Diagonal Ridge Pattern of Different Age Populations Found in Gaia-DR2 with LAMOST Main-sequence Turnoff and OB-type Stars

Galactic modeling requires the consideration of evolution and an asymmetric potential, as pointed out by Antoja et al. (2018), who have revealed in our Galaxy many intriguing signals such as snail shells, arches, and ridges, etc. The so-called Galactoseismology (Widrow et al. 2012, 2014) concludes the nonequilibrium and nonstationary potential of the Milky Way, observed in many density or velocity asymmetries in Liu et al. (2018), Wang et al. (2018a, 2018b, 2018c, 2019a, 2020a, 2020b, 2020c), Xu et al. (2015), Gaia Collaboration et al. (2018b), Carrillo et al. (2019), Trick et al. (2019), López-Corredoira & Sylos Labini (2019), López-Corredoira et al. (2020), and references therein, which are significant for us to understand the dynamical history of the Milky Way. There is no doubt we are entering into a golden era of Galactoseismology by embracing Gaia (Gaia Collaboration et al. 2018a) parallax and proper motions.

The inspiring snails and ridges imply that the disk is phase mixing from an out of equilibrium state (Antoja et al. 2018). Hence, quadrupole patterns and phase spirals at different Galactic positions have been revealed by Wang et al. (2019b), showing that external perturbations by the Sagittarius dwarf galaxy might be its dynamical origin. Time stamps have suggested that snails happened between 0.5 and 6 Gyr ago, thus leading to the consideration that young stars may have memory of the interstellar medium (Tian et al. 2018). Phase space snail shells in different cold and hot orbit distributions are also dissected in Li & Shen (2020). Unfortunately, these works using the LAMOST survey (Cui et al. 2012; Deng et al. 2012; Zhao et al. 2012; Liu et al. 2014) did not investigate more details for the intriguing ridges.

For the phase mixing patterns and structures, scenarios are mainly classified into two types: (1) the external perturbations (Minchev et al. 2009; Antoja et al. 2018; Binney & Schönrich 2018; Bland-Hawthorn et al. 2019; Craig et al. 2019; Laporte et al. 2019), e.g., the Sagittarius dwarf galaxy perturbation; (2) the internal dynamics (Quillen et al. 2018; Khoperskov et al. 2019; Monari et al. 2019; Barros et al. 2020), e.g., buckling of the stellar bar accompanied by bending waves without an external intruder.

Both the spiral arms and Sagittarius perturbation simulations for ridges are shown in Khanna et al. (2019). Outer Lindblad resonance of the bar could create the prominent ridges (Fragkoudi et al. 2019) and it could be used to compare with the ridge map in Kawata et al. (2018). Multiple ridges were also found in Hunt et al. (2018) with 2D transient spiral arms. Arches might be the projection of ridges in the V_R, V_ϕ plane (Antoja et al. 2018) and both are connected together (Ramos et al. 2018). Some recent works have also shown that the ridges could be produced by only internal mechanisms, such as spirals without external contributors (Michtchenko et al. 2019; Barros et al. 2020). So far, it is still too ambiguous for us to have a clear picture of the ridges, arches, and vertical waves, or of the origins or relations. And whether they are from internal or external or both mechanisms (e.g. Bland-Hawthorn & Tepper-Garcia 2020) is very unclear. In this work, we focus on the ridge pattern, tracing it in time stamps in a multidimensional parameter space, trying to get more details of its features and better constraining its origin. There are other recent works discussing the snails, but relatively fewer works focused on the ridge, and those do not include the time tagging analysis we present here.

The cornerstone Gaia-DR2 mission (Gaia Collaboration et al. 2018a) has already measured precise proper motions and distances for more than 1.3 billion stars. Gaia data in combination with the statistical distribution of stellar ages of millions of stars from LAMOST (Cui et al. 2012; Deng et al. 2012; Zhao et al. 2012; Liu et al. 2014) provide a good sample to study the ridge pattern, by which we can track the variation of the feature in different age populations from multiple perspectives and thus provide an unprecedented understanding of it.

