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# M-subdwarf Research. II. Atmospheric Parameters and Kinematics

Shuo Zhang, A. -Li Luo, Georges Comte, Rui Wang, Yin-Bi Li, Bing Du, Wen Hou, Li Qin, John Gizis, Jian-Jun Chen, et al.

► To cite this version:

Shuo Zhang, A. -Li Luo, Georges Comte, Rui Wang, Yin-Bi Li, et al. M-subdwarf Research. