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

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.

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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_error > 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.

$$\begin{eqnarray}&&{p}_{\mathrm{ph}}(D| J-K,K,l,b)={p}_{\mathrm{sp}}(D| J-K,K,l,b),\end{eqnarray} \tag{ 1 }$$

where J − K and K stand for the color index and K_s -band magnitude in 2MASS (Skrutskie et al. 2006), respectively.

Then, the stellar densities for the photometric data, ν_ph, and for the spectroscopic data, ν_sp, are associated with each other through

$$\begin{eqnarray}&&\begin{array}{l}{\nu }_{\mathrm{sp}}(D| J-K,K,l,b)=\\ {\nu }_{\mathrm{ph}}(D| J-K,K,l,b)S(J-K,K,l,b),\end{array}\end{eqnarray} \tag{ 2 }$$

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

$$\begin{eqnarray}&&S(J-K,K,l,b)=\displaystyle \frac{{n}_{\mathrm{sp}}(J-K,K,l,b)}{{n}_{\mathrm{ph}}(J-K,K,l,b)},\end{eqnarray} \tag{ 3 }$$

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 ν_sp along a line of sight, i.e.,

$$\begin{eqnarray}&&{\nu }_{\mathrm{sp}}(D| J-K,K,l,b)=\displaystyle \frac{1}{{\rm{\Omega }}{D}^{2}}\sum _{i}^{{n}_{\mathrm{sp}}(J-K,K,l,b)}{p}_{i}(D),\end{eqnarray} \tag{ 4 }$$

where _pi (D) is the probability density function of D for the ith 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 △(J − K) = 0.1 and △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).

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).

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

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 = [−15 15] and l = [0° to 90°, 270° to 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.

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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 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 −51 to 5.1, respectively. These values are within our range for the OB stellar disk. We will discuss this further later in the paper.

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 ± 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_⊙ 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 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).

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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.

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 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 (Z₀) 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 Z₀ 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.

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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.

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

In order to test the effect of the method including a decomposition 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. Interestingly, 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.

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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.

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4.5.2. Possible Scenarios for the Flaring

4.5.3. Relations between the Young Stellar Disk and Gas Disk