11institutetext:  Institute of Theoretical Physics and Astronomy, Vilnius
University, Sauletekio av. 3, 10257, Vilnius, Lithuania 22institutetext: Main
Astronomical Observatory, National Academy of Sciences of Ukraine, 27
Akademika Zabolotnoho St, 03680, Kiev, Ukraine 33institutetext: Departamento
de Física de la Tierra y Astrofísica, Instituto de Física de Partículas y del
Cosmos, IPARCOS. Universidad Complutense de Madrid (UCM), E-28040, Madrid,
Spain

# Searching for Milky Way twins: Radial abundance distribution as a strict
criterion

L. S. Pilyugin Searching for Milky Way twins: Radial abundance distribution as
a strict criterionSearching for Milky Way twins: Radial abundance distribution
as a strict criterionSearching for Milky Way twins: Radial abundance
distribution as a strict criterionSearching for Milky Way twins: Radial
abundance distribution as a strict criterion G. Tautvaišienė Searching for
Milky Way twins: Radial abundance distribution as a strict criterionSearching
for Milky Way twins: Radial abundance distribution as a strict criterion M. A.
Lara-López Searching for Milky Way twins: Radial abundance distribution as a
strict criterionSearching for Milky Way twins: Radial abundance distribution
as a strict criterion

We search for Milky Way-like galaxies among a sample of approximately 500
galaxies. The characteristics we considered of the candidate galaxies are the
following: stellar mass $M_{\star}$, optical radius $R_{25}$, rotation
velocity $V_{rot}$, central oxygen abundance (O/H)0, and abundance at the
optical radius (O/H)${}_{R_{25}}$. If the values of $R_{25}$ and $M_{\star}$
of the galaxy were close to that of the Milky Way, then the galaxy was
referred to as a structural Milky Way analogue (sMWA). The oxygen abundance at
a given radius of a galaxy is defined by the evolution of that region
(astration level, that is, the fraction of gas converted into stars, as well
as gas exchange with the surroundings), and we then assumed that the
similarity of (O/H)0 and (O/H)${}_{R_{25}}$ in two galaxies suggests a
similarity in their (chemical) evolution. If the values of (O/H)0 and
(O/H)${}_{R_{25}}$ in the galaxy were close to that of the Milky Way, then the
galaxy was referred to as an evolutionary Milky Way analogue (eMWA). If the
galaxy was simultaneously an eMWA and sMWA, then the galaxy was considered a
Milky Way twin. We find that the position of the Milky Way on the (O/H)0 –
(O/H)${}_{R_{25}}$ diagram shows a large deviation from the general trend in
the sense that the (O/H)${}_{R_{25}}$ in the Milky Way is appreciably lower
than in other galaxies of similar (O/H)0. This feature of the Milky Way
evidences that its (chemical) evolution is not typical. We identify four
galaxies (NGC 3521, NGC 4651, NGC 2903, and MaNGA galaxy M-8341-09101) that
are simultaneously sMWA and eMWA and can therefore be considered as Milky Way
twins. In previous studies, Milky Way-like galaxies were selected using
structural and morphological characteristics, that is, sMWAs were selected. We
find that the abundances at the centre and at the optical radius (evolutionary
characteristics) provide a stricter criterion for selecting real Milky Way
twins.

###### Key Words.:

galaxies: spiral -– galaxies: fundamental parameters – galaxies: abundances –
ISM: abundances

##  1 Introduction

The position of the Milky Way in the context of the general galaxy population
is an important subject of study, as it concerns identifying whether the Milky
Way is really a typical spiral galaxy and the way(s) in which it differs if it
is not. In a number of investigations, there have been attempts to establish
how typical the Milky Way is amongst galaxies and how many Milky Way-like
galaxies exist. Milky Way-like galaxies are usually referred to as Milky Way
analogues (MWAs). Boardman et al. (2020a) noted that there is no single and
commonly accepted definition of an MWA; rather, the definition can change
depending on the goals of a particular study. Different characteristics of the
Milky Way can be used when comparing it to other galaxies (de Vaucouleurs &
Pence 1978; Hammer et al. 2007; Mutch et al. 2011; Licquia et al. 2015;
McGaugh 2016; Licquia et al. 2016; Fraser-McKelvie et al. 2019; Boardman et
al. 2020a; Fielder et al. 2021), and galaxies may be identified as being Milky
Way-like on the basis of having similar qualitative characteristics to the
Milky Way or on the basis of their position relative to the Milky Way in a
given parameter space.

de Vaucouleurs & Pence (1978) identified four nearby galaxies (NGC 1073, NGC
4303, NGC 5921, and NGC 6744) as MWAs since their photometric parameters
(morphological type $T$, isophotal diameter, effective diameter, absolute $B$
magnitude, and mean colour index ($B-V$)) are in remarkably close agreement
with the corresponding values of the Milky Way. Mutch et al. (2011) selected
MWAs using stellar mass and the structural parameter $f_{DeV}$ as the
selection criteria, where the structural parameter $f_{DeV}$ describes the
fraction of light that corresponds to the de Vaucouleurs component of the
light profile and is correlated with the morphological type of galaxy as well
as with the bulge-to-total ratio ($B/T$). Licquia et al. (2015) selected a
large MWA sample from the Eighth Data Release (Aihara et al. 2011) of the
Sloan Digital Sky Survey III (SDSS-III; York et al. 2000) on the basis of
stellar mass and current star formation rate. Boardman et al. (2020a)
presented a sample of 62 galaxies identified as MWAs on the basis of their
stellar masses and bulge-to-total ratios from the Mapping Nearby Galaxies at
Apache Point Observatory (MaNGA) survey (Bundy et al. 2015). The selection of
MWAs using only two characteristics of the Milky Way as the selection criteria
is based on the Copernican assumption that the Milky Way is not extraordinary
amongst galaxies, that is, any property of the Milky Way is similar to that of
the MWA galaxies selected (Mutch et al. 2011; Licquia et al. 2015; Boardman et
al. 2020a).

It is evident that when the process of selecting MWAs involves using a larger
number of parameters as well as more stringent constraints on a given
parameter, it yields a sample of MWA galaxies with properties that are closer
to the true properties of the Milky Way. However, the use of a greater number
of selection criteria (or an overly strict definition of “analogue”) yields
few, if any, MWA galaxies (Boardman et al. 2020b). Indeed, Fraser-McKelvie et
al. (2019) found only 176 MWAs amongst over a million galaxies in the Sloan
Digital Sky Survey (SDSS) Data Release 7 (Abazajian et al. 2009) when
selecting based on stellar mass, bulge-to-total ratio ($B/T$), and morphology
(the presence of spiral arms and the presence of a bar). Boardman et al.
(2020a) did not find a single MWA in the SDSS-IV MaNGA survey (Bundy et al.
2015) when attempting to select based on a combination of stellar mass, star
formation rate, bulge-to-total ratio ($B/T$), and disc scale length. Those
results suggested that some parameter(s) of the Milky Way galaxy may be
unusual or that the combination of its properties may be rare.

Hammer et al. (2007) compared the Milky Way to disc galaxies within the same
mass range, using its location in the Tully-Fisher (variant of $V_{rot}$
versus $k$-band luminosity) and other diagrams. They found for all
relationships that the Milky Way galaxy is systematically offset by 1$\sigma$,
showing a significant deficiency in stellar mass, angular momentum, disc
radius, and Fe/H in the stars in its outskirts at a given $V_{rot}$, i.e. on
the basis of its location in the ($L_{k}$, $V_{rot}$, and $R_{25}$) volume,
the fraction of spirals like the Milky Way was found to be around 7%. In
contrast, McGaugh (2016) found that the Milky Way appears to be a normal
spiral galaxy that obeys scaling relations, such as Tully-Fisher, and the
size-mass relation. He noted that the galaxy NGC 3521 has a baryonic mass,
rotation velocity, and scale disc length that are very similar to those of the
Milky Way; these quantities are identical within the uncertainties. McGaugh
(2016) concluded that NGC 3521 is a near twin to the Milky Way. Licquia et al.
(2016) considered the three variants of the Tully-Fisher relation (rotation
velocity versus $i$-band luminosity, stellar mass, and baryonic mass) and
found that our Galaxy’s properties are in excellent agreement with those
Tully-Fisher relations. They also examined the three-dimensional relation
(rotation velocity-luminosity-radius) using the disc scale length as a measure
of size for spiral galaxies. Licquia et al. (2016) found that the Milky Way
lies farther from the relation in comparison to 90% of other spiral galaxies,
yielding evidence that it is unusually compact for its rotation velocity and
luminosity. The expected disc scale length for the Milky Way from the relation
is approximately 5 kpc, nearly twice as large as the observed value. Thus,
there is a hint that some parameter(s) of the Milky Way (e.g. size) may not be
perfectly typical and that the combination of the parameters may be rather
rare.

The characteristics of a galaxy can be conditionally divided into two types.
The parameters of the first type (e.g. morphology, luminosity, stellar mass,
rotation velocity) describe the structure and global characteristics of a
galaxy at the present-day epoch and can be called ”structural parameters.” The
parameter of the second type is related to the oxygen abundance of a galaxy.
The oxygen abundance at a given radius of a galaxy is defined by the evolution
of this region of a galaxy (fraction of gas converted into stars, i.e.
astration level, and matter exchange with the surroundings). Then the oxygen
abundance can be considered as an indicator of a galaxy’s evolution and can be
called an ”evolutionary parameter.” A galaxy located close to the Milky Way in
the field(s) of the first type of parameters is referred to in this work as a
structural Milky Way analogue (sMWA). A galaxy located close to the Milky way
in the field of the second type of parameters is referred to as an
evolutionary Milky Way analogue (eMWA). If a galaxy is simultaneously an sMWA
and an eMWA, then such a galaxy is considered a twin of the Milky Way.

In fact, sMWAs were selected and examined in the papers cited above. The
oxygen abundance at the optical radius of the Milky Way is appreciably lower
in comparison to other galaxies with similar central oxygen abundance (see
below). This feature of the Milky Way evidences that its (chemical) evolution
is not typical. Therefore, it is highly useful to study the evolutionary
analogues of the Milky Way. The goal of the current study is to search for and
examine the galaxies that are simultaneously sMWAs and eMWAs. We considered
three structural parameters: optical radius, stellar mass, and rotation
velocity. Since rotation curve data are not available for some galaxies or the
rotation velocity has been measured with a large uncertainty (e.g. in face-on
galaxies with low-inclination angles) the position in the $M_{\star}$ –
$R_{25}$ – $V_{rot}$ has not been determined. The stellar mass – optical
radius diagram was therefore used to select the sMWAs. The central abundance
versus abundance at the optical radius diagram served in the search for eMWAs.
We compared the Milky Way with a sample of spiral galaxies for which radial
abundance distributions, optical radii, stellar masses, and rotation curves
were derived by us or compiled from the literature. Our sample of the
comparison galaxies involves the nearby galaxies and the galaxies from the
MaNGA survey. The obtained candidates of Milky Way twins are examined in more
detail.

This paper is organised in the following way: the Milky Way characteristics
are described in Sect. 2. In Sec. 3, a sample of (comparison) galaxies is
reported. The selection of the Milky Way-like galaxies is given in Sect. 4.
The discussion is in Sect. 5, and Sect. 6 contains a brief summary.

##  2 Characteristics of the Milky Way Galaxy

###  2.1 Milky Way optical radius R25

The maximum size of the Galactic stellar disc of the Milky Way is not yet
known. Some studies have suggested an abrupt drop-off of the stellar density
of the disc at galactocentric distances $R$ $\ga$ 15 kpc. Minniti et al.
(2011) considered the clump giants of the disc as standard candles, calibrated
from Hipparcos parallaxes. They concluded that there is an edge in the stellar
disc of the Milky Way at $R$ = 13.9$\pm$0.5 kpc along various lines of sight
across the Galaxy. Based on the Two Micron All Sky Survey (2MASS) data, Amôres
et al. (2017) found a disc truncation at approximately 16.1$\pm$1.3 kpc. If
age dependence for disc parameters is considered, then the disc truncation is
19.4$\pm$1.4 kpc or 18.7$\pm$1.6 kpc. The density drops by 90% within 1 kpc,
and therefore the cutoff is sharp. In practice, this means that no disc stars,
or very few of them, should be found beyond this limit.

In contrast, López-Corredoira et al. (2018) revealed the presence of disc
stars at $R>26$ kpc. Chrobáková et al. (2020) calculated the stellar density
using star counts obtained from Gaia Data Release 2 up to a galactocentric
distance of $R$ = 20 kpc. They found that the stellar density maps can be
fitted by an exponential disc in the radial direction $h_{d}$ = 2.07$\pm$0.07
kpc, with a weak dependence on the azimuth, up to 20 kpc without any cutoff.
The flare and warp are clearly visible. They found the stellar density in the
solar neighbourhood $\rho$ = 0.064 stars/pc3 where the solar neighbourhood is
defined as the area where 7.5 kpc $<R<$ 8.5 kpc and $-0.05<z<0.05$ kpc.
Chrobáková et al. (2020) noted that this does not mean that radial truncations
are not possible in spiral galaxies, as there are other galaxies in which they
have been observed many years ago (van der Kruit & Searle 1981), though the
Milky Way is not one of them. Is should be noted that an exponential
distribution was also observed for the gas density of the Milky Way without
any truncation up to a distance of 40 kpc from the centre (Kalberla & Dedes
2008).

The optical radius can be estimated from the radial distributions of the
surface stellar mass density in the disc described by Eq. 1 by adopting
($M/L$)B = 1.4 (Flynn et al. 2006). The radial distribution of the surface
stellar mass density in the disc is described by the expression

$\Sigma_{\star}=\Sigma_{\star,R_{0}}\exp\left(-\frac{R-R_{0}}{h_{d}}\right),$
(1)

where $\Sigma_{\star,R_{0}}$ is the surface stellar mass density at the solar
galactocentric distance ($R_{0}$ = 8.178$\pm$0.013 kpc, Gravity Collaboration
2019) and $h_{d}$ is the disc scale length. It should be noted that a two-
component disc (thin and thick discs of different scale lengths) is usually
considered (e.g. McMillan 2017). The single exponential disc is adopted here.

