# The Flare and Warp of the Young Stellar Disk Traced with LAMOST DR5 OB-type Stars

Yang Yu, Hai-Feng Wang, Wen-Yuan Cui, Lin-Lin Li, Chao Liu, Bo Zhang, Hao Tian, Zhen-Yan Huo, Jie Ju, Zhi-Cun Liu, et al.

► To cite this version:

Yang Yu, Hai-Feng Wang, Wen-Yuan Cui, Lin-Lin Li, Chao Liu, et al. The Flare and Warp of the Young Stellar Disk Traced with LAMOST DR5 OB-type Stars. The Astrophysical Journal, 2021, 922, 10.3847/1538-4357/ac1e91. insu-03720851

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# The Flare and Warp of the Young Stellar Disk Traced with LAMOST DR5 OB-type Stars

Yang Yu (于扬)¹,², Hai-Feng Wang (王海峰)¹,³,⁴,⁵, Wen-Yuan Cui (崔文元)², Lin-Lin Li (李林林)², Chao Liu (刘超)⁵, Bo Zhang (章博)⁵,⁶, Hao Tian (田浩)⁵, Zhen-Yan Huo (霍振燕)², Jie Ju (巨洁)², Zhi-Cun Liu (柳志存)⁵, Fang Wen (温芳)², and Shuai Feng (冯帅)²

¹Equal first authors

²Department of Physics, Hebei Normal University, Shijiazhuang 050024, People's Republic of China; wenyuancui@126.com, cuiwenyuan@hebtu.edu.cn

³GEPI, Observatoire de Paris, Université PSL, CNRS, Place Jules Janssen F-92195, Meudon, France

⁴South-Western Institute for Astronomy Research, Yunnan University, Kunming, 650500, People's Republic of China

⁵National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, People's Republic of China

⁶Department of Astronomy, Beijing Normal University, Beijing, 100875, People's Republic of China

Received 2021 February 1; revised 2021 August 4; accepted 2021 August 16; published 2021 November 23

## Abstract

We present an analysis of the spatial density structure for the outer disk from 8–14 kpc with the LAMOST DR5 13,534 OB-type stars and observe similar flaring on the north and south sides of the disk, implying that the flaring structure is symmetrical about the Galactic plane, for which the scale height at different Galactocentric distances is from 0.14 to 0.5 kpc. By using the average slope to characterize the flaring strength, we find that the thickness of the OB stellar disk is similar but that flaring is slightly stronger compared to the thin disk as traced by red giant branch stars, possibly implying that secular evolution is not the main contributor to the flaring but rather perturbation scenarios such as interactions with passing dwarf galaxies could be possible. When comparing the scale height of the OB stellar disk on the north and south sides with the gas disk, the former one is slightly thicker than the latter one by ≈33 and 9 pc, meaning that one could tentatively use young OB-type stars to trace the gas properties. Meanwhile, we determine that the radial scale length of the young OB stellar disk is 1.17 ± 0.05 kpc, which is shorter than that of the gas disk, confirming that the gas disk is more extended than the stellar disk. What is more, by considering the midplane displacements ($Z_0$) in our density model we find that almost all values of $Z_0$ are within 100 pc, with an increasing trend as Galactocentric distance increases.

Unified Astronomy Thesaurus concepts: Milky Way disk (1050)

## 1. Introduction

Disk galaxy structure and origins are central problems in galaxy formation and evolution. Star counts are commonly used to explore the structure of a disk galaxy such as our home galaxy, the Milky Way (MW), and it also has proved to be a very effective tool in revealing structures and substructures such as flares, warps, truncations, spiral arms, etc.; therefore, star counts will push our understanding of the Galaxy's formation and evolution (van der Kruit & Freeman 2011; Bland-Hawthorn & Gerhard 2016). A dual exponential model is widely used to study the spatial structure of disk: one for the thin disk and the other one for the thick disk (Gilmore & Reid 1983; Jurić et al. 2008; Bovy et al. 2012; Rix & Bovy 2013; Bland-Hawthorn & Gerhard 2016; Bovy et al. 2016). An alternative form, that is, a *sech* function, is also often used in the vertical density profile model (van der Kruit 1988; van der Kruit & Freeman 2011; Wang et al. 2018b).

With the help of red giant branch (RGB) stars, Wang et al. (2018b) revealed that the Galactic disk radial profile is composed by three sections of an exponential law with the scale lengths of $2.12 \pm 0.26$, $1.18 \pm 0.08$, and $2.72$ kpc, respectively, at $R < 11$, $11 \le R \le 14$, and $R > 14$ kpc. Meanwhile, they also found the scale length of the thick disk is larger than that of the thin disk, and some density asymmetries might be explained, to some extent, by shifting either the midplane displacements of the thin or the thick disk. What is more, they also detected clear flaring features, i.e., the scale height increases with increasing distance, from 8 to 19 kpc.

Jurić et al. (2008) found that the scale length of the thin disk is shorter than that of the thick disk based on the Sloan Digital Sky Survey. Similar results were shown in Chen et al. (2017) by using photometric data from the Xuyi Schmidt Telescope Photometric Survey of the Galactic Anti-Centre and the Sloan Digital Sky Survey. However, Wan et al. (2017) suggested that the younger geometrical thin disk with an exponential scale length of 4.7 kpc is larger than the older thick disk with a scale length of 3.4 kpc of the exponential scale length with two components, which has been argued by Bovy et al. (2012) using mono-abundance population methods. The geometry definition mentioned in this work is based on the density profile (Martig et al. 2016).