This paper is organized as follows. In Section 2, we introduce how we select the main-sequence turnoff (MSTO) and OB stars sample and describe its properties concisely. The results and a discussion are presented in Section 3. Finally, we conclude this work in Section 4.

A sample of around 0.93 million MSTO stars with subgiant star contribution from the LAMOST Galactic spectroscopic surveys, including the disk region, Galactic anticenter region, etc., is selected based on the stars' positions in their locus in the T_eff − M_V plane. With the help of LAMOST DR4 spectra and the Kernel Principal Component Analysis method, accuracies of radial velocities reach 5 km s⁻¹. The ages are determined by matching with stellar isochrones using the Yonsei-Yale (Y2) isochrones and Bayesian algorithm with the help of T_eff, log g, [Fe/H], and [α/Fe] and the similar method of Jørgensen & Lindegren (2005). Interstellar extinction was derived using the star pairs method and the technique is able to determine E(B−V) to an accuracy of 0.01 mag (Yuan et al. 2015); distance estimates range between 10% and 30%. Overall, the sample stars have a median error of 34% for the age estimates and the typical uncertainties of the stellar parameters, such as T_eff, log g, [Fe/H], and [α/Fe], measured from the LAMOST data are 100 K, 0.1 dex, 0.1 dex, and 0.05 dex, respectively (Xiang et al. 2017a, 2017b, 2017c). The OB star selection is easily determined by spectral line index space in LAMOST and the distance here is from Gaia; more details can also be found in Liu et al. (2019) and the data were used to unravel some velocity asymmetries in Cheng et al. (2019).

The second data release of the Gaia mission with unprecedented high-precision proper motions with typical uncertainties of 0.05, 0.2, and 1.2 mas yr⁻¹ for stars with G-band magnitudes ≤14, 17, and 20 mag, respectively, has made it possible to map the Galaxy's kinematics and Galactoseismology with hitherto the largest spatial extent (Gaia Collaboration et al. 2016, 2018a).

3D velocities are derived by assuming the location of the Sun is R_⊙ = 8.34 kpc (Reid et al. 2014) and Z_⊙ = 27 pc (Chen et al. 2001); Tian et al. (2015) solar motion values are [U_⊙, V_⊙, W_⊙] = [9.58, 10.52, 7.01] km s⁻¹, and other solar motions (e.g., Huang et al. 2015) will not change our conclusion at all. The circular speed of the LSR is adopted as 238 km s⁻¹ (Schönrich 2012) and Cartesian coordinates on the basis of coordinate transformation described in Galpy (Bovy 2015). We use LAMOST distance for MSTO stars by absolute magnitude and extinction measurement and Gaia parallax or distance only for OB stars. López-Corredoira & Sylos Labini (2019) have tested zero-point bias in the parallaxes of Gaia-DR2; they suggested that the effect of the systematic error in the parallaxes is negligible during their work. We also do not think the small zero-point bias will affect our conclusion with similar tests to López-Corredoira & Sylos Labini (2019). Actually, our sample is within 4–5 kpc from the Sun and the parallax is larger than 0.2–0.25 mas. The small zero-point bias cannot change our conclusion.

We show the MSTO sample in Figure 1. It shows the T_eff versus log g distributions colored by age, we can see that most of the stars have surface gravity larger than 3, and younger stars have higher effective temperature than the old ones. Figure 2 shows the star count distribution in the R, Z plane. It shows that the number of northern stars is greater than that of southern stars with the calculations. In order to build a reliable sample containing stellar astrophysical parameters and precise kinematical information, we use criteria from the LAMOST spectroscopic survey and Gaia catalogs as follows:

• (1)  
  $| Z|$ < 1.5 kpc and 7.5 < R < 12 kpc;
• (2)  
  SNR > 20;
• (3)  
  age less than 14 Gyr and larger than 0;
• (4)  
  v_ϕ = [50, 350] km s⁻¹; and
• (5)  
  parallax > 0 and the relative error <0.20.