Flynn et al. (2006) found a local stellar disc surface density of 35.5
$M_{\sun}$/pc2, while McKee et al (2015) found the value of 33.4
$M_{\sun}$/pc2. The solar neighbourhood is located in the interarm region, and
the “counted” local stellar disc surface density should be corrected for the
spiral arm enhancement in order to find the azimuthal average of the surface
stellar mass density at the solar galactocentric distance, that is, a 10%
enhancement should be added to the “counted” local stellar disc surface
density (Flynn et al. 2006; Kubryk et al 2015). This results in a stellar disc
surface density at the solar galactocentric distance of 39 $M_{\sun}$/pc2
(Flynn et al. 2006) and 37 $M_{\sun}$/pc2 (McKee et al 2015). We adopted
$\Sigma_{\star,R_{0}}$ = 38 $M_{\sun}$/pc2. Bland-Hawthorn & Gerhard (2016)
analysed 130 papers on disc parameters, with scale lengths ranging from 1.8 to
6.0 kpc. Their analysis of the main papers (15 in all) on this topic led to
$h_{d}$ = 2.6 $\pm$ 0.5 kpc.

Regarding the conversion of the solar units $L_{\sun}$/pc2 to magB/arcsec2, we
note that the $\mu_{B}$ = 25.0 magB/arcsec2 corresponds to 6.44 $L_{\sun}$/pc2
with the adopted $M_{B,\sun}$ = 5.45 (the relation is $\mu_{B}$(mag/arcsec2) =
–2.5log$L_{B}$ ($L_{\sun}$/pc2) +27.022). The value of the surface brightness
of $\mu_{B}$ = 25.0 magB/arcsec2 corresponds to the stellar surface mass
density of $\sim$9.0 $M_{\sun}$/pc2, assuming ($M/L$)B = 1.4 (Flynn et al.
2006). The value of the optical radius $R_{25}$ is around 12 kpc for the
$h_{disc}$ = 2.6 kpc and the stellar disc surface mass density at the solar
galactocentric distance of 38 $M_{\sun}$/pc2. This value of the optical radius
is close to the early estimation of the optical radius ($R_{25}$ = 11.5 kpc)
obtained by de Vaucouleurs & Pence (1978). We adopted $R_{25}$ = 12.0 kpc for
the Milky Way.

###  2.2 Stellar mass $M_{\star}$ and black hole mass MBH of the Milky Way

The stellar mass of the Milky Way is the sum of the stellar masses of disc and
bulge. Two comments on the determination of the stellar mass of the Milky Way
should be presented. First, the mass of a single component exponential disc of
a given scale length can be estimated through the simple relation (McMillan
2017):

$M_{\star,d}=2\pi\Sigma_{\star,0}h_{d}^{2},$ (2)

where $\Sigma_{\star,0}$ is the central surface mass density of the disc and
$h_{d}$ is the scale length of the surface mass density distribution. However,
a two-component disc (thin and thick disc) is usually considered. Therefore,
the above expression should be applied to each component of the disc. Second,
it is often used to derive not the mass of the pure bulge, but the sum of the
mass of the bulge and disc within the bulge region.

Table 1:  Estimations of the stellar mass of the Milky Way from different publications.  | disc | bulge | total
---|---|---|---
| (1010M☉) | (1010M☉) | (1010M☉)
Flynn et al. (2006) |  |  | 5.18$\pm$0.32
Bovy & Rix (2013) | 4.6$\pm$0.3 | 0.6 | 5.2
Licquia & Newman (2015) | 5.17$\pm$1.11 | 0.91$\pm$0.07 | 6.08$\pm$1.14
Licquia & Newman (2016) | 4.8${}^{+1.5}_{-1.1}$ | 0.91$\pm$0.07 | 5.7${}^{+1.5}_{-1.1}$
McMillan (2017) |  | 0.91$\pm$0.09 | 5.43$\pm$0.57
Cautun et al. (2020) | 4.10$\pm$0.40 | 0.94$\pm$0.10 | 5.04$\pm$0.50

Estimations of the stellar mass of the Milky Way have been reported in many
papers (Flynn et al. 2006; Bovy & Rix 2013; Licquia & Newman 2015, 2016;
Bland-Hawthorn & Gerhard 2016; McMillan 2017; Cautun et al. 2020, among
others). Estimations from some papers are listed in Table. 1. We adopted the
following value of the stellar mass of the Milky Way: $M_{\star}$ =
5.2$\times$1010 $M_{\sun}$ or log($M_{\star}/M_{\sun}$) = 10.716. The mass of
the black hole at the centre of the Milky Way is equal to $M_{BH}$ =
4.15$\times$106 $M_{\sun}$ or log($M_{BH}/M_{\sun}$) = 6.618 (Gravity
Collaboration 2019).

###  2.3 Rotation velocity Vrot

Figure 1:  Rotation curves of the Milky Way from Burton & Gordon (1978),
Eilers et al. (2019), Ablimit et al. (2020) (two variants), and Sofue (2020).

The rotation curve of the Milky Way has been obtained by many studies (e.g.
Burton & Gordon 1978; Eilers et al. 2019; Ablimit et al. 2020; Sofue 2020).
Fig. 1 shows the rotation curves from one early investigation (Burton & Gordon
1978) and from three recent papers (Eilers et al. 2019; Ablimit et al. 2020;
Sofue 2020). Burton & Gordon (1978) have determined the Galactic rotation
curve in the galactocentric distance range up to 10 kpc using molecular gas
velocities combined with atomic gas velocities. Eilers et al. (2019) have
measured the circular velocity curve of the Milky Way with the highest
precision to date across galactocentric distances of 5 $\la R\la$ 25 kpc. They
used precise parallaxes, spectral data, and photometric information from the
Apache Point Observatory Galactic Evolution Experiment (APOGEE), the Wide-
field Infrared Survey Explorer (WISE), 2MASS data, and Gaia for 23,000
luminous red giant stars. Ablimit et al. (2020) analysed about 3,500 classical
Cepheids identified from different surveys. They used two kinematical methods
to measure the Galactic rotation curve in the galactocentric distance range
from $\sim$4 to $\sim$19 kpc. Sofue (2020) constructed an unified rotation
curve of the Milky Way from the Galactic centre to the galactocentric distance
of about 100 kpc by averaging the published rotation curves that are based on
the molecular gas velocities and on the velocities of approximately 16,000 red
clump giants in the outer disc combined with velocities of around 5,700 halo K
giants.

The obtained values of the maximum rotation velocity are between $\sim$230 km
s-1 and $\sim$245 km s-1. The value of the rotation velocity of the Milky Way
that we adopted is $V_{rot}$ = 235 km s-1, or log$V_{rot}$ = 2.371.

###  2.4 Oxygen abundance

Figure 2:  Radial oxygen abundance distribution in the Milky Way. Panel a:
Radial abundance gradients obtained by Arellano-Córdova et al. (2020) and
Arellano-Córdova et al. (2021). The black circles designate the H ii regions
from Arellano-Córdova et al. (2020). The dashed black curve is the quadratic
fit to those data. The blue squares mark the H ii regions from Arellano-
Córdova et al. (2021). The solid blue line shows the linear fit to all the
data. Panel b: Radial abundance distribution in the Milky Way obtained in this
work (see text). The black circles denote the H ii regions used in the
determination of the radial abundance gradient (solid line). The open circles
designate the H ii regions excluded from the determination of the abundance
gradient.

The oxygen abundances of 42 H ii regions of the Milky Way determined through
the direct $T_{e}$ method have been recently reported by Arellano-Córdova et
al. (2020, 2021). Panel (a) in Fig. 2 shows the radial distribution of the
oxygen abundances in the Milky Way obtained by the cited authors. The black
circles denote the H ii regions from Arellano-Córdova et al. (2020). The
dashed black curve is the quadratic fit to those data

$12+\log(\rm O/H)=8.64-0.009\times R-0.0014\times R^{2}.$ (3)

The blue squares in panel (a) of Fig. 2 designate the H ii regions from
Arellano-Córdova et al. (2021). The solid blue line is the linear fit to all
the data

$12+\log(\rm O/H)=8.84(\pm 0.09)-0.042(\pm 0.009)\times R.$ (4)

It is believed that the $T_{e}$ method, which is based on the measurements of
temperature sensitive line ratios, should give accurate oxygen abundances. In
practice, however, $T_{e}$-based oxygen abundances of the same H ii region
derived in different works can differ for two reasons: First, there may be
errors in the line intensity measurements. Second, the $T_{e}$-based oxygen
abundances depend on the relations used to convert the values of the line
fluxes to the electron temperatures and to the ion abundances. The determined
abundances also depend on the adopted relationship between the electron
temperature in low-ionisation zones and electron temperatures in the high-
ionisation part of the nebula. Differences between the oxygen abundances in a
given H ii region produced by different relations used in the $T_{e}$ method
can be appreciable. For example, Esteban et al. (2017) found an oxygen
abundance of 12 + log(O/H)${}_{T_{e}}$ = 8.14$\pm$0.05 in the Galactic H ii
region Sh 2-83, while Arellano-Córdova et al. (2020) found 12 +
log(O/H)${}_{T_{e}}$ = 8.28$\pm$0.08 in the same region using the same
spectroscopic measurements. Berg et al. (2015) detected auroral lines in 45 H
ii regions in the nearby galaxy NGC 628. They determined the $T_{e}$-based
abundances in those H ii regions and estimated the radial abundance gradient.
They found the central (intersect) oxygen abundance 12 + log(O/H)0 =
8.83$\pm$0.07 in NGC 628. In their recent paper (Berg et al. 2020), they
recalculated the ionic and total $T_{e}$-based abundances in the same H ii
regions and determined the central (intersect) oxygen abundance 12 + log(O/H)0
= 8.71$\pm$0.06 in NGC 628.

In this paper, the oxygen abundance of the Milky Way is compared to the oxygen
abundances in galaxies determined through the $R$ calibration from Pilyugin &
Grebel (2016). The $T_{e}$-based oxygen abundances in H ii regions used as the
calibrating data points in the construction of the $R$ calibration were
derived using the $T_{e}$-method equations reported in Pilyugin et al. (2012).
Therefore the $T_{e}$-based oxygen abundance in the Milky Way and the $R$
calibration-based abundances in other galaxies correspond to this unique
abundance scale (Pilyugin & Grebel 2016; Pilyugin et al. 2022) if only the
$T_{e}$-based oxygen abundances in H ii regions in the Milky Way are
determined using the $T_{e}$-method equations from Pilyugin et al. (2012). We
then redetermined the oxygen abundances in H ii regions of the Milky Way. The
line intensity measurements in the spectra of the H ii regions were taken from
the same sources as in Arellano-Córdova et al. (2020) and Arellano-Córdova et
al. (2021). If the measurements of two auroral lines ([O iii]$\lambda$4363 and
[N ii]$\lambda$5755) were available for the H ii region, then the two values
of the oxygen abundance were determined. The first value of the abundance is
based on the electron temperature in high-ionisation parts of the nebula
estimated using the auroral line [O iii]$\lambda$4363 and the electron
temperature in the low-ionisation parts of the nebula obtained from the
relationship between the electron temperature in low-ionisation zones and
electron temperatures in high-ionisation parts of the nebula. The second value
of the abundance is based on the electron temperature in low-ionisation zones
estimated from the measured auroral line [N ii]$\lambda$5755 and the electron
temperature in high-ionisation zones determined from the relationship between
electron temperatures.

The obtained oxygen abundances are presented in the lower panel of Fig. 2.
Because there is no visual evidence for a break in the O/H gradient, we
characterised the O/H gradient in the Milky Way with a single linear
regression. The points with deviations in excess of 0.3 dex from the
regression (open circles in the lower panel of Fig. 2) were rejected when
determining the final relation. The obtained relation,

$12+\log(\rm O/H)=8.76(\pm 0.04)-0.044(\pm 0.004)\times R,$ (5)

is shown by the solid line in the lower panel of Fig. 2. The scatter in O/H
around this relation is 0.092 dex for the 54 data points. The derived O/H –
$R$ relation (Eq. 5) resulted in the value of the oxygen abundance at the
optical radius ($R_{25}$ = 12 kpc) of 12 + log(O/H)${}_{R_{25}}$ = 8.24.

We emphasise that we do not pretend that the values of the $T_{e}$-based
abundances for the Milky Way recomputed here are more accurate than the
original abundance values derived by Arellano-Córdova et al. (2020) and
Arellano-Córdova et al. (2021). Our aim is that the abundances of all the
galaxies used here correspond to the same metallicity scale. This is mandatory
for the current study.

We also note that the derived value of the central (intersect) oxygen
abundance in the Milky Way may be slightly overestimated. The measured radial
distributions of the surface mass density of atomic H i and molecular H2
hydrogen in the Milky Way suggests that the gas can be entirely exhausted
(fully converted into stars) within a radius of approximately 1 kpc (McMillan
2017). If this is the case, then the gas-phase oxygen abundance reaches the
maximum (attainable) value at the radius of around 1 kpc and remains constant
within this radius.

Thus, we adopted the following values for the Milky Way characteristics. The
stellar mass is $M_{\star}$ = 5.2$\times$1010 M☉ or log$M_{star}$ = 10.716.
The rotation velocity is $V_{rot}$ = 235 km s-1 or log$V_{rot}$ = 2.371. The
optical radius is $R_{25}$ = 12 kpc or log$R_{25}$ = 1.079. The mass of the
black hole is MBH = 4.15$\times$106 M☉ or logMBH = 6.618. The central oxygen
abundance is 12 + log(O/H)0 = 8.76. The oxygen abundance at the optical radius
is 12 + log(O/H)${}_{R_{25}}$ = 8.24.

