What does the Milky Way look like?

VLBI at radio wavelengths has been used to detect a large amount of masers associated with HMSFRs, and they can be used to map the spiral structure of the MW from the solar neighborhood to the GC and beyond. Table 1 lists the coordinates and parallaxes of 204 HMSFR masers measured with VLBI techniques, including the National Radio Astronomy Observatory’s Very Long Baseline Array, the Japanese VLBI Exploration of Radio Astrometry project, the European VLBI Network, and the Australian Long Baseline Array. For the masers listed in Table 1, 199 were summarized by R19, and five have been newly reported by Xu et al. (2021b) and Bian et al. (2022) in the past two years. The typical parallax accuracy of the masers is $\sim$20 $\mu$as, and 19 of them even have accuracies of 10 $\mu$as or better.

High-mass stars are generally located near their birthplaces, and thus they can also be used to trace the Galactic spiral structure. Employing the same method as used by Gaia Collaboration et al. (2022), we adopted the effective temperature, spectral type, distance from the galactic plane, and the astrometric fidelity indicator, $f_{a}$ (Rybizki et al., 2022), to select O–B-type star candidates from Gaia DR3 (Gaia Collaboration et al., 2022). We only use stars with a parallax precision better than 20%, i.e., parallax_over_error $>$ 5. After applying this criterion, we obtained a total of 495 965 O–B stars.

Then, RR-Lyrae stars identified by vari_rryrae in Gaia DR3 were removed. Next, we filter the tangential velocity $\nu_{\rm tan}=A_{\nu}(\mu_{\alpha*}^{2}+\mu_{\delta}^{2})^{1/2}/\varpi$ with $\nu_{\rm tan}<180$ km s^-1, the same as Gaia Collaboration et al. (2018), where $\mu_{\alpha*}$ and $\mu_{\delta}$ are the proper motions in the R.A. and decl., respectively, $\varpi$ is the parallax, and $A_{\nu}$ = 4.74  km yr s^-1. After filtering based on the above criteria, 488 449 O–B-type stars are left. In this work, we only consider stars hotter than 20 000 K, which corresponds to O–B2-type stars whose typical ages are younger than 20 Myr (Chen et al., 2013). The final sample is composed of 23 807 O–B2 stars. We perform a parallax zero-point correction for all O–B2-type stars in the sample, as indicated by (Lindegren et al., 2021). The median standard error of the parallaxes of the O–B2-type stars is 17 $\mu$as.

Since YOCs ($\textless$ 20 Myr) can trace the spiral arms well (Hao et al., 2021), we only use OCs younger than 20 Myr as tracers in this work. In recent years, taking full advantage of the high-precision astrometric data provided by Gaia, numerous studies have identified thousands of OCs in the MW, and their ages cover a wide range, from several megayears to a few gigyears. Based on many previous works, Hao et al. (2021) compiled a catalog containing more than 3 700 OCs using Gaia Early Data Release 3. Soon after, 704 and 628 newly found OCs in the Gaia area were reported by Hao et al. (2022) and Castro-Ginard et al. (2022), respectively. In this work, we have synthesized the above three catalogs and obtained a large sample of 5 021 OCs, of which 1 011 OCs have ages younger than 20 Myr. We apply a parallax zero-point correction for the member stars of each OC, and then use the average parallax of all members as the OC’s parallax (Lindegren et al., 2021). Similar to the O–B2-type star sample, we only use YOCs with parallax accuracies better than 20%, resulting in a final number of 981 YOCs. The median standard error of parallax of YOCs is $\sim$23 $\mu$as.

The spiral arms of the MW show quasi-continuous structure in CO and HI in Galactic longitude–local standard of rest (LSR) velocity ($l$–$v$) maps. We initially assign masers to spiral arms by comparing the $(l,v)$ positions of the sources with the $(l,v)$ loci of arm segments provided by Reid et al. (2016). Although a plan view of the MW from $l$–$v$ plots cannot accurately place HMSFR masers into spiral arms, one can, in most cases, assign HMSFR masers to spiral arms by their association with CO and HI emission features. In addition, the Galactic latitudes and parallax distances can be helpful for confirming the arm assignments of HMSFR masers and avoiding any anomalous kinematic effects.