The scale height of the thin disk is around 220–450 pc and that of the thick disk is between 700 and 1200 pc in the solar vicinity, as measured using either an exponential model or a *sech* function for the vertical component (Bland-Hawthorn & Gerhard 2016). As we move forward to larger Galactic distances, the value increases due to flaring effects; in another words, because the disk flares, the exponential scale height increases with increasing Galactocentric radius. Recently, with 250,000 OB stars from the Gaia (Gaia Collaboration et al. 2016) and 2MASS (Skrutskie et al. 2006) photometric catalogs, Li et al. (2019) showed that the scale length is $2.10 \pm 0.01$ kpc and scale height is 132–450 pc.

It appears that secular heating of the stellar disk caused by the scattering of the spiral structures (Sellwood & Carlberg 1984; Carlberg & Sellwood 1985) or giant molecular clouds (Jenkins & Binney 1990; Jenkins 1992) might cause the shorter scale
height of the younger populations compared to that of the older ones (Liu & van de Ven 2012; Yu & Liu 2017). The well-known flare was explained by the migration of stars (Solway et al. 2012); the larger vertical excursions due to the decreased gravitational pull in the outer disk can lead to the flaring (Bovy et al. 2016). An alternating explanation was dynamical heating (Quinn et al. 1993). However, as first proposed by Minchev et al. (2012), flaring by radial migration does happen, but the corresponding features are completely wiped out by mergers, as shown in Figure 2 of Minchev et al. (2014). Following by this work, Minchev et al. (2015, 2016, 2018) suggested that migration suppresses flaring in the presence of external perturbations in cold dark matter (CDM) cosmology (Quillen et al. 2009). This is in agreement with some other cosmological simulations, e.g., those of Grand et al. (2016), Ma et al. (2017).

As far as we know, there are two potential causes of the flaring in general: one is secular evolution, e.g., mentioned in the works of Minchev et al. (2012, 2014) and Narayan & Jog (2002), and the other is perturbation, e.g., by passing dwarf galaxies or satellites as denoted in Kazantzidis et al. (2008), Villalobos & Helmi (2008), Laporte et al. (2018), and so on.

There is almost a consensus that a warp exists in the MW, in the sense the disk bends upwards and downwards in the north and south hemisphere separately. The kinematical and spatial signals of the stellar warp as a function of radius and azimuth angle are shown in some works (López-Corredoira et al. 2014; Chen et al. 2019; Liu et al. 2017b). The dynamical signals of the warp corresponding to an increasing trend of vertical velocity with vertical angular momentum was displayed in Schönrich & Dehnen (2018) and Huang et al. (2018), and Wang et al. (2020a) also proposed that most likely the main S-shaped structure of the warp is a long-lived, unsteady feature.

According to our current understanding, it seems that previous studies of the structure of the disk tended to use older tracers for the reason that the number of old stars is quite large, especially for the outer disk, which makes it easier to describe the density distribution of the disk (e.g., López-Corredoira et al. 2002, López-Corredoira & Molgó 2014, Bovy et al. 2016, Wang et al. 2018b and reference therein). Up to now, we are still not sure of the exact flaring mechanisms and the detailed flaring features in the north and south stellar disk. Before the era of the Large Sky Area Multi-Object fiber Spectroscopic Telescope (LAMOST; also known as the Guo Shou Jing telescope) and Gaia, we could not get a large sample of OB stars due to some reasons such as sample purity, sampling rates of the disk region, precise distances, atmospheric parameters, line indices, high-precision photometry, and so on. In this work, we use young OB-type stars to explore the spatial structure of the young thin disk, which will help us to better understand the formation of the stellar disk.

The structure of this paper is as follows. In Section 2, we describe how we select OB-type stars and correct for the selection effects. In Section 3, we introduce the vertical star counts model for this work. In Section 4, we show the results for the flaring disk and discussions. Finally, we summarize this work in Section 5.

## 2. Sample and Selection Effects

### 2.1. The OB-type Stars Catalog

The LAMOST sky survey (Cui et al. 2012; Deng et al. 2012; Zhao et al. 2012) has observed a total of 4154 sky regions and

released 9,026,365 spectra in the phase I. The DR5 catalog includes spectral parameters of 5,348,712 stars with $T_{eff}$, log g, and [Fe/H]. Since 2018, LAMOST has been conducting the second 5 year survey with a medium resolution of 7500.

OB-type stars are composed of massive ($M > 8M_{⊙}$) stars, hot subdwarfs, white dwarfs, and post-AGB stars, etc. Among them, the massive stars have not moved out of their star-forming regions because of their short lives. Liu et al. (2019) identified 16,032 OB-type stars selected in spectral line indices space, including 22,901 spectra with signal-to-noise ratios larger than 15 in the g band, 948 hot subdwarf spectra, and 160 white dwarf spectra. The sample in this catalog has been tested by independent human eyes one by one, and thus has a high accuracy. The completeness for OB stars earlier than B7 contained in LAMOST DR5 is better than 89% ± 22%, and this sample is used here; it is by now the largest spectroscopic OB-type star sample. This sample has been used in Cheng et al. (2019) and Wang et al. (2020c) for studies of disk asymmetries.

We cross-match the OB-type star catalog with Gaia DR2 (Gaia Collaboration et al. 2018a) so that the distances of around 16,000 stars can be obtained. We suggest the small parallax zero-point bias will not affect our final conclusion due to the fact that our sample is mainly within 5 kpc of the Sun and the parallaxes are larger than 0.2 mas, so the small parallax zero-point bias of around 0.05 mas or even smaller cannot change our conclusion; the zero-point bias increases with distance for Gaia, but it is very small within 4–5 kpc (Gaia Collaboration et al. 2018b), which is our range. That said, we have already performed a test prove our conclusions are robust. The sky coverage and the number counts distributions of the sample we use in this work are denoted in Figure 1.