##  3 A sample of comparison galaxies

Table 2:  Characteristics of nearby galaxies.

galaxy | $R_{25}$ | $i$ | PA | $d$ | $V_{rot}$ | log$M_{\star}$ | $R_{25}$ | 12+log(O/H)0 | 12+log(O/H)${}_{R_{25}}$ | log$M_{BH}$
---|---|---|---|---|---|---|---|---|---|---
| arcmin | degree | degree | Mpc | km s-1 | $M_{\sun}$ | kpc |  |  | $M_{\sun}$
NGC 0224 | 95.27 | 77 | 38 | 0.82 | 253 | 11.00 | 22.72 | 8.715 | 8.337 | 8.15
NGC 0253 | 13.77 | 76 | 235 | 3.70 | 211 | 10.54 | 14.82 | 8.493 | 8.414 | 7.00
NGC 0300 | 10.94 | 42 | 106 | 1.94 | 85 | 9.32 | 6.17 | 8.444 | 8.019 | –
NGC 0598 | 35.40 | 54 | 201 | 0.94 | 125 | 9.69 | 9.68 | 8.489 | 8.037 | –
NGC 0628 | 5.24 | 6 | 25 | 9.91 | – | 10.36 | 15.09 | 8.667 | 8.257 | –
NGC 0753 | 1.26 | 50 | 128 | 72.40 | 210 | 10.91 | 26.45 | 8.586 | 8.522 | –
NGC 0925 | 5.24 | 66 | 287 | 9.29 | 115 | 9.75 | 14.15 | 8.440 | 8.080 | –
NGC 1058 | 1.51 | 15 | 145 | 10.60 | – | 9.40 | 4.66 | 8.649 | 8.384 | –
NGC 1068 | 3.54 | 35 | 73 | 13.97 | – | 10.91 | 14.38 | 8.696 | 8.594 | 6.75
NGC 1097 | 4.67 | 46 | 134 | 13.58 | 253 | 10.76 | 18.43 | 8.661 | 8.523 | 8.38
NGC 1232 | 3.71 | 30 | 270 | 21.50 | 220 | 10.67 | 23.18 | 8.741 | 8.254 | –
NGC 1313 | 6.12 | 48 | 0 | 4.32 | 112 | 9.46 | 7.69 | 8.163 | 8.016 | –
NGC 1365 | 5.61 | 46 | 222 | 19.60 | 300 | 10.78 | 31.98 | 8.619 | 8.411 | 6.60
NGC 1512 | 4.46 | 42 | 262 | 18.83 | 179 | 10.72 | 24.41 | 8.741 | 8.362 | 7.78
NGC 1598 | 0.72 | 55 | 123 | 55.80 | 110 | 10.21 | 11.73 | 8.665 | 8.390 | –
NGC 1672 | 3.30 | 43 | 134 | 19.40 | – | 10.73 | 18.64 | 8.639 | 8.510 | 7.08
NGC 2403 | 10.94 | 63 | 124 | 3.19 | 134 | 9.65 | 10.15 | 8.465 | 7.934 | –
NGC 2442 | 2.75 | 29 | 27 | 21.50 | – | 10.84 | 17.18 | 8.606 | 8.556 | 7.28
NGC 2805 | 3.16 | 36 | 123 | 28.70 | 106 | 9.98 | 26.34 | 8.477 | 8.106 | –
NGC 2835 | 3.30 | 41 | 1 | 12.22 | – | 10.00 | 11.74 | 8.498 | 8.193 | 6.72
NGC 2903 | 5.87 | 65 | 204 | 8.90 | 215 | 10.52 | 15.21 | 8.707 | 8.369 | 7.06
NGC 2997 | 4.46 | 33 | 108 | 11.30 | 185 | 10.49 | 14.66 | 8.725 | 8.362 | 5.84
NGC 3031 | 10.69 | 59 | 330 | 3.63 | 215 | 10.69 | 11.29 | 8.638 | 8.489 | 7.81
NGC 3184 | 3.71 | 16 | 179 | 11.62 | 210 | 10.41 | 12.53 | 8.721 | 8.395 | –
NGC 3351 | 3.71 | 41 | 192 | 9.96 | 196 | 10.37 | 10.74 | 8.696 | 8.619 | 6.52
NGC 3359 | 3.62 | 53 | 350 | 22.60 | 145 | 10.18 | 23.81 | 8.401 | 7.966 | –
NGC 3521 | 4.16 | 73 | 340 | 10.70 | 227 | 10.70 | 12.94 | 8.78a | 8.29a | 6.85
NGC 3621 | 4.88 | 65 | 345 | 7.06 | 140 | 10.06 | 10.03 | 8.704 | 8.124 | 6.00
NGC 4254 | 2.68 | 34 | 68 | 13.10 | 183 | 10.42 | 10.23 | 8.662 | 8.408 | –
NGC 4258 | 9.31 | 72 | 331 | 7.58 | 200 | 10.71 | 20.53 | 8.600 | 8.443 | 7.58
NGC 4303 | 3.23 | 27 | 318 | 16.99 | 150 | 10.51 | 15.95 | 8.658 | 8.261 | 6.58
NGC 4321 | 3.71 | 27 | 153 | 15.21 | 270 | 10.75 | 16.40 | 8.616 | 8.537 | 6.67
NGC 4395 | 6.59 | 46 | 324 | 4.51 | 80 | 9.42 | 8.65 | 8.063 | 8.078 | 5.64
NGC 4501 | 3.46 | 64 | 141 | 16.80 | 280 | 11.00 | 16.90 | 8.774 | 8.445 | 7.13
NGC 4625 | 1.09 | 31 | 303 | 11.75 | 60 | 9.08 | 3.74 | 8.624 | 8.489 | –
NGC 4651 | 1.99 | 53 | 77 | 19.00 | 215 | 10.42 | 11.00 | 8.652 | 8.275 | –
NGC 5055 | 5.87 | 59 | 102 | 8.87 | 192 | 10.73 | 15.16 | 8.693 | 8.414 | 8.92
NGC 5068 | 3.62 | 35 | 342 | 5.20 | – | 9.41 | 5.48 | 8.474 | 8.316 | –
NGC 5194 | 5.61 | 22 | 173 | 8.58 | 219 | 10.66 | 14.00 | 8.700 | 8.557 | –
NGC 5236 | 6.44 | 24 | 225 | 4.89 | 190 | 10.53 | 9.16 | 8.688 | 8.567 | –
NGC 5248 | 3.08 | 47 | 109 | 14.87 | 196 | 10.41 | 13.34 | 8.517 | 8.550 | 6.30
NGC 5457 | 14.42 | 18 | 37 | 6.85 | – | 10.58 | 28.73 | 8.688 | 7.895 | 6.41
NGC 6384 | 3.08 | 55 | 31 | 25.90 | 230 | 10.76 | 23.23 | 8.783 | 8.410 | –
NGC 6744 | 9.98 | 50 | 16 | 9.39 | 200 | 10.77 | 27.25 | 8.840 | 8.200 | 6.89
NGC 6946 | 5.74 | 33 | 243 | 7.34 | 186 | 10.45 | 12.26 | 8.648 | 8.390 | –
NGC 7331 | 5.24 | 76 | 168 | 14.70 | 244 | 11.00 | 22.39 | 8.590 | 8.545 | 8.02
NGC 7518 | 0.71 | 47 | 294 | 47.56 | – | 10.17 | 9.77 | 8.675 | 8.572 | –
NGC 7529 | 0.43 | 29 | 157 | 63.20 | – | 9.87 | 7.82 | 8.637 | 8.374 | –
NGC 7591 | 0.98 | 68 | 148 | 67.30 | 199 | 10.57 | 19.08 | 8.638 | 8.553 | –
NGC 7793 | 5.24 | 50 | 290 | 3.62 | 95 | 9.40 | 5.51 | 8.477 | 8.134 | –
IC 0342 | 10.69 | 31 | 37 | 3.45 | 170 | 10.37 | 10.73 | 8.713 | 8.287 | –
IC 5201 | 4.26 | 67 | 206 | 9.20 | 98 | 9.88 | 11.39 | 8.349 | 7.819 | –
IC 5309 | 0.67 | 63 | 20 | 55.70 | 152 | 10.21 | 10.93 | 8.614 | 8.565 | –

Notes. The notation ”a” indicates that the abundance distribution was traced
using P calibration-based abundances.

The characteristics of the Milky Way are compared with a sample of galaxies.
Our sample of the comparison involves two subsamples: a sample of nearby
galaxies and a sample of galaxies from the MaNGA survey. Those subsamples are
described in this section.

###  3.1 Nearby galaxies

The spectral measurements of H ii regions in nearby galaxies are compiled in
Pilyugin et al. (2004, 2014). This data compilation served as the base for the
construction of the comparison sample of nearby galaxies. To have the oxygen
abundances in a unique metallicity scale, only the galaxies where the radial
abundance gradient was determined through the $R$ calibration from Pilyugin &
Grebel (2016) were considered, with one exception (see below). Therefore, only
the spectra with measured emission lines [O ii]$\lambda\lambda$3727,3729 from
the compilation in Pilyugin et al. (2014) were taken into consideration. New
spectral measurements of H ii regions in the galaxies were added (if
available).

The galaxy NGC 3521 is the one exception, as the abundances in ten H ii
regions were estimated through the $P$ calibration and were added to the
abundances in three H ii regions determined through the $R$ calibration
(Section 4.4.1). The relative accuracy of the $P$ calibration-based abundances
is around 0.1 dex, that is, the oxygen abundances estimated through the $P$
calibration agree with the $T_{e}$-based abundances within $\sim$0.1 dex
(Pilyugin & Thuan 2005). However, the $P$ calibration encounters the following
difficulty: It is well known that the relation between the oxygen abundance
and the strong oxygen line intensities is double valued, with two distinct
parts, traditionally known as the upper and lower branches of the $R_{23}$ –
O/H diagram (e.g. Pagel et al. 1979; Pilyugin 2000, 2001). Two distinct
relations between the oxygen abundance and the strong oxygen line intensities
have been established: one for the upper branch (the high-metallicity
calibration) and one for the lower branch (the low-metallicity calibration).
There is a transition zone between the upper and lower branches (from 12 +
log(O/H) $\sim$ 8.3 to 12 + log(O/H) $\sim$ 8.0) where the $P$ calibration
cannot be applied (e.g. Pilyugin & Thuan 2005). Thus, one has to know a priori
on which of the two branches the H ii region lies. In the case of NGC 3521, we
overcame this difficulty in the following way. It is known that discs of
spiral galaxies show radial oxygen abundance gradients, in the sense that the
oxygen abundance is higher in the central part of the disc and decreases with
galactocentric distance. Abundances determined through the $R$ calibration in
three H ii regions in the inner part of NGC 3521 are 12 + log(O/H) $\sim$ 8.6.
We thus started from the H ii regions in the inner part of NGC 3521 and moved
outward until the radius where the oxygen abundance decreases to 12 + log
(O/H) $\sim$ 8.3 (the start of the transition zone between the upper and lower
branches). An unjustified use of the upper branch calibration in the
determination of the oxygen abundance in low-metallicity H ii regions would
result in wrong estimations. Therefore, we used the $R$ calibration
everywhere, which is workable over the whole metallicity scale, while we used
the $P$ calibration in one galaxy only.

The distances to galaxies, the angular optical radii, the angles of the
orientation of the galaxy in space, the stellar masses, the rotation curves,
and the masses of the central black holes were taken from the literature. The
rotation curves of a number of nearby galaxies (e.g. with small inclination
angles) were either not available or estimated with large uncertainties. The
estimations of the masses of the central black holes were available for a
small fraction of galaxies only.

The sample of nearby galaxies are reported in Table. 2; the list includes 53
galaxies. Table 2 lists the general characteristics of each galaxy. The first
column provides the name for each galaxy. The optical (isophotal) radius
$R_{25}$ in arcmin of each galaxy is reported in the second column. The
inclination and the position angle of the major axis are listed in columns
three and four. The distance is reported in column five. The rotation velocity
is given in column six. The stellar mass is reported in column seven. The
optical radius in kiloparsecs, estimated from the data in columns two and
five, is given in column eight. The oxygen abundances at the centre
12+log(O/H)0 and at the optical radius 12+log(O/H)${}_{R_{25}}$ are listed in
columns nine and ten. The mass of the black hole at the centre of the galaxy
is reported in column 11. Notes on the individual galaxies and the references
to the sources of the data are given in Appendix A. The radial abundance
distributions and rotation curves of several candidate Milky Way twins are
presented in Section 4.4.

###  3.2 MaNGA galaxies

Figure 3:  Properties of the MaNGA galaxy M-8934-12701. Panel a1: Surface
brightness distribution across the image of the galaxy in sky coordinates
(pixels). The value of the surface brightness is colour-coded. The circle
shows the kinematic centre of the galaxy, the dark solid line indicates the
position of the major kinematic axis of the galaxy, and the solid ellipse is
the optical radius for kinematic angles. The red cross is the photometric
centre, the red dashed line indicates the position of the major photometric
axis, and the red dashed ellipse is the optical radius for photometric angles.
Panel a2: Photometric profile (points) and its fit (line) within the optical
radius. Panel b1: Line-of-sight velocity field in sky coordinates. Panel b2:
Rotation velocity curve (points) and its fit (line) within the optical radius.
Panel c1: Oxygen abundance map. Panel c2: Radial abundance distribution. The
grey points denote the abundances for the individual spaxels, the solid line
is the simple linear fit to those data, while the dashed line is the broken
linear fit to the same data. Panel d1: Map of the gas velocity dispersion
$\sigma$. Panel d2: Radial distribution of the gas velocity dispersion
$\sigma$ in the disc. The coloured circles denote the gas velocity dispersion
for the individual spaxels of H ii region-like (blue symbols), intermediate
(red symbols), and AGN-like (black symbols) spectra classification. Panel e1:
Map of the measured flux in the H$\alpha$ emission line per spaxel in units of
10-17 erg/s/cm2/spaxel. Panel e2: Radial distribution of the measured
H$\alpha$ flux. The coloured circles denote the flux for the individual
spaxels of H -region-like (blue symbols), intermediate (red symbols), and AGN-
like (black symbols) spectra classification. Panel f1: Map of the BPT spectra
classification. The BPT types of radiation for the individual spaxels are
colour-coded. Panel f2: BPT diagram for the individual spaxels colour-coded by
H ii region-like (blue symbols), intermediate (red symbols), and AGN-like
(black symbols) spectra. Solid and short-dashed curves mark the demarcation
line between AGNs and H ii regions defined by Kauffmann et al. (2003) and
Kewley et al. (2001), respectively. The long-dashed line is the dividing line
between Seyfert galaxies and LINERs defined by Cid Fernandes et al. (2010).

