AN ADVANCED APPROACH FOR DEFINITION OF
THE ”MILKY WAY GALAXIES-ANALOGUES”

Morphological type of our Galaxy was determined as SAB(rs)bc by de Vaucouleurs & Pence (1978). The SBc type (T=4) is usually considered for MWAs study.

Main structural parameters and metallicity: giant disk galaxy having four (two ?) spiral arms with twist angles, bar, bulge, inner ring, and halo. The thickness of thin and thick disks are usually considered as 220–450 pc and 2.6 kpc, respectively (Bland-Hawthorn & Gerhard, 2016).

Metallicity as a key parameter of the chemodynamical evolution reveals many factors, which define the MW structural parameters. Hammer et al. (2007) found a systematic offset in the position of the Milky Way in the parameter space within 1$\sigma$ for all Tully-Fisher ratios, which shows a significant deficiency in stellar mass, angular momentum, disk radius, and $Fe/H$ in the stars in periphery region at a given $V_{rot}$. In contrast, McGaugh (2016) suggests that the Milky Way is a normal spiral galaxy obeying the Tully–Fisher and the size-mass relation. Licquia et al. (2016) examine the three-dimensional diagram ($V_{rot}$ – luminosity – radius) and found that the Milky Way lies farther from this relation than around 90 % of other spiral galaxies, yielding evidence that MW is extremely compact for its rotation velocity and luminosity possessing a cold bar (Quillen, 1996). The recent studies by Queiroz et al. (2021) with the GAIA data highlight the differences of the stellar population in the MW bar and bulge.

The chemical properties of MW are not typical in several aspects. On the one hand, the MW is one of the most oxygen-rich spiral galaxies in the sense that the metallicity in the center is close to the maximum attainable value (Pilyugin et al., 2007). On the other hand, the oxygen abundance along the optical radius is noticeably lower than in galaxies with a similar central metallicity (Pilyugin et al., 2023). At the same time, MW has a very steep metallicity gradient compared to most giant spiral galaxies, in which the change in oxygen excess along the optical radius is quite small (Pilyugin & Tautvaišienė, 2024).

Chandra et al. (2023) considered the MW three-phase chemodynamical evolution exploring a sample of 10 million red giant stars with low-resolution Gaia XP spectra and operating with angular momentum as a function of metallicity. They compared it with those of MWAs from the Illustris(TNG50) cosmological simulation taking into account these three MW evolutionary phases: the disordered protogalaxy, the kinematically hot old disk, and the kinematically cold young disk. They proposed three physical mechanisms for explanation (spinup, merger, and cooldown), which satisfies conditions of the Gaia-Sausage-Enceladus (GSE) last major merger with our Galaxy at $z\approx$ 2. In the frame of this three-phase scenario, Semenov et al. (2024) proposed an explanation of yet one MW feature: the MW disk was formed quite early, within the first few billion years of its evolution. It is consistent with the overall population of MWA-mass disk galaxies.

Among other MW chemodynamical features, which were compared with MWAs obtained in TNG50 cosmological simulations we note recent fundamental research by Rix et al. (2024). Using Gaia XP spectra they found a universal feature for MW and MWAs: their extremely metal-rich giant stars ($M/H_{XP}$ ¿ 0) are mostly concentrated in a compact central dynamically hot knot with $R<$ 1.5 kpc. Taking into account that MW metal-poor stars are also concentrated in the central few kiloparsecs region, future studies with the SDSS-V as write these authors will allowing to estimate the stellar population more precisely. Another ”side” of our Galaxy, the halo at 10-80 kpc, was studied by Han et al. (2024) with the H3 Survey data. They found the strong kinematic asymmetries of distributions and, consequently, cold and hot kinematically fractions of stars with radial velocity dispersions 70 km/s and 160 km/s, respectively.

As for the inner ring feature, (Wylie et al., 2022) in their recent meticulous work with a sample of APOGEE DR16 inner Galaxy stars studied the outer bar region. They considered the orbits of stars in the ”state of the art bar-bulge potential with a slow pattern speed” constructing the maps of their metallicity [Fe/H], density, and ages. They conclude that MW inner ring-like structure is on average middle-age and has a metal-rich gradient along the bar’s major axis. Its location is between the planar bar and corotation radius.

The following photometric parameters are usually taken into account for MWA search: luminosity class (II); isophotal diameter $D_{25}$ = 26.8 kpc (Goodwin et al., 1998), where the isophotal radius is usually adopted as $R_{25}$ = 12 kpc; the stellar disk up to 1.35 kpc (Rix & Bovy, 2013). To learn the ”Maps of the Milky Way based on Gaia DR3 from 10 pc to 200 kpc” one can go to the next url: https://gruze.org/posters_dr3/.

