Ripple patterns in in-plane velocities of OB stars from LAMOST and Gaia

TL;DR

This study analyzes the 3D velocity distribution of about 12,000 OB stars in the Galactic disk, revealing ripple patterns in radial and azimuthal velocities that are not aligned with known spiral arms or induced by the central bar.

Contribution

First detailed mapping of OB star velocities across 6-15 kpc revealing non-axisymmetric ripple patterns unrelated to known spiral structures or the Galactic bar.

Findings

Ripple pattern in radial velocity reaches -8 km/s at 9 kpc

Azimuthal velocity shows similar ripple with phase difference

Outer ripple does not align with known spiral arms

Abstract

With about 12 000 OB type stars selected from the LAMOST and Gaia survey, we study their 3 dimensional velocity distribution over the range of galactocentric radius from 6 to 15 kpc in the Galactic disk plane. A clear ripple pattern in the radial velocity ($V_R$) map is shown. The median $V_R$ reaches $-8$ km s$^{-1}$ at $R\sim9$ kpc, then increases to $\sim0$ km s$^{-1}$ at $R\sim12$ kpc, and later declines to below $-10$ km s$^{-1}$ beyond $R\sim13$ kpc. The median azimuthal velocity ($V_\phi$) map shows a similar pattern but has roughly $1/4$ phase difference with the radial velocity. Although the ripple of negative $V_R$ at $\sim9$ kpc extends to about 40$^\circ$ in the azimuth angle, it does not align with either the Local or the Perseus spiral arm. Moreover, the farther ripple beyond 13 kpc does not match the Outer spiral arm either. This indicates that the non-axisymmetric kinematic features are not induced by perturbations of known spiral structures. The central rotating bar can not lead to such patterns in the outer disk either. External perturbation of a dwarf galaxy or a dark matter sub-halo can induce such patterns but requires more evidence from both observations and simulations. The $V_\phi$ map in the $Z$--$V_Z$ plane of the OB stars is also investigated. Despite asymmetry to some degree, no spiral pattern is found. This is reasonable since most of the OB stars have ages much younger than 100 Myrs, which is smaller than one orbital period around the Galactic center.

Figures

c](#S3.F3.sf3) and [Figure 4](#S3.F4) (green line). Unlike $\tilde{V}_{R}$, $\tilde{V}_{\phi}-V_{\rm LSR}$ shows three dips at around $X=7$, $11$ kpc and $>15$ kpc. We can conclude from [Figure 4](#S3.F4) that the ripple of $\tilde{V}_{\phi}-V_{\rm LSR}$ has roughly $1/4$ phase difference with the ripple of $\tilde{V}_{R}$. It clearly shows that the dip of $\tilde{V}_{\phi}-V_{\rm LSR}$ at $X\sim 11$ kpc is located between the dip of $\tilde{V}_{R}$ at $\sim 9$ kpc and the peak of $\tilde{V}_{R}$ at $\sim 12$ kpc. Meanwhile, the local peak of $\tilde{V}_{\phi}-V_{\rm LSR}$ at around $13$ kpc i

a](#S3.F5.sf1) shows the map of the median $\tilde{V}_{\phi}$ with subtraction of $V_{\rm LSR}$ in the $Z$–$V_{Z}$ plane for all OB stars, while [Figure 5b](#S3.F5.sf2) displays the similar map but only with stars in the same cylinder selected by Bland-Hawthorn et al. ([2018](#bib.bib7)). We see that $\tilde{V}_{\phi}-V_{\rm LSR}$ varies in the $Z$–$V_{Z}$ plane with amplitude of $4\sim 8$ km s*-1*. The lowest $\tilde{V}_{\phi}-V_{\rm LSR}$ ($-2\sim-4$ km/s) appears at ($Z\sim-0.25$ kpc, $\tilde{V}_{Z}$$\sim 0$ km s*-1*), and the highest values ($2\sim 4$ km s*-1*) appear at roughly the mirror