Figure 4:  Properties of the MaNGA galaxy M-8341-09101. The notations are the
same as in Fig. 3.

Using the publicly available spectroscopy obtained by the MaNGA survey (Bundy
et al. (2015), Albareti et al (2017), Data Release 15), the rotation curves,
surface brightness profiles, radial distributions of the oxygen abundance, and
the gas velocity dispersion were determined for a large sample of late-type
galaxies (Pilyugin et al. 2018, 2019, 2020, 2021). As an example, Fig. 3 and
Fig. 4 show the obtained maps and radial distributions of different
characteristics of the MaNGA galaxies M-8934-12701 and M-8341-09101. The
characteristics of the MaNGA galaxies were determined using our own emission
line measurements. The emission line parameters for those galaxies are also
available from the MaNGA Data Analysis Pipeline (DAP) measurements. The
geometrical parameters of the galaxies (coordinates of the rotating centre,
the position angle of the major kinematic angle, and the inclination angle)
were obtained for a number of galaxies using both our measurements and the DAP
measurements (we used the datacubes from the publicly available Data Release
16) (Pilyugin et al. 2021). We also carried out a quantitative comparison
between spaxel properties (oxygen abundance and gas velocity dispersion) based
on our measurements and the DAP measurements. The geometrical parameters and
spaxel properties of the galaxies based on our measurements agree with those
based on the DAP measurements (Pilyugin et al. 2021). Thus, our data on the
MaNGA galaxies are robust.

The distances to the galaxies were taken from the NASA/IPAC Extragalactic
Database (ned)111The NASA/IPAC Extragalactic Database is operated by the Jet
Propulsion Laboratory, California Institute of Technology, under contract with
the National Aeronautics and Space Administration.
http://ned.ipac.caltech.edu/. The ned distances use flow corrections for
Virgo, the Great Attractor, and the Shapley Supercluster infall (adopting a
cosmological model with $H_{0}=73$ km/s/Mpc, $\Omega_{m}=0.27$, and
$\Omega_{\Lambda}=0.73$). We note that we considered a rather nearby sample of
galaxies, and therefore the choice of parameters for the cosmological model is
not very crucial. We chose the spectroscopic stellar masses $M_{\star}$ of the
SDSS and BOSS (i.e. the Baryon Oscillation Spectroscopic Survey in SDSS-III;
see Dawson et al. 2013). The spectroscopic masses were taken from the table
stellarMassPCAWiscBC03 and were determined using the Wisconsin method (Chen et
al. 2012) with the stellar population synthesis models from Bruzual & Charlot
(2003).

The oxygen abundances were determined through the $R$ calibration (Pilyugin &
Grebel 2016) using the spaxel spectra. The measured line fluxes
$F_{\lambda}^{obs}$ were corrected for the interstellar reddening
$F_{\lambda}$ = $F_{\lambda}^{obs}\times 10^{C_{{\rm H}{\beta}}f_{\lambda}}$,
where $C_{{\rm H}{\beta}}$ is the logarithmic extinction at H$\beta$. The
value of $C_{{\rm H}{\beta}}$ was estimated through a comparison between the
measured and the theoretical $F_{{\rm}H\alpha}/F_{{\rm H}\beta}$ ratios,

$C_{{\rm H}\beta}=(\log(F_{{\rm}H\alpha}/F_{{\rm H}\beta})^{teor}-\log(F_{{\rm
H}\alpha}/F_{{\rm H}\beta})^{obs})/(f_{{\rm H}\alpha}-f_{{\rm H}\beta}),$ (6)

using the reddening law (function $f_{\lambda}$) of Cardelli et al. (1989)
with $R_{V}$ = 3.1. The theoretical value for the $(F_{{\rm}H\alpha}/F_{{\rm
H}\beta})^{teor}$ line ratio (= 2.87) was taken from Osterbrock & Ferland
(2006), assuming the case $B$ recombination. If the measured value of the
ratio $F_{{\rm}H\alpha}/F_{{\rm H}\beta}$ was lower than the theoretical one,
then the reddening was assumed to be zero.

We classified the excitation of the spaxel spectrum using its position on the
standard diagnostic Baldwin–Phillips–Terlevich (BPT) diagram [N
ii]$\lambda$6584/H$\alpha$ versus the [O iii]$\lambda$5007/H$\beta$, as
suggested by Baldwin, Phillips, Terlevich (1981). As in our previous studies
(Zinchenko et al. 2019; Pilyugin et al. 2020, 2021), the spectra located to
the left (below) the demarcation line of Kauffmann et al. (2003) are referred
to as the SF-like or H ii region-like spectra; those located to the right
(above) the demarcation line of Kewley et al. (2001) are referred to as the
AGN-like spectra; and the spectra located between both demarcation lines are
classified as intermediate (INT) spectra. The oxygen abundances were
determined only in spaxels with H ii region-like spectra.

The final sample of MaNGA galaxies was selected by visual inspection,
considering the obtained surface brightness profile, rotation curve, and
abundance distribution for each galaxy. The spaxels with measured emission
lines and surface brightness needed to be well distributed across the galactic
disc, that is, covering more than $\sim$2/3$R_{25}$. This condition allowed us
to estimate values of the rotation velocity, the surface brightness, and the
oxygen abundance both at the centre and at the optical radius since the
extrapolation is relatively small (if any). Unfortunately, this condition
resulted in the loss of galaxies where ongoing star formation does not occur
over a significant fraction of galaxy. We note that only the spaxel spectra
where the used lines are measured with a $S/N$ $>$ 3 were considered.
Therefore, the spaxels with reliable measured spectra can cover less than
$\sim$2/3$R_{25}$, even if the total spaxel spectra beyond 2/3$R_{25}$ are
available. The deprojected fractional galactocentric distances (normalised to
the optical radius $R_{25}$) of each spaxel were estimated using the kinematic
angles for galaxies with inclination angles of $i$ $\ga$ 30 degrees and
photometric angles for face-on galaxies with inclination angles of $i$ $\la$
30 degrees.

For the current study, galaxies from the MaNGA sample were selected when the
radial oxygen abundance distribution was satisfactory approximated by a single
linear relation. The approximations of the radial abundance distribution in
each galaxy for both the simple linear fit and the broken linear fit were
estimated (panels (c2) in Fig. 3 and Fig. 4). We used the differences between
the intersect values of the oxygen abundances given by the single linear
relation and the abundances given by the broken linear relation at the galaxy
centre $\Delta$(O/H)0 and at the optical radius $\Delta$(O/H)${}_{R_{25}}$ as
the selection criteria. The absolute values of $\Delta$(O/H)0 and
$\Delta$(O/H)${}_{R_{25}}$ are usually within 0.05 dex for the galaxies
(Zinchenko et al. 2016; Pilyugin et al. 2017). The galaxies where the sum of
the absolute values of $\Delta$(O/H)0 and $\Delta$(O/H)${}_{R_{25}}$ exceed
0.1 dex were rejected.

Thus, our final sample of comparison galaxies includes 504 galaxies, of which
451 are MaNGA galaxies and 53 are nearby galaxies. Unfortunately, the rotation
curves are available only for 423 galaxies (e.g. rotation curves are not
derived for low-inclination MaNGA galaxies), and the stellar mass estimations
are available only for 495 out of 504 galaxies.

##  4 Milky Way among galaxies

###  4.1 Comparison of the Milky Way properties with our reference sample

Figure 5:  Comparison of the characteristics of the Milky Way and galaxies
from our sample. Panel a: Stellar masses $M_{\star}$ as a function of rotation
velocity $V_{rot}$ (Tully-Fisher diagram). The grey points in each panel
denote individual MaNGA galaxies, while the goldenrod points correspond to
nearby galaxies in our sample. The solid line is the linear fit to all the
data, while the dotted lines are $\pm\sigma$ deviations. The red circle marks
the position of the Milky Way. Panel b: Optical radius $R_{25}$ as a function
of rotation velocity $V_{rot}$. Panel c: Optical radius $R_{25}$ as a function
of stellar mass $M_{\star}$. Panel d: Black hole mass $M_{BH}$ as a function
of stellar mass $M_{\star}$. Panel e: Central oxygen abundance (O/H)0 as a
function of stellar mass $M_{\star}$. Panel f: Oxygen abundance at the optical
radius (O/H)${}_{R_{25}}$ as a function of stellar mass $M_{\star}$.

Figure 5 shows the comparison between the characteristics of the Milky Way and
the galaxies in our sample. In panel (a), we plot the stellar mass of the
galaxy $M_{\star}$ as a function of its rotation velocity $V_{rot}$ (Tully-
Fisher diagram). Since the gas mass in spiral galaxies with stellar masses
similar to the Milky Way is lower than the stellar mass by around an order of
magnitude (Parkash et al. 2018), the stellar mass can also be considered in
the first approximation as the representative of the baryonic mass of the
galaxy. The grey points in the figure denote the data for individual MaNGA
galaxies, while the goldenrod points correspond to nearby galaxies from our
sample. The linear fit to all the data is given by the expression

$\log M_{\star}=2.003(\pm 0.152)+3.742(\pm 0.068)\times\log V_{rot}$ (7)

and is shown with the solid line in panel (a) of Fig. 5. The mean value of the
scatter in the $M_{\star}$ around the relation is $\sigma$ = 0.220 dex for the
414 points. The red circle marks the position of the Milky Way. The deviation
of the Milky Way stellar mass from the relation is –0.170 dex, or
–0.77$\sigma$.

Panel (b) of Fig. 5 shows the optical radius of the galaxy $R_{25}$ in
kiloparsecs as a function of its rotation velocity $V_{rot}$. The linear fit
to all the data,

$\log R_{25}=-0.973(\pm 0.075)+0.922(\pm 0.034)\times\log V_{rot},$ (8)

is shown with the solid line in panel (b) of Fig. 5. The mean value of the
scatter in the $R_{25}$ values around the relation is $\sigma$ = 0.112 dex for
the 423 points. The red circle marks the position of the Milky Way. The
deviation of the Milky Way optical radius from the relation is $-0.134$ dex,
or $-1.21\sigma$.

In panel (c) of Fig. 5, we plot the optical radius of the galaxy $R_{25}$ in
kiloparsecs versus the stellar mass $M_{\star}$. The obtained $R_{25}$ –
$M_{\star}$ relation is given by

$\log R_{25}=-1.561(\pm 0.074)+0.256(\pm 0.007)\times\log M_{\star}$ (9)

and is shown with the solid line in panel (c) of Fig. 5. The mean value of the
scatter in the $R_{25}$ values around the relation is $\sigma$ = 0.100 dex for
the 495 points. The red circle marks the position of the Milky Way. The
deviation of the Milky Way optical radius from the relation is $-0.101$ dex,
or $-1.00\sigma$.

Panel (d) of Fig. 5 shows the black hole mass $M_{BH}$ as a function of
stellar mass $M_{\star}$. Unfortunately, the estimations for the central black
hole mass are available only for a small fraction of the nearby galaxies.

Panel (e) of Fig. 5 shows the central oxygen abundance (O/H)0 in the galaxy as
a function of stellar mass $M_{\star}$. The points designate the data for
individual galaxies (grey – MaNGA and goldenrod – nearby galaxies) from our
sample. The red circle marks the position of the Milky Way. Panel (f) of Fig.
5 shows the oxygen abundance at the optical radius (O/H)${}_{R_{25}}$ as a
function of stellar mass $M_{\star}$.

Figure 6:  Histograms of the radial oxygen abundance gradients for our sample
of galaxies. Panel a: Normalised histogram of the radial oxygen abundance
gradients for our sample of galaxies (MaNGA + nearby). The solid line denotes
the histogram of the obtained gradients, while the dashed line corresponds to
the Gaussian fit to those data. The arrow marks the value of the radial
abundance gradient of the Milky Way. Panel b: Normalised histograms of the
radial oxygen abundance gradients for subsamples of MaNGA (dotted line) and
nearby (solid line) galaxies. The histograms were normalised to the same value
as the histogram in panel (a).

Inspection of Fig. 5 showed that the most prominent deviation of the position
of the Milky Way from the general trends of the galaxies in our sample takes
place in the (O/H)0 – $M_{\star}$ and (O/H)${}_{R_{25}}$ – $M_{\star}$
diagrams. The difference between oxygen abundances at the optical radius and
at the centre log(O/H)${}_{R_{25}}$ – log(O/H)0 is, by definition, the radial
abundance gradient in the galaxy expressed in units of dex/$R_{25}$. Panel (a)
in Fig. 6 shows the normalised histogram of the radial oxygen abundance
gradients for our sample of galaxies. The solid line denotes the histogram of
the measured gradients in bins of 0.025 dex/$R_{25}$, and the dashed line is
the Gaussian fit to those data. The arrow marks the value of the radial
abundance gradient of the Milky Way. The mean value of the gradients in our
sample of galaxies is –0.20 dex/$R_{25}$, and the scatter is $-0.10$
dex/$R_{25}$. Sánchez et al. (2014) examined the radial abundance gradients in
the sample of CALIFA galaxies and found that all galaxies without clear
evidence of an interaction present a common gradient in the oxygen abundance
with a characteristic slope of $-0.16$ dex/$R_{25}$ and a dispersion of 0.12
dex/$R_{25}$. Thus, the distribution of the gradients for our sample of
galaxies is similar to the distribution from Sánchez et al. (2014). Panel (a)
in Fig. 6 shows that the gradient in the Milky Way is in the far wing (or in
the tail) of the distribution of gradients. The deviation of the gradient in
the Milky Way ($-0.5$ dex/$R_{25}$) from the mean value of the gradients for
our sample of galaxies ($-0.2$ dex/$R_{25}$) is $-0.3$ dex/$R_{25}$, which is
–3$\sigma$. The ratio of the oxygen abundance at the centre to the oxygen
abundance at the optical radius is (O/H)0/(O/H)${}_{R_{25}}$ $\sim$3 for the
Milky Way, which is twice as large as the mean value of ratios for our sample
of galaxies. It should be noted that the (O/H)0/(O/H)${}_{R_{25}}$ ratio in
the well studied nearby galaxy NGC 5457 (M 101) is twice as high as that in
the Milky Way. Panel (b) in Fig. 6 shows the normalised histograms of the
radial oxygen abundance gradients for subsamples of MaNGA (dotted line) and
nearby (solid line) galaxies. The histograms have been normalised to the same
value as the histogram in panel (a).

###  4.2 Searching for Milky Way twin candidates using strict criteria

The optical radius, stellar mass, and rotation curve specify the structure of
a galaxy. These characteristics of a galaxy are related to each other. In
general, any two of these characteristics can be used to search for galaxies
with a similar structure. Rotation velocities are not available for a fraction
of the galaxies in our sample. Therefore, a stellar mass versus optical radius
diagram was used as the basic diagram to compare the structure of the Milky
Way and other spiral galaxies. Galaxies located close to the Milky Way on the
$M_{\star}$ – $R_{25}$ diagram are referred to as structural Milky Way
analogues (sMWAs).

The oxygen abundance at a given radius of a galaxy is defined by the
evolutionary stage (the astration level) of that region and by the matter
exchange with the surroundings. One can expect that if the oxygen abundances
at the centre and at the optical radius (evolutionary stages at the centre and
at the optical radius) are similar in two galaxies, then those galaxies have
evolved in a more or less similar way. Then the central abundance - abundance
at the optical radius diagram can be used to compare the evolution of the
Milky Way and other spiral galaxies. Galaxies located close to the Milky Way
on the (O/H)0 – (O/H)${}_{R_{25}}$ diagram are referred to as evolutionary
Milky Way analogues (eMWAs). If a galaxy is simultaneously an sMWA and an
eMWA, then such a galaxy can be considered a Milky Way twin candidate.

We defined the distance between the positions of a galaxy and the Milky Way in
the $R_{25}$ –$M_{\star}$ diagram

$D_{MR}=[(\log R_{25}-\log R_{25,MW})^{2}+(\log M_{\star}-\log
M_{\star,MW})^{2}]^{\frac{1}{2}}.$ (10)

The value of DMR is some kind of measure (index) of the structural difference
between a galaxy and the Milky Way. We also defined the distance between the
position of each galaxy and the Milky Way in the (O/H)${}_{R_{25}}$ – (O/H)0
diagram

$D_{\rm
OH}=[(Z_{0}-Z_{0,MW})^{2}+(Z_{R_{25}}-Z_{R_{25},MW})^{2}]^{\frac{1}{2}},$ (11)

where the notation Z = 12 + log(O/H) is used for the sake of brevity. The
value of the DOH is some kind of measure (index) of the evolutionary
difference between a galaxy and the Milky Way.

Figure 7:  Milky Way twin candidates according to the strict criteria. Panel
a: Index of the structural differences between galaxies and the Milky Way DMR
(Eq. 10) as a function of the index of the evolutionary difference DOH (Eq.
11). The points are individual MaNGA (grey) and nearby (goldenrod) galaxies.
The dashed lines indicate DMR = 0.1 and DOH = 0.1. Panel b: Central oxygen
abundance versus abundance at the optical radius. The galaxies with DOH $\leq$
0.1 (eMWAs) are marked with red crosses. The galaxies with DMR $<$ 0.1 (sMWAs)
are indicated with blue plus signs. The green circle denotes the Milky Way.
Panel c: Optical radius versus stellar mass diagram. The notations are the
same as in panel (b). Panel d: Optical radius versus rotation velocity
diagram. The notations are the same as in panel (b).

We plot the index of the structural difference between the galaxy and the
Milky Way DMR as a function of the index of the evolutionary difference DOH
for our sample of galaxies in panel (a) of Fig. 7. In this section, we select
the Milky Way-like galaxies using a strict criteria for similarity. We adopted
galaxies with DOH $\leq$ 0.1 as eMWAs and galaxies with DMR $\leq$ 0.1 as
sMWAs. Panel (b) of Fig. 7 shows the (O/H)0 – (O/H)${}_{R_{25}}$ diagram.
Panel (c) shows the $R_{25}$ – $M_{\star}$ diagram, and panel (d) shows the
$R_{25}$ – $V_{rot}$ diagram.

Inspection of Fig. 7 shows that the eMWAs are rather rare, while the sMWAs are
more numerous. This implies that the Milky Way shows a rather atypical
(chemical) evolution. A prominent feature of the Milky Way is its high
metallicity (oxygen abundance) at the centre of the disc, which is close to
the maximum attainable oxygen abundances in galaxies, while the oxygen
abundance at the optical radius is significantly lower in comparison to other
galaxies of similar central oxygen abundances. We found that seven galaxies
from our sample (six nearby galaxies, NGC 628, NGC 1232, NGC 3521, NGC 4303,
NGC 6744, and IC 342, plus the MaNGA galaxy M-8934-12701) satisfy the
condition DOH $\leq$ 0.1 and are hence considered eMWAs. The characteristics
of nearby galaxies are listed in Table. 2. The MaNGA galaxy M-8934-12701 is at
a distance of 240.8 Mpc. The characteristics of M-8934-12701 are the
following: the stellar mass is log$M_{\star}$ = 10.75; the rotation velocity
is $V_{rot}$ = 235 km s-1; the optical radius is $R_{25}$ = 18.85 kpc; the
central oxygen abundance is 12 + log(O/H)0 = 8.74; and the oxygen abundance at
the optical radius is 12 + log(O/H)${}_{R_{25}}$ = 8.28. Fig. 3 shows the maps
and radial distributions of the properties in the MaNGA galaxy M-8934-12701.

At the same time, we found that 35 galaxies from our sample satisfy the
condition DRM $\leq$ 0.1. Close examination of Fig. 7 showed that six out of
seven eMWAs are not sMWAs. The values of the stellar mass and rotation
velocity in three eMWAs are relatively close to that in the Milky Way, but
their optical radii are significantly larger in comparison to the optical
radius of the Milky Way ($R_{25}$ = 23.18 kpc in NGC 1232, $R_{25}$ = 27.25
kpc in MGC 6744, and $R_{25}$ = 18.85 in the MaNGA galaxy M-8934-12701 versus
$R_{25}$ = 12.0 in the Milky Way). Three other eMWAs have noticeably lower
values of stellar mass (log$M_{\star}$ =10.36 in NGC 628, log$M_{\star}$
=10.51 in NGC 4303, and log$M_{\star}$ =10.37 in IC 342 versus log$M_{\star}$
=10.72 in the Milky Way) and rotation velocity ($V_{rot}$ = 150 km s-1 in NGC
4303 and $V_{rot}$ = 170 km s-1 in IC 342 versus $V_{rot}$ = 235 km s-1 in the
Milky Way). We note that in previous studies, Milky Way-like galaxies were
selected using the structural and morphological characteristics of galaxies,
that is, sMWAs were selected. We found that the abundances at the centre and
at the optical radius (evolutionary characteristics) provide a more strict
criterion for selecting real Milky Way twins.

We found that only the galaxy NGC 3521 is simultaneously both an sMWA and an
eMWA. All the characteristics considered (stellar mass, optical radius,
rotation velocity, central oxygen abundance, and abundance at the optical
radius) of NGC 3521 are close to that of the Milky Way. The masses of black
holes in those galaxies are also close to each other. Thus, the galaxy NGC
3521 can be a real Milky Way twin candidate. A detailed comparison of the
galaxy NGC 3521 with the Milky Way is given in Section 4.4.

###  4.3 Searching for Milky Way twin candidates using weak criteria

Figure 8:  Milky Way twin candidates according to the weak criteria. Panel a:
Central oxygen abundance versus abundance at the optical radius diagram. The
grey points are individual MaNGA galaxies, and the goldenrod pints denote the
nearby galaxies. The galaxies with $\Delta$(O/H)${}_{0}\leq$ 0.1 dex and
$\Delta$(O/H)${}_{R_{25}}\leq$ 0.1 dex (eMWAs) are marked with the red
crosses. The eMWAs with $\Delta R_{25}\leq$ 0.114 dex, $\Delta M_{\star}\leq$
0.3 dex, and $\Delta V_{rot}\leq$ 0.079 dex (Milky Way twin candidates) are
marked with the blue plus signs. The green circle denotes the Milky Way. Panel
b: Optical radius versus stellar mass diagram. The notations are the same as
in panel (a). Panel c: Optical radius versus rotation velocity diagram. The
notations are the same as in panel (a).

Boardman et al. (2020a) noted that the selection of Milky Way analogues using
a larger number of simultaneous selection parameters, as well as more
stringent constraints on a given parameter, yields a sample of Milky Way-like
galaxies with properties that are closer to the true properties of the Milky
Way. At the same time, the use of a larger number of the selection criteria
(or an overly strict definition of the “analogue”) yields few to no Milky Way-
like galaxies (Boardman et al. 2020b). The fact that we found only one Milky
Way candidate twin in the previous section can be the result of an overly
strict definition of a Milky Way twin. In this section we search for Milky Way
twins using a more weak (less strict) criteria.

The difference between the determined values of the parameter for two galaxies
does not necessarily coincide with the real difference of the parameter for
those galaxies, but it can also involve the uncertainty in the parameter
determinations. Therefore, in the search for Milky Way twins, the uncertainty
in the parameter determinations should be taken into account in the choice of
the allowed difference. Unfortunately, the characteristics of many nearby
galaxies can involve significant uncertainties, as noted in many papers. For
instance, McQuinn et al. (2017) noted “surprisingly, many of the best-studied
spiral galaxies in the Local Volume have distance uncertainties that are much
larger than can be achieved with modern observation techniques.” The
uncertainty in the distance to the galaxies results in uncertainties in the
optical radius in kiloparsecs, as well as in the luminosity and consequently
in the stellar mass. The uncertainty in the luminosity to stellar mass
conversion also makes a significant (maybe dominant) contribution to the
uncertainty in the estimation of the stellar mass of the galaxy.

We noted previously that for this current study, we selected our sample of
MaNGA galaxies where radial oxygen abundance distribution could be
approximated satisfactorily by a single linear relation. Belfiore et al.
(2017) found that the galaxy inclination and the point spread function can
generate a flattening in the radial abundance gradient in the MaNGA galaxies,
since flux from different galactocentric radii is summed up when the galaxy is
projected in the plane of the sky. The metallicity depletion at the galaxy
centre depends on the PSF and galaxy inclination, and it can be as large as
$\sim$0.04 dex.

It is difficult to specify the rotation of a galaxy with a single parameter
because there is a wide variety of shapes in the rotation curves of galaxies.
The rotation velocity of the flat part of the rotation curve Vflat is often
used as the characteristic value for the galaxy rotation. However, there is
not a commonly accepted way to determine Vflat. Even for galaxies with well
measured rotation curves, the estimations of Vflat in different publications
can differ by around 20 km$s^{-1}$. For example, there are several
measurements for the rotation curve of NGC 5055 (Thornley & Mundy 1997; Blais-
Ouellettte et al. 2004; de Blok et al. 2008). The estimations of the Vflat for
NGC 5055 are Vflat = 192 km s-1 (Leroy et al. 2008), Vflat = 197 km s-1 (Frank
et al. 2016), and Vflat = 179 km s-1 (Lelli et al. 2016).

In this section, we search for Milky Way twins using the following (weak)
selection criteria: 1) The absolute value of the difference between the oxygen
abundance at the centre of the galaxy and that for the Milky Way should be
lower than 0.15 dex, $\Delta$(O/H)0 (= abs(log(O/H)0 – log(O/H)0,MW)) $\leq$
0.15. 2) The absolute value of the difference between the oxygen abundance at
the optical radius of the galaxy and that for the Milky Way should be lower
than 0.15 dex, $\Delta$(O/H)${}_{R_{25}}$ (= abs(log(O/H)${}_{R_{25}}$ –
log(O/H)${}_{R_{25},MW}$)) $\leq$ 0.15. 3) The optical radii of the galaxy and
the Milky Way should agree within $\sim$30%, $\Delta R_{25}$ (=
abs(log$R_{25}$ – log$R_{25,MW}$)) $\leq$ 0.114. 4) The difference between the
stellar mass of the galaxy and that of the Milky Way should be less than a
factor of approximately two, $\Delta M_{\star}$ (= abs(log$M_{\star}$ –
log$M_{\star,MW}$)) $\leq$ 0.3. 5) The rotation velocities of the galaxy and
that of the Milky Way agree within $\sim$20%, $\Delta V_{rot}$ (=
abs(log$V_{rot}$ – log$V_{rot,MW}$)) $\leq$ 0.079. The allowed differences of
the parameters (criteria) that we adopted in the search for Milky Way twins
are somewhat arbitrary.

All five parameters are available for 414 galaxies from our sample (the
rotation curve is not determined for low-inclination galaxies). We found that
46 galaxies satisfy criteria 1 and 2. Those galaxies (eMWAs) are shown in Fig.
8 with red crosses. At the same time, only four out of 46 eMWAs (NGC 3521, NGC
4651, NGC 2903, and MaNGA galaxy M-8341-09101) satisfy criteria 3 through 5.
Those galaxies (Milky Way twin candidates) are shown in Fig. 8 with blue plus
signs.

A comparison between Fig. 7 and Fig. 8 showed that the general behaviour of a
sample of eMWAs selected with the weak criteria is similar to that of the
sample of eMWAs selected with the strict criteria. Only a small fraction of
the weak eMWAs (4 out of 46) are sMWAs. For the majority of eMWAs, either the
optical radii is significantly larger in comparison to the optical radius of
the Milky Way or the stellar mass (and/or rotation velocity) is significantly
lower than that of the Milky Way.

###  4.4 Abundance distributions and rotation curves of the Milky Way twin
candidates

In this section, we compare the radial abundance distributions and rotation
curves of the Milky Way twin candidates (NGC 3521, NGC 4651, NGC 2903, and
MaNGA galaxy M-8341-09101) with that of the Milky Way. Zhou et al. (2023)
found that the MaNGA galaxy M-8983-03703 is a Milky Way-like galaxy in the
context of their star formation and chemical evolution histories. Hence, this
galaxy is also considered here.

####  4.4.1 NGC 3521

Figure 9: Comparison between the properties of NGC 3521 and the Milky Way.
Panel a: Comparison between the radial oxygen abundance distributions. The
blue circles denote the $T_{e}$-based abundances in individual H ii regions in
the Milky Way (comes from panel (b) of Fig. 2), and the solid line is the best
fit to those data. The dark triangles mark the $R$ calibration-based
abundances in H ii regions in NGC 3521. The crimson plus signs are the $P$
calibration-based abundances in H ii regions in NGC 3521, and the dotted line
is the linear fit to those data points. Panel b: Comparison between rotation
curves. The points denote the rotation curve of the Milky Way from Eilers et
al. (2019). The line shows the rotation curve of the NGC 3521 from de Blok et
al. (2008).

The galaxy NGC 3521 is an SABb galaxy (morphological type code $T$ =
4.0$\pm$0.2). It is included in The H i Nearby Galaxy Survey (THINGS) list
(Walter et al. 2008). We adopted the following parameters of NGC 3521 used or
obtained by the THINGS survey: distance $d$ = 10.7 Mpc; optical radius of 4.16
arcmin; physical optical radius $R_{25}$ = 12.94 kpc (Walter et al. 2008);
inclination angle $i$ = 73$\degr$; position angle of the major axis PA =
340$\degr$ (de Blok et al. 2008); stellar mass $M_{\star}$ = 5.01 $\times$
1010 M☉, or log($M_{\star}/M_{\sun}$) = 10.70 (Leroy et al. 2008); and
rotation velocity $V_{rot}$ = 227 km s-1 (de Blok et al. 2008; Leroy et al.
2008). The black hole mass in NGC 3521 is log($M_{BH}/M_{\sun}$) =
6.85$\pm$0.58 (Davis et al. 2014).

The measurements of the emission lines, which are necessary for the
determination of the abundance through the $R$ calibration, are available for
only three H ii regions in the NGC 3521 (Bresolin et al. 1999). However, NGC
3521 was taken into consideration for two reasons: First, McGaugh (2016) noted
that NGC 3521 is the closest structural analogue to the Milky Way, having a
similar luminosity, scale length, and rotation curve. Second, the measurements
of the emission lines $R_{2}$ and $R_{3}$, which allow for estimation of the
abundance through the $P$ calibration, are available for ten H ii regions in
NGC 3521 (Zaritsky et al. 1994). The oxygen abundances determined through the
$R$ calibration in three H ii regions from Bresolin et al. (1999) are denoted
with the triangles in panel (a) of Fig. 9. In order to estimate the oxygen
abundances using the oxygen lines $R_{2}$ and $R_{3}$ measured by Zaritsky et
al. (1994) in ten H ii regions in NGC 3521, we obtained the calibration
relation (O/H)P = $f$($R_{2},R_{3}$) for the upper branch (Pilyugin 2001;
Pilyugin & Thuan 2005) using the calibration data points from Pilyugin &
Grebel (2016) and supplemented by the recent measurements of H ii regions in
NGC 5457 from Croxall et al. (2016) and Esteban et al. (2020)

$\displaystyle\begin{array}[]{lll}12+\log(O/H)_{P}&=&8.6059+0.4143\,P\\\
&+&(0.2662-1.2014\,P)\,X\\\ &-&(0.6786-0.8121\,P)\,X^{2}\\\ \end{array},$ (15)

where $P$ = $R_{3}/R_{23}$ is the excitation parameter, $R_{23}$ = $R_{3}$ \+
$R_{3}$, and $X$ = log(1 + $R_{23}$). The oxygen abundances determined through
the $P$ calibration in H ii regions from Zaritsky et al. (1994) are shown with
plus signs in panel (a) of Fig. 9. The radial distribution of those oxygen
abundances was approximated by the relation

$12+\log(\rm O/H)=8.786(\pm 0.041)-0.494(\pm 0.069)\times R_{g}$ (16)

with a scatter of 0.042 dex for the 10 data points.

Thus, the values of the optical radii of NGC 3521 ($R_{25}$ = 12.9 kpc) and
the Milky Way ($R_{25}$ = 12.0 kpc) are close to each other. The value of the
stellar mass of the NGC 3521 (log($M_{\star}/M_{\sun}$) = 10.7) is close to
the value of the stellar mass of the Milky Way (log($M_{\star}/M_{\sun}$) =
10.716). The mass of the black hole at the centre of NGC 3521
(log($M_{BH}/M_{\sun}$) = 6.85) is close to that in the Milky Way
(log($M_{BH}/M_{\sun}$) = 6.62). The radial distributions of the oxygen
abundances (panel (a) of Fig. 9) and rotation curves (panel (b) of Fig. 9) in
those galaxies agree satisfactorily with each other. However, in order to make
a solid conclusion as to whether the galaxy NGC 3521 is a twin of the Milky
Way, the radial distribution of the $R$ calibration-based abundances in NGC
3521 should be established, that is, the measurements of the spectra including
emission lines necessary for abundance determinations through the $R$
calibration should be carried out. The distance to NGC 3521 and its optical
radius should also be more precise.

####  4.4.2 NGC 4651

Figure 10: Comparison of properties between NGC 4651 and the Milky Way. Panel
a: Comparison between radial oxygen abundance distributions. The blue circles
denote the Te-based abundances in individual H ii regions in the Milky Way
(comes from panel (b) of Fig. 2), and the solid line is the best fit to those
data. The crimson plus signs are the $R$ calibration-based abundances in H ii
regions in NGC 4651, and the dotted line is the linear fit to those data
points. Panel b: Comparison between rotation curves. The points denote the
rotation curve of the Milky Way from Eilers et al. (2019). The rotation curve
of NGC 4651 from Epinat et al. (2008) is shown with plus signs (approaching
side) and crosses (receding side).

The galaxy NGC 4651 is an Sc galaxy (morphological type code $T$ =
5.1$\pm$0.6). The inclination angle of NGC 4651 is $i$ = 53$\degr$, and the
position angle of the major axis is PA = 77$\degr$ (Epinat et al. 2008). The
optical radius is 1.99 arcmin (de Vaucouleurs et al. 1991). At the distance of
$d$ = 19.0 Mpc (Foster et al. 2014), the physical optical radius is $R_{25}$ =
11.00 kpc. The stellar mass is $M_{\star}$ = 2.61 $\times$ 1010 $M_{\sun}$, or
log($M_{\star}/M_{\sun}$) = 10.42 (Leroy et al. 2019) (or $M_{\star}$ = 1.7
$\times$ 1010 $M_{\sun}$ or log($M_{\star}/M_{\sun}$) = 10.23 (Foster et al.
2014)). The rotation velocity of NGC 4651 is 215 km s-1 (Epinat et al. 2008).

The radial distribution of the oxygen abundances estimated through the $R$
calibration in H ii regions from Skillman et al. (1996) was approximated by
the relation

$12+\log(\rm O/H)=8.652(\pm 0.039)-0.377(\pm 0.083)\times R_{g}$ (17)

with a scatter of 0.039 dex for the six data points (panel (a) in Fig. 10).

The values of the optical radii of NGC 4651 ($R_{25}$ = 11.0 kpc) and the
Milky Way ($R_{25}$ = 12.0 kpc) are close to each other. The radial
distributions of the oxygen abundances (panel (a) of Fig. 10) and the rotation
curves (panel (b) of Fig. 10) in those galaxies agree satisfactorily to each
other. While the rotation velocity of NGC 4651 is rather close to that of the
Milky Way, the value of the stellar mass of NGC 4651
(log($M_{\star}/M_{\sun}$) = 10.42) is appreciably lower (by a factor of
approximately two, or even more) than the stellar mass of the Milky Way
(log($M_{\star}/M_{\sun}$) = 10.716). If the estimations of the stellar mass
of NGC 4651 are correct, then NGC 4651 can be considered a low(-stellar) mass
evolutionary analogue of the Milky Way.

####  4.4.3 NGC 2903

Figure 11: Comparison of properties between NGC 2903 and the Milky Way. Panel
a: Comparison between radial oxygen abundance distributions. The blue circles
denote the Te-based abundances in individual H ii regions in the Milky Way
(comes from panel (b) of Fig. 2), and the solid line is the best fit to those
data. The crimson plus signs are the $R$ calibration-based abundances in H ii
regions of NGC 2903, and the dotted line is the linear fit to those data
points. Panel b: Comparison between rotation curves. The points denote the
rotation curve of the Milky Way from Eilers et al. (2019). The rotation curve
of NGC 2903 from de Blok et al. (2008) is shown with the line.

The galaxy NGC 2903 is an Sbc spiral galaxy (morphological type code $T$ =
4.0$\pm$0.1). Its inclination angle is $i$ = 65$\degr$, and the position angle
of the major axis is PA = 204$\degr$ (de Blok et al. 2008). The optical radius
of NGC 2903 is $R_{25}$ = 5.87 arcmin (Walter et al. 2008). The distance to
NGC 2903 is $d$ = 8.9 Mpc (Drozdovsky & Karachentsev 2000), and it results in
a physical optical radius of $R_{25}$ = 15.21 kpc. The stellar mass of NGC
2903 based on the mean value from Jarrett et al. (2019) and Leroy et al.
(2021) and rescaled to the adopted distance is $M_{\star}$ = 3.33 $\times$
1010 $M_{\sun}$, or log($M_{\star}/M_{\sun}$) = 10.52. The mass of the black
hole in NGC 2903 is log($M_{BH}/M_{\sun}$) = 7.06${}^{+0.28}_{-7.06}$ (van den
Bosch 2016). The rotation velocity of NGC 2903 is 215 km s-1 (de Blok et al.
2008).

The abundance gradient traced by the $R$ calibration-based abundances in the H
ii regions from the compilation in Pilyugin et al. (2014) is

$12+\log(\rm O/H)=8.707(\pm 0.018)-0.338(\pm 0.035)\times R_{g}$ (18)

with a scatter of 0.047 dex for the 25 data points.

The values of the optical radii of NGC 2903 ($R_{25}$ = 15.21 kpc) and the
Milky Way ($R_{25}$ = 12.0 kpc) are close to each other, and the rotation
curves (panel (b) of Fig. 11) in those galaxies agree satisfactorily to each
other. However, the value of the stellar mass of NGC 2903
(log($M_{\star}/M_{\sun}$) = 10.52) is appreciably lower than the stellar mass
of the Milky Way (log($M_{\star}/M_{\sun}$) = 10.716). There is also an
appreciable difference between the radial distributions of the oxygen
abundances (panel (a) of Fig. 11) in the galaxies. Thus, NGC 2903 is a Milky
Way twin only to some extent.

####  4.4.4 MaNGA galaxy M-8341-09101

Figure 12: Comparison between the properties of the MaNGA galaxy M-8341-09101
and the Milky Way. Panel a: Comparison between the radial oxygen abundance
distributions. The blue circles denote the Te-based abundances in individual H
ii regions in the MW (comes from panel (b) of Fig. 2) and the solid line is
the best fit to those data. The grey points are the $R$ calibration-based
abundances in the spaxels of M-8341-09101 and the dashed line is the linear
fit to those data points. Panel b: Comparison between rotation curves. The
points denote the rotation curve of the Milky Way from Eilers et al. (2019).
The rotation curve of M-8341-09101 is shown by the line.

The distance to the MaNGA galaxy M-8341-09101 is 216.3 Mpc. The central oxygen
abundance in M-8341-09101 is 12 + log(O/H)0 = 8.63, and the oxygen abundance
at the optical radius is 12 + log(O/H)${}_{R_{25}}$ = 8.33. The comparison of
the radial distribution of the oxygen abundances in the galaxy M-8341-09101
and in the Milky Way is shown in panel (a) of Fig. 12. One can see that the
difference between the radial distribution of the oxygen abundances in the two
galaxies is significant.

The optical radius of M-8341-09101 ($R_{25}$ = 13.3 kpc) is close to the
radius of the Milky Way ($R_{25}$ = 12.0 kpc). The stellar mass of
M-8341-09101 (log($M_{\star}/M_{\sun}$) = 10.75) is close to that of the Milky
Way (log($M_{\star}/M_{\sun}$) = 10.716). The comparison between the rotation
curves in M-8341-09101 and the Milky Way is shown in panel (b) of Fig. 12.
Comparison between Fig. 12 and Fig. 11 suggested that the properties (rotation
curve and the radial abundance distribution) of the galaxy M-8341-09101 and
NGC 2903 are close to each other, that is, the galaxy M-8341-09101 is more
similar to NGC 2903 than to the Milky Way.

####  4.4.5 MaNGA galaxy M-8983-03703

Figure 13: Comparison between the radial oxygen abundance distributions in the
MaNGA galaxy M-8983-03703 and the Milky Way. The blue squares are the median
values of O/H in bins of 0.05 in the fractional radius $R/R_{25}$ of
M-8983-03703, and the bars show the scatter in O/H around the median values of
the bins. The red circles are abundances estimated from other MaNGA
measurements (M-7495-12704) of this galaxy. The median values of the oxygen
abundances for different measurements were obtained for the same bin, but the
positions of the symbols (circles and squares) were shifted slightly along the
x-axis for the sake of clarity. The black crosses denote the $T_{e}$-based
abundances of individual H ii regions in the Milky Way, while the solid line
is the best fit to those data within the optical radius.

Zhou et al. (2023) found that the MaNGA galaxy M-8983-03703 is a Milky Way-
like galaxy in the context of their star formation and chemical evolution
histories. Fig. 13 shows the comparison between the radial oxygen abundance
distributions in the MaNGA galaxy M-8983-03703 and the Milky Way. The field-
of-view of M-8983-03703 measurement covers the central part of the galaxy
only. There is another MaNGA measurement (M-7495-12704) of this galaxy that
covers a much larger fraction of the galaxy. The radial oxygen abundance
distribution obtained from M-7495-12704 is also shown in Fig. 13. One can see
that the difference between the radial distributions of the oxygen abundances
in M-8983-03703 (and M-7495-12704) and in the Milky Way is very large. Hence
M-8983-03703 cannot be considered as Milky Way twin candidate.