The total mass of our Galaxy has various estimates depending on methods and entire MW region for this estimate: from 8.5$\times$10¹¹ $M_{Sun}$ (Peñarrubia et al., 2014) up to 1.4$\times$10¹² $M_{Sun}$ (Grand et al., 2019). The virial mass at Galactocentric distance less than 21.1 kpc is $M_{vir}$ = 0.2 $\times$ 10${}^{12}M_{Sun}$ (see, for example, Watkins et al. (2019) for estimation by halo globular clusters motion). The stellar mass is $M_{*}$$=5\times$ $10^{10}M_{Sun}$ (log$M_{*}$ = 10.7) and star formation rate $SFR$ = (1.78 $\pm$ 0.36) $M_{Sun}$ yr^-1 with taking the linear scale length ($B/T$, $R_{eff}$) into consideration (Tuntipong et al., 2024); number of stars $N_{*}$ = (1–4) $\times 10^{11}$ when the disk stars were detected with Gaia DR2 even beyond 25 kpc from the MW center. The dark matter density at Sun’s position $M_{DM}$ = 0.0088 $M_{Sun}$ pc^-3 (Kafle et al., 2014) but a dark matter area may extend up to $\approx$ 600 kpc (Deason et al., 2020).

We propose to search for such a parameter of the Milky Way in the parameter space, which shows the maximum deviation from the corresponding relation for spiral galaxies. This parameter is used as the main criterion for the selection of MWA galaxies. Because the search for MWA galaxies is feasible using any parameters of the MW, we propose to increase their number both for the search for MWAs and for the specification of the MWAs properties.

In most of the research, as you see, the MW galaxies-analogues were selected based on two/three parameters: stellar mass and some additional parameter, usually bulge-to-disk (bulge-to-total) ratio, the star formation rate. In addition to these MW features, we would like to highlight a weak nuclear activity and low mass of the supermassive black hole (SMBH), 3D-kinematics for the rotation velocity, isolation criteria, and several known multiwavelrngth properties.

3D-kinematics of star’s movement can serve as an indicator for MWAs search. In series of works, Fedorov et al. (2021, 2023), Dmytrenko et al. (2023), Denyshchenko et al. (2024) investigated region of the Milky Way in coordinate ranges 120^∘ $<$ $\theta$ $<$ 240^∘, 0 kpc $<$ $R$ $<$ 16 kpc, -1 kpc $<$ $Z$ $<$ 1 kpc with Gaia EDR3 using samples of red giants and sub-giants whose centroids are in the MW plane. For the first time, these authors derived the dependence of the centroid’s kinematic parameters on the Galactocentric coordinates as well as the parameters for rotational velocity $\partial$$V_{R}$/$\partial$$\theta$ and $\partial$V$\theta$/$\partial$$\theta$.

Our approach includes the task of investigating the 3D-kinematics of a large part of the MW based on GAIA DR3 data within the Ogorodnikov-Milne model and using the determined strain and rotation rate tensors to establish the spiral pattern of the MW. The studied galactic space will be bounded by the Galactocentric coordinates 4 kpc $<$ $R$ $<$ 14 kpc, 140^∘ $<$ $\theta$ $<$ 220^∘ and -3 kpc $<$ $Z$ $<$ 3 kpc. This is the region dominated by older stars, which are more evenly distributed than younger blue stars. Using the obtained components of the spatial velocities of the centroids and kinematic parameters we will able to construct $V_{rot}(R)$ and their slope within this region and to determine the parameters of the spiral arms including the coordinates of the vertices of various star regions. These results can serve as indicators for applying machine learning in tasks for search of MWAs with the kinematically cold rotating disk.

We remind that our Galaxy possesses both a weak nuclear activity and small mass of the supermassive black hole: $M_{SMBH}$ = 4.61 $\times$ 10${}^{6}M_{Sun}$ (Ghez et al., 2008; Becerra-Vergara et al., 2021). The central object Sgr A* usually shows quiescent state, but sometimes does show rapid outbursts or flares of radiation (see, e.g., Genzel et al. (2010); Dodds-Eden et al. (2011), and references therein). This is the case of a low-luminosity galactic nucleus, radiating at $\approx$10^–8 of the Eddington level. In the such regime of activity, the MW core has no typical AGN-like gas-dusty torus but has so-called ”circumnuclear disk” (CND) as a torus-like dusty-molecular gas around Sgr A$\star$ extending from $\approx$ 1 pc to $\approx$ 5 pc (Etxaluze et al., 2011; Lau et al., 2013; Tsuboi et al., 2018).