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3.1. Ridge Pattern Investigation for MSTO Stars

For this section, we investigate the ridge pattern in the different parameter space plots. We show in Figure 3 density (f), radial velocity (v_R), and vertical velocity (v_z) distributions in the plane of the rotational velocity in the y-axis and radial distance in the x-axis; the magenta dotted curves represent constant angular momentum of L_Z = (1650, 1800, 2080) kpc km s⁻¹ including the contribution of V_LSR (Schönrich 2012). The radial distance range displayed here is from 7.5 to 12 kpc. We can see that there are no clear ridge features for the density pattern due to the selection effects, sample precision, etc. However, the ridge pattern is very prominent and strong for the radial velocity distribution shown in the middle subfigures, shown as negative blue strips accompanied with positive red stripes, the patterns and trends of which are similar to some previous works, e.g., Khanna et al. (2019). In addition, it denotes clearly that the sensitive time of the inspiring ridge feature to the possible perturbation is 0–14 Gyr due to the fact that we could detect the ridge signals in the range of 0–14 Gyr.

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It is remarkable that the angular momentum per unit mass of the ridge pattern varies with age when compared with the constant magenta lines in radial velocity subfigures showing in the middle one. As we can see in the top panel of the middle of Figure 3, there are three magenta lines corresponding to the three ridges colored by blue and red strips. Here we define these three strips as ridge A, ridge B, and ridge C from the top to the bottom. For ridge A in the top, we can see when the age is less than 6 Gyr. The pattern could be matched with the constant angular momentum line for the general trend by focusing on the range of 9–10.5 kpc, but when we move forward with age larger than 6 Gyr, the ridge pattern, especially for the range of 9–10.5 kpc, is deviating the magenta lines with around 10 km s⁻¹ in all population bins. The corresponding errors are small and almost all of them are less than 2–4 km s⁻¹. For ridge B, the overall trend of the ridge pattern could be matched with the second magenta lines in all populations without significant deviations, implying that there is no significant variation compared with the constant angular momentum line. For ridge C, the minimum one, it is also matched with the third magenta lines well and has no clear variation like ridge A by focusing on the range of 9–10.5 kpc to guide our the eye. We suggest the relatively variable ridge A (τ > 6 versus τ < 6 Gyr) and relatively invariable ridge B, C are showing two kinds of ridges that possibly originated from different physical scenarios, which is helpful for us to unveil the origins of the ridge.

So there are two relatively stable ridges and one variable ridge from the current figures and in order to try to see this ridge variation clearly, according to Friske & Schöenrich (2019), in Figure 4 we also use the L_Z versus v_ϕ panel colored by v_R to investigate the ridge pattern. We can see that there are also three ridge patterns from the left to the right and colored by red, blue, and blue. These ridge patterns correspond to the three ridges of Figure 3. We can see that the left two ridges are relatively stable but the shift of the right ridge located around 2180 kpc km s⁻¹ of L_Z is detected, especially when the age is larger than 3 Gyr. Please note that here we use the 2180 but not the 2080 vertical line for L_Z due to the fact that the angular momentum must have larger errors than the radial distance with the contribution of velocity and distance errors for L_Z, so the pattern here has some differences from Figure 3, we use a relatively larger value for the right vertical magenta line in order to see the variable pattern in the right relatively clearly and try to match the pattern of Figure 3, which would not affect our conclusions. Friske & Schöenrich (2019) suggested that the L_Z shift of resonances with the age is expected, because of higher energy E (or action J) of the older stars. We also propose that the shift of the ridge again supports that there might have two kinds of ridges.

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When we keep going with the v_z pattern in the same plane, as shown in the right panel of Figure 3, what we could see is that weak ridge features are observed in the vertical motions especially around the bottom magenta line, although it is not as strong as radial velocity, which is also not as clear as the results of Khanna et al. (2019), showing a clear pattern in the vertical velocity distribution. The ridge stars in Khanna et al. (2019) mainly consist of midplane stars less than 0.2 kpc, which is different from our results here using stars less than 1.5 kpc (in order to get more stars and see the ridge pattern in v_R clearly). When we use similar but more stringent selection conditions, the sample is too small to see a very clear pattern like in Figure 3 due to the increasing Poisson noise and observational errors, etc.

