shaped radio bubble from Ulvestad & Wilson (1989). The
radio contour is $\rm 0.0003\,Jy/beam$.

In Figure 9, we compare the distribution of $f_{\rm Y}$ with the [O iii]
outflow component, extended soft X-ray emission reported by Xu & Wang (2022),
and the nuclear radio bubble documented by Ulvestad & Wilson (1989). Colbert
et al. (2005) and Xu & Wang (2022) found that there exists extended soft X-ray
emission around the nucleus. Xu & Wang (2022) further revealed that the
circumnuclear ($r\sim 750\,\rm pc$) soft X-ray emission could be dominated by
the hot gas associated with the AGN outflow traced by the nuclear figure-
eight-shaped radio bubble.

In the northern region near the nucleus, the highest $f_{\rm Y}$ (median
$f_{\rm Y}\sim 0.6$) is observed at the outskirts of the northern radio bubble
(right panel of Figure 9), indicating an AGN positive feedback scenario. This
finding is similar to the result detected by Venturi et al. (2023) in the
Teacup galaxy, where a younger stellar population was identified at the
periphery of a large ionized gas bubble compared to the rest of the galaxy.
Except for the northern and western regions, the circumnuclear region ($<1$
kpc) exhibits the lowest $f_{\rm Y}$ ($<0.01$) but strong soft X-ray and [O
iii] outflow component emission. There is a significant amount of molecular
gas in this region (Zanchettin et al., 2023), but very few young stars have
formed. This result also suggests a possible AGN negative feedback scenario in
the circumnuclear region.

####  4.1.1 Coupling efficiency

Some numerical simulations suggest that the coupling efficiency $\dot{E}_{\rm
out}/L_{\rm bol}$ should be larger than $0.5\%$ (e.g. Hopkins & Elvis, 2010)
to exert a noticeable feedback effect on the host galaxy. The AGN in NGC 2992
is a well-known source with intense variability, exhibiting X-ray 2-10 keV
luminosity variations between $3.8\times 10^{41}\rm\,erg\,s^{-1}$ and
$1.4\times 10^{43}\rm\,erg\,s^{-1}$ over timescales of decades (e.g. Marinucci
et al., 2018; Middei et al., 2022). Applying the bolometric correction from
Marconi et al. (2004), we can estimate the bolometric luminosity of $L_{\rm
bol}=2.7\times 10^{42}\rm\,erg\,s^{-1}$–$1.6\times 10^{44}\rm\,erg\,s^{-1}$.

Recently, Zanchettin et al. (2023) estimated the kinetic power of the ionized
gas outflow to be $\dot{E}_{\rm out}=1.2\times 10^{42}\rm\,erg\,s^{-1}$ from
[O iii] emission line using the same MUSE data. By adopting this value, the
coupling efficiency can range from $0.75\%$ to $45\%$, depending on the
bolometric luminosity. Even though the lower limit of the coupling efficiency
is larger than the threshold suggested by Hopkins & Elvis (2010). Hence, the
galactic ionized gas outflow in NGC 2992 could impact the host galaxy
according to the computed coupling efficiency.

####  4.1.2 Timescales

The dynamical timescale of the ionized gas outflow can be estimated by $t_{\rm
out}=d/v$, where $d$ is the size of the outflow and $v$ is the average
velocity of the outflow. Assume that $d=7\rm\,kpc$ and $v=200\rm\,km\,s^{-1}$
(see also Zanchettin et al., 2023), we can calculate $t_{\rm out}\sim
34\rm\,Myr$. This dynamical timescale is close to the timescale of the young
stellar population, which is less than $40\rm\,Myr$ according to both BC03 and
FSPS synthesis (Figure 8 and Figure 7). García-Lorenzo et al. (2001)
identified two [O iii] arcs moving at a velocity of $\sim 70\rm\,km/s$,
consistent with the northwest and southeast bubbles observed in the nuclear
radio emission. By assuming that the radio bubbles are expanding at a velocity
of $\sim 70\rm\,km/s$ with a size of $\sim 700\rm\,pc$, we can estimate the
expansion timescale of the radio bubble to be $\sim 10\rm\,Myr$, which aligns
closely with the timescale of the young stellar population. This suggests that
the AGN outflow could affect the formation of the young stellar population.

###  4.2 Interaction between NGC 2992 and NGC 2993

In simulations, major merger processes can induce gas inflow towards the
central regions of galaxies, thereby boosting circumnuclear star formation and
triggering nuclear activities (e.g. Hopkins & Quataert, 2010). The star
formation rate in merging galaxies is expected to increase, particularly in
the central region (e.g. Ellison et al., 2013; Steffen et al., 2021).
Additionally, in galaxy mergers, the metallicity gradient may be altered as a
result of gas inflow (e.g. Thorp et al., 2019).

Duc et al. (2000) suggested that NGC 2992 and NGC 2993 are observed at an
early stage of the interaction, $\sim$100 Myr after the first pericentre
passage. The timescale of interaction is estimated to be 2-3 times longer than
that of the young stellar population and ionized outflow (see Sect 4.1.2).
However, considering the time required for the gas to respond, the interaction
between these galaxies could potentially trigger the formation of the young
stellar population and AGN activities in NGC 2992. Friedrich et al. (2010)
suggested that galaxy interaction could trigger nuclear star formation.
Additionally, Guolo-Pereira et al. (2021) discovered a young, metal-poor
stellar population in the nucleus of NGC 2992, proposing that gas inflows
resulting from the interaction between NGC 2992 and NGC 2993 stimulate both
star formation and AGN activities.

Although the metallicity derived from FSPS and BC03 synthesis are different,
the trends of $<Z>_{\rm Y}$ along the north direction of the major axis
obtained from both syntheses show negative trends, potentially indicating gas
inflow in this region. This region is situated at the base of the tidal tail
connecting NGC 2992 and the tidal dwarf galaxy Arp 245N (Figure 1). Previous
studies have indicated that the SFR can be enhanced at the base of tidal tails
(e.g. Hancock et al., 2009; Smith et al., 2014). The $f_{\rm Y}$ in the
northern region of the stellar disk is higher than that in the southern
region, suggesting that the star formation may be enhanced by gas inflow in
the northern region.

###  4.3 Contamination from the AGN continuum?

The correlation between the ionization cones and the distribution of stellar
populations raises concerns about potential contamination from the AGN
continuum, which could impact the accuracy of the fitting results. Guolo-
Pereira et al. (2021) conducted tests on the AGN continuum contamination in
the nuclear region of NGC 2992 using GMOS data. They utilized a featureless
power-law continuum ($F_{\lambda}\propto\lambda^{1.7}$) to account for AGN
emission and combined it with stellar population templates to fit the spaxels
within the nuclear region ($r<1.1\arcsec$). Their findings indicate that the
contribution of the AGN continuum to the total light diminishes with
increasing radius, becoming negligible beyond $r\sim 1\arcsec$. In the nuclear
region, where the AGN contribution is significant, the derived stellar
populations would appear younger if the featureless continuum is not included
in the fitting process (Guolo-Pereira et al., 2021). Based on their results,
the AGN continuum contribution outside the nuclear region can be ignored.

We also tested the contribution of the AGN continuum in some spaxels by
combining a power law component ($F_{\lambda}\propto\lambda^{1.7}$) in the
continuum fitting. As expected, the power-law component was negligible in
these spectra. If we assume that the AGN continuum does impact the continuum
fitting, it would lead to an underestimation of the mean age of stellar
populations in the ionization cones, thereby strengthening the findings of
this study.

##  5 Conclusions

In this work, we study the spatially resolved properties of stellar
populations of NGC 2992 using the archival VLT/MUSE data. Two stellar
templates are employed to fit the stellar continuum. The extinction in the V
band and the stellar kinematics obtained from the continuum fitting are shown.
The spatially resolved maps and radial profiles along the major and minor axes
of light-weighted stellar age, light-weighted metallicity $<Z>$, fraction of
the young stellar population $f_{\rm Y}$ (age $<100\,\rm Myr$), and average
age and metallicity ($<Z>_{\rm Y}$) of the young stellar population are
presented. The main results and conclusions are summarized as follows:

  1. 1.

Both the results obtained from BC03 and FSPS synthesis indicate the presence
of a very young stellar population (age $<40$ Myr) within the dust lane and
nearly along the major axis. The metallicities derived from the two stellar
population syntheses differ, with BC03 synthesis indicating a super-solar
metallicity across the stellar disk, while FSPS synthesis reveals a sub-solar
metallicity.

  2. 2.

Positive trends of the average stellar age and $f_{\rm Y}$ are found along
both major and minor axes, indicative of an inside-out star formation
scenario. Positive trends of $<Z>_{\rm Y}$ are observed in all directions
except for the north of the major axis in both BC03 and FSPS synthesis. Along
the northern direction of the major axis, $<Z>_{\rm Y}$ displays a negative
trend, suggesting a gas inflow in this region.

  3. 3.

Along the minor axis, where the AGN outflow is prominent, the fraction of the
young stellar population ($f_{\rm Y}$) is low. In the circumnuclear region,
the highest value of $f_{\rm Y}$ is found at the outskirts of the northern
radio bubble (Figure 9). Based on discussions regarding the coupling
efficiency and timescales, we propose that the AGN outflow in NGC 2992 might
have both negative and positive feedback effects on the formation of young
stars especially in the circumnuclear region ($<1$ kpc) (Sec 4.1).

  4. 4.

The young stellar population is detected along the major axis of the galaxy,
showing spatial alignment with the dust lane and molecular gas disk. This
observation could be linked to the interaction between NGC 2992 and NGC 2993,
potentially causing gas inflow in the gas disk, consequently triggering the
formation of young stars.

In the future, further multi-wavelength observational studies are needed to
validate the results of this work.

##  6 Acknowledgments

We thank the anonymous referee for helpful comments that significantly
improved the clarity of our work. We thank Dr. Yulong Gao, Tianwen Cao, Ran
Wang, and Siyi Feng for their helpful discussion. We acknowledges the National
Key R&D Program of China (Grant No. 2023YFA1607904 and No. 2022YFF0503402).
X.X. acknowledges the China Postdoctoral Science Foundation (No. 2023M741639).
J.W. acknowledges the NSFC grants 12333002, 12033004, and 12221003. Z.L.
acknowledges the National Natural Science Foundation of China (grant
12225302). Based on observations collected at the European Southern
Observatory under ESO program 094.B-0321.

## References

  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, Astronomy and Astrophysics, 558, A33, doi: 10.1051/0004-6361/201322068
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, The Astronomical Journal, 156, 123, doi: 10.3847/1538-3881/aabc4f
  * Bacon et al. (2010) Bacon, R., Accardo, M., Adjali, L., et al. 2010, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7735, Ground-based and Airborne Instrumentation for Astronomy III, ed. I. S. McLean, S. K. Ramsay, & H. Takami, 773508, doi: 10.1117/12.856027
  * Bacon et al. (2014) Bacon, R., Vernet, J., Borisova, E., et al. 2014, The Messenger, 157, 13
  * Baldwin et al. (1981) Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, Publications of the Astronomical Society of the Pacific, 93, 5, doi: 10.1086/130766
  * Bressan et al. (1993) Bressan, A., Fagotto, F., Bertelli, G., & Chiosi, C. 1993, Astronomy and Astrophysics Supplement Series, 100, 647
  * Bruzual & Charlot (2003) Bruzual, G., & Charlot, S. 2003, Monthly Notices of the Royal Astronomical Society, 344, 1000, doi: 10.1046/j.1365-8711.2003.06897.x
  * Calzetti et al. (2000) Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, The Astrophysical Journal, 533, 682, doi: 10.1086/308692
  * Cano-Díaz et al. (2012) Cano-Díaz, M., Maiolino, R., Marconi, A., et al. 2012, Astronomy and Astrophysics, 537, L8, doi: 10.1051/0004-6361/201118358
  * Cappellari (2023) Cappellari, M. 2023, Monthly Notices of the Royal Astronomical Society, 526, 3273, doi: 10.1093/mnras/stad2597
  * Cappellari & Copin (2003) Cappellari, M., & Copin, Y. 2003, Monthly Notices of the Royal Astronomical Society, 342, 345, doi: 10.1046/j.1365-8711.2003.06541.x
  * Chabrier (2003) Chabrier, G. 2003, Publications of the Astronomical Society of the Pacific, 115, 763, doi: 10.1086/376392
  * Choi et al. (2016) Choi, J., Dotter, A., Conroy, C., et al. 2016, The Astrophysical Journal, 823, 102, doi: 10.3847/0004-637X/823/2/102
  * Colbert et al. (2005) Colbert, E. J. M., Strickland, D. K., Veilleux, S., & Weaver, K. A. 2005, The Astrophysical Journal, 628, 113, doi: 10.1086/430734
  * Conroy & Gunn (2010) Conroy, C., & Gunn, J. E. 2010, The Astrophysical Journal, 712, 833, doi: 10.1088/0004-637X/712/2/833
  * Conroy et al. (2009) Conroy, C., Gunn, J. E., & White, M. 2009, The Astrophysical Journal, 699, 486, doi: 10.1088/0004-637X/699/1/486
  * Cresci et al. (2015) Cresci, G., Mainieri, V., Brusa, M., et al. 2015, The Astrophysical Journal, 799, 82, doi: 10.1088/0004-637X/799/1/82
  * Davidson & Flachaire (2008) Davidson, R., & Flachaire, E. 2008, Journal of Econometrics, 146, 162, doi: https://doi.org/10.1016/j.jeconom.2008.08.003
  * Davies et al. (2007) Davies, R. I., Müller Sánchez, F., Genzel, R., et al. 2007, The Astrophysical Journal, 671, 1388, doi: 10.1086/523032
  * Dotter (2016) Dotter, A. 2016, The Astrophysical Journal Supplement Series, 222, 8, doi: 10.3847/0067-0049/222/1/8
  * Duc et al. (2000) Duc, P. A., Brinks, E., Springel, V., et al. 2000, The Astronomical Journal, 120, 1238, doi: 10.1086/301516
  * Ellison et al. (2013) Ellison, S. L., Mendel, J. T., Patton, D. R., & Scudder, J. M. 2013, Monthly Notices of the Royal Astronomical Society, 435, 3627, doi: 10.1093/mnras/stt1562
  * Fabian (2012) Fabian, A. C. 2012, Annual Review of Astronomy and Astrophysics, 50, 455, doi: 10.1146/annurev-astro-081811-125521
  * Feruglio et al. (2010) Feruglio, C., Maiolino, R., Piconcelli, E., et al. 2010, Astronomy and Astrophysics, 518, L155, doi: 10.1051/0004-6361/201015164
  * Feruglio et al. (2015) Feruglio, C., Fiore, F., Carniani, S., et al. 2015, Astronomy and Astrophysics, 583, A99, doi: 10.1051/0004-6361/201526020
  * Fiore et al. (2017) Fiore, F., Feruglio, C., Shankar, F., et al. 2017, Astronomy and Astrophysics, 601, A143, doi: 10.1051/0004-6361/201629478
  * Fitzpatrick (1999) Fitzpatrick, E. L. 1999, Publications of the Astronomical Society of the Pacific, 111, 63, doi: 10.1086/316293
  * Fluetsch et al. (2019) Fluetsch, A., Maiolino, R., Carniani, S., et al. 2019, Monthly Notices of the Royal Astronomical Society, 483, 4586, doi: 10.1093/mnras/sty3449
  * Freudling et al. (2013) Freudling, W., Romaniello, M., Bramich, D. M., et al. 2013, Astronomy and Astrophysics, 559, A96, doi: 10.1051/0004-6361/201322494
  * Friedrich et al. (2010) Friedrich, S., Davies, R. I., Hicks, E. K. S., et al. 2010, Astronomy and Astrophysics, 519, A79, doi: 10.1051/0004-6361/200913924
  * García-Lorenzo et al. (2001) García-Lorenzo, B., Arribas, S., & Mediavilla, E. 2001, Astronomy and Astrophysics, 378, 787, doi: 10.1051/0004-6361:20011243
  * Guolo-Pereira et al. (2021) Guolo-Pereira, M., Ruschel-Dutra, D., Storchi-Bergmann, T., et al. 2021, Monthly Notices of the Royal Astronomical Society, 502, 3618, doi: 10.1093/mnras/stab245
  * Hancock et al. (2009) Hancock, M., Smith, B. J., Struck, C., Giroux, M. L., & Hurlock, S. 2009, The Astronomical Journal, 137, 4643, doi: 10.1088/0004-6256/137/6/4643
  * Harrison et al. (2014) Harrison, C. M., Alexander, D. M., Mullaney, J. R., & Swinbank, A. M. 2014, Monthly Notices of the Royal Astronomical Society, 441, 3306, doi: 10.1093/mnras/stu515
  * Hopkins & Elvis (2010) Hopkins, P. F., & Elvis, M. 2010, Monthly Notices of the Royal Astronomical Society, 401, 7, doi: 10.1111/j.1365-2966.2009.15643.x
  * Hopkins et al. (2008) Hopkins, P. F., Hernquist, L., Cox, T. J., & Kereš, D. 2008, The Astrophysical Journal Supplement Series, 175, 356, doi: 10.1086/524362
  * Hopkins & Quataert (2010) Hopkins, P. F., & Quataert, E. 2010, Monthly Notices of the Royal Astronomical Society, 407, 1529, doi: 10.1111/j.1365-2966.2010.17064.x
  * Irwin et al. (2017) Irwin, J. A., Schmidt, P., Damas-Segovia, A., et al. 2017, Monthly Notices of the Royal Astronomical Society, 464, 1333, doi: 10.1093/mnras/stw2414
  * Joye & Mandel (2003) Joye, W. A., & Mandel, E. 2003, in Astronomical Society of the Pacific Conference Series, Vol. 295, Astronomical Data Analysis Software and Systems XII, ed. H. E. Payne, R. I. Jedrzejewski, & R. N. Hook, 489
  * Kakkad et al. (2023) Kakkad, D., Stalevski, M., Kishimoto, M., et al. 2023, Monthly Notices of the Royal Astronomical Society, 519, 5324, doi: 10.1093/mnras/stac3827
  * Kakkad et al. (2022) Kakkad, D., Sani, E., Rojas, A. F., et al. 2022, Monthly Notices of the Royal Astronomical Society, 511, 2105, doi: 10.1093/mnras/stac103
  * Keel (1996) Keel, W. C. 1996, The Astrophysical Journal Supplement Series, 106, 27, doi: 10.1086/192326
  * Le Borgne et al. (2003) Le Borgne, J. F., Bruzual, G., Pelló, R., et al. 2003, Astronomy and Astrophysics, 402, 433, doi: 10.1051/0004-6361:20030243
  * Lipari et al. (2009) Lipari, S., Sanchez, S. F., Bergmann, M., et al. 2009, Monthly Notices of the Royal Astronomical Society, 392, 1295, doi: 10.1111/j.1365-2966.2008.14148.x
  * López-Cobá et al. (2020) López-Cobá, C., Sánchez, S. F., Anderson, J. P., et al. 2020, The Astronomical Journal, 159, 167, doi: 10.3847/1538-3881/ab7848
  * Malkan et al. (1998) Malkan, M. A., Gorjian, V., & Tam, R. 1998, The Astrophysical Journal Supplement Series, 117, 25, doi: 10.1086/313110
  * Marconi et al. (2004) Marconi, A., Risaliti, G., Gilli, R., et al. 2004, Monthly Notices of the Royal Astronomical Society, 351, 169, doi: 10.1111/j.1365-2966.2004.07765.x
  * Marinucci et al. (2018) Marinucci, A., Bianchi, S., Braito, V., et al. 2018, Monthly Notices of the Royal Astronomical Society, 478, 5638, doi: 10.1093/mnras/sty1436
  * Middei et al. (2022) Middei, R., Marinucci, A., Braito, V., et al. 2022, Monthly Notices of the Royal Astronomical Society, 514, 2974, doi: 10.1093/mnras/stac1381
  * Mingozzi et al. (2019) Mingozzi, M., Cresci, G., Venturi, G., et al. 2019, Astronomy and Astrophysics, 622, A146, doi: 10.1051/0004-6361/201834372
  * Paxton et al. (2019) Paxton, B., Smolec, R., Schwab, J., et al. 2019, The Astrophysical Journal Supplement Series, 243, 10, doi: 10.3847/1538-4365/ab2241
  * Robleto-Orús et al. (2021) Robleto-Orús, A. C., Torres-Papaqui, J. P., Longinotti, A. L., et al. 2021, The Astrophysical Journal, 906, L6, doi: 10.3847/2041-8213/abd32f
  * Sánchez-Blázquez et al. (2006) Sánchez-Blázquez, P., Peletier, R. F., Jiménez-Vicente, J., et al. 2006, Monthly Notices of the Royal Astronomical Society, 371, 703, doi: 10.1111/j.1365-2966.2006.10699.x
  * Schlafly & Finkbeiner (2011) Schlafly, E. F., & Finkbeiner, D. P. 2011, The Astrophysical Journal, 737, 103, doi: 10.1088/0004-637X/737/2/103
  * Scholtz et al. (2020) Scholtz, J., Harrison, C. M., Rosario, D. J., et al. 2020, Monthly Notices of the Royal Astronomical Society, 492, 3194, doi: 10.1093/mnras/staa030
  * Scholtz et al. (2021) —. 2021, Monthly Notices of the Royal Astronomical Society, 505, 5469, doi: 10.1093/mnras/stab1631
  * Silk (2013) Silk, J. 2013, The Astrophysical Journal, 772, 112, doi: 10.1088/0004-637X/772/2/112
  * Silk & Mamon (2012) Silk, J., & Mamon, G. A. 2012, Research in Astronomy and Astrophysics, 12, 917, doi: 10.1088/1674-4527/12/8/004
  * Silk & Rees (1998) Silk, J., & Rees, M. J. 1998, Astronomy and Astrophysics, 331, L1, doi: 10.48550/arXiv.astro-ph/9801013
  * Smith et al. (2014) Smith, B. J., Soria, R., Struck, C., et al. 2014, The Astronomical Journal, 147, 60, doi: 10.1088/0004-6256/147/3/60
  * Steffen et al. (2021) Steffen, J. L., Fu, H., Comerford, J. M., et al. 2021, The Astrophysical Journal, 909, 120, doi: 10.3847/1538-4357/abe2a5
  * Thorp et al. (2019) Thorp, M. D., Ellison, S. L., Simard, L., Sánchez, S. F., & Antonio, B. 2019, Monthly Notices of the Royal Astronomical Society, 482, L55, doi: 10.1093/mnrasl/sly185
  * Trippe et al. (2008) Trippe, M. L., Crenshaw, D. M., Deo, R., & Dietrich, M. 2008, The Astronomical Journal, 135, 2048, doi: 10.1088/0004-6256/135/6/2048
  * Ulvestad & Wilson (1984) Ulvestad, J. S., & Wilson, A. S. 1984, The Astrophysical Journal, 285, 439, doi: 10.1086/162520
  * Ulvestad & Wilson (1989) —. 1989, The Astrophysical Journal, 343, 659, doi: 10.1086/167737
  * Veilleux & Osterbrock (1987) Veilleux, S., & Osterbrock, D. E. 1987, The Astrophysical Journal Supplement Series, 63, 295, doi: 10.1086/191166
  * Veilleux et al. (2001) Veilleux, S., Shopbell, P. L., & Miller, S. T. 2001, The Astronomical Journal, 121, 198, doi: 10.1086/318046
  * Veilleux et al. (2013) Veilleux, S., Meléndez, M., Sturm, E., et al. 2013, The Astrophysical Journal, 776, 27, doi: 10.1088/0004-637X/776/1/27
  * Venturi et al. (2023) Venturi, G., Treister, E., Finlez, C., et al. 2023, Astronomy and Astrophysics, 678, A127, doi: 10.1051/0004-6361/202347375
  * Weilbacher et al. (2020) Weilbacher, P. M., Palsa, R., Streicher, O., et al. 2020, Astronomy and Astrophysics, 641, A28, doi: 10.1051/0004-6361/202037855
  * Xu & Wang (2022) Xu, X., & Wang, J. 2022, The Astrophysical Journal, 938, 127, doi: 10.3847/1538-4357/ac912f
  * Zanchettin et al. (2023) Zanchettin, M. V., Feruglio, C., Massardi, M., et al. 2023, Astronomy and Astrophysics, 679, A88, doi: 10.1051/0004-6361/202245729
  * Zubovas & Bourne (2017) Zubovas, K., & Bourne, M. A. 2017, Monthly Notices of the Royal Astronomical Society, 468, 4956, doi: 10.1093/mnras/stx787


#  Exploring the effect of hadron cascade-time on particle production in Xe+Xe
collisions at $\sqrt{s_{\rm{NN}}}$ = 5.44 TeV using a multi-phase transport
model

Girija Sankar Pradhan1 Rutuparna Rath1 Ronald Scaria1 Raghunath
Sahoo1,2,111Corresponding author<EMAIL_ADDRESS>1Department of
Physics, Indian Institute of Technology Indore, Simrol, Indore 453552, India
2CERN, CH 1211, Geneva 23, Switzerland

###### Abstract

Heavy-ion collisions at ultra-relativistic energies provide extreme conditions
of energy density and temperature to produce a deconfined state of quarks and
gluons. Xenon (Xe) being a deformed nucleus further gives access to the effect
of initial geometry on final state particle production. This study focuses on
the effect of nuclear deformation and hadron cascade-time on the particle
production and elliptic flow using A Multi-Phase Transport (AMPT) model in
Xe+Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV. We explore the effect of
hadronic cascade-time on identified particle production through the study of
$p_{\rm T}$-differential particle ratios. The effect of hadronic cascade-time
on the generation of elliptic flow is studied by varying the cascade-time
between 5 and 25 fm/$c$. This study shows the final state interactions among
particles generate additional anisotropic flow with increasing hadron cascade-
time especially at very low and high-$p_{\rm T}$.

###### pacs:

12.38.Mh, 25.75.Ld, 25.75.Dw

##  I Introduction

The primary goal of ultra-relativistic heavy-ion collisions is to create a
system of deconfined quarks and gluons known as quark-gluon-plasma (QGP) under
extreme conditions of high temperature and/or baryon density, and characterise
its properties. It is very important to understand the particle production
mechanism in ultra-relativistic heavy-ion collisions for which several
experimental set-ups are designed at places such as Relativistic Heavy-ion
Collider (RHIC) at BNL, USA and Large Hadron Collider (LHC) at CERN,
Switzerland. In such collisions, huge initial energy density and pressure are
created which drive the expansion of the system through various complex
processes involving different degrees of freedom of the system. During this
expansion, multiple interactions of quarks and gluons may lead to a
thermalized system that further undergoes collective expansion and
hadronization to form composite hadrons from the deconfined partons. The
hadronized final state particles carry information about the initial-state
effects of the system produced during heavy-ion collisions. The initial state
geometry of produced system gives rise to spatial anisotropy which later
results in the momentum anisotropy of the final state particles in non-central
collisions. Anisotropic flow quantifies the momentum anisotropy of the
produced system, which is one of the signatures of QGP. The strength of this
anisotropic flow can be estimated from the flow coefficients ($v_{\rm n}$) in
the Fourier expansion of the momentum distribution of the final state
particles given by,

$E\frac{d^{3}N}{dp^{3}}=\frac{d^{2}N}{2\pi p_{\rm T}dp_{\rm
T}dy}\bigg{[}1+2\sum_{n=1}^{\infty}v_{n}~{}cos[n(\varphi-\psi_{n})]\bigg{]}.$
(1)

Where, the second-order Fourier coefficient of the anisotropic flow is called
elliptic flow ($v_{2}$), which is sensitive to the equation of state (EoS) and
transport properties Snellings:2011sz . Here $\varphi$ is the azimuthal angle
of emission of a final state particle and $\psi_{n}$ is the angle with respect
to the reaction plane– the plane created by the impact parameter and beam
axis. The elliptic flow ($v_{2}$) has been studied extensively using different
colliding systems such as Au+Au, Cu+Cu, U+U, Xe+Xe and Pb+Pb by RHIC and the
LHC with a wide range of collision energies varying from 7.7 GeV to 5.44 TeV
Feng:2016emh ; v2_phenix3 ; v2_phenix4 ; AMPT_Scaling ; v2_star2 ; AMPT_PbPb ;
Tripathy:2018rln . The shape of the colliding nuclei may also contribute to
the initial state geometry of the produced system, which may subsequently
affect the elliptic flow. A comparison of $v_{2}$ between spherical nuclei and
a deformed one in the central collisions can establish the origin of elliptic
flow due to the initial state effect. Recently, LHC has collided intrinsically
deformed nuclei Xenon (Xe) at $\sqrt{s_{\rm NN}}$ = 5.44 TeV, which also
bridges the final state charged particle multiplicity gap between the smaller
systems (p+p and p+Pb) and larger system (Pb+Pb). For the most central
collisions (0–5$\%$), the $v_{2}$ is found to be $\sim$ 35$\%$ higher in Xe+Xe
as compared to Pb+Pb Acharya:2018ihu . Further, the violation of quark
participant scaling of identified particle $v_{2}$ is also observed for the
Xe+Xe system like other colliding systems having spherical nuclei Kim:2018ink
; Tripathy:2018bib .

The space-time evolution of the system produced in heavy-ion collisions goes
through different stages and the phase between the chemical and kinetic
freeze-out boundaries is known as the hadronic phase. At the chemical freeze-
out boundary the inelastic processes cease and the particle abundances are
fixed which further experience elastic collisions with other particles present
in the system till they arrive at the kinetic freeze-out boundary. Inside the
hadronic phase, the strength of the scatterings depends on the cross-section
of the system constituents and the lifetime of the hadronic phase. The
momentum distribution of final state hadrons may also vary due to multiple
scatterings in the hadronic phase. This may also contribute to the momentum
anisotropy of the final state particles which results in the change in
$v_{2}$. This effect can be better studied by varying the lifetime of the
hadronic phase, which is possible to carry out with theoretical models like A
Multi-Phase Transport model (AMPT). Earlier, the effect of the hadronic phase
on the $v_{2}$ and resonance production has been observed by considering
spherical nuclei Singha:2015fia ; Nayak:2017gpi . It would be interesting to
look into the identified and charged particle $v_{2}$ with different hadronic
cascade-time ($\tau_{\rm HC}$) as a function of transverse momentum ($p_{\rm
T}$) and centrality using the intrinsically deformed nuclei, like Xe. It
should be noted here that the space-time evolution of the produced fireball in
heavy-ion collisions is governed by the initial energy density, which is
controlled by the available centre-of-mass energy and the number of
participating nuclei. Accordingly, the hadronic phase lifetime and the
cascade-time (we use these terms interchangeably without the violation of the
meaning thereof) becomes a function of collision energy and collision geometry
of the initial state of the collision.

The study of particle ratios with different mass, quark content and
baryons/mesons can be helpful to understand the particle production mechanism
in heavy-ion collisions. The $p_{\rm T}$-differential particle ratios help to
investigate various reasons for particle production at different $p_{\rm T}$
scales Rath:2018ytr . At lower $p_{\rm T}$ region, the spectral shapes of
identified particles strongly depend on the radial flow that has been observed
at the LHC in central heavy-ion collisions which are well explained by
hydrodynamically motivated models Abelev:2013vea ; Bozek:2012qs . The
collective expansion of the system pushes the heavier mass particles from
low-$p_{\rm T}$ to intermediate-$p_{\rm T}$, which subsequently shows an
enhancement of the ratio of the heavier to lighter particles. At intermediate
$p_{\rm T}$ region, a clear enhancement of baryon over meson has been observed
especially for p/$\pi$ ratios in the most central Pb+Pb collisions as compared
to pp-collisions. Baryons to meson ratio are further enhanced by the
coalescence mechanism which also requires radial flow where coalescence of
three quarks results in the creation of larger $p_{\rm T}$ baryons compared to
two quark/antiquark mesons. These $p_{\rm T}$-differential particle ratios can
also be affected due to the interactions of identified particles in the
hadronic phase through subsequent elastic scatterings. The intensity of such
phenomena mostly depends on the hadronic phase lifetime and the elastic cross-
section of the identified particles. The high-$p_{\rm T}$ sector is dominated
by the jet fragmentation and pQCD processes.

Here, we present a comprehensive study on the effect of the hadronic phase
lifetime (or hadronic cascade-time, as is known otherwise) on the $p_{\rm
T}$-differential particle ratios along with $p_{\rm T}$-differential and
integrated elliptic flow. In this study, we have used AMPT (string melting
version) to generate events at different hadronic phase times varying from 5
to 25 fm/$c$, which will be discussed in detail in Section II. Further, we
have discussed the results in the Section III, which is followed by the
Section IV with a summary of this study.

Figure 1: (Color online) $p\rm{{}_{T}}$-differential particle ratios of
$K^{\pm}$, $p(\bar{p})$, $\phi$ and $\Lambda(\bar{\Lambda})$ to $\pi^{\pm}$ in
Xe+Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV for 20–30 $\%$ centrality
class. Different symbols show various hadron cascade-times. The vertical lines
on the data points are the statistical uncertainties.

##  II Formalism

### A Mutli-Phase Transport (AMPT) model

In this study, we have used A Multiphase Transport (AMPT) model which is a
hybrid transport model AMPT1 ; AMPT2 ; AMPT3 . It has four components, namely:
Heavy-Ion Jet INteraction Generator (HIJING) that is used for the
initialization of collisions ampthijing , Zhang’s Parton Cascade model (ZPC)
that helps in parton transport after initialization, Lund string fragmentation
model or quark coalescence model to carry-out the hadronization mechanism and
finally A Relativistic Transport (ART) model to complete the hadron transport.
The differential cross-section of the produced minijet particles in p+p
collisions is calculated in the HIJING model which is given by,

$\displaystyle\frac{d\sigma}{dp_{T}^{2}\,dy_{1}\,dy_{2}}=$ $\displaystyle K$
$\displaystyle\,\sum_{a,b}x_{1}f_{a}(x_{1},p_{T1}^{2})\,x_{2}f_{b}(x_{2},p_{T2}^{2})$
(2) $\displaystyle\times$
$\displaystyle\frac{d\hat{\sigma}_{ab}}{d\hat{t}}\,,$

where $\sigma$ and $\hat{t}$ are the produced particles cross-section and the
momentum transfer during partonic interactions in p+p collisions,
respectively. $x_{i}$’s and $f(x,p_{T}^{2})$’s represent the momentum fraction
of the mother protons which are carried by interacting partons and the parton
density functions (PDF) accordingly. With the help of parametrized shadowing
function and nuclear overlap function of the in-built Glauber model, the
partons produced in the p+p collisions are transformed to A+A and p+A
collisions within HIJING. We use Woods-Saxon (WS) Loizides:2017ack
distribution to define the distribution of nucleons inside the spherical
nuclei like Au and Pb. Whereas, for the deformed nuclei like Xenon, we have
used a modified Woods-Saxon (MWS) density distribution in the HIJING that
includes deformation parameter, $\beta_{n}$, along with spherical harmonics,
$Y_{nl}(\theta)$, in the WS function mws_1 ; mws_2 ; mws_3 ; mws_4 ; mws_5 .
Nucleon density is usually written as a three parameter Fermi distribution
density_fermitype , which is defined as,

$\rho(r)=\rho_{0}\bigg{[}\frac{1+w(r/R)^{2}}{1+exp[(r-R)/a]}\bigg{]}\,.\\\ $
(3)

Here $\rho_{0}$ is the nuclear matter density in the centre of the nucleus,
$w$ is the deviation from a smooth spherical surface and $a$ is the skin depth
or surface thickness. The parameter, $R$, is the radius of the nucleus from
its centre and $r$, is a position variable and distance of any point from the
centre of the nucleus. Spherical nuclei are considered to have a uniform
distribution of nucleons within their spherical volume and a smooth surface
for which the value of $w$ becomes zero. Hence, the reduced nucleonic density
function wdsx  for a spherical nucleus can be written as,

$\rho(r)=\frac{\rho_{0}}{1+exp[(r-R)/a]}\,.\\\ $ (4)

The radius parameter, $R$, can be modified for an axially symmetric or prolate
deformed nucleus like Xe. The modified Woods-Saxon nuclear radius wdsx_deform
is given by,

$R_{A\Theta}=R[1+\beta_{2}Y_{20}(\theta)+\beta_{4}Y_{40}(\theta)],$ (5)

where the $\beta_{i}$’s are deformation parameters. In case of Xenon nucleus,
the deformation parameters, $\displaystyle\beta_{2}$= 0.162 and
$\displaystyle\beta_{4}$= -0.003, which are taken from Ref. atomic_data_table
; Giacalone:2017dud . The spherical harmonics, $Y_{20}$, and $Y_{40}$ are
given by speherical_harmonic ,

$\displaystyle Y_{20}(\theta)$ $\displaystyle=$
$\displaystyle\frac{1}{4}\sqrt{\frac{5}{\pi}}(3\ cos^{2}\theta-1)$
$\displaystyle Y_{40}(\theta)$ $\displaystyle=$
$\displaystyle\frac{3}{16\sqrt{\pi}}(35\ cos^{4}\theta-30\
cos^{2}\theta+3)\,.$ (6)

Figure 2: (Color online) $p\rm{{}_{T}}$-differential particle ratios of
$K^{\pm}$, $p(\bar{p})$, $\phi$ and $\Lambda(\bar{\Lambda})$ to $\pi^{\pm}$ in
Xe+Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV for 50–60$\%$ centrality
class. Different symbols show various hadron cascade-times. The vertical lines
on the data points are the statistical uncertainties.

The positions of nucleons within the distribution, $\rho(r)$, are illustrated
using the volume element $r^{2}sin\theta\ dr\ d\theta\ d\phi$ thesis_chris ;
ptribedy . For random orientation of nuclei, position configurations are
measured using both polar angle, (angle between major axis and beam axis)
$\Theta$ in $[0,\pi]$ and azimuthal angle, (angle between major axis and
impact parameter) $\Phi$ within limits $[0,2\pi]$. Both target and projectile
nuclei are rotated event-by-event in $\Theta$ and $\Phi$ space. In this paper,
calculations have been done only with random orientation which means,
unpolarized and averaged value over random $\Theta$ and $\Phi$ define_config .

The produced particles are then passed through the ZPC amptzpc , that
transports the quarks and gluons using Boltzmann transport equation which is
given by,

$\displaystyle p^{\mu}\partial_{\mu}f(x,p,t)=C[f]$ (7)

The leading order equation showing interactions among partons is approximately
given by,

$\frac{d\hat{\sigma}_{gg}}{d\hat{t}}\approx\frac{9\pi\alpha_{s}^{2}}{2(\hat{t}-\mu^{2})^{2}}\,.$
(8)

Where $\sigma_{gg}$ is the gluon scattering cross-section and $\alpha_{s}$ is
the strong coupling constant. Here, $\mu^{2}$ is the cutoff used to avoid
infrared divergences that may occur if the momentum transfer, $\hat{t}$, goes
to zero during scattering.

In the AMPT-SM version, colored strings melt into low momentum partons which
take place at the start of the ZPC and are calculated using the Lund FRITIOF
model of HIJING. These resulting partons undergo multiple scattering when any
two partons are within minimum separation which is given by $\displaystyle
d\,\leq\,\sqrt{\sigma/\pi}$, where $\sigma$ is the scattering cross-section of
the partons. Further, using the coalescence mechanism, the transported partons
are hadronized amptreco ; ampthadron2 ; ampthadron3 . Finally, the produced
hadrons undergo evolution through the ART model, where interactions take place
among meson-meson, baryon-baryon and meson-baryon before we get the final
state hadrons amptart1 ; amptart2 . For our work, we have used the AMPT
version 2.26t7 (released: 28/10/2016) where we have fixed the partonic
scattering cross-section ($\sigma_{gg}$) = 10 mb and the Lund string
fragmentation parameters $a$ and $b$ are set to their default values of 2.2
and 0.5/GeV2, respectively. It is worthwhile to note that we have kept the
hadron level decay flagged as off for $\phi$ and $\rm{K}_{s}^{0}$ to study
these particles in the final state. In the AMPT, the hadron cascade-time is
controlled by the parameter named NTMAX and DT. By varying DT, we have
generated the data in the AMPT-SM for the hadron cascade-times from 5 to 25
fm/$c$ within a time interval of 5 fm/$c$. Since the hadronic phase lifetime
for the default version of the AMPT is 30 fm and the lower limit obtained from
the study of re-scattering effect using resonances with experimental data is
$\sim$ 2–4 fm ALICE:2019xyr ; XX ; Sahu:2019tch , we have taken such an
interval of hadron cascade-time for our studies.

##  III Results and discussions

In this work, we have investigated $p\rm{{}_{T}}$-differential particle
ratios, $p\rm{{}_{T}}$-differential and $p\rm{{}_{T}}$-integrated elliptic
flow for identified and charged particles for different centralities,
respectively. The results are obtained for Xe+Xe collision at $\sqrt{s_{\rm
NN}}$ = 5.44 TeV by analysing the AMPT-SM generated events in which we have
taken care of the deformation effect of Xe-nuclei. Events are generated for a
wide range of hadronic cascade-time ranging from 5 to 25 fm/$c$ within a time
interval of 5 fm/$c$. Here, we have studied the $p\rm{{}_{T}}$-differential
identified particle ratios with respect to ($\pi^{+}+\pi^{-}$) and
(p+$\bar{\rm{p}}$). Furthermore, we have tried to see the quark participant
scaled elliptic flow for identified particles such as ($\pi^{+}+\pi^{-}$),
($K^{+}+K^{-}$), (p+$\bar{\rm{p}}$), $\phi$ and
($\Lambda+\bar{\rm{\Lambda}}$). Hadronic cascade-time can be sensitive to the
$p\rm{{}_{T}}$-differential identified particle ratios depending upon their
scattering cross-section in the hadronic phase and the lifetime of the
hadronic phase. Further, the multiple scattering of the final state particles
may modify their azimuthal direction and transverse momentum which will be
reflected on the $p\rm{{}_{T}}$-differential and $p\rm{{}_{T}}$-integrated
elliptic flow. Hence, our primary goal is to quantify the effect of hadronic
cascade-time ($\tau_{HC}$) on the observables like $p\rm{{}_{T}}$-differential
particle ratios and elliptic flow in the Xe+Xe collision system. This study
will enrich our understanding of particle production dynamics and the effect
of final state hadronic cascade-time in view of the finite hadronic phase
lifetime at the LHC energies, even in small collision systems.

###  III.1 Identified $p\rm{{}_{T}}$-differential particle ratios

Figure 3: (Color online) $p\rm{{}_{T}}$-differential particle ratios of $\phi$
to p in Xe+Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV for 20–30 $\%$
(upper) and 50–60 $\%$ (lower) centrality classes. Different symbols show
various hadron cascade-time. The vertical lines in the data points are the
statistical uncertainties.

Figures 1 and 2 show the ratio to pion in 20–30$\%$ and 50–60$\%$ centrality
classes for the particles like $K^{+}+K^{-}$, p+$\bar{\rm{p}}$, $\phi$ and
$\Lambda+\bar{\rm{\Lambda}}$ as a function of transverse momentum in different
hadronic cascade-time. The production rate of these identified particles as
compared to pion increases with $p\rm{{}_{T}}$ which attain a maximum value in
the intermediate $p\rm{{}_{T}}$ (2–3 GeV/$c$). This similar behaviour is also
observed for all the hadronic cascade-time. At lower transverse momentum
region ($p\rm{{}_{T}}~{}<1~{}{\rm GeV}/c$), we see a significant effect of the
hadronic cascade-time on $\phi$/$\pi$ and p/$\pi$ which have a maximum
deviation of $\sim$ 40$\%$ for $\tau_{HC}$ = 5 fm/$c$ with respect to 25
fm/$c$. However, this trend reverses for $p\rm{{}_{T}}~{}>1~{}{\rm GeV}/c$.
Moreover, the hadronic cascade-time has less effect on the strange particle
ratios like K/$\pi$ and $\Lambda$/$\pi$. For 50–60$\%$ centrality class, the
deviation for $\phi$/$\pi$ ratio is higher at lower $p\rm{{}_{T}}$ region as
compared to 20–30$\%$ centrality class.

Furthermore, we have investigated the effect of hadronic cascade-time on the
$\phi/p$ $p\rm{{}_{T}}$-differential ratio, which has a nearly similar mass.
Figure 3 represents $\phi$/p ratio as a function of $p\rm{{}_{T}}$ in
20–30$\%$ and 50–60$\%$ centrality classes for different hadron cascade-times.
The ratio increases with $p\rm{{}_{T}}$ and starts saturating after
$p\rm{{}_{T}}$ = 1 GeV/$c$ for both the centrality classes that further
enhances at high-$p_{\rm T}$. A similar trend is followed by all the hadronic
cascade-times. From the lower panel of the figure, we observe a clear
dependence on the $\tau_{HC}$ especially for 50–60$\%$ centrality class which
gradually increases as we decrease the value of $\tau_{HC}$ and shows a
maximum deviation $\sim$ 30$\%$ for $\tau_{HC}$ = 5 fm/$c$ as compared to 25
fm/$c$.

This study signifies the importance of different processes in the hadronic
phase and their impact on the $p\rm{{}_{T}}$-differential identified particle
ratios. This motivates us to further investigate the effect of hadronic
cascade-time on one of the important observables known as elliptic flow and
the results will be discussed in the next section, III.2.

###  III.2 Elliptic flow ($v_{2}$)

To be inline with the experimental procedure of estimating elliptic flow, in
this study, we have used the two-particle correlation method for a direct
comparison of AMPT data. The details of the two-particle correlation method
are described elsewhere Mallick:2020ium . For Pb+Pb collisions at
$\sqrt{s_{\rm NN}}$ = 2.76 TeV, a two-particle correlation method was also
used to predict $v_{\rm 2}$ for identified hadrons using AMPT Xu:2011fi . In
addition, the same method was also successfully used for estimating higher-
order anisotropic flows, as well as dihadron correlations in Pb+Pb collisions
at $\sqrt{s_{\rm NN}}$ = 2.76 TeV using the AMPT model Xu:2011jm . The two-
particle correlation method has the added edge of construction with a proper
pseudo-rapidity cut. This removes substantial residual non-flow effects in the
elliptic flow. Non-flow effects are azimuthal correlations, which usually
occur from jets and resonance decays, and are not associated with the symmetry
planes. Figure 4 shows the charged particle elliptic flow as a function of
$p\rm{{}_{T}}$ for both 20–30$\%$ and 50–60$\%$ centrality classes. Here, we
have compared the $p\rm{{}_{T}}$-differential elliptic flow generated for the
two extreme cases, $\tau_{HC}$ = 5 fm/$c$ and 25 fm/$c$ for both the
centrality classes. With different centrality classes and cascade-times, the
elliptic flow increase with $p\rm{{}_{T}}$ and obtain a maximum value for
$p\rm{{}_{T}}$ around 2–2.5 GeV/$c$. We observe higher $v_{\rm 2}$ for the
peripheral collisions (50–60$\%$) as compared the semi-central collisions
(20–30$\%$). The results are compared with the $p\rm{{}_{T}}$-differential
elliptic flow of the charged particles obtained from ALICE for both 20–30$\%$
and 50–60$\%$ centrality classes. In both the cases, the trend is
qualitatively explaining the ALICE data and a higher elliptic flow is observed
for 50–60 $\%$ centrality class, which is in line with the experimental
observations.

Figure 4: (Color online) $p\rm{{}_{T}}$-differential elliptic flow of charged
particles in Xe+Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV for 20-30$\%$
and 50-60$\%$ centrality classes. Different symbols show various hadron
cascade-times. The results are compared with the ALICE data Acharya:2018ihu .

This can be understood from the effect of initial momentum anisotropic due to
the geometry of the overlapping region generated after the collisions which
are higher for the peripheral collisions. While considering different hadronic
cascade-times, we observe a similar behavior of the
$p\rm{{}_{T}}$-differential elliptic flow in both 20–30$\%$ and 50–60$\%$. For
both the centralities, with higher cascade-time, the azimuthal distribution of
the final state particles is more anisotropic for high and very low-$p_{\rm
T}$ region. However, in the intermediate-$p_{\rm T}$ region seems to be not
affected by the hadronic cascade-time significantly.

Figure 5: (Color online) $n_{\rm q}$-scaled $p\rm{{}_{T}}$-differential
elliptic flow of the identified charged particles in Xe+Xe collisions at
$\sqrt{s_{\rm NN}}$ = 5.44 TeV for 20–30$\%$ (top) and 50–60$\%$ (bottom)
centrality classes for hadron cascade-time of 25 fm/c. Different symbols show
various identified hadrons. The results are compared with the ALICE data
ALICE:2021ibz .

The particle production via quark coalescence can be verified by studying the
elliptic flow of baryons and mesons at intermediate $p\rm{{}_{T}}$ after
scaling both $p\rm{{}_{T}}$ and $v_{\rm 2}$ by the number of constituent
quarks ($n_{\rm q}$). In AMPT with the string melting mode, mesons and baryons
are formed when a quark and antiquark pair and three quarks come close in
phase space, respectively. In such conditions, the elliptic flow for baryons
is higher at the intermediate $p\rm{{}_{T}}$ range compared to mesons due to
the recombination effect. Figure 5 represents the constituent quark scaled
$v_{2}$ as a function of $p\rm{{}_{T}}$/$n_{\rm q}$. For this study, the
elliptic flow and $p\rm{{}_{T}}$ are scaled by 2 for mesons like pions, kaons
and $\phi$, while the same are scaled by 3 for baryons such as protons and
$\Lambda$. We can clearly see the violation of the scaling behavior in both
20–30$\%$ and 50–60$\%$ centrality classes at $\tau_{HC}$ = 25 fm/$c$, which
are in line with the deviations that are already reported in ALICE
ALICE:2021ibz  and several experimental studies performed at LHC energies
Acharya:2018zuq . We have explicitly checked that this violation is also
observed for $\tau_{HC}$ = 5 fm/$c$, indicating the fact that hadron cascade-
time has no role on the quark-participant scaling violation in the elliptic
flow.

Figure 6: (Color online) $p\rm{{}_{T}}$-integrated elliptic flow of the
charged particles in Xe+Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV for
0-10$\%$, 10-20$\%$, 20-30$\%$, 30-40$\%$, 40-50$\%$ and 50-60$\%$ centrality
classes. Different symbols show various hadron cascade-times.

Furthermore, to investigate the effect of hadronic cascade-time on the bulk
part of the system with centrality, we have studied the
$p\rm{{}_{T}}$-integrated elliptic flow of the charged particles. Inspired by
the ALICE kinematic acceptance, we have considered the charged tracks with
$p\rm{{}_{T}}$ lying between 0.2 to 3 GeV/$c$. Figure 6 shows the
$p\rm{{}_{T}}$-integrated elliptic flow as a function of centrality for
different values of $\tau_{\rm HC}$. While going from central to peripheral
collisions, the $p\rm{{}_{T}}$-integrated $v_{2}$ increases for all the
hadronic cascade-times. To quantify the dependence on hadronic cascade-time,
we have shown the ratio with respect to 25 fm/$c$ in the lower panel of Figure
6. We do not observe significant dependence of the $p\rm{{}_{T}}$-integrated
$v_{2}$ on the hadronic cascade-time, though we see a clear dependence on
hadronic cascade-time in case of the $p\rm{{}_{T}}$-differential $v_{2}$.

##  IV Summary

In this study, we have explored the effect of hadronic cascade-time
($\tau_{\rm HC}$) on the $p\rm{{}_{T}}$-differential identified particle
ratios, $p\rm{{}_{T}}$-differential and $p\rm{{}_{T}}$-integrated elliptic
flow in Xe+Xe collision at $\sqrt{s_{\rm{NN}}}$ = 5.44 TeV using the data
generated from the AMPT-SM version. In the AMPT-SM, the participation of soft
partons originating from the string melting process in partonic scatterings
results in an increased elliptic flow as compared to the default AMPT. In
addition, it allows modifying the final state hadronic phase lifetime by
varying the number of time steps in a hadron cascade and/or the length of the
time step. The significance of the hadronic cascade-time on particle
production depends on the scattering cross-section among the final state
particles and the duration of the hadronic phase. This study has more
significance in looking into the larger hadronic phase lifetime at the LHC
energies. We see a significant dependence of identified particle ratios and
elliptic flow on the $\tau_{\rm HC}$ when studied as a function of $p_{\rm T}$
and centrality. The important findings of this study are summarised below:

  * •

Significant dependence of $p\rm{{}_{T}}$-differential particle ratios for
$\phi/\pi$ and $p/\pi$ on $\tau_{\rm HC}$ is observed at low $p_{\rm T}$,
which is higher for $\phi/\pi$ ratio. With higher $\tau_{\rm{HC}}$, the low
$p\rm{{}_{T}}$ particles shift towards intermediate and higher $p\rm{{}_{T}}$
region due to more interactions which is reflected in the particle ratios.

  * •

To cancel out the mass dependence on $\tau_{\rm HC}$, we have looked into the
$\phi/p$ $p\rm{{}_{T}}$-differential particle ratio. We see a scaling of this
ratio for 50-60$\%$ centrality class with $\tau_{\rm HC}$. However, for mid-
central collisions, we see a significant dependence of $\tau_{\rm HC}$ on
$\phi/p$ ratio at intermediate $p\rm{{}_{T}}$ region.

  * •

The $p\rm{{}_{T}}$-differential charged particle elliptic flow is higher for
$\tau_{\rm HC}$ = 25 fm/$c$ compared to 5 fm/$c$ at very low and high-$p_{\rm
T}$ region. This indicates added anisotropy in the azimuthal distribution of
the charged particles might be originating from multiple scattering in the
hadronic phase with higher $\tau_{\rm HC}$.

