Hot Subdwarf Stars Identified in Gaia DR2 with Spectra of LAMOST DR6 and DR7. II.Kinematics

We analyzed a sample of 182 single-lined hot subdwarf stars observed in Gaia DR2 and LAMOST DR6 and DR7 (Lei et al. 2020). The sample included 89 sdB, 37 sdOB, 26 sdO, 24 He-sdOB, 3 He-sdO, and 3 He-sdB stars. The surface temperature T_eff, gravity $\mathrm{log}\,g$, helium abundance $y=n\mathrm{He}/n{\rm{H}}$ were also collected from Table 1 by Lei et al. (2020) and are shown in Table 1. As described in Luo et al. (2019), these 182 stars can be divided into four groups based on their helium abundances. Generally, the stars were classified as He-rich and He-deficient with respect to the solar helium abundance $\mathrm{log}y=-1$. Furthermore, He-rich and He-deficient stars can also be independently divided into two groups via $\mathrm{log}(y)=0$ and $\mathrm{log}(y)=-2.2$. The classification scheme could inherently associate these four helium groups with different formation channels in the ${T}_{\mathrm{eff}}-\mathrm{log}(y)$ diagram (Németh et al. 2012; Luo et al. 2019). As described by Németh et al. (2012), composite spectrum binaries with F and G type companions are relatively easy to identify because they have characteristic features, very different from subdwarfs and a comparable optical brightness. Identifying composite spectra with late G and K type companions is a challenge because of their significantly lower contributions and weaker lines. For these reasons, the identification of composite spectra with late type companions also heavily depends on the quality of the spectra. We excluded double-lined composite spectrum systems with noticeable Ca ii H&K (λ3933 Å and λ3968 Å), Mg i (λ5183 Å), or Ca ii (λ8650 Å) absorption lines. Unfortunately, the near-infrared region is seriously polluted by sky emission lines in LAMOST spectra and we could not use the Ca ii triplet lines.

Table 1.  Atmospheric Parameters, Space Positions, Orbital Parameters and Galactic Velocities for 182 Single-lined Hot Subdwarf Stars Observed in Gaia DR2 and LAMOST DR6 and DR7

Num	Label	Explanations
1	LAMOST	LAMOST target
2	R.A.deg	Barycentric R.A. (J2000)a
3	DEdeg	Barycentric decl. (J2000)a
4	Teff	Stellar effective temperatureb
5	$e\_{T}_{\mathrm{eff}}$	Standard error in Teff
6	$\mathrm{log}g$	Stellar surface gravityb
7	$e\_\mathrm{log}g$	Standard error of Stellar surface gravity
8	$\mathrm{log}(y)$	Stellar surface He abundance y = nHe/nHb
9	$e\_\mathrm{log}(y)$	Standard error in $\mathrm{log}(y)$
10	type	Spectra typeb
11	pmRA	Proper motion in RA
12	$e\_{pmRA}$	Standard error pmRA
13	pmDE	Proper motion in DE
14	$e\_{pmDE}$	Standard error in pmDE
15	D	Gaia DR2 stellar distance
16	$e\_D$	Standard error in stellar distance
17	RVel	Radial velocity from LAMOST spectra
18	$e\_{RVel}$	Standard error in radial velocity
19	X	Galactic position toward Galactic center
20	$e\_X$	Standard error in X
21	Y	Galactic position along Galactic rotation
22	$e\_Y$	Standard error of Y
23	Z	Galactic position toward north Galactic pole
24	$e\_Z$	Standard error of Z
25	U	Galactic radial velocity positive toward Galactic center
26	$e\_U$	Standard error in U
27	V	Galactic rotational velocity along Galactic rotation
28	$e\_V$	Standard error in V
29	W	Galactic velocity toward north Galactic pole
30	$e\_W$	Standard error in W
31	Rap	Apocenter radiusc
32	$e\_{R}_{\mathrm{ap}}$	Standard error in Rap
33	Rperi	Pericenter radiusc
34	$e\_{R}_{\mathrm{peri}}$	Standard error in Rperi
35	zmax	Maximum vertical heightc
36	$e\_{z}_{\max }$	Standard error in zmax
37	e	Eccentricityc
38	ee	Standard error in e
39	Jz	Z−component of angular momentumc
40	$e\_{J}_{{\rm{z}}}$	Standard error in Jz
41	zn	Normalized z-extent of the orbitc
42	$e\_{z}_{{\rm{n}}}$	Standard error in zn
43	Pops	Population classificationd
44	PTH	probability in thin disk
45	PTK	probability in thick disk
46	PH	probability in halo