Stars with all heights contribute to the ridge but in this case, the vertical information might be completely washed out (Khanna et al. 2019). We could test whether there is a possibility that the factors mentioned here and in the last paragraph might also affect the distribution of [Fe/H], [α/Fe], v_z. As shown in Figure 5, the [Fe/H], [α/Fe] (z = [−1.5 1.5] kpc), and v_z (z = [−0.2 0.2] kpc) distributions display that there are still weak ridge features in the metallicity and abundance, especially for the top panels in the left and middle figures. We have plotted red and blue strips in the range of 8–10 kpc and around 220 km s⁻¹. Other features are not so clear, but we could still detect some signals, e.g., the third row of the left panel and the second row of the middle panel. By using a narrow range of stars, we could detect a weaker signal around the bottom magenta line for the vertical distribution in the right panel of Figure 5.

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Summing up, in the v_ϕ, R plane for our sample, we see the well-known ridge pattern in radial velocity accompanied by the signals in the [Fe/H], [α/Fe], and v_z distributions, with the time tagging analysis not yet shown in previous works. They display observational evidence that the different ridges might have different angular momentum that is variable (or not) with time, which shows for the first time that there are possibly two types of ridges with different properties and origins.

3.2. Ridge Pattern Investigation by OB Stars

As mentioned in the last section, the ridge pattern has been sensitive to perturbation for 0–14 Gyr. In order to know more about its population features, we make full use of LAMOST's different samples. We use OB stars (Liu et al. 2019) to chart the distributions of density and radial velocity in the (R, v_ϕ) plane, which is displayed in Figure 6. It clearly denotes that there is an obvious ridge strip colored with blue on the right, especially for the radial velocity in the range of R from 9 to 11 kpc and v_ϕ from 170 to 200 km s⁻¹, the ridge is similar to one of the ridges in MSTO stars. As a mater of fact, the OB stars' ridges do not need to correspond to the MSTO ridges exactly due to the different population effects.

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3.3. Discussions

As manifested and implied in Wang et al. (2020b) and references therein, we suggest many mechanisms might be coupled together to cause the complex and abundant vertical asymmetries with bending and breathing modes accompanied with mean nonzero radial motions and asymmetrical rotations for the disk regions. All of these might be under the same comprehensive dynamical distribution function. In-plane asymmetries and vertical motions are coupled together as shown clearly in Antoja et al. (2018) and Khanna et al. (2019), but whether other different locations and populations are still coupling together is not clear. Antoja et al. (2018) used a relatively narrow range in the solar neighborhood to discover the snails in the z, v_z plane and arches, shells, and box in v_R, v_ϕ, v_z plane, thus then drew the coupling conclusion, but it is not clear for the ridges' coupling phenomenon in the R, v_ϕ plane corresponding to the larger distance range during that work. Furthermore, we might examine the details of the chemistry for ridges alone.

A relatively clear picture was proposed by Khanna et al. (2019), who made use of all stars of the GALAH southern sky survey, the test particle simulation, and the N-body simulation to explore the relations of ridges, arches, and vertical waves, which have differences for the sky coverage and tracers with us. Here we provide the ridge pattern sensitive time to the perturbations in our sample, and suggest the angular momentum variation of the ridge in different age populations and ridge distributions on the north and south sides in Figure 7, etc., by using the LAMOST sky survey and only MSTO and OB stars.

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Khanna et al. (2019) suggested that the ridges, arches, and vertical waves are coupled together, and they implied that the v_R are strongly correlated with each other and some signals are also detected in [Fe/H], [α/Fe], and v_z, which are consistent with our main results. Meanwhile, they also pointed out clearly that phase mixing of disrupting spiral arms can generate both the ridges and arches accompanied with the points that different ridges could have originated from different scenarios in theoretical view, but if they want to unify the coupling planar and vertical motions, an intermediate satellite like Sagittarius perturbation is favored. In this work, we detect that the angular momentum of one ridge pattern is relatively variable with age but the other two are relatively stable, displaying that the two kinds of ridges might have different origins and be accompanied by the vertical signals.