### 2.2. The OB-type Stars Selection Correction

We adopt the method to correct selection effects developed by Liu et al. (2017a), and it was tested with simulation data. This method has been used in several works based on LAMOST giant stars, e.g., Xu et al. (2018) and Wang et al. (2018b). Before applying the selection correction, we further clean the OB samples by adopting the criteria below:

1. Parallax/Parallax<sub>error</sub> > 2.5 and parallax > 0;

2. $J_{error}$, $K_{error}$ < 0.1 mag;

3. $K < 14.3$ mag;

After applying these criteria in consideration of the parameter accuracy and the limiting magnitude or the completeness of the photometric survey, there are 13,534 OB-type stars left for this analysis. Next, we assume that, at a given line of sight in Galactic coordinates (l, b) and a color–magnitude box, the probability finding a star at distance D in the LAMOST survey data should be roughly the same as in the photometric 2MASS (Skrutskie et al. 2006) data. Based on these assumptions and Bayesian theory, we could obtain a selection factor, and thus we could calculate the corrected density. Not only could this method be used in the study of spatial density, but it could also be used in the study of in mono-abundance population structures. Below, we briefly introduce the main principle to show how we correct for selection effects.

$$p_{ph}(D|J - K, K, l, b) = p_{sp}(D|J - K, K, l, b), \quad (1)$$

where $J - K$ and $K$ stand for the color index and $K_{s}$-band magnitude in 2MASS (Skrutskie et al. 2006), respectively.
<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>Figure 1. The top figure shows the normalized number counts distribution of OB-type stars without considering selection effects during this work. The bottom one is the sky coverage of our OB-type stars adopted from Liu et al. (2019). The area of the sky is mainly the Galactic anticenter direction; the sample is mainly in the range $l = [140^{\circ} 210^{\circ}]$, $b = [-3^{\circ} 5^{\circ}]$, with a relatively small contribution from other areas.</figcaption></figure>

Then, the stellar densities for the photometric data, $\nu_{ph}$, and for the spectroscopic data, $\nu_{sp}$, are associated with each other through

$$ \nu_{sp}(D|J-K, K, l, b) = \nu_{ph}(D|J-K, K, l, b)S(J-K, K, l, b), \quad (2) $$

where S represents the selection function of the spectroscopic data. The selection function can be determined by

$$ S(J - K, K, l, b) = \frac{n_{sp}(J - K, K, l, b)}{n_{ph}(J - K, K, l, b)}, \quad (3) $$

where $n_{sp}$ and $n_{ph}$ are the star counts of the spectroscopic and photometric data in the $J-K$ versus $K$ plane from 2MASS (Skrutskie et al. 2006), respectively. Then, we could obtain the corrected stellar density by combining the selection factor and the spectroscopic number density in the catalog.

Because the spectroscopic stars are usually very limited in a line of sight, and the uncertainty of distances to the stars cannot be ignored, a kernel density estimation (KDE) is applied to derive $\nu_{sp}$ along a line of sight, i.e.,

$$ \nu_{sp}(D|J - K, K, l, b) = \frac{1}{\Omega D^2} \sum_{i}^{n_{sp}(J - K, K, l, b)} p_i(D), \quad (4) $$

where $p_i(D)$ is the probability density function of $D$ for the $i$th star.

In general, $D$ is the distance from the Sun, and we normalize the probability for $D$ along the line of sight from 0 to infinity. The uncertainty of this method is about 25% including an extinction contribution. The size of each bin for star counts is $\Delta(J-K) = 0.1$ and $\Delta K = 0.25$, and the $J-K$ versus $K$ plane is from 2MASS. Please see more details about this method in our previous papers (Wan et al. 2017; Liu et al. 2017a, 2018; Wang et al. 2018b).

### 3. Star Counts Model

In this section, we will introduce how we construct the density model of the disk used in this work. The Galactic disk mainly consists of two components, a thin and thick disk (Gilmore & Reid 1983). However, the OB-type stars in our sample are all young stars with lower galactic latitudes. Therefore, they really cannot contribute to the old thick disk, so we choose to use only a single exponential vertical profile. Wang et al. (2018b) used the nonparametric method of normalizing the radial density part into the midplane density, thus allowing them to simplify the 2D density plane to a 1D density slice and to reveal that the outer disk is more complex than previously thought. In this work, we use a similar method, but we consider the north and south sides separately and introduce the midplane displacement $Z_0$ as an additional free parameter. Then, we slice the OB-type star sample into bins along the direction of the Galactocentric distance $R$, which are centered at $R = 8.5, 9.5, 10.5, 11.5, 12.5$, and $13.5$ kpc. The width of each bin is 1 kpc, based on consideration of the sampling rates and Poisson noise.

We use a normalized exponential model to fit the stellar density distribution assuming north-south vertical symmetry as follows:

$$ \nu(Z|R) = \begin{cases} \nu_0(R)e^{-\frac{(Z-Z_0)}{h_n(R)}} & Z > Z_0 \\ \nu_0(R)e^{-\frac{(Z-Z_0)}{h_s(R)}} & Z < Z_0 \end{cases}. \quad (5) $$

Here, $\nu_0(R)$ is the total volume density when $Z = Z_0$, $h_n(R)$ is the scale height on the north side of the young disk, $h_s(R)$ is the scale height on the south side of the disk, and $Z_0(R)$ is the true midplane displacement. We assume $Z = Z_0$ is a free parameter in the data and the sample is separated by $b = 0$ or $Z = 0$ due to the fact that we do not know the true value of the midplane displacement and we want to explore it using our method. This way, we can explore the scale height of the north and south and the true midplane $Z_0$ simultaneously. And up to now, we are also not sure of the $Z = Z_0$ value at different distances, and it is not clear whether the scale heights of the north and south sides of the disk are similar or not. In order to derive all of the unknown parameters at each $R$ bin, we first set up the histogram of the mean vertical stellar density along the $Z$ grid. Then, we sample the likelihood distribution as:

$$ \mathcal{L}(\{\nu_{\text{obs}}(Z_i|R)\} | \nu_0, h_n, h_s, Z_0) = \prod_i \exp \left[ -\frac{1}{2}(\nu_{\text{obs}}(Z_i|R) - \nu_{\text{model}}(Z_i|R, \nu_0, h_n, h_s, Z_0))^2 \right]. \quad (6) $$