Notes. The full table can be found in the online version of the paper.

^aAt Epock 2000.0 (ICRS). ^bFrom Lei et al. (2020). ^cForm the numerical orbit integration. ^dH = Halo; TK = thick disk; TH = thin disk.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Binary systems affect the calculations of Galactic velocities and orbits. Although our study focuses on studying only single-lined hot subdwarf stars, we cannot exclude the possibility of having unknown and unresolved binary systems based on a single epoch radial velocity measurement. We consider all stars to be members of the thin-disk, thick-disk, or halo populations until they are further constrained.

We utilized the spectra of LAMOST DR6 and DR7 to measure the radial velocities of the 182 hot subdwarf stars. The LAMOST spectra are similar to the SDSS data with a resolution of R ∼ 1800 and wavelength coverage of 3800–9100 Å. The data are described in detail in Luo et al. (2012, 2014). The published radial velocities in the LAMOST catalog are not reliable for hot subdwarf stars because hot subdwarfs are not included in LAMOST stellar templates for RVs. Therefore, we remeasured the radial velocities of these 182 stars and present them in Table 1.

Gaia DR2 provided high-precision positions (α and δ), proper motions (${\mu }_{\alpha }\cos \delta$ and ${\mu }_{\delta }$), and parallaxes ($\bar{\omega }$) (Gaia Collaboration et al. 2018a, 2018b, 2018c) for all 182 stars. Distances (D) were calculated using $D=1/\bar{\omega }$. These parameters are shown in Table 1. However, for 20 stars reliable distances cannot be obtained by simply inverting the parallax. Therefore, their distances were replaced with estimated values from the Gaia DR2 distance catalog (Bailer-Jones et al. 2018).

Figure 1 displays the space positions of the four hot subdwarf helium groups in the X − Z diagrams. The left panel of Figure 1 reveals that the space distributions of the two He-deficient groups do not show any obvious differences. Most stars tend to cluster around the disk and only a few stars are found in the halo. The star density quickly decreases from the disk to the halo and a sharp cutoff appears at $| Z| \sim 1.5\,\mathrm{kpc}$, which is considered the vertical scale height of the thick disk (Ma et al. 2017).

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In contrast, the right panel of Figure 1 shows that the space distributions of the two groups of He-rich stars have a noticeable difference at $| Z| \gt 1.5\,\mathrm{kpc}$ where the star density of He-rich stars with $\mathrm{log}(y)\geqslant 0$ is significantly higher than that of stars with $-1\leqslant \mathrm{log}(y)\lt 0$. The difference in space distribution also indicates that the two groups of He-rich stars likely originate from different formation channels.

Comparisons of the left and right panel in the Figure 1 demonstrate that the space density of the two group of He-rich stars has a larger dispersion than the groups of He-deficient stars, which suggests that He-rich and He-deficient hot subdwarf stars have different kinematic origins.

Figure 2 exhibits the distribution of the four hot subdwarf helium groups in the U − V velocity diagram. The U − V velocity diagram demonstrates that He-deficient stars can be found mostly around the LSR, while He-rich stars are more widely scattered in the whole region. In order to identify the Galactic population memberships of the stars, we also plot the two dotted ellipses as shown in Figure $\,1$ of Martin et al. (2017). They mark the 3σ limits of thin-disk and thick-disk WDs (Pauli et al. 2006), respectively.