Equations

$$V_{\mathrm{ad}}=\sqrt{\frac{\gamma kT}{m}}=1.2\text{ km/s},$$

$$V_{\mathrm{iso}}=\sqrt{\frac{kT}{m}}=0.9\text{ km/s},$$

$${\tau }_{\mathrm{vertical}}=\frac{H_{\mathrm{vertical}}}{V_{\mathrm{sound}}}=\frac{150\text{ pc}}{1\text{ km/s}}\approx 150\text{ Myr}.$$

$${\tau }_{\mathrm{H}}=\frac{H_{\mathrm{r}}}{V_{\mathrm{sound}}}=\frac{3.15\text{ kpc}}{1\text{ km/s}}\approx 3.1\text{ Gyr}.$$

Full text

Galaxy: disk — Galaxy: kinematics and dynamics — Galaxy: structure

1 Introduction

Following Gaia DR2, the phase-mixing features in the $Z$–$V_{Z}$ phase space of the Milky Way was discovered (Antoja et al., 2018) and confirmed (Bland-Hawthorn et al., 2018; Tian et al., 2018). This is likely caused by the perturbation of a satellite galaxy passing through the Galactic disk. Antoja et al. (2018) suggests that the encounter with the dwarf galaxy happened between 300 and 900 Myrs ago, while Tian et al. (2018) and Bland-Hawthorn et al. (2018) favor that the event occurred $\sim 500$ Myrs ago.

The possible effect of interaction with satellite galaxies has been explored a long time ago (Edelsohn & Elmegreen, 1997). Since the discovery of the phase-mixing phenomenon, both toy-models and N-body simulations have been performed, and found that the external perturber may induce coupled effects in both vertical and in-plane directions (D’Onghia et al., 2016; Binney & Schönrich, 2018; Bland-Hawthorn et al., 2018).

In addition, non-axisymmetric features in the velocity and density distributions have also been explored. The radial velocity, $V_{R}$, asymmetry was firstly detected with stars from the Radial Velocity Experiment (RAVE) survey (Siebert et al., 2011), later confirmed with various stellar tracers from different surveys (Carlin et al., 2013; Sun et al., 2015a; Tian et al., 2017; Liu et al., 2018; Williams et al., 2013; Katz et al., 2018). Various theoretical explanations have been offered: perturbation by the central rotating bar (Fux, 2001; Tian et al., 2017; Liu et al., 2018), spiral arms (Siebert et al., 2012; Katz et al., 2018), or a merging satellite galaxy (Carlin et al., 2013).

Vertical density and velocity oscillations have also been extensively studied (e.g., Widrow et al. (2012); Xu et al. (2015); Wang et al. (2018b); Bennett & Bovy (2018); Carlin et al. (2013); Sun et al. (2015a); Wang et al. (2018a)). Theoretical explanations have been proposed, including the interaction with the Sagittarius (Gómez et al., 2013) and vertical perturbation by spiral structures (Nelson, 1976; Debattista, 2014; Faure et al., 2014).

It is noted that most previous studies are based on old stellar populations with age of at least $1$ Gyr. Investigating asymmetric kinematics in young populations can play an important role since they can reflect the perturbed kinematics of the gaseous disk. In this work we use OB stars, which have ages from a few million to a few tens of millions years, to explore asymmetric motions in the 3 dimensional velocity map beyond 6 kpc from the Sun in the Galactic plane.

The paper is organized as follows: the procedure for data selection and analysis is in Section 2, results and discussions are in Section 3, and conclusions are drawn in Section 4.

2 Data

The data are combined with parameters from two surveys, line-of-sight velocities from LAMOST DR5 (Zhao et al., 2012; Deng et al., 2012; Luo et al., 2015) and proper motions from the Gaia DR2 (Gaia Collaboration et al., 2016, 2018). We employed around 16 000 OB stars with spectral signal-to-noise ratio larger than 15 selected from LAMOST DR5 (Liu et al. submitted). The distance of these OB stars are derived by Bailer-Jones et al. (2018). To keep the reliability of the distances, we only use OB stars with relative distance uncertainty $\sigma_{d}/d<0.4$, in which $d$ and $\sigma_{d}$ are distance and its uncertainty. In fact, most stars have $0.07<\sigma_{d}/d<0.15$, which is considerably lower than the cut-off value ($0.4$).