In Figure 1, we have overlaid the HMSFR masers on the $l$–$v$ plot of HI emission. Figure 2 shows the Galactic longitude–latitude $(l,b)$ positions of the maser sources, and Figure 3 presents a plan view of the MW. In these three figures, the white dots indicate spurs or sources for which the arm assignments are unclear. The arm assignments for most sources, in terms of the $(l,v)$ matches, are clear and consistent with the parallax distances. It is worth mentioning that the maser sources assigned to the Norma and Scutum Arms in previous work (R19) are mixed together in the $l$–$v$, $l$–$b$, and $x$–$y$ plots (as shown by the zoomed-in subfigures in Figures 1, 2, and 3), respectively. Therefore, in this work, these sources are assigned to the same arm, namely the Norma Arm. Besides, R19 indicated that the Sagittarius Arm has a 2 kpc long gap centered at $l\approx 43$^∘ near ($x$, $y$) = (2,  6) kpc (see Figure 3), and the arm segment on the left of the gap belongs to the Sagittarius Arm. As this arm segment is connected to the Carina Arm, here we have assigned the masers to the Carina Arm.

Since the radial velocities ($v$) of different spiral arms are almost equal to 0 km s^-1 in the direction of the GC (340^∘ $<l<$ 20^∘) and anti-GC (160^∘ $<l<$ 200^∘), the Galactic latitudes and parallax distances are used as the primary indicators for arm assignment. For sources within 5 kpc of the Sun, their arm assignments can be determined confidently based on their accurate parallax distances. However, for some distant sources, their parallax distances may be consistent with two or even three spiral arms within their 1$\sigma$ uncertainties, so their Galactic latitudes can provide strong evidence to resolve this issue. G019.60$-$00.23 is a good example of this situation. Around $l\approx 20$^∘, $b$ and $v$ of the Sagittarius and Perseus Arms are ($-$0.08^∘, 39 km s^-1) and (0.08^∘, 26 km s^-1), respectively (Reid et al., 2016). Near ($x$, $y$) = (4, $-$4) kpc, G019.60$-$00.23 has a velocity of $\sim$41 km s^-1, implying it may belong to either the Sagittarius Arm or the Perseus Arm judging from the $(l,v)$ match in Figure 1 and the ($x$, $y$) match in Figure 3. Considering that the Galactic latitude of G019.60$-$00.23 is $-$0.23^∘, we rule out assigning this maser to the Perseus Arm based on the latitude difference of 0.31^∘ ($Z$-height of 70 pc at a distance of 13 kpc). The Sagittarius Arm matches this maser in both latitude and $v$, and thus we assign G019.60$-$00.23 to the Sagittarius Arm. The same technique for arm assignment is also adopted for the sources G229.57$+$00.15 and G240.31$+$00.07, whose Galactic latitudes are 0.15^∘ and 0.07^∘, respectively. From the $l$–$v$ plot (Figure 1) and the plan view of the MW (Figure 3), they could be in either the Perseus Arm or the Outer Arm. At $l\approx 230$^∘ and $\approx 240$^∘, the Galactic latitudes of the Perseus Arm are $-$2.10^∘ and $-$2.44^∘ (Reid et al., 2019), and the corresponding values are 0.17^∘ and 0.19^∘ for the Outer Arm (Reid et al., 2019). Hence, the differences of 2.25^∘ and 2.51^∘ ($Z$-height of $\sim$200 pc at a distance of 5 kpc) in the Galactic latitude rule out the sources as belonging to the Perseus Arm, and instead they likely reside in the Outer Arm. The arm assignment of each source is listed in Table 1, and the numbers of the sources in the spiral arms are listed in Table 2.

The high-precision parallaxes of young stars provided by Gaia are excellent tracers, and can be used to map the spiral structure near the Sun. To reveal the MW’s spiral structure better, we use a bivariate kernel density estimator (Feigelson & Babu, 2012) to outline the stellar density structures around the Sun. Meanwhile, considering the exponential distribution of stars in the Galactic disk, we adopt a weight related to the Galactocentric radius, which is set as $w_{a}(R)=C\exp(R/R_{d})$. Here, $C$ is the constant factor and $R_{d}$ is the disk scale, assumed to be 3 kpc (Binney & Tremaine, 2008). Assuming that the weight at solar circle is 1, we simply set $C=\exp(-8.15/R_{d})$. Adopting a local bandwidth of 0.4 kpc, which is similar to Poggio et al. (2021), the density structures indicated by the O–B2-type stars (color background) and YOCs (contours) are shown in Figure 4. The color backgrounds and contours are concordant. The distributions of the O–B2-type stars and YOCs are highly structured rather than homogeneous.

Owing to a lack of radial velocities of many O–B2-type stars, we could not assign them to spiral arms based on the Galactic $l$–$v$ maps as masers. Instead, we adopt a new method to judge which spiral arm an O–B2-type star belongs to according to the probability of the O–B2-type star being located in one of the spiral arms shown in the plan view of the MW. Here, the probability is calculated by a Gaussian function, i.e.,

where $\Delta d$ is the distance to the spiral arm, $\sigma_{x}$ is the uncertainty of the distance, and $\sigma_{a}$ is the arm width, which defaults to 0.3 kpc in this work. Finally, we only select stars with probabilities larger than 10%, corresponding to them being less than 1.7$\sigma$ away from the nearest spiral arm.