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In order to illustrate the kinematics of the total velocity for the four hot subdwarf helium groups, Figure 3 displays the kinetic energy $2{E}_{\mathrm{kin}}/m={U}^{2}+{V}^{2}+{W}^{2}$ versus rotational velocity (V) diagram. The higher the value of the kinetic energy $2{E}_{\mathrm{kin}}/m$, the more elliptic the orbit of the star. We also plotted the isovelocity curves perpendicular to the Galactic rotation, where ${V}_{\perp }={({U}^{2}+{V}^{2})}^{1/2}$. The higher the value of the V_⊥, the hotter is the kinematic temperature. As described by Luo et al. (2019), most of stars are clustered around the LSR in a "banana" shaped region alongside the ${V}_{\perp }=0\,\mathrm{km}\,{{\rm{s}}}^{-1}$ isovelocity curve, which means that they are kinematically cool and likely have more circular orbits. A few stars are located farther away from the ${V}_{\perp }=0\,\mathrm{km}\,{{\rm{s}}}^{-1}$ isovelocity curve, where He-rich stars with $\mathrm{log}(y)\geqslant 0$ have a higher fraction. These are kinematically hot stars with likely more eccentric orbits. The sample also exhibits a sharp cut near $110\,\mathrm{km}\,{{\rm{s}}}^{-1}$. The few stars to the left of this velocity limit show a larger scatter and belong to the halo population (Altmann et al. 2004). In this region, the proportion of He-rich stars with $\mathrm{log}(y)\geqslant 0$ is more than 25%.

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Table 2 lists the mean values and standard deviations of the Galactic velocity components for the four hot subdwarf helium groups. We find that He-rich stars with $\mathrm{log}(y)\geqslant 0$ show the largest standard deviations of the Galactic velocity components in all four hot subdwarf helium groups and He-rich stars with $-1\leqslant \mathrm{log}(y)\lt 0$ display the second largest standard deviation. The two groups of He-deficient stars exhibit similar values of standard deviations.

Table 2.  Mean Values and Standard Deviations of the Galactic Velocities and the Galactic Orbital Parameters: Eccentricity (e), Normalized z-extent (z_n), Maximum Vertical Amplitude (z_max), Apocenter (R_ap) and Pericenter (R_peri) for the Four Hot Subdwarf Helium Groups

Subsample	N	$\bar{U}$	${\sigma }_{U}$	$\bar{V}$	σV	$\bar{W}$	σW	$\overline{{U}^{2}+{V}^{2}+{W}^{2}}$	${\sigma }_{{U}^{2}+{V}^{2}+{W}^{2}}$	$\overline{e}$	σe	$\overline{{z}_{{\rm{n}}}}$	${\sigma }_{{z}_{{\rm{n}}}}$	$\overline{{z}_{\max }}$	${\sigma }_{{z}_{\max }}$	$\overline{{R}_{{ap}}}$	${\sigma }_{{R}_{{ap}}}$	$\overline{{R}_{\mathrm{peri}}}$	${\sigma }_{{R}_{\mathrm{peri}}}$
All stars	182	30	62	203	35	0	36	46 458	16 817	0.23	0.13	0.12	0.08	1.14	0.70	9.94	1.84	5.98	2.45
$\mathrm{log}(y)\geqslant 0$	20	39	76	148	82	4	60	42 938	20 150	0.41	0.32	0.29	0.22	2.42	1.75	10.17	2.46	4.79	3.22
$-1\leqslant \mathrm{log}(y)\lt 0$	12	3	43	204	44	−2	49	47 907	19 653	0.27	0.20	0.22	0.23	2.38	2.37	10.96	1.51	6.86	2.99
$-2.2\leqslant \mathrm{log}(y)\lt -1$	57	35	57	205	33	−1	31	46 568	12 457	0.20	0.10	0.12	0.08	0.99	0.53	9.64	1.46	6.13	2.15
$\mathrm{log}(y)\lt -2.2$	89	29	63	203	35	3	35	46 962	16 640	0.24	0.14	0.12	0.07	1.17	0.73	9.94	1.89	6.02	2.25

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These results are in good agreement with the findings of Luo et al. (2019). The diverse range of kinematic velocities support the argument that He-rich hot subdwarf stars with $\mathrm{log}(y)\geqslant 0$ likely originate from different formation channels.