Radial velocity was derived from $H\delta$ and $H\gamma$ absorption lines of the stellar spectra by using a forward model based on TLUSTY synthetic spectra library (Lanz & Hubeny, 2007) conducted by Liu et al. (in preparation). Given effective temperature, surface gravity, metallicity, radial velocity, and stellar rotation, this model can predict $H\delta$ and $H\gamma$ line profiles. The radial velocity and other stellar parameters of the spectrum in interest can be determined by comparing to the predicted lines. The typical uncertainty of radial velocity is $\sim 5$ km s*-1*.

The three velocity components in Galactocentric cylindrical coordinates, $V_{R}$, $V_{\phi}$, and $V_{Z}$, are calculated from the radial velocity, distance and proper motions adopting that the motion of the Sun with respect to the local standard of rest (LSR) is (9.58, 10.52, 7.01) km s*-1* (Tian et al., 2015) and the rotational speed of LSR at $V_{\rm LSR}=238$ km s*-1* (Reid et al., 2014).

Most OB stars are massive stars in the disk and as young as a few tens of millions years, whereas a few low-mass post-AGB and blue horizontal branch stars from the halo population are contaminations. It is not easy to distinguish them from low resolution spectra, but can be identified by locations and kinematics. We only select stars within $|Z|<1.0\text{ kpc}$ and with large enough angular momenta with respect to the $Z$-axis ($L_{z}$). Figure 1 shows the distribution of $L_{z}$. Only a small fraction of stars have low $L_{z}$, which may be from the thick disk or the halo. We thus empirically exclude stars with $L_{z}<1500$ km s*-1* kpc*-1*.

We arbitrarily select one spectrum for stars with multiple observations, and obtain 12 360 OB stars after the above selections. Their spatial distribution in the $X$–$Y$ plane is illustrated in Figure 2. The galactocentric coordinates are selected such that the Sun is at $X=8.34$ kpc and $Y=0$ kpc. The locations of spiral arms are from Reid et al. (2014) and Sun et al. (2015b). The number density is obtained using the adaptive probability density estimation method with a bi-weight kernel (Skuljan et al., 1999). For our sample, the optimal value for the smoothing parameter is $h=0.788$ kpc.

3 Results

3.1 Ripple patterns in velocity map

Figure 3(a), (c) and (e) respectively show the velocity fields of $\tilde{V}_{R}$, $\tilde{V}_{\phi}$ and $\tilde{V}_{Z}$ estimated with the same technique as for the number density, while panels (b), (d) and (f) show the uncertainties of the corresponding velocity fields estimated from bootstrapping. We arbitrarily selected 80% stars as a subsample and added corresponding Gaussian noise to their velocities. The adaptive probability density estimation was rebuilt for this subsample to derive the velocity fields. The process was repeated 1000 times, and the standard deviations at each point in the $X$–$Y$ plane are calculated and taken as uncertainties. Note that they are different from the velocity dispersions by definition.

We integrated the three velocity fields within $-2.5<Y<2.5$ kpc and plotted the average velocity with respect to $X$ in Figure 4 to better illustrate the radial variation of velocities. The uncertainties are estimated with the same methods as mentioned above.

3.1.1 Asymmetry in $V_{R}$

A few local ripple-like patterns are identified in the map of $\tilde{V}_{R}$ Figure 3a. That is, $\tilde{V}_{R}$ displays with two negative-velocity strips (blue) with a zero-value strip in between. At $X\sim 9$ kpc, $\tilde{V}_{R}$ declines to $\sim-8$ km/s, and increases back to $\sim 0$ at around $X=12$ kpc, and finally drops to below $-10$ km s*-1* when $X>15$ kpc. Both negative $\tilde{V}_{R}$ features are detected with a $>5\sigma$ confidence level according to the map of $\epsilon_{\tilde{V}_{R}}$ shown in Figure 3b. These features are better shown in Figure 4 with the red lines.