##  5 Discussion

We found that the position of the Milky Way in the central abundance versus
the abundance at optical radius diagram, Fig. 7, shows a significant shift
from the general trend. A prominent feature of the Milky Way is a high
metallicity (oxygen abundance) at the centre of the disc, which is close to
the maximum attainable oxygen abundance in galaxies, while the oxygen
abundance at the optical radius is significantly lower in comparison to
galaxies of similar central oxygen abundances, that is, the radial abundance
gradient (in dex/$R_{25}$) in the Milky Way is significantly steeper than in
other galaxies of similar (high) central metallicity. This evidences in favour
of a rather atypical (chemical) evolution of the Milky Way. In this section,
we discuss a possible reason for the atypical radial abundance gradient in the
Milky Way.

The chemical evolution of a given region of a galaxy is defined by the star
formation history and mass exchange with its surroundings. In the standard
$\Lambda$ cold dark matter ($\Lambda$CDM) scenario, successive mergings are
considered one of the main mechanisms for assembling mass in galaxies (White &
Rees 1978; Blumenthal et al. 1984). Galaxy-galaxy interactions and mergers can
have a significant effect on galaxy evolution, altering different
characteristics of a galaxy. In particular, the gas inflows are predicted to
lead to a redistribution of metals, reducing the central gas-phase metallicity
and producing an overall flatter abundance gradient (Rupke et al. 2010a;
Sillero et al. 2017; Bustamante et al. 2018). These predictions are in
agreement with observational data. Measurements of central metallicities of
interacting galaxies and galaxy pairs confirm that they have lower central
metallicities than isolated galaxies of similar stellar mass (e.g. Rupke et
al. 2008; Ellison et al. 2008; Garduño et al. 2021). However, Barrera-
Ballesteros et al. (2015) found central oxygen abundances in a sample of
interacting galaxies similar to those in a control sample. It has been found
(Rupke et al. 2010b; Kewley et al. 2010; Rosa et al. 2014; Croxall et al.
2015; Torres-Flores et al 2020) that merging and interacting systems exhibit
shallow oxygen abundance gradients compared to isolated spiral galaxies.
Boardman et al (2022, 2023) concluded that galaxies that have experienced
smooth gas accretion histories produce negative metallicity gradients over
time and that the increased merging activity disrupts this process, leading to
flatter metallicity gradients. One could suggest that the lack of mergers and
interactions is a necessary condition for a galaxy to have a high abundance at
the centre and a steep radial abundance gradient. In such a case, the high
central metallicity and steep gradient in the Milky Way would be evidence that
the Milky Way has evolved without mergers and interactions.

Empirical investigations of the merger history of the Milky Way have been
carried out in the past decades. The Sagittarius (Ibata et al. 1994) and Cetus
mergers (Newberg et al. 2009) were discovered. Large stellar surveys, such as
Gaia (Gaia Collaboration et al. 2016, 2018, 2021) and the Apache Point
Observatory Galactic Evolution Experiment, which is one of the programmes in
the SDSS (Majewski et al. 2017; Abdurro’uf et al. 2022), have provided
homogeneous astrometric, photometric, and spectroscopic data sampling for a
large amount of stars in the Milky Way. This has allowed for the detection and
characterisation of substructures in the Milky Way that are remnants of the
progenitor galaxies that merged with the Milky Way and contributed to its
stellar population. Hence, it has become increasingly possible to investigate
the merging history of the Milky Way in great detail. Belokurov et al. (2018)
and Helmi et al. (2018) argue that the inner halo is dominated by debris from
a major accretion event that occurred between 8 and 11 Gyr ago. A captured
galaxy was slightly more massive than the Small Magellanic Cloud. This object
is referred to as the Gaia-Enceladus-Sausage. Several other merger galaxies
have been discovered: Thamnos (Koppelman et al. 2019), Sequoia (Myeong et al.
2019), Kraken (Kruijssen et al. 2019, 2020), and Pontus (Malhan et al. 2022).
The Gaia-Enceladus-Sausage is the most recent major merger (Borre et al. 2022;
Dropulic et al. 2023). Since this event, the Milky Way has evolved without
significant mergers for the last $\sim$10 Gyr and, consequently, one can
expect that the redistribution of metals does not take place in the Milky Way
disc. Thus, the Milky Way meets the necessary conditions (i.e. lack of the
mergers and interactions) in order to have a high abundance at its centre and
a steep radial abundance gradient. The presence of close satellites
(Magellanic Clouds) may appear to be in conflict with this picture. However,
van den Bergh (2006) argues that the Large and Small Magellanic Clouds may be
interlopers from a remote part of the Local Group rather than true satellites
of the Milky Way (i.e. the Large Magellanic Cloud is on its first approach to
the Milky Way).

Close examination of Fig. 7 shows that among galaxies with central oxygen
abundances close to the Milky Way, the radial abundance gradients (in terms of
dex/$R_{25}$, difference between the oxygen abundance at the optical radius
and at the centre) for two galaxies in our sample exceed the radial abundance
gradient of the Milky Way. Those galaxies are NGC 6744, with 12 + log(O/H)0 =
8.84 and 12 + log(O/H)${}_{R_{25}}$ = 8.20 and consequently grad(O/H) = –0.64
dex/$R_{25}$, and NGC 5457 (M 101), with 12 + log(O/H)0 = 8.71 and 12 +
log(O/H)${}_{R_{25}}$ = 7.87 and consequently grad(O/H) = $-0.84$
dex/$R_{25}$. These galaxies are huge compared to the Milky Way, as the
optical radius of NGC 6744 is $R_{25}$ = 27.25 kpc, while the optical radius
of NGC 5457 is $R_{25}$ = 28.73 kpc. The stellar masses of NGC 5457
(3.81$\times$1010 $M_{\sun}$) and NGC 6744 (5.92$\times$1010 $M_{\sun}$) are
slightly lower or similar to that of the Milky Way (5.2$\times$1010
$M_{\sun}$). It should be emphasised that it is not necessary for a large
galaxy to show a steep radial abundance gradient. Indeed, the galaxy NGC 753
of radius $R_{25}$ = 26.45 kpc shows a radial gradient of $-0.12$
dex/$R_{25}$, and the galaxy NGC 1365 of radius $R_{25}$ = 31.98 kpc shows a
radial abundance gradient of $-0.21$ dex/$R_{25}$. The stellar masses of NGC
753 (8.13$\times$1010 $M_{\sun}$) and NGC 1365 (6.0$\times$1010 $M_{\sun}$)
are slightly higher or similar to that of the Milky Way.

One can expect that the shallow gradients in the majority of large galaxies
can be attributed to the fact that the abundances within those galaxies are
redistributed due to the mergers or interactions. Robotham et al. (2014) used
a subset of the Galaxy And Mass Assembly II redshift sample to compare the
effect of in situ star formation versus mass accretion through mergers and
found that galaxies of low masses are likely to obtain most of their mass
through star formation, whilst massive galaxies are likely to obtain most of
their mass build-up through the accretion of smaller galaxies. Conselice et
al. (2022) measured the pair fraction and merger fractions for galaxy mergers
of different mass ratios and quantified the merger rate for massive galaxies
(with stellar masses higher than 1011M☉). They found that over the last
$\sim$10 Gyr, major mergers with mass ratios greater than 1:4 occurred
0.85${}^{+0.19}_{-0.20}$ times on average, while minor mergers down to ratios
of 1:10 occurred on average 1.43${}^{+0.5}_{-0.3}$ times per galaxy.

Thus, one can suggest that the steep radial abundance gradient in the Milky
Way can be attributed to the fact that the Milky Way has evolved without
significant mergers and interactions for the last $\sim$10 Gyr. However, it is
not clear whether the evolution without mergers and interactions is a
sufficient condition for a steep abundance gradient in a galaxy.

##  6 Conclusions

We searched for Milky Way-like galaxies, comparing the following
characteristics: stellar mass $M_{\star}$, optical radius $R_{25}$, rotation
velocity $V_{rot}$, central oxygen abundance (O/H)0, and abundance at the
optical radius (O/H)${}_{R_{25}}$. Our sample of comparison galaxies contained
504 galaxies: 53 nearby galaxies and 451 MaNGA galaxies.

If the values of the optical radius and the stellar mass of the galaxy were
close to that of the Milky Way, then the galaxy was referred to as a
structural Milky Way analogue, sMWA. The oxygen abundance at a given radius of
a galaxy is defined by the evolution of this region (fraction of gas converted
into stars, i.e. astration level, and gas exchange with the surroundings). One
can expect that the similarity of the central oxygen abundance and the
abundance at the optical radius in two galaxies suggests a similar (chemical)
evolution. If the values of (O/H)0 and (O/H)${}_{R_{25}}$ in a galaxy were
close to that of the Milky Way, then the galaxy was referred to as an
evolutionary Milky Way analogue, eMWA. If the galaxy was simultaneously an
eMWA and an sMWA, then it could be considered a Milky Way twin.

We find that the position of the Milky Way on the (O/H)0 – (O/H)${}_{R_{25}}$
diagram shows a large deviation from the general trend outlined by galaxies of
our comparison sample in the sense that the (O/H)${}_{R_{25}}$ of the Milky
Way is appreciably lower than in other galaxies of similar (O/H)0. This
feature in the Milky Way evidences that its (chemical) evolution is not
typical.

The majority of the eMWAs are not sMWAs. Either the optical radii of the eMWAs
are significantly larger in comparison to the Milky Way or the eMWAs have
appreciably lower values of stellar mass and rotation velocity than the Milky
Way.

We found four galaxies (NGC 3521, NGC 4651, NGC 2903, and MaNGA galaxy
M-8341-09101) that are simultaneously an sMWA and an eMWA, that is, they can
be considered Milky Way twins. The galaxy NGC 3521 is possibly the most
similar to the Milky Way. The characteristics we considered (stellar mass,
optical radius, rotation velocity, oxygen abundance) of NGC 3521 are similar
to those of the Milky Way. The masses of black holes in those galaxies are
also similar to each other.

In previous studies, Milky Way-like galaxies were selected using structural
and morphological characteristics of galaxies, that is, sMWAs were selected.
We find that the abundances at the centre and at the optical radius
(evolutionary characteristics) provide a stricter criterion for selecting real
Milky Way twins.

## Acknowledgements

We are grateful to the referee, Dr. N. Boardman, for his constructive
comments.
LSP acknowledges support from the Research Council of Lithuania (LMTLT), grant
no. P-LU-PAR-23-28.
MALL acknowledges support from the Spanish grant PID2021-123417OB-I00, and the
Ramón y Cajal program funded by the Spanish Government (RYC2020-029354-I)
This research has made use of the NASA/IPAC Extragalactic Database (NED),
which is funded by the National Aeronautics and Space Administration and
operated by the California Institute of Technology.
We acknowledge the usage of the HyperLeda database (http://leda.univ-
lyon1.fr).
Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the
Participating Institutions, the National Science Foundation, and the U.S.
Department of Energy Office of Science. The SDSS-III web site is
http://www.sdss3.org/.
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 Observatories of China, New Mexico State
University, New York University, University of Notre Dame, Observatário
Nacional / MCTI, The Ohio State University, Pennsylvania State University,
Shanghai Astronomical Observatory, United Kingdom Participation Group,
Universidad Nacional Autónoma de México, University of Arizona, University of
Colorado Boulder, University of Oxford, University of Portsmouth, University
of Utah, University of Virginia, University of Washington, University of
Wisconsin, Vanderbilt University, and Yale University.

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##  Appendix A Characteristics of nearby galaxies

In this section we report the general characteristics (the inclination angle
of a galaxy, the position angle of the major axis, distance, angular and
physical optical radii, stellar mass, rotation velocity, and the black hole
mass) and the source of the data for the sample of nearby galaxies. We
estimated the abundances in H ii regions through the $R$ calibration from
Pilyugin & Grebel (2016) and determined the O/H - $R_{g}$ relation for each
galaxy where $R_{g}$ is a fractional radius normalised to the optical radius
$R_{25}$. The mean value of the uncertainty in the (O/H)R abundance obtained
through the $R$ calibration is $\sim$0.05 dex (Pilyugin & Grebel 2016). We
assumed a deviation of the abundance from the O/H-$R_{g}$ relation larger than
0.15 dex could be attributed to the large uncertainty in the line measurements
or could be an indicator of a peculiarity in the abundance of the H ii region.
Therefore, the points with deviations larger than 0.15 dex in (O/H) were
rejected and not used in the determination of the final O/H-$R_{g}$ relation.
The nearby galaxies discussed in the Section 4.4 (NGC 2903, NGC 3521, and NGC
4651) are not considered in this section. The compiled and derived
characteristics of nearby galaxies are listed in Table. 2.

###  A.1 NGC 224 (M 31)

Galaxy NGC 224 (M 31, Andromeda galaxy) is an Sb galaxy (morphological type
code $T$ = 3.0$\pm$0.4). The inclination angle of NGC 224 is $i$ = 77$\degr$,
and the position angle of the major axis is PA = 38$\degr$ (Corbelli et al.
2010). The optical radius is 95.27 arcmin (de Vaucouleurs et al. 1991). At the
distance of $d$ = 0.82 Mpc (Anand et al. 2021), the physical optical radius of
the NGC 224 is $R_{25}$ = 22.72 kpc. The stellar mass is $M_{\star}$ = 1.0
$\times$ 1011 $M_{\sun}$, or log($M_{\star}/M_{\sun}$) = 11.00 (Jarrett et al.
2019). The black hole mass is log($M_{BH}/M_{\sun}$) =
8.15${}^{+0.22}_{-0.11}$ (Davis et al. 2019). The rotation velocity of NGC 224
is 253 km s-1 (Corbelli et al. 2010). The radial distribution of the oxygen
abundances based on the H ii regions from the compilation in Pilyugin et al.
(2014) was approximated by the relation

$12+\log(\rm O/H)=8.715(\pm 0.016)-0.377(\pm 0.028)\times R_{g}$ (19)

with a scatter of 0.060 dex for 204 data points.