Here, $Z_i$ is the $i$th point of the $Z$ grid, $\nu_{\text{obs}}$ is the stellar density calculated from the observation, $\nu_{\text{model}}$ is the stellar density of the theoretical model, and the corresponding errors
<table><caption>**Table 1**
Best-fitting Parameters of Different *R* Bins with Vertical Density Distribution Models</caption><thead><tr><th><i>R</i> (kpc)<br>(1)</th><th>ln<i>ν</i><sub>0</sub>(kpc<sup>-3</sup>)<br>(2)</th><th><i>h</i><sub>n</sub> (kpc)<br>(3)</th><th><i>h</i><sub>s</sub> (kpc)<br>(4)</th><th><i>Z</i><sub>0</sub> (kpc)<br>(5)</th></tr></thead><tbody><tr><td>8 &lt; <i>R</i> &lt; 9</td><td>6.72 ± 0.009</td><td>0.22 ± 0.002</td><td>0.14 ± 0.001</td><td>-0.08 ± 0.002</td></tr><tr><td>9 &lt; <i>R</i> &lt; 10</td><td>6.011 ± 0.005</td><td>0.20 ± 0.001</td><td>0.15 ± 0.001</td><td>0.01 ± 0.001</td></tr><tr><td>10 &lt; <i>R</i> &lt; 11</td><td>5.03 ± 0.009</td><td>0.17 ± 0.002</td><td>0.17 ± 0.002</td><td>0.02 ± 0.001</td></tr><tr><td>11 &lt; <i>R</i> &lt; 12</td><td>3.87 ± 0.018</td><td>0.23 ± 0.003</td><td>0.20 ± 0.005</td><td>0.03 ± 0.004</td></tr><tr><td>12 &lt; <i>R</i> &lt; 13</td><td>3.17 ± 0.040</td><td>0.30 ± 0.011</td><td>0.30 ± 0.023</td><td>0.08 ± 0.013</td></tr><tr><td>13 &lt; <i>R</i> &lt; 14</td><td>2.24 ± 0.100</td><td>0.45 ± 0.062</td><td>0.50 ± 0.126</td><td>0.09 ± 0.045</td></tr></tbody></table>

are calculated by a bootstrap method. We have four free parameters in the fitting process: ln($\nu_0(R)$), $h_n(R)$, $h_s(R)$, and $Z_0(R)$.

## 4. Results and Discussions

The Markov Chain Monte Carlo (MCMC) method provided by emcee (Foreman-Mackey et al. 2013) is used for sampling the likelihood distribution. The best-fitting value of the free parameters is selected as the peak of the likelihood distribution, and the estimated uncertainty is determined by the values of the 15th and 85th percentiles of the likelihood distribution. The MCMC fitting results are shown in Table 1, which lists the four best-fitting parameters at different *R* bins. As an example, we show the likelihood distribution of the parameters for 8–9 kpc and the fitting results of the model and data in Figure 2.

### 4.1. The North–South Flaring Disk Compared with the Stellar Disk

The scale height of the young stellar disk is shown in Figure 3. As we can see, the north and south scale heights of the young stellar disk increase from 0.14 to 0.5 kpc in the range of 8–14 kpc; this is a clear flaring signature, so we can say we detect the features of flaring in the young stellar disk. In addition it is shown that the pattern of the north and south disk is similar or just slightly different: the average difference of the scale height in the north and south is 19 pc, and there is not a large difference between the slopes of both sides, suggesting that the flaring of the disk might be symmetrical. In this work, we use the average slope of the scale height versus distance to describe the flaring strength, which has been used in Wan et al. (2017).

Previous works are also compared in the figure, and we can see that the thickness of the young stellar disk is similar to or only slightly different from that of the thin disk traced by RGB stars in Wang et al. (2018b). The clear differences between the young stellar disk of OB stars and the thin disk or disk distribution of López-Corredoira et al. (2002) and López-Corredoira & Molgó (2014) are also displayed here. The reason for the difference could be, naturally, that different populations and methods are used in these works; e.g., here, we use the young OB-type stars and a nonparametric method, while López-Corredoira et al. (2002) used photometric red clump stars without considering the two components of the disk, and López-Corredoira & Molgó (2014) adopted the F8V–G5V stars to study changes of the scale heights of the thin and thick disks with different methods. Importantly, we detect the almost symmetrical flaring signature in the young stellar disk of the OB sample, and it is similar to or even slightly stronger than that of the old stellar thin disk traced by RGB samples. Please also notice that our OB-star sample is distributed in the

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 2.** The top panel shows the likelihood distribution of the parameters (ln($\nu_0$); (kpc$^{-3}$), $h_z$ (kpc), and $Z_0$ (kpc)) for 8–9 kpc, drawn from the MCMC simulation. The uncertainties in the estimates are determined using the 15th and 85th percentiles of the MCMC samples. The bottom panel shows the fitting results and relative errors of the model and data. It appears that there are some oscillations in the solar neighborhood.</figcaption></figure>

Galactic anticenter, and we just use the projection distance, that is to say, *R* and *Z*, and the comparison data in Figure 3 originate from roughly the same regions, mainly from the north hemisphere. There are some clearly different regions for the
<figure><img src="image_7.png" /></figure>

**Figure 3.** The figure shows the scale-height distribution of OB-type stars and other tracers as a function of radial distance. The red pentagrams represent the northern OB-type stars, and the black pentagrams is the southern OB-type stars. The green triangles show the thin disk scale height of Wang et al. (2018b), and the green rectangles show the thick disk scale height of Wang et al. (2018b). Brown and blue lines are the thin disk and thick disk of López-Corredoira & Molgó (2014), respectively. The yellow line shows the results of López-Corredoira et al. (2002). These data compared here originate from the same regions, and the average slopes describing the strength of the flaring are labeled in the bottom left, with different colors corresponding to different results.

gas disk, but we can still compare the disk scale length and
scale height.