Compared to the spiral arms, the ripple patterns are not aligned with them in the $X$–$Y$ plane. The near negative $\tilde{V}_{R}$ strip overlaps with the local arm at ($X\sim 9$, $Y\sim 0$) kpc. It does not follow the arm to ($X=7.5$, $Y=3.5$) kpc, but extends along $X\sim 9$ kpc and overlaps with part of the Perseus arm at $Y\sim 3$ kpc. At $Y>3$ kpc, it goes beyond the Perseus arm. Similarly, the farther negative $\tilde{V}_{R}$ strip is located at larger radius than the Outer arm. In the bottom row of Figure 3, we tested the robustness of the ripple as a function of distance uncertainty. We cut the data with $\sigma_{d}/d<0.1$, 0.2, and 0.5. The 9 kpc $\tilde{V}_{R}$ strip exists in all three cases and show similar trend for the case with $\sigma_{d}/d<0.2$. This strongly indicates that the pattern is real.

The strip centered at $X=9$ kpc is consistent with previous discoveries (Siebert et al., 2011; Carlin et al., 2013; Tian et al., 2017; Liu et al., 2017b, 2018; Katz et al., 2018). Siebert et al. (2012) and Katz et al. (2018) suggested that this asymmetric radial velocity is produced by the perturbation of nearby spiral structures. Theoretical studies (Debattista, 2014; Faure et al., 2014) found that if this is the case, then the spatial distribution of the asymmetric $\tilde{V}_{R}$ should be naturally correlated with the coherent spiral structures. Therefore, the uncorrelated spatial distribution between the negative $\tilde{V}_{R}$ strip and the local or Perseus arm shows that the perturbation of the spiral arms is not the main driver of the ripples.

Compared to D’Onghia et al. (2016), we find the ripple patterns are similar to their simulations (see the top-right plot in their Figure 4), which demonstrate a perturbed disk by an interaction with a satellite.

Note that the strip at $X>15$ kpc approaches the regime that the parallax from Gaia is less precise. The larger uncertainties of parallax and the uncertainties of proper motions have been considered in the estimation of the uncertainty of $\tilde{V}_{R}$ shown in Figure 3b. According to this figure, the typical error of the median radial velocity at $X\sim 15$ kpc is around 3-4 km s*-1*. The smaller values of error are mostly due to two reasons. First, the radial velocity is mostly contributed by the line-of-sight velocity derived from the LAMOST spectra, which is independent of parallax. Second, the large number of OB stars detected reduces the uncertainty of the velocity, even though the typical error of the line-of-sight velocity is $\sim 5$ km s*-1*. Therefore, the strip shown at $X>15$ kpc is real. Similar to the strip displayed at $X\sim 9$ kpc, the misalignment of the farther strip with the Outer arm implies that the spiral arms are not responsible for the ripples.

3.1.2 Asymmetry in $\tilde{V}_{\phi}-V_{\rm LSR}$ and $\tilde{V}_{Z}$

Similar ripple patterns are also seen in $\tilde{V}_{\phi}-V_{\rm LSR}$, as shown in Figure 3c and Figure 4 (green line). Unlike $\tilde{V}_{R}$, $\tilde{V}_{\phi}-V_{\rm LSR}$ shows three dips at around $X=7$, $11$ kpc and $>15$ kpc. We can conclude from Figure 4 that the ripple of $\tilde{V}_{\phi}-V_{\rm LSR}$ has roughly $1/4$ phase difference with the ripple of $\tilde{V}_{R}$. It clearly shows that the dip of $\tilde{V}_{\phi}-V_{\rm LSR}$ at $X\sim 11$ kpc is located between the dip of $\tilde{V}_{R}$ at $\sim 9$ kpc and the peak of $\tilde{V}_{R}$ at $\sim 12$ kpc. Meanwhile, the local peak of $\tilde{V}_{\phi}-V_{\rm LSR}$ at around $13$ kpc is beyond the peak of $\tilde{V}_{R}$ located at $\sim 12$ kpc.

Indeed, if the disturber, internal (e.g. spiral structure) or external (e.g. a dwarf galaxy), introduces an in-plane gravitational force to the stars, the decomposition of the perturbation force along the radial and azimuthal direction would naturally induce additional radial and azimuthal motions with $1/4$ phase difference to the stars.