Table 3.  Population Classification and Relative Contributions of the Four Hot Subdwarf Helium Groups

Subsample	N	Thin Disk	Thick Disk	Halo
All stars	182	83	73	26
$\mathrm{log}(y)\geqslant 0$	19	5	8	6
$-1\leqslant \mathrm{log}(y)\lt 0$	13	7	2	4
$-2.2\leqslant \mathrm{log}(y)\lt -1$	60	32	20	8
$\mathrm{log}(y)\lt -2.2$	90	39	43	8

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Two important orbital parameters are the z-component of the angular momentum J_z and the eccentricity e of the orbit. They are used to distinguish different populations. Figure 4 shows the distribution of the four hot subdwarf helium groups in the ${J}_{z}-e$ diagram. We also show the two regions defined by Pauli et al. (2003): Region A confines thin-disk stars clustering to an area of low eccentricity, and J_z around 1800 kpc km s⁻¹; Region B encompasses thick-disk stars with higher eccentricities and lower angular momenta. Outside these two regions, defined as region C, halo star candidates are found. The majority of stars show a continuous distribution from Region A to Region B without an obvious dichotomy. Only a few stars lie in Region C and they they are separated by a noticeable gap from Region B and Region C. In Region C, He-rich stars with $\mathrm{log}(y)\geqslant 0$ have a very high fraction.

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In Table 2 we give the mean values and standard deviations of the orbital parameters: eccentricity, normalized z-extent, maximum vertical amplitude, apocenter, and pericenter. The standard deviation of the orbital parameters is similar to that of the Galactic velocity components. He-rich stars with $\mathrm{log}(y)\geqslant 0$ show the largest standard deviation of the orbital parameters and He-rich stars with $-1\leqslant \mathrm{log}(y)\lt 0$ display the second largest standard deviation. The two groups of He-deficient stars show similar values of standard deviations. These results are in good agreement with earlier findings (Martin et al. 2017; Luo et al. 2019).

We primarily adopted the U − V diagram, ${J}_{z}-e$ diagram, and the maximum vertical amplitude z_max to distinguish the Galactic populations of hot subdwarfs. To ensure correct population assignments, all orbits were visually inspected to supplement the automatic classifications. The detailed classification scheme was described by Martin et al. (2017) and Luo et al. (2019). Thin-disk stars are situated within the 3σ thin-disk contour in the U − V diagram and Region A in the ${J}_{z}-e$ diagram. Their orbits show a small extension in the Galactocentric distance R and the Galactic plane Z directions and have ${z}_{\max }\lt 1.5\,\mathrm{kpc}$. Thick disk stars lie within the 3σ thick-disk contour and in Region B. The extensions of their orbits in the R and the Z directions are larger than that of thin-disk stars, but do not reach the region of halo stars. Halo stars lie outside Region A and B, as well as outside the 3σ thick-disk contour. Their orbits show high extensions in R and Z. There are also some halo stars with an extension in R larger than $18\mathrm{kpc}$, or the vertical distance from the Galactic plane Z larger than $6\mathrm{kpc}$. Table 3 gives the number of stars in the four hot subdwarf helium groups classified as halo, thin, or thick-disk stars and Figure 5 displays their fractions in the halo, thin disk, and thick disk.