## 4.2. The North–South Flaring Disk $h_z$ Compared With the Gas Disk

The scale height of the young stellar disk compared with the H I and H₂ gas disk of Kalberla et al. (2007) and Nakanishi & Sofue et al. (2006) is shown in Figure 4. For the Nakanishi & Sofue et al. (2006) sample, the data mainly cover $b = [-1.5, 1.5]$ and $l = [0°, 90°, 270°, 360°]$, and the Kalberla et al. (2007) sample covers an all-sky disk region by discarding $b > 30°$ and Galactic distance $R = [-3.5, 3.5]$ kpc. It is shown that the young stellar disk, in an overall trend, is slightly thicker than the gas disk, but it is not significantly different in terms of scale height, which is expected since we declare that OB-type stars can be used to trace gas properties and dynamics, and this will be shown in our series of works. The OB-type stars are very young and have not moved out of their star formation areas, so there is no doubt that the structure shown by the OB-type stars has inherited some properties of the gas clouds that are forming stars. We also find that the H I disk is different from the H₂ disk, due to a temperature difference, possibly. The distances of our OB stars are from Gaia; the extinction is very small, and the Gaia distances are precise within 8–14 kpc. If we agree there is some influence on our results caused by extinction and not-perfect selection effects, then the error bars will be enlarged and thus the true differences will possibly be reduced. This strengthens our points to some extent; that is, we can use OB stars to infer some properties of the gas disk.

The most important tracer for molecular gas in galaxies is the CO spin line of different isotopes, especially the 2.6 mm line of CO. High-sensitivity CO observations are essential for describing the structure of the disk in galaxies, and sometimes we also choose to convert CO to H₂. In Sun et al. (2019), they also confirmed the gas thin disk (FHWM ≈90 pc) and revealed the gas thick disk scale height was around 280 pc, consistent

<figure><img src="image_8.png" /></figure>

**Figure 4.** The figure shows the OB-type star scale height distribution compared with the gas disk as a function of the radial distance. The red line is the north-side scale height, and the black line is the southern scale height. The green line is the Kalberla et al. (2007) southern scale height of the H I gas disk, while the blue rectangles and pentagram are also the Kalberla et al. (2007) northern H I thickness distribution. Yellow pentagrams correspond to the H₂ results in Nakanishi & Sofue et al. (2006). The average slope of the scale height ($h_z$) versus distance ($R$) describing the strength of flaring is labeled in the bottom left.

with the H I gas disk scale height (250–300 pc). They also pointed out molecular gas properties might be related to massive star evolution, which supports our point that the gas disk properties could be inherited by the young OB-type stars, so the young stellar disk can be compared with the gas disk to investigate more intriguing details. Recently, Su et al. (2021) found that the molecular gas disk has two components, a gas thin disk and thick disk, with scale heights of 85 and 280 pc in the region of $l$ from 16° to 52° and $b$ from −5°1 to 5.°1, respectively. These values are within our range for the OB stellar disk. We will discuss this further later in the paper.

## 4.3. The Scale Length of the OB-type Stellar Disk Compared with the Gas Disk

The stellar density of the disk, general speaking, is exponentially distributed in the radial direction and gradually decreases with increasing distance. We fit the logarithm of the stellar density in the direction of the anticenter belonging to the radial range of $R = 8–14$ kpc. The scale length of the OB-type stars is $1.17 \pm 0.05$ kpc, and the comparison with previous works studying the H₂ gas disk (which have been converted from CO data; Dame et al. 1987; Bronfman et al. 1988; Digel 1991; Nakanishi & Sofue et al. 2006; Pohl et al. 2008) is shown in Figure 5. It should be pointed out that, for the gas density, we directly use the data points from other works in the literature. Some works give the number density in units of $cm^{-3}$ and this gas density is often calculated by dividing column density by radius size; however, here we have actually used the surface mass density ($M_\odot pc^{-2}$), which is also suitable for comparisons of the scale length. In order to compare with stellar disk in one figure, the gas density value and the stellar density value of Wang et al. (2018b) are shifted up in the y-axis. It shows that the young stellar disk scale length is shorter than that of the gas disk when comparing the values labeled in the figure, except for the work of Bronfman et al. (1988) with only three points in a narrower range. These other studies imply that generally the gas disk is more extended than the stellar
<figure><img src="image_9.png" /><figcaption>**Figure 5.** The figure shows the midplane density distribution as a function of distance. The linear fitting results are shown as dashed lines with different colors; the scale lengths of different works for the H₂ gas disk (Dame et al. 1987; Bronfman et al. 1988; Digel 1991; Nakanishi & Sofue et al. 2006; Pohl et al. 2008) are labeled in the bottom left, and the H₂ value is converted from CO (Heyer & Dame 2015). The left y-axis corresponds to the stellar disk and the right axis is the gas surface density. The gas density is adjusted by shifting up 5.5, and the Wang et al. (2018b) values are shifted up 10 in order to compare in one figure.</figcaption></figure>

disk. We may also deduce from here that the stellar disk might be more compact, similar to the hot dust distribution, than the gas and cold dust disk. For the gas disk region mentioned in this part, the range of Dame et al. (1987) is covered by 10°–20° in latitude at all longitudes and includes all or nearly all large, nearby clouds at higher latitudes. Latitudes from –2° to 2° and longitudes from 300° to 348° correspond to the region of the Bronfman et al. (1988) sample, but we only use the north data beyond 8 kpc. Based on smoothed particle hydrodynamical simulations and the compiled data (Dame et al. 2001), Pohl et al. (2008) made full use of the CO survey, which covered a total area of 9353 deg², more than one-fifth of the entire sky and nearly one-half of the area within 30° of the Galactic plane. Digel (1991) used data located in the outer Galaxy within the disk region with $l = [65°, 116°]$. Here, the H₂ gas surface density is converted from CO surveys using uniform assumptions regarding the Galactic rotation curve, solar radius, and the CO-to-H₂ conversion factor; all of these data are from the review of Heyer & Dame (2015).

In addition, we notice that the scale length of the OB-type stellar disk here is different from the results given by Li et al. (2019): it is 2.10 ± 0.01 kpc, and the scale height is 132–450 pc. Both are morphological or geometrical definitions, and we suggest the difference is due to the fact that Li et al. (2019) used Gaia DR2 and 2MASS photometric data, which must include both the early-type and late-type OB stars. What we want to emphasize here is that our sample lacks late-type stars and mainly consists of early-type stars as a result of the selection methods, so the scale lengths from these two works have some differences.

### 4.4. The Midplane Displacements of the Disk

The gas warp was detected as shown in Kerr (1957), Bosma (1981), and Briggs et al. (1990). Recently, with the help of classical Cepheids, Chen et al. (2019) have revealed an intuitive three-dimensional (3D) map of the stellar warp by made using star counts methods; it covers all of the sky out to

<figure><img src="image_10.png" /><figcaption>**Figure 6.** The figure displays the midplane displacement distribution as a function of R. Almost all values are within 100 pc, and the slope shown in the bottom left is 0.020. Please notice that the slope is just for a quantitative analysis, and is different from the flaring strength.</figcaption></figure>

20 kpc. Meanwhile, Skowron et al. (2019a, 2019b) have also showed us number density stellar warp signals in different distances and azimuthal angles located in the northern and southern sky and declared that the amplitude of the northern part of the warp is very prominent and stronger than that of the southern part. What is more, the kinematical and height signal of the stellar warp and the origins of gas infall have been also unraveled in Wang et al. (2020c) with the help of a sample mainly from the LAMOST Galactic anticenter in the northern hemisphere. Another study of warp signals with different tracers and methods can also be found in Poggio et al. (2018), who used a Gaia sample mainly on the north side. Poggio et al. (2020) then used an all-sky Gaia sample of 12 million giant stars to detect the warp precession for the first time. However, Chrobáková & López-Corredoira (2021) recently recalculated the warp precession and found that there is no need for a precession. They used different warp parameters but the same approach and Gaia DR2 kinematic data.

In this work, we introduce the midplane displacement ($Z_0$) to Equations (5) and (6) to do the decomposition and fit the OB-type stars in radial slices displayed in Figure 6. Intriguingly, we find that the midplane displacements exist and different locations have different $Z_0$ values, but almost all are within 100 pc, with the value approximately equal to 0 around the solar location in the range of 8–9 kpc.

More importantly, we find the offset increases with distance and infer that there is a possibility it might reflect suspected signals such as the warp here. If it is true, we can say this work detects a similar warp signal in the young stellar population and that the warp should happen at an early time. However, this evidence is from only one figure, and we cannot rule out other possibilities due to the limited range of the sample and other possible perturbations. In short, the pattern might be caused by the warp, or perhaps it is caused by the heating of some perturbations that are different from warp dynamical mechanisms; sometimes we actually cannot determine whether the vertical signal is from a warp, or external perturbations (Wang et al. 2020a, 2020b), or other unknown causes, but this is also not the main target of this paper. Please notice that the zero-point bias might affect the exact value here, but it will not change the pattern shown in this work. The significance of the signal needs to be investigated more in the future, but we do
not want to rule out some possibilities here; our motivation is to
study the flaring.

By using a similar method introduced in Xu et al. (2015),
Wang et al. (2018b) proposed that some disk oscillations are
very complicated but could still be explained, to some extent,
by a shifting of either the thin or the thick disk. So, in this
work, we consider that a shift in the young stellar disk is
reasonable and the value of the midplane displacement (Z₀) is
also not strange at all. In general, our midplane shifting pattern
is actually similar to that in Figure 5 of the recent work by Xu
et al. (2020) based on the kinematics method.

4.5. Discussions

4.5.1. Comparisons to the Disk without the North and South Sides

In order to test the effect of the method including a decom-
position of the north and south sides, we have made a
comparison of the features of the north and south disk scale
heights to the values found without considering separate north
and south sides. As shown in Figure 7, the scale heights, scale
lengths, and midplane offsets are compared from the top to the
bottom. For the scale heights, there are no large differences and
the general pattern is the same. Similarly, the midplane offsets
also show the same trend but with some differences. Interest-
ingly, the midplane density and the scale length are matched
very well. All of these comparisons show that our method using
north and south sides will not change our main conclusion for
this work, especially regarding the flaring.

By combining all stars in the range 8–14 kpc without radial
slices, we have also performed the fitting results for the young
stellar disk. The scale height of the young stellar disk is
0.16 kpc and the midplane offset of the disk is 11 pc; the fitting
results are quite well determined and shown by us in Figure 8.