We fit a spiral pattern to the spiral-arm segments by adopting a log-periodic spiral, defined as,

where $R$ is the Galactocentric radius at the Galactocentric azimuth, $\beta$, (defined as 0 toward the Sun and increasing in the direction of Galactic rotation) for an arm with radius $R_{\rm ref}$ at reference azimuth $\beta_{\rm ref}$, and pitch angle $\psi$. We fit a straight line to $(x,y)=(\beta,\ln(R/R_{\rm ref}))$ using a Bayesian Markov Chain Monte Carlo (MCMC) procedure to estimate the parameters $R_{\rm ref}$ and $\psi$.

The $\chi^{2}$ test is employed to evaluate the fitted result of the spiral arms, i.e.,

Here, the subscripts “obs” and “mod” on the $R$, respectively mean the radius gleaned from the observational data and from the model, respectively; the subscript $i$ represents the $i$th source, $\sigma$ is the radius dispersion for $(R_{\rm mod}-R_{\rm obs})$, and $N$ is the number of sources.

Each log-periodic spiral arm has been depicted by the locations of the masers using the method described by R19. We also constrain the fitted arms to pass the observed arm tangencies (Hou & Han, 2015). After assigning the O–B2-type stars to the spiral arms in the solar neighborhood (the Outer, Perseus, Local, and Carina Arms) based on their probabilities of being located in the referenced spiral arm, we fit the arm parameters ($R_{\rm ref}$ and $\psi$) using Eq. 2. The referenced azimuth, $\beta_{\rm ref}$, is arbitrarily set to zero when using the O–B2-type stars to fit the spiral arms. Since the structures indicated by the O–B2-type stars seem to be consistent with those inferred by the masers, we use the spiral arms traced by the masers as the initial reference. Afterward, we assign the O–B2-type stars to the fitted arms and repeat the above procedures until the fitted spiral arms converge. The best-fitting parameters of the masers and O–B2-type stars are listed in Table 2. Figure 3 presents the spiral arms depicted by the masers as well as the arm tangencies, and Figure 4 shows the spiral arms depicted by the O–B2-type stars.

The precise locations of the masers, O–B2-type stars, and YOCs have revealed the spiral structure of the MW. As shown in Figure 5, the Norma Arm traced by these masers passes the arm tangency at $l$ $\sim$ 30.6^∘ in the first Galactic quadrant. Due to a lack of masers and young stars in the fourth Galactic quadrant, we adopt a constant pitch angle to extend the Norma Arm outward and it passes through the arm tangency at $l$ $\sim$ 305.5^∘; the conjectural arm is depicted by the dotted line in Figure 5. There is an additional arm tangency at $l$ $\sim$ 311.5^∘ near the tangency of the Norma Arm (305.5^∘). Two adjacent tangencies are likely created by one spiral arm dividing into two spiral arms (Minniti et al., 2021). Therefore, near the direction of $l$ $\sim$ 310^∘–340^∘, the Norma Arm likely bifurcates out of the Centaurus Arm. Owing to a lack of high-precision data, the Centaurus Arm has been inferred by using the arm tangency at $l$ $\sim$ 311.5^∘, as depicted by the dotted line in Figure 5. After extending the Perseus Arm inward with a constant pitch angle, it naturally meets the arm tangency at $l$ $\sim$ 328.8^∘, which is symmetric with the Norma Arm, as shown by the dotted line in Figure 5. Employing the best-fitting pitch angle (see Table 2), the Sagittarius Arm is expected to intersect with the Perseus Arm in the direction of $l$ $\sim$ 10^∘–30^∘ and extend upwards passing the arm tangency at $l$ $\sim$ 49.3^∘. Around $l$ $\sim$ 10^∘–30^∘, in fact, the masers in the Sagittarius and Perseus Arms exhibit consistent trend in the $l$–$b$ and $l$–$v$ plots, which could provide support for the above intersection. To sum up, the Norma and Perseus Arms are likely the two symmetric arms in the inner MW. As they extend from the inner Galaxy to the outer parts, they bifurcate, and connect to the Centaurus and Sagittarius Arms, respectively.