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The general trends in the distributions of the four hot subdwarf helium groups observed in LAMOST DR6 and DR7 can be matched with the results reported in LAMOST DR5 (Luo et al. 2019). A study on the structure of the Milky Way (Xiang et al. 2017) demonstrated that the different Galactic populations (thin-disk, thick-disk, and halo) reflect different age stellar populations. The binary population synthesis calculations of Han (2008) gave the fractions of hot subdwarf stars from three different formation channels (stable RLOF, CE ejection, and the merger of double HeWDs) at various stellar population ages. Although the exact values of the fractions are not consistent with the predictions of binary population synthesis (Han et al. 2003; Han 2008), we could make a comparison of the overall tendency of the fractional distributions.

The frequency of He-rich hot subdwarf stars with $\mathrm{log}(y)\geqslant 0$ monotonically increases from 6% in the thin disk to 23% in the halo. This trend is in a good agreement with the predictions of the merger channel of double HeWDs. Although many observations could outline two groups of He-deficient stars in the ${T}_{\mathrm{eff}}-\mathrm{log}\,g$ and ${T}_{\mathrm{eff}}-\mathrm{log}(y)$ diagrams separated by a gap in He abundance at $\mathrm{log}(y)=-2.2$ (Edelmann et al. 2003; Lisker et al. 2005; Stroeer et al. 2007; Hirsch 2009; Geier et al. 2011, 2015b; Németh et al. 2012; Luo et al. 2016, 2019; Lei et al. 2018, 2020), their formation channels are not understood well. Németh et al. (2012) found that hot subdwarf binary systems with F and G type companions, which are predominantly long-period binary candidates from the stable RLOF channel, appear in the two groups of He-deficient stars but show higher fractions among sdB stars with $-2.2\leqslant \mathrm{log}(y)\lt -1$. However, reviews of larger samples (Kawka et al. 2015; Kupfer et al. 2015) found that both short-period and long-period hot subdwarf binary systems occur in each sdB group. We found that the fraction of He-deficient stars with $\mathrm{log}(y)\lt -2.2$ is in good agreement with the predictions of the CE ejection channel and the fraction of He-deficient sdB stars with $-2.2\leqslant \mathrm{log}(y)\lt -1$ agrees with the predictions of the stable RLOF channel if the excluded composite binary systems were all considered to have sdB stars with $-2.2\leqslant \mathrm{log}(y)\lt -1$ in LAMOST DR5. The vast majority of the identified composite spectra show signatures of F or early G type companions. To determine the nature of hot subdwarfs in these systems we will need spectral decomposition. The distribution of single-lined He-deficient hot subdwarf stars observed in LAMOST DR6 and DR7 (Lei et al. 2020) is in good agreement with the distribution of single-lined He-deficient stars derived from LAMOST DR5 data (Luo et al. 2019). These samples support the predicted fractional contributions of the formation channels (Han et al. 2003; Han 2008).

Finally, the formation of He-rich hot subdwarf stars with $-1\leqslant \mathrm{log}(y)\lt 0$ remains a puzzle. The fraction of He-rich hot subdwarf stars with $-1\leqslant \mathrm{log}(y)\lt 0$ increases to 15% in the halo after decreasing from $\sim 8 \%$ in the thin disk to $\sim 3 \%$ in the thick disk, which is consistent with that of LAMOST DR5. Their frequency implies that He-rich hot subdwarf stars with $-1\leqslant \mathrm{log}(y)\lt 0$ in the thin disk and the halo may have different formation channels. Recent observations (Jeffery et al. 2017; Dorsch et al. 2019; Jeffery & Miszalski 2019; Naslim et al. 2020) found that He-rich hot subdwarf stars with $-1\leqslant \mathrm{log}(y)\lt 0$ show a strong enrichment of heavy elements. The reason for this enrichment is still unclear. Future kinematic studies may help shed light on the poorly understood physical processes behind the strong enrichment of heavy elements.