We adopt as a working hypothesis that the features of the MW are caused by its evolution without major merging for the last 10 Gyr. We consider the isolation criterion of MWA galaxies on the scales of neighboring galaxies (Tully & Fisher, 1987) to study the role of satellites in the evolution of MWA galaxies. The Milky Way can be considered as an isolated galaxy during the long time of its evolution. The results of the high-resolution N-body simulations of last major merger (Naidu et al., 2021) allowed in particular to determine both the orbital parameters of merging with two density profile breaks at $\approx$ 15-18 kpc and 30 kpc as well as distribution of stellar and dark matter mass between GSE and Milky Way.

What is about minor mergers? What is the influence of the Magellanic Clouds (the gas reservoirs) on the MW evolution? (van den Bergh, 2006) assumes that the 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 (LMC) is on its first approach to the MW. Font et al. (2021) and Jones et al. (2024) investigated the significance of satellite effects and analyzed star formation rates in galaxy systems similar to the MW-like satellite system using the projected satellite–host galaxy distances. Exploiting the data from SAGA II catalog, CFHT and VLA observations, Jones et al. (2024) defined eight such MW-like systems when a satellite is undergoing ram pressure stripping in process of collision with circumgalactic medium of its host galaxy.

What is for the future collision of the Milky Way with Andromeda galaxy ((Dubinski et al., 1996; van der Marel et al., 2019)) in around 5 Gyr? (Sawala et al., 2024) used the Gaia and HST observational data to determine the dynamical process of merging the MW-M31 system. These authors predicted that M33 and LMC as other members of the Local Group are able to make this merger less likely because the LMC orbit runs perpendicular to the MW-M31 system orbit. Moreover, they found that existing uncertainties in the present kinematic and dynamic (masses) data for Local Group galaxies give 50 %-50 % probability of MW-M31 merger during the next 10 Gyr. The certain role can plays not only the correct distance moduli determination (see, for example, Elyiv et al. (2020)), the MW-M31 orbital geometry ((Banik et al., 2022)), but the position of Local Void lying adjacent to the Local Group ((Tully & Fisher, 1987; Lindner et al., 1995; Mazurenko et al., 2024)) and the MW moving away this void.

To study the role of interaction with neighboring (dwarf/normal) galaxies in the evolution of MWA galaxies, the isolation parameters are available for nearby galaxies in catalogs of isolated galaxies (Sorgho et al., 2024). For example, the isolated galaxies selected from 2MIG catalog exhibit multiwavelength properties, which are characterized by a weak nuclear activity as compare with galaxies in the dense environment ((Pulatova et al., 2015; Melnyk et al., 2015; Vol’Vach et al., 2011; Dobrycheva et al., 2018)) and faint luminocity in spectral ranges especially in radio- and X-ray ranges ((Pulatova et al., 2023; Vasylenko et al., 2020)).

For the most MW-like galaxy NGC 3521 (MW-twin in terms of baryon mass, rotation velocity, scaled disk length, metallicity), the observational data from the Ukrainian UTR-2 radio telescope ((Konovalenko et al., 2016)) will be quite useful in decameter range both to have a full spectral energy distribution of the NGC 3521 and to explain the Galactic background radio emission, the North Polar Spur (Miroshnichenko, 2009). The archive of UTR-2 radio telescope contains large volumes of 24-hour survey data for 4-5 positions on inclination.

An interesting expected result to find the view of MW from the outside observer can be achieved using machine learning for classification by a range of photometric parameters (morphology details, optical radius, luminosity concentration index to the center, color indices, etc.) and image feature as the bar and bulge, structure of spiral arms, inclination angle, etc. ((Vavilova et al., 2021; Khramtsov et al., 2022; Vavilova et al., 2022; Dobrycheva et al., 2023)). The obtained 3-D kinematics of the MW red-giant and sub-giant stars, and the parameters of multiwavelength radiation of MWAs could be considered as additional indicators.

The samples of candidates to the MW galaxies-analogues should contain the MW features as much as possible. It allows optimizing the necessary and sufficient conditions for revealing MWAs. Thanks to this, the number of candidates for MWA galaxies will increase quantitatively, and their study will, in turn, allow us to understand the appearance and features of the MW as the extragalactic object. Cosmological simulations TNG50, in own turn, allow clarifying whether single/different evolutionary tracks lead to the MWA formation.