4.5.2. Possible Scenarios for the Flaring

With the release of Gaia DR2 data, Antoja et al. (2018) found
phase mixing features of the MW disk, possibly due to the
disturbance caused by the vibration of the dwarf galaxy passing
through the disk 300–900 Myr ago. The lifetime of OB stars is
mostly <100 Myr, and the gas disk forming the OB-type star
could possibly be disturbed by the dwarf galaxy such that some
imprints might be inherited by the OB-type stars (Cheng et al.
2019). Cheng et al. (2019) also introduced two types of
interference sources: first, internal disturbances such as spiral
structures, huge molecular clouds, or central rods; second, external
disturbances such as a dwarf galaxy or satellites passing through
the MW. In addition to the aforementioned disturbances, Cheng
et al. (2019) proposed another case: a few megayears ago, the dark
matter subhalo perturbed the disk and left marks on these young
stars. Similar perturbation scenarios to the disk such as a warp,
stream, satellites, dwarf galaxies, or dark matter subhalos are also
mentioned in Wang et al. (2018a, 2019, 2020a, 2020c), Khanna
et al. (2019), Bland-Hawthorn et al. (2019), López-Corredoira
et al. (2020), and Xu et al. (2020) and reference therein.

Flaring is possibly related to disk heating, and there are
many mechanisms proposed in the past several years. For
example, spiral arms could be an important contributor to the
in-plane motions, but without influencing the vertical motions
(Sellwood & Carlberg 1984; Sellwood 2013). Giant molecular

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

**Figure 7.** Comparison of the disk parameters determined using the north and south sides to values found without considering the scale heights of the north and south sides simultaneously, which are indicated by red or black pentagrams and green squares, respectively. The top panel shows the scale height, and the middle one shows the midplane density, with the slope of the scale height and scale length versus the distance labeled. The bottom panel shows the midplane offsets with the slopes labeled; clearly, the pattern is stable.
<figure><img src="image_14.png" /><figcaption>**Figure 8.** The panel shows the likelihood distribution of the parameters ($\ln(\nu_0)$; ($kpc^{-3}$), $h_z$ (pc), $Z_0$ (kpc)) for 8–14 kpc data drawn from the MCMC simulation without considering north and south sides simultaneously. The uncertainties in the estimates are determined using the 15th and 85th percentiles of the MCMC samples.</figcaption></figure>

clouds (GMCs) could heat the disk and redirect the velocity of stars out of the plane (Lacey 1984). The bar might not be important beyond the solar neighborhood, but cannot be ignorable in the inner bulge region (Moetazedian & Just 2016). Migration might heat the disk and contribute to the flaring, which was mentioned in recent work (Bovy et al. 2016), but the different scenarios proposed by Minchev et al. (2012, 2018) suggest that migration is not important for heating and flaring. External perturbations such as a dwarf galaxy can heat the disk (House et al. 2011) and can be the mechanism for the flaring (Kazantzidis et al. 2008); in addition, mergers and perturbations from satellite galaxies and subhalos can induce radial mixing in the outer disk (Quillen et al. 2009). For our work, we focus on the average slope of the scale height versus distance which is used to describe the strength of the flaring features in different populations. Then, we can attempt to infer which mechanism of the flaring is more important. We agree that the different heating mechanisms can affect the thickness of the disk differently, but distinguishing them is not a target of our paper; hopefully in the future we can combine kinematics and star counts to investigate more details about this intriguing question.

Here again, as we mentioned in the introduction, we attempt to classify the mechanisms of the flaring into two types: one is the secular evolution of the disk, for which we expect the younger population to have a weaker flaring strength than the older population, and the other one could be perturbations caused by many agents, for which we do not expect any effect on the flaring strength with age. Against this general background, we can then discuss which mechanism is more important; we also know the physical details may be more complicated, and we are not planning to rule out other physical scenarios from the current analysis.

Therefore, from the current results, we clearly detect that the flaring strength of the young OB stellar population is similar to

or even slightly stronger than that of the old RGB population. This is found by focusing on the thin disk by using the slope of the scale height versus distance to describe the strength of the flaring. The average value of the slope is 0.042 (northern OB stars) versus 0.065 (southern OB stars) versus 0.020 (RGB stars), and the qualitative conclusion is similar to that of Wang et al. (2018b): they also found the flaring strength of red clump giant stars is similar to the RGB pattern for the thin disk. By comparing the flaring strengths of the thin disk and thick disk, both Wan et al. (2017) and Wang et al. (2018b) detected similar flaring features for these two different populations. That is to say, we suggest that secular evolution is not the main contributor in our works, and for the quantitative analysis of Wang et al. (2018b) shown in this paper, the value of the slope is the same for the thin and thick disks, as shown in Figure 3.

And for the current work, if we look carefully at Figure 3 by only focusing on the thin disk stellar population, the purple solid line represents the F/G-type stars, the green line with triangles represents K-type/RGB stars, and the red and black lines with pentagrams shown the OB-type stars. It is not possible for us to see a trend in which the flaring is stronger for older populations: by focusing on the variation of the scale height or the slope of the scale height with distance, the quantitative analysis for the strength of the flaring indicates values of 0.042 or 0.065 for OB stars, 0.145 for F/G-type stars, and 0.020 for K-type stars, which is also not consistent with the secular evolution scenario. Meanwhile, if we concentrate on the thick disk stellar population, the blue line represents F/G-type stars, and the green line with rectangles represents RGB/K-type stars. The former sample is generally younger than the latter one, but it appears that both have similar flaring features with slopes of 0.023 and 0.020. It is hard to explain this using secular evolution scenarios. All of these pieces of evidence again indicate that secular evolution, a prediction of which is that the flaring strength is different for different populations, with older stellar populations showing stronger flaring, is not the main contributor, although we cannot completely rule out the contributions of this scenario up to now. In other words, perturbations such as those caused by a dwarf galaxy might be the more probable of the two current two classifications.