Liu et al. (2017b) showed a similar azimuthal velocity map with young stars. However, because their young F-type stars only covers less than 1 kpc around the Sun, they did not find that the velocity pattern is unrelated to the local arm at larger distance.

The ripple pattern is not clearly displayed in the distribution of the vertical velocity, but other interesting features are seen in the $\tilde{V}_{Z}$ map. A region with a relatively high upward motion ($>5$ km s*-1*) beyond $X=13$ kpc is discovered with $3\sim 5\sigma$ confidence level (see Figure 3e and more clearly in Figure 4).

Liu et al. (2017a) discovered similar vertical motion using red clump stars along the Galactic anti-center direction and attributed it to the Galactic warp. Poggio et al. (2018) reported a gradient of similar scale at 8-14 kpc. Furthermore, similar to their findings, the upward vertical velocity also shows a larger amplitude in the second quadrant of the disk plane, i.e. $Y>0$ in our coordinates. This implies that the line-of-node of the warp may be located in the third quadrant.

3.1.3 A substructure along $l=90^{\circ}$ ?

Beside the features discussed above, a suspected substructure is found in the velocity map along the Galactic longitude of $l=90^{\circ}$ beyond $Y>5$ kpc along the longitude. The OB stars in this region show \tilde{V}_{R}$$>+10 km s*-1*, \tilde{V}_{\phi}-V_{\rm LSR}$$<-15 km s*-1*, and \tilde{V}_{Z}$$<-5 km s*-1*. In other word, this group of stars is moving away from the Galactic center and downward to the south with slower azimuthal velocity. The feature is close to the edge of the detection of the sample. Therefore, it is not clear whether this is real.

3.2 Spiral feature in the phase space

Following Tian et al. (2018), who tried to find the spiral feature in the phase space for younger stars so that the time of the occurrence of the perturbation can be better constrained, we examine the distribution of $\tilde{V}_{\phi}$ in the $Z$–$V_{Z}$ phase space with our samples.

Figure 5a shows the map of the median $\tilde{V}_{\phi}$ with subtraction of $V_{\rm LSR}$ in the $Z$–$V_{Z}$ plane for all OB stars, while Figure 5b displays the similar map but only with stars in the same cylinder selected by Bland-Hawthorn et al. (2018). We see that $\tilde{V}_{\phi}-V_{\rm LSR}$ varies in the $Z$–$V_{Z}$ plane with amplitude of $4\sim 8$ km s*-1*. The lowest $\tilde{V}_{\phi}-V_{\rm LSR}$ ($-2\sim-4$ km/s) appears at ($Z\sim-0.25$ kpc, \tilde{V}_{Z}$$\sim 0 km s*-1*), and the highest values ($2\sim 4$ km s*-1*) appear at roughly the mirroring position of the lowest region with respect to $Z=0$. However, it does not show a clear spiral pattern as seen in other works. This is reasonable since the OB stars are too young to finish even one orbital period around the Galactic center.

4 Discussions and conclusions

It seems that the ripple patterns in the map of in-plane velocities is the result of a perturbation. In principle, the disturber could be classified as internal, such as spiral structures, giant molecular clouds or a central rotating bar, or external, such as pass-by dwarf galaxies or dark matter sub-halos. In the next paragraphs we attempt to briefly discuss these possibilities in turn.

As discussed in the previous section, it is clear that the ripple patterns shown in the map of $\tilde{V}_{R}$ and $\tilde{V}_{\phi}$ do not follow the present-day gaseous spiral arms. Thus, they are the result of perturbations induced by current spiral structures according to Siebert et al. (2012). However, it is noted that they assume a steady spiral structure in their simulation, while the origin of the spiral structures is far from clear (Baba et al., 2018; Tchernyshyov et al., 2018; Sellwood et al., 2018). Therefore, our results may not clearly exclude the perturbation of spiral arms originated from other mechanism but only rule out a steady density wave spiral structure.

Liu et al. (2018) revealed that a bar with pattern speed of 60 km s*-1* kpc*-1* is also capable of producing the dip in $\tilde{V}_{R}$ centered at $X\sim 9$ kpc through a test particle simulation, but could not produce the farther decline beyond $13$ kpc. Thus, the bar alone is not the reason.