In addition to the Perseus Arm, the masers also trace several other spiral arms in the outer Galaxy region, including the Outer, Local, Carina, and Sagittarius Arms. The Outer, Perseus, Local, and Carina Arms are confirmed by O–B2-type stars and YOCs, which also densify and complement the spiral arms depicted by the masers. In Figure 5, the spiral arms depicted by the O–B2-type stars have been indicated by black solid lines. The Local Arm has a propensity to bend down in the third quadrant and may extend forward. Due to a lack of data, we are currently unable to determine whether the Outer Arm is connected to one of the inner arms. As shown in Figure 5, the Carina Arm may be not connected to the Sagittarius Arm. Using masers and the arm tangency at $l$ $\sim$ 283.5^∘, we have depicted the Carina Arm and inferred its structure in the fourth quadrant, which is confirmed by the fitted result of the young objects in the Gaia data. On the whole, the spiral structure in the solar neighborhood traced by the multifarious young objects nearly agrees with the structure depicted by R19. Considering the inner two symmetric arms and several arm segments in the outer Galaxy regions, the MW should be considered as a multiple-arm spiral galaxy.

Previous studies have indicated that there are slight offsets between the spiral arms traced by objects of different ages (e.g., Vallée, 2014; Hou & Han, 2015). Indeed, as shown in Figure 5, there is a similar situation between the spiral arms drawn by masers and those by young objects; however, these differences are not expected to have an effect on the overall Galactic morphology determined in this work. The consistency of the spiral arms indicated by the various tracers also reinforces the validity of these arms. According to previous research on external galaxies, the pitch angle of a long spiral arm can be variable (Honig & Reid, 2015). Although a constant pitch angle is typically adopted to depict the Perseus Arm, if it is not constant, it is not likely to change the global structure of the MW when considering the widespread distribution of the masers related to the Perseus Arm.

In the solar neighborhood, the multiple spiral arms of the MW depicted by the masers, O–B2 stars, and YOCs are almost concordant with the results outlined by R19, and the young objects observed by Gaia densify and extend the spiral structure constructed by using the VLBI maser data alone. In the inner region of the Galaxy, R19 proposed that our Galaxy has four major spiral arms, namely the Norma, Scutum, Sagittarius, and Perseus Arms, while this work suggests that there are two major spiral arms, the Norma and Perseus Arms. Since the HMSFR masers assigned to the Norma and Scutum Arms in R19 are mixed together, these sources are considered as belonging to the same arm, i.e., the Norma Arm. After extending inward into the inner regions of the MW, the Sagittarius and Perseus Arms are expected to intersect in the direction of $l$ $\sim$ 10^∘–30^∘, instead of being two spiral arms separated from each other. Therefore, the Sagittarius Arm in this work is considered to be a bifurcation of the Perseus Arm.

Considering that the MW is a typical SBbc- or SBc-type galaxy (Binney & Tremaine, 2008), we select 185 external galaxies with morphologies identified as SBbc- and SBc-type from the SIMBAD database, and compare their morphologies with that of the MW. For more details, please see Appendix B. The properties of the sample of external MW-like galaxies, which contains 73 (40%) flocculent, 99 (54%) multiple-arm, 12 (6%) grand-design, and one unidentified case, have been visually inspected. For multiple-arm galaxies, we have also counted the number of their inner spiral arms, as shown in Figure 6. Statistically, only 2% of the multiple-arm galaxies have four inner arms. But relatively speaking, 83% of the multiple-arm galaxies clearly present two inner arms. As mentioned above, the MW galaxy likely has two inner symmetric arms and several arm segments in the outer regions, showing a multiple-arm morphology. So, in this case, the morphology of the MW is similar to those of most multiple-arm galaxies in the universe.

In most multiple-arm galaxies, there is usually a change in the appearance of the spirals midway out in the disk because of symmetric bifurcations or broadenings of the inner spiral arms. Generally, the inner spiral arms of a galaxy are considered to be within 0.5 $R_{25}$ or twice the radius of galactic bar, where $R_{25}$ is the radius at which the surface brightness is 25 mag arcsec^-2 (Elmegreen & Elmegreen, 1995). The $R_{25}$ value of the MW is about 11.5 kpc (de Vaucouleurs & Pence, 1978), and recent research has reported that the radius of the Galactic bar is $\sim$ 3.1 kpc (Hilmi et al., 2020). Since the nearly symmetric bifurcations of the inner two arms of the MW are situated at distances of 5.0–6.5 kpc from the GC, the features of the inner two arms of our Galaxy are concordant with the statistical patterns of external galaxies. Additionally, we find that the inner two arms of 73% of the external multiple-arm, barred galaxies start from the ends of the galactic bars. Because there are not enough young objects observed in the Galactocentric region, it is still not possible to determine whether or not the Norma and Perseus Arms start at the ends of the Galactic bar. The potential connections are depicted by chain lines in Figure 5.