###  A.2 NGC 253

Galaxy NGC 253 is an SABc galaxy (morphological type code $T$ = 5.1$\pm$0.4).
The inclination angle of NGC 253 is $i$ = 76$\degr$, and the position angle of
the major axis PA = 235$\degr$ (Lucero et al. 2015). The optical radius is
13.77 arcmin (de Vaucouleurs et al. 1991). At a distance of $d$ = 3.70 Mpc
(Anand et al. 2021), the physical optical radius of NGC 253 is $R_{25}$ =
14.82 kpc. The stellar mass (mean value) is $M_{\star}$ = 3.50 $\times$ 1010
$M_{\sun}$, or log($M_{\star}/M_{\sun}$) = 10.54 (Jarrett et al. 2019; Leroy
et al. 2021). The black hole mass is log($M_{BH}/M_{\sun}$) = 7.00$\pm$0.19
(Davis et al. 2019). The rotation velocity of NGC 253 is 211 km s-1
(Hlavacek–Larrondo et al. 2011a; Lucero et al. 2015). The radial distribution
of the oxygen abundances traced by the H ii regions from Webster & Smith
(1983) was approximated by the relation

$12+\log(\rm O/H)=8.493(\pm 0.144)-0.079(\pm 0.182\times R_{g}$ (20)

with a scatter of 0.061 dex for eight data points.

###  A.3 NGC 300

Galaxy NGC 300 is an Scd galaxy (morphological type code $T$ = 6.9$\pm$0.4).
The inclination angle of NGC 300 is $i$ = 42$\degr$, and the position angle of
the major axis PA = 106$\degr$ (Carignan 1985). The optical radius is 10.94
arcmin (de Vaucouleurs et al. 1991). At a distance of $d$ = 1.94 Mpc (Bono et
al. 2010), the physical optical radius of NGC 300 is $R_{25}$ = 6.17 kpc. The
stellar mass (the mean value for estimations from Jarrett et al. (2019) and
Leroy et al. (2021) rescaled to the adopted distance) is $M_{\star}$ = 2.10
$\times$ 109 $M_{\sun}$, or log($M_{\star}/M_{\sun}$) = 9.32. The rotation
velocity of NGC 300 is 85 km s-1 (Hlavacek–Larrondo et al. 2011b; Ponomareva
et al. 2016) The radial distribution of the oxygen abundances estimated using
the H ii regions from the compilation in Pilyugin et al. (2014) and
supplemented by the measurements from Toribio San Cipriano et al (2016) was
approximated by the relation

$12+\log(\rm O/H)=8.444(\pm 0.017)-0.424(\pm 0.034\times R_{g}$ (21)

with a scatter of 0.062 dex for 46 data points.

###  A.4 NGC 598 (M 33)

Galaxy NGC 598 (M 33) is an Sc galaxy (morphological type code $T$ =
5.9$\pm$0.4). The inclination angle of NGC 598 is $i$ = 54$\degr$, and the
position angle of the major axis is PA = 201$\degr$ (Kam et al. 2017). The
optical radius is 35.40 arcmin (de Vaucouleurs et al. 1991). At a distance of
$d$ = 0.94 Mpc (Anand et al. 2021), the physical optical radius of NGC 598 is
$R_{25}$ = 9.68 kpc. The stellar mass is $M_{\star}$ = 4.87 $\times$ 109
$M_{\sun}$, or log($M_{\star}/M_{\sun}$) = 9.69 (Jarrett et al. 2019). The
rotation velocity of the NGC 598 is 125 km s-1 (Kam et al. 2017). The radial
abundance distribution traced by the H ii regions from the compilation in
Pilyugin et al. (2014) was approximated by the relation

$12+\log(\rm O/H)=8.489(\pm 0.020)-0.452(\pm 0.053)\times R_{g}$ (22)

with a scatter of 0.056 dex for 35 data points.

###  A.5 NGC 628 (M 74)

The nearby galaxy NGC 628 (M 74, the Phantom Galaxy) is an isolated Sc spiral
galaxy (morphological type code $T$ = 5.2$\pm$0.5). It is a face-on galaxy.
Its inclination angle is $i$ = 6$\degr$, and the position angle of the major
axis PA = 25$\degr$ (Kamphuis & Briggs 1992). The optical radius of NGC 628 is
$R_{25}$ = 5.24 arcmin (de Vaucouleurs et al. 1991). The H i disc extends out
to more than three times the optical radius (Kamphuis & Briggs 1992). There
are recent distance estimations for NGC 628 obtained through the tip of the
red giant branch method based on Hubble Space Telescope measurements. Jang &
Lee (2014) found the distance to NGC 628 to be 10.19 $\pm$ 0.14 (random) $\pm$
0.56 (systematic) Mpc. McQuinn et al. (2017) measured the distance to NGC 628
to be 9.77 $\pm$ 0.17 (statistical uncertainty) $\pm$ 0.32 (systematic
uncertainty) Mpc. Sabbi et al. (2018) determined the distances for the central
pointing ($d$ = 8.6 $\pm$ 0.9 Mpc) and for the outer field ($d$ = 8.8 $\pm$
0.7 Mpc). In this work, we adopted the distance to the NGC 628 used in our
previous paper: $d$ = 9.91 Mpc (Pilyugin et al. 2014), which is close to the
values obtained by Jang & Lee (2014) and McQuinn et al. (2017). The optical
radius of NGC 628 is $R_{25}$ = 15.09 kpc with the adopted distance. The mean
value of the stellar mass from Leroy et al. (2008) and Leroy et al. (2021)
rescaled to the adopted distance is $M_{\star}$ = 2.3 $\times$ 1010
$M_{\sun}$, or log($M_{\star}/M_{\sun}$) = 10.36. The radial abundance
distribution for the H ii regions from McCall et al. (1985); Ferguson et al.
(1998); van Zee et al. (1998); Bresolin et al. (1999); Berg et al. (2015) was
approximated by the relation

$12+\log(\rm O/H)=8.667(\pm 0.016)-0.409(\pm 0.028)\times R_{g}$ (23)

with a scatter of 0.047 dex for 78 data points.

###  A.6 NGC 753

Galaxy NGC 753 is an SABc galaxy (morphological type code $T$ = 4.9$\pm$1.0).
The inclination angle of NGC 753 is $i$ = 50$\degr$, the position angle of the
major axis is PA = 128$\degr$ (Amram et al. 1994). The optical radius is 1.26
arcmin (de Vaucouleurs et al. 1991). At a distance of $d$ = 72.4 Mpc (Leroy et
al. 2019), the physical optical radius of NGC 753 is $R_{25}$ = 26.45 kpc. The
value of the rotation velocity is $\sim$210 km s-1 (Amram et al. 1994). The
stellar mass is $M_{\star}$ = 8.13 $\times$ 1010 $M_{\sun}$, or
log($M_{\star}/M_{\sun}$) = 10.91 (Leroy et al. 2019). The abundance gradient
traced by the H ii regions from Henry et al. (1996) is

$12+\log(\rm O/H)=8.586(\pm 0.065)-0.064(\pm 0.095\times R_{g}$ (24)

with a scatter of 0.055 dex for eight data points.

###  A.7 NGC 925

Galaxy NGC 925 is an Scd galaxy (morphological type code $T$ = 7.0$\pm$0.3).
The inclination angle of NGC 925 is $i$ = 66$\degr$, and the position angle of
the major axis is PA = 287$\degr$ (de Blok et al. 2008). The optical radius is
5.24 arcmin (de Vaucouleurs et al. 1991). At a distance of $d$ = 9.29 Mpc
(Saha et al. 2006), the physical optical radius of NGC 925 is $R_{25}$ = 14.15
kpc. The stellar mass is $M_{\star}$ = 5.62 $\times$ 109 $M_{\sun}$, or
log($M_{\star}/M_{\sun}$) = 9.75 (Leroy et al. 2019). The rotation velocity of
NGC 925 is 115 km s-1 (Ponomareva et al. 2016). The radial abundance
distribution based on the H ii regions from van Zee et al. (1998) was
approximated by the relation

$12+\log(\rm O/H)=8.440(\pm 0.017)-0.360(\pm 0.027)\times R_{g}$ (25)

with a scatter of 0.047 dex for 34 data points.

###  A.8 NGC 1058

Galaxy NGC 1058 is an Sc galaxy (morphological type code $T$ = 5.1$\pm$0.9).
The inclination angle of NGC 1058 is $i$ = 15$\degr$, and the position angle
of the major axis is PA = 145$\degr$ (García-Gómez et al. 2004). The optical
radius is 1.51 arcmin (de Vaucouleurs et al. 1991). At a distance of $d$ =
10.6 Mpc (Schmidt et al. 1994), the physical optical radius of NGC 1058 is
$R_{25}$ = 4.66 kpc. The stellar mass (rescaled to adopted distance) is
$M_{\star}$ = 2.51 $\times$ 109 $M_{\sun}$, or log($M_{\star}/M_{\sun}$) =
9.40 (Leroy et al. 2019). The radial abundance distribution traced by the H ii
regions from Ferguson et al. (1998); Bresolin (2019) was approximated by the
relation

$12+\log(\rm O/H)=8.649(\pm 0.023)-0.265(\pm 0.043)\times R_{g}$ (26)

with a scatter of 0.046 dex for 22 data points.

###  A.9 NGC 1068 (M 77)

Galaxy NGC 1068 (M 77) is an Sb galaxy (morphological type code $T$ =
3.0$\pm$0.3). The inclination angle of NGC 1068 is $i$ = 35$\degr$, and the
position angle of the major axis PA = 73$\degr$ (Leroy et al. 2021). The
optical radius is 3.54 arcmin (de Vaucouleurs et al. 1991). At a distance of
$d$ = 13.97 Mpc (Anand et al. 2021), the physical optical radius of NGC 1068
is $R_{25}$ = 14.38 kpc. The stellar mass is $M_{\star}$ = 8.13 $\times$ 1010
$M_{\sun}$, or log($M_{\star}/M_{\sun}$) = 10.91 (Leroy et al. 2021). The mass
of the black hole in the NGC 1068 is log($M_{BH}/M_{\sun}$) = 6.75$\pm$0.08
(Davis et al. 2019). The radial distribution of the oxygen abundances in the H
ii regions from the compilation in Pilyugin et al. (2014) was approximated by
the relation

$12+\log(\rm O/H)=8.696(\pm 0.018)-0.102(\pm 0.062)\times R_{g}$ (27)

with a scatter of 0.035 dex for 13 data points.

###  A.10 NGC 1097

Galaxy NGC 1097 is an SBb galaxy (morphological type code $T$ = 3.3$\pm$0.5).
The inclination angle of NGC 1097 is $i$ = 46$\degr$, and the position angle
of the major axis is PA = 134$\degr$ (Ondrechen et al 1989). The optical
radius is 4.67 arcmin (de Vaucouleurs et al. 1991). At a distance of $d$ =
13.58 Mpc (Anand et al. 2021), the physical optical radius of NGC 1097 is
$R_{25}$ = 18.43 kpc. The stellar mass is $M_{\star}$ = 5.75 $\times$ 1010
$M_{\sun}$, or log($M_{\star}/M_{\sun}$) = 10.76 (Leroy et al. 2021). The
black hole mass is log($M_{BH}/M_{\sun}$) = 8.38$\pm$0.04 (Davis et al. 2019).
The rotation velocity of NGC 1097 is 253 km s-1 (Ondrechen et al 1989). The
abundance gradient estimated using the H ii regions from the compilation in
Pilyugin et al. (2014) was approximated by the relation

$12+\log(\rm O/H)=8.661(\pm 0.009)-0.138(\pm 0.040)\times R_{g}$ (28)

with a scatter of 0.022 dex for 15 data points.

###  A.11 NGC 1232

Galaxy NGC 1232 is an SABc galaxy (morphological type code $T$ = 5.0$\pm$0.4).
The inclination angle of NGC 1232 is $i$ = 30$\degr$, and the position angle
of the major axis is PA = 270$\degr$ (van Zee & Bryant 1999). The optical
radius is 3.71 arcmin (de Vaucouleurs et al. 1991). At a distance of $d$ =
21.5 Mpc (van Zee & Bryant 1999), the physical optical radius of NGC 1232 is
$R_{25}$ = 23.18 kpc. The stellar mass rescaled to the adopted distance is
$M_{\star}$ = 4.70 $\times$ 1010 $M_{\sun}$, or log($M_{\star}/M_{\sun}$) =
10.67 (Leroy et al. 2019). The rotation velocity of the NGC 1232 is 220 km s-1
(van Zee & Bryant 1999). The radial abundance distribution traced by the H ii
regions from the compilation in Pilyugin et al. (2014) was approximated by the
relation

$12+\log(\rm O/H)=8.741(\pm 0.028)-0.487(\pm 0.048)\times R_{g}$ (29)

with a scatter of 0.050 dex for 29 data points.

###  A.12 NGC 1313

Galaxy NGC 1313 is an SBcd galaxy (morphological type code $T$ = 7.0$\pm$0.4).
The inclination angle of NGC 1313 is $i$ = 48$\degr$, and the position angle
of the major axis PA = 0$\degr$ (Ryder et al. 1995). The optical radius is
6.12 arcmin or 367.2 arcsec (Ho et al. 2011). At a distance of $d$ = 4.32 Mpc
(Anand et al. 2021), the physical optical radius of NGC 1313 is $R_{25}$ =
7.69 kpc. The stellar mass (mean value) is $M_{\star}$ = 2.91 $\times$ 109
$M_{\sun}$, or log($M_{\star}/M_{\sun}$) = 9.46 (Jarrett et al. 2019; Leroy et
al. 2019). The rotation velocity of the NGC 1313 is 112 km s-1 (Ryder et al.
1995). The abundance gradient based on the H ii regions from the compilation
in Pilyugin et al. (2014) was approximated by the relation

$12+\log(\rm O/H)=8.163(\pm 0.025)-0.148(\pm 0.049)\times R_{g}$ (30)

with a scatter of 0.071 dex for 37 data points.

###  A.13 NGC 1365

Galaxy NGC 1365 is an Sb galaxy (morphological type code $T$ = 3.2$\pm$0.7).
Its inclination angle is $i$ = 46$\degr$, and the position angle of the major
axis is PA = 222$\degr$ (Ondrechen & van der Hulst 1989). The optical radius
of NGC 1365 is $R_{25}$ = 5.61 arcmin (de Vaucouleurs et al. 1991). The
distance to NGC 1365 is $d$ = 19.6 Mpc (Saha et al. 2006). The physical
optical radius at the adopted distance is $R_{25}$ = 31.98 kpc. The stellar