Giant molecular clouds may also be potential disturbers and can induce spiral structures according to D’Onghia et al. (2013). However, this scenario can not be investigated until more simulations about how giant molecular clouds affect the stellar kinematics are performed.

Considering the external disturbers, many recent works in Section 1 argued that Sagittarius is one of the possible disturbers. However, it is unlikely that these OB stars were directly affected due to their young age. Instead, the encounter might affect the gaseous disk, which may eventually affect the orbits of the OB stars formed from it. As pointed out by Binney & Schönrich (2018) and Bland-Hawthorn et al. (2018), the pass-by satellite attracts the disk stars both in vertical and in-plane direction. The in-plane perturbation may raise complicated spiral structures with rich ripple-like in-plane velocities as seen in the simulation by Bland-Hawthorn et al. (2018) (See their Figure 25). Unlike the stellar disk, dissipation may play an important role in the gaseous disk.

As a qualitative estimate, the speed of sound can be used to obtain an approximate time timescale of dissipation. The cold neutral medium (CNM) has a typical temperature of $T=100\text{ K}$ and hydrogen inside is in atomic state (Ferrière, 2001). Thus, we can treat CNM as ideal gas and estimate the speed of sound in adiabatic and isothermal processes.

[TABLE]

[TABLE]

where $\gamma=5/3$ for hydrogen in atomic state, $k$ is the Boltzmann constant, and $m$ is the mass of the hydrogen atom. Thus, $V_{\rm sound}=1\text{ km/s}$ is a reasonable approximation for the speed of sound in the CNM.

The scale height of HI region at the position of the Sun is $\sim 0.15$ kpc (Kalberla & Kerp, 2009). Therefore, a vertical perturbation would dissipate in a time scale of

[TABLE]

Considering that the encounter was $\sim 500$ Myrs ago, it is possible that a great proportion of the vertical impact in the gaseous disk has been dissipated. This can explain the lack of spiral features in the vertical phase space shown in Figure 5a.

On the other hand, the in-plane perturbation due to the encountering satellite can induce spiral structures in the gaseous disk, similar to the stellar disk. However, due to dissipation of the gas, the spiral structures may be finally damped as mentioned in Section 6.4 of Binney & Tremaine (2008). A very rough estimate of the time scale of dissipation in the in-plane direction can be made using the size of the gaseous disk and the speed of sound. Considering the scale length of gaseous disk is $\sim 3.15$ kpc (Kalberla & Kerp, 2009), the timescale of dissipation can be approximated as

[TABLE]

This means that although a perturbation to the disk occurred a few hundred Myrs ago, the marks of the in-plane perturbation sculpted in the gaseous disk may later be inherited by the new born OB stars from these gas clouds.

An alternative scenario is that another dark matter sub-halo disturbed the disk a few tens of Myrs ago and imprinted the ripple pattern in these young stars. If this is the case, similar patterns should also be seen in relatively old stellar populations.

In summary, we explored the kinematic structure of the Milky Way galaxy with OB stars. While they do not show a clear indication of the phase-mixing spiral in the $Z$–$V_{Z}$ plane, we found clear ripple patterns in the in-plane map of $\tilde{V}_{R}$ and $\tilde{V}_{\phi}$. The roughly $1/4$ phase difference between the ripple features in $\tilde{V}_{R}$ and $\tilde{V}_{\phi}$ implies that these patterns should be a result of an in-plane perturbation. We considered a few possible disturbers, including internal and external origins, and find that neither of them can be the exclusive reason for the ripple structure, although perturbation of stationary spiral structures can be ruled out since the ripples are not aligned with the known spiral structures.

We appreciate the anonymous referee for his/her helpful suggestions which improved the paper. We thank Youjun Lu, Zhao-Yu Li, Juntai Shen, and Elena D’Onghia for helpful discussions and comments. This work is supported by the National Key Basic Research and Development Program of China No. 2018YFA0404501 and NFSC under grants 11821303, 11390372, 11761131004 (SM), 11333003 (CL and SM), 11873057 (CL) and 11773009 (WC). Guoshoujing 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 the National Astronomical Observatories, Chinese Academy of Sciences. This work has 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.