Radial velocity surveys (e.g., Maxted et al. 2001; Morales-Rueda et al. 2003; Copperwheat et al. 2011; Geier et al. 2011) of sdB stars showed that about 50% of sdB stars reside in close binary systems with either a cool MS star or a WD companion. Napiwotzki et al. (2004) reported a binary fraction of 39% of sdB stars from the ESO Supernova type Ia Progenitor survey (SPY). Recently, Kawka et al. (2015) reported a binary fraction of 37% of hot subdwarf stars selected from the GALEX all-sky survey and showed RV amplitudes ranging from a few tens to hundreds of km s⁻¹. The kinematic analysis based on just one epoch in RV is therefore intrinsically uncertain. With the binary population statistics of Kawka et al. (2015), we performed Monte Carlo simulations for our sample. We applied the binary fraction of 37% for single-lined subdwarf stars and the distribution of RV amplitudes to correct for systematics due to the unknown RV. For each binary system, we assumed a circular orbit in the form ${RV}(t)=\gamma +K\sin \phi$, where K is the RV amplitude, γ is the system velocity, and ϕ is the orbital phase. The orbital phase ϕ was chosen from a uniform distribution from 0 to 2π. 3000 system RVs were produced for each individual star. Combing the distances, proper motions, and their errors, we calculated their Galactic space velocity components and orbits. We obtained the probabilities of the Galactic populations on each individual star and listed in Table 1. The upper right panel of Figure 5 shows the RV variability selection-effect-corrected fractional distributions of the four hot subdwarf helium groups for the halo, thick-disk, and thin-disk populations. The impact of the RV variability selection effect on the fractional distributions is less than 5% of the number of stars in a group.

Using the effective temperature (T_eff) and surface gravity (g) we determined the total luminosity (in L_⊙) by assuming for all stars a sample-average mass of $0.47{M}_{\odot }$ (Fontaine et al. 2012). The upper left panel of Figure 6 displays the luminosity versus distance of the sample. There is no clear correlation between luminosity and distance for the sample.

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Thanks to Gaia DR2, Geier et al. (2019) compiled an all-sky catalog of $39,800$ hot subdwarf star candidates using the means of color, absolute magnitude, and reduced proper motion cuts. Except for the Galactic plane, the catalog is nearly complete up to about $1.5\,\mathrm{kpc}$. The upper right panel of Figure 6 illustrates the absolute Gaia G magnitude ${M}_{{\rm{G}}}=G+5\mathrm{log}(D)-10-{A}_{G}$ versus distance D (in pc). In order to avoid contamination due to WDs at the faint limit, we restricted the sample to objects with $-0.65\leqslant {M}_{{\rm{G}}}\lt -0.5$. The lower left panel of Figure 6 displays the distribution function of ${M}_{{\rm{G}}}$ for objects that lie in three distance intervals, respectively. The last two intervals show quite similar distribution functions and the Kolmogorov–Smirnov (K–S) test gives a P value of 0.99. Therefore, the objects with $500\lt D\lt 1500$ in Gaia DR2 are expected to be volume complete. The lower right panel of Figure 6 shows comparisons of the distribution function of ${M}_{{\rm{G}}}$ for hot subdwarf stars with $500\lt D\lt 1500$ in Gaia DR2, objects in LAMOST DR5 (Luo et al. 2019), DR6 and DR7 (Lei et al. 2020). We consider the sample of hot subdwarfs in LAMOST DR5 to be complete. In the lower left panel of Figure 5 we give the volume selection-effect-corrected fractional distributions of the four hot subdwarf helium groups for the halo, thick-disk, and thin-disk populations. The influence of the volume selection effect on the results is estimated to be less than 5% of the number of stars within a group. We also present the volume and RV variability selection effect corrected fractional distributions of the four hot subdwarf helium groups for the halo, thick-disk, and thin-disk populations in the lower left panel of Figure 5. A total impact of these two effects is less than 8% of the number of stars within each group. We can see that the overall tendency of the fractional distributions of the four hot subdwarf helium groups in the halo, thin disk, and thick disk from DR6 and DR7 are consistent with the findings reported by Luo et al. (2019) based on LAMOST DR5.