  * •

In line with the experimental results obtained at the LHC energies, we do not
observe any scaling behavior with the number of constituent quarks ($n_{\rm
q}$) on elliptic flow. The hadron cascade-time has no effect on the quark-
participant scaling violation in the elliptic flow, which is supposed to be an
initial state effect in contrast to the hadronic rescattering, which is a
final state effect.

  * •

To see the effect of hadronic cascade-time over the bulk of the medium, we
have estimated the $p\rm{{}_{T}}$-integrated charged particle elliptic flow in
different centrality classes. We found the $p\rm{{}_{T}}$-integrated charged
particle elliptic flow is almost independent of the hadronic cascade-time.
This might be due to the compensation of anisotropy over different
$p\rm{{}_{T}}$ regions.

More precisely, we observe the effect of hadron cascade-time on
$p\rm{{}_{T}}$-differential identified particle ratios,
$p\rm{{}_{T}}$-differential and integrated charged particle elliptic flow. We
see an interplay of different hadronic phase effects such as scattering cross-
sections, hadronic phase lifetime and momentum anisotropy inherited from
initial collision geometry on these observables.

## Acknowledgements

RR and GSP acknowledge the financial supports by DST-INSPIRE program of
Government of India. Ronald Scaria acknowledges CSIR, Government of India for
financial supports. Raghunath Sahoo acknowledges the financial supports under
the CERN Scientific Associateship and the financial grants under DAE-BRNS
Project No. 58/14/29/2019-BRNS of Government of India. The authors would like
to acknowledge the usage of resources of the LHC grid computing facility at
VECC, Kolkata and usage of resources of the LHC grid Tier-3 computing facility
at IIT Indore. We would like to thank N. Mallick and S. Prasad for helping in
the estimation of elliptic flow in the two-particle correlation method. Mr.
Vikash Yadav is acknowledged for making an initial exploration of the idea
used in this paper as a part of his master’s thesis.

## References

  * (1) R. Snellings, New J. Phys. 13, 055008 (2011).
  * (2) Z. Feng, G. M. Huang and F. Liu, Chin. Phys. C 41, 024001 (2017).
  * (3) A. Adare et al. [PHENIX Collaboration], Phys. Rev. Lett. 98, 162301 (2007).
  * (4) A. Adare et al. [PHENIX Collaboration], Phys. Rev. C 85, 064914 (2012).
  * (5) S. Singha and M. Nasim, Phys. Rev. C 93, 034908 (2016).
  * (6) B. I. Abelev et al. [STAR Collaboration], Phys. Rev. C 75, 054906 (2007).
  * (7) Liang Zheng et al. Eur. Phys. J. A 53, 124 (2017).
  * (8) S. K. Tripathy, M. Younus, Z. Naik and P. K. Sahu, Nucl. Phys. A 980, 81 (2018).
  * (9) S. Acharya et al. [ALICE Collaboration], Phys. Lett. B 784, 82 (2018).
  * (10) B. Kim [ALICE Collaboration], Nucl. Phys. A 982, 279 (2019).
  * (11) S. Tripathy, S. De, M. Younus and R. Sahoo, Phys. Rev. C 98, 064904 (2018).
  * (12) S. Singha, B. Mohanty and Z. W. Lin, Int. J. Mod. Phys. E 24, 1550041 (2015).
  * (13) K. Nayak, S. Singha, M. Nasim and B. Mohanty, DAE Symp. Nucl. Phys. 62, 962 (2017).
  * (14) R. Rath, S. Tripathy, R. Sahoo, S. De and M. Younus, Phys. Rev. C 99, 064903 (2019).
  * (15) B. Abelev et al. [ALICE Collaboration], Phys. Rev. C 88, 044910 (2013).
  * (16) P. Bozek and I. Wyskiel-Piekarska, Phys. Rev. C 85, 064915 (2012).
  * (17) Z. w. Lin and C. M. Ko, Phys. Rev. C 65, 034904 (2002).
  * (18) Zi-Wei Lin et al., Phys. Rev. C 72, 064901 (2005).
  * (19) L. W. Chen, V. Greco, C. M. Ko and P. F. Kolb, Phys. Lett. B 605, 95 (2005).
  * (20) X. N. Wang and M. Gyulassy, Phys. Rev. D 44, 3501 (1991).
  * (21) C. Loizides, J. Kamin and D. d’Enterria, Phys. Rev. C 97, 054910 (2018).
  * (22) H. Masui, B. Mohanty and N. Xu, Phys. Letts. B 679 440 (2009).
  * (23) M. R. Haque, Z. Lin and B. Mohanty, Phys. Rev. C 85, 034905 (2012).
  * (24) P. Dasgupta, R. Chatterjee and D. K. Srivastava, Phys. Rev C 95, 064907 (2017).
  * (25) O.S.K. Chaturvedi et. al. Eur. Phys. J. Plus 132, 430 (2017).
  * (26) Arpit Singh et al, Eur. Phys. J. C 78 419 (2018).
  * (27) R. Hofstadter, Nobel Lecture, December 11, 1961.
  * (28) Roger D. Woods and David S. Saxon, Phys. Rev. 95, 577 (1954).
  * (29) D. L. Hendrie, N.K. Glendenning, B.G. Harvey, O.N. Jarvis, H.H. Duhm, J. Saudinos, J. Mahoney, Phys. Letts B 26, 127 (1968).
  * (30) P.Moller, J.R.Nix, W.D.Myers and W.J.Swiatecki, Atomic Data and Nuclear Data Tables 59, 185 (1995).
  * (31) G. Giacalone, J. Noronha-Hostler, M. Luzum and J. Y. Ollitrault, Phys. Rev. C 97, 034904 (2018).
  * (32) C 5, Quantum Theory of Angular Momentum, By D A Varshalovich, A N Moskalev, V K Khersonskii, Singapore: World Scientific (1988).
  * (33) PhD Thesis, Christopher Edward Flores, University of California, Davis http://nuclear.ucdavis.edu/thesis/CEF_Thesis_Final.pdf.
  * (34) B. Schenke, P. Tribedy, and R. Venugopalan, Phys. Rev. C 89, 064908 (2014).
  * (35) C. Nepali, G. Fai, and D. Keane, Phys. Rev. C 76, 051902 (2007).
  * (36) B. Zhang, Comput. Phys. Commun. 109, 93 (1998).
  * (37) V. Greco, C. M. Ko and P. Levai, Phys. Rev. Lett. 90, 202302 (2003).
  * (38) R. J. Fries, B. Muller, C. Nonaka and S. A. Bass, Phys. Rev. Lett. 90, 202303 (2003).
  * (39) R. J. Fries, B. Muller, C. Nonaka and S. A. Bass, Phys. Rev. C 68, 044902 (2003).
  * (40) B. Li, A. T. Sustich, B. Zhang and C. M. Ko, Int. J. Mod. Phys. E 10, 267 (2001).
  * (41) B. A. Li and C. M. Ko, Phys. Rev. C 52, 2037 (1995).
  * (42) S. Acharya et al. (ALICE Collaboration), Phys. Lett. B 802, 135225 (2020).
  * (43) B. Abelev et al. (ALICE Collaboration ) Phys. Rev. C 91, 024609 (2015).
  * (44) D. Sahu, S. Tripathy, G. S. Pradhan and R. Sahoo, Phys. Rev. C 101, 014902 (2020).
  * (45) N. Mallick, R. Sahoo, S. Tripathy and A. Ortiz, J. Phys. G 48, 045104 (2021).
  * (46) J. Xu and C. M. Ko, Phys. Rev. C 83, 034904 (2011).
  * (47) J. Xu and C. M. Ko, Phys. Rev. C 84, 044907 (2011).
  * (48) S. Acharya et al. [ALICE Collaboration], JHEP 10, 152 (2021).
  * (49) S. Acharya et al. [ALICE Collaboration], JHEP 09, 006 (2018).