We have also finished a test in Figure 7. The heat maps of various quantities show the stars' radial velocity distribution in the (R, v_ϕ) plane in different age populations the whole sample (left), southern stars of the ridge (middle), and northern stars of the ridge (right). It appears that there are no clear north–south asymmetries shown here.

By investigating the origin of moving groups and diagonal ridges with the help of simulations of stellar orbits and birthplaces, Barros et al. (2020) pointed out that the diagonal ridges could have originated from the spiral resonances. There is no evidence of incomplete phase mixing in the vertical direction of the disk found in Michtchenko et al. (2019) and their results could be explained by internal mechanisms without external perturbations. Recently, Kushniruk et al. (2020) investigated the HR 1614 moving groups and proposed that several different mechanisms such as resonances of the bar, spiral structure, phase mixing of dissolving spiral structure, phase mixing due to an external perturbation should be combined to explain this feature. Laporte et al. (2020) have investigated the ridge and moving groups and found that the long bar could produce the ridge features qualitatively, meanwhile with the point that the internal and external mechanisms are shaping the Galactic disk. All these works need to explain the dependence of the ridge features on the stellar ages found in this paper. Our results provide additional constraints on the theoretical models, and encourage further theoretical studies to distinguish these scenarios based on the new observational constraints.

In this work, using LAMOST−Gaia combined stars, we clearly corroborate the existence of the ridge structure in the radial velocity distribution in the v_ϕ, R plane. More importantly, with the help of three ridge detailed analysis, evidence of the two kinds of ridge patterns possibly with different dynamical origins is first revealed. This is shown by the ridge angular momentum being relatively variable or not variable in different age populations. The two kinds of ridges are clearer in the v_R, L_Z plane, implying again that different ridges might have different physical scenarios. Moreover, the ridge patterns also show some features in [Fe/H], [α/Fe], v_z distributions.

We further investigate the kinematic analysis of the ridge pattern with different stellar ages, and find that the asymmetry is sensitive to the perturbations for 0–14 Gyr. With the help of younger populations of OB stars, we also detect ridge signals in radial velocity distribution. This is the first time stamps have worked on the ridge and different levels of sensitivity for different stellar populations in response to the possible dynamical perturbation are unveiled again in this work. These features are nontrivial and we will investigate them in more detail, e.g., we will go a farther distance, beyond 12 kpc, to characterize them in more dimensions, which is not the target of the current work.

We would like to thank the anonymous referee for very helpful and insightful comments. This work is supported by the National Key Basic R&D Program of China via 2019YFA0405500 and the National Natural Science Foundation of China via grants 11773009, 12003027. H.F.W. is supported by the LAMOST Fellow project and the National Natural Science Foundation of China via grant 12003027, funded by the China Postdoctoral Science Foundation via grants 2019M653504 and 2020T130563, the Yunnan Province Postdoctoral Directed Culture Foundation, and the Cultivation Project for LAMOST Scientific Payoff and Research Achievement of CAMS-CAS. M.L.C. was supported by grant PGC-2018-102249-B-100 of the Spanish Ministry of Economy and Competitiveness. Y.H. acknowledges the National Natural Science Foundation of China U1531244,11833006, 11811530289, U1731108, 11803029, and 11903027 and the Yunnan University grant Nos. C176220100006 and C176220100007. H.W.Z. is supported by the National Natural Science Foundation of China under grant No. 11973001. H.F.W. is fighting for the plan "Mapping the Milky Way Disk Population Structures and Galactoseismology (MWDPSG) with large sky surveys" in order to establish a theoretical framework in the future to unify the global picture of the disk structures and origins with a possible comprehensive distribution function. We pay our respects to elders, colleagues, and others for comments and suggestions; thanks to all of them. The Guo Shou Jing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, LAMOST) is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by National Astronomical Observatories, Chinese Academy of Sciences. This work has also made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular, the institutions participating in the Gaia Multilateral Agreement.