Recently, based on the smooth particle hydrodynamical simulations with clumpy episodes, Silva et al. (2020) discovered broken exponentials is existing in the low-[$\alpha$/Fe] population and more importantly, flare significantly for low-[$\alpha$/Fe] stars but only weakly for high-[$\alpha$/Fe] populations. Meanwhile they also found that for low-[$\alpha$/Fe] thin disk stars, the flaring level decreases with age, which is also contrary to the secular evolution and it is similar with GMC perturbation scenario.

With the help of LAMOST K-giant stars and two types of simulations, Xu et al. (2020) pointed out that external perturbations might influence the outer disk beyond solar neighborhood, and they revealed that the flaring could be qualitatively explained by perturbations, which supports our viewpoints here about the flaring. Combining young OB-type stars and old K-giant stars, we could infer that the time period in which disk features are sensitive to possible perturbations could range from relatively soon after the OB-star population formed to the relatively late times after the formation of the K-giant population.

Although we are far from determining the exact flaring mechanisms, we suggest here that possible perturbations such as those mentioned above could heat the disk and then cause
the disk flaring; therefore, we could detect clear flaring signatures in the disk. More importantly, in this work we discover these possible heating mechanisms might be thicken- ing the disk on both sides in some similar ways, especially in the outer disk, and this will encourage us to gain a better understanding of the well-known flaring disk, especially from a theoretical point of view.

### 4.5.3. Relations between the Young Stellar Disk and Gas Disk

We also find evidence of a relationship between the young OB-type stars and the gas disk by comparing their structure parameters. It is shown in Figure 4 that the scale height of the OB-type stars is slightly thicker than that of the gas by 9 pc in the south and 33 pc in the north (the median values); this small difference supports the truth that OB stars are very young and only last a few million years and during this time the stars should not have had time to significantly move from their birth locations. So, young stars and gas could share similar properties, and we can use young OB stars to trace some physics in the gas. As for the reason the OB stellar disk is a little thicker than the gas disk, we speculate there are two possibilities. One is that the stars are hotter than the gas, so the stellar disk is thicker; the other is that the stars are perturbed by some agents that are possibly more effective on stars. The latter possibility is also consistent with the perturbations scenarios if we assume that the OB stellar disk is heated by perturbations after it formed from the gas. As far as we know, we do not see other works that show similarities between the young stellar disk and the gas disk, so that it might encourage our community to explore this further. We are planning to investigate more and to farther distances for the stellar, gas, and dust disks. In this work, because the sampling rate is low for distances larger than 14 kpc, we only focus on a limited distance range here.

In short, we detect clear flaring signatures of the young stellar disk that are possibly mainly caused by perturbations. This evidence of symmetrical flaring in the young stellar disk is clearly of vital importance for us to understand flaring mechanisms and even gas disk physics.

## 5. Summary

In this work, we explore the spatial structures of the young stellar disk with the LAMOST DR5 OB-type stars catalog, based on the Bayes method for correcting selection effects and a nonparametric method for disk decomposition, both of which have been robustly tested in our previous works. We discover that the north-south flaring in the outer disk is symmetrical and the scale height ranges from 0.14 to 0.5 kpc at different distances from 8 to 14 kpc. The flaring strength of the younger stellar disk is similar to or slightly stronger than that of the thin disk traced by older red giant branch stars, with an average slope characterizing the strength of 0.042 or 0.065 (OB) and 0.020 (RGB), which indicates that flaring might not be mainly caused by secular evolution scenarios that predict that the flaring of old populations should be stronger than that of the younger ones. In addition, we speculate that the mechanism might have influence both sides of the disk in similar ways.

We also find that the OB stellar disk is slightly thicker than the gas disk by 9 pc in the south and 33 pc in the north for the median value, implying that we can attempt, to some extent, to use OB-type stars to infer the gas disk properties in the future. What is more, we determine that the stellar disk might be more

compact than the gas disk by showing that the scale length of OB-type stars is shorter than that of the gas. We believe that more comparisons of the young stellar disk and the gas disk will be nontrivial to uncover more secrets about the formation of the disk.

Finally, it is shown that the midplane displacements($Z_0$) of the thin disk has a clear increasing trend with increasing distance in the range 8–14 kpc, which is possibly a signal of a warp, but we are still not sure of its origins and significance due to the fact that we cannot discriminate between the warp contributions and perturbation contributions or other unknowns from the current limited distance range and analysis. All of these pieces of observational evidence of the young stellar thin disk shown here will encourage us to uncover more about the flaring mechanisms and gas disk physics: more works will be presented in the future.

We would like to thank the anonymous referee, Lixia Yuan, Yang Su, Miaomiao Zhang, Ningyu Tang, Yan Sun, Ivan Minchev, and Leandro Beraldo e Silva for their very helpful and insightful comments and discussions. This work is supported by the National Key Basic R&D Program of China via 2019YFA0405500 and 2019YFA0405501, and by the National Natural Science Foundation of China (NSFC) under grants 11773009, 11873057, 11390371, 11673007, and 12003027. W.Y.C. is also supported by the “333 talents project” of Hebei Province. H.F.W. is also supported by the LAMOST Fellow project, 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. The authors gratefully acknowledge the support of the K.C. Wong Education Foundation. 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 the 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.

## ORCID iDs

Yang Yu (于扬) https://orcid.org/0000-0001-9329-7015
Hai-Feng Wang (王海峰) https://orcid.org/0000-0001-8459-1036

Wen-Yuan Cui (崔文元) https://orcid.org/0000-0003-1359-9908

Chao Liu (刘超) https://orcid.org/0000-0002-1802-6917

Bo Zhang (章博) https://orcid.org/0000-0002-6434-7201

Hao Tian (田浩) https://orcid.org/0000-0003-3347-7596

Shuai Feng (冯帅) https://orcid.org/0000-0002-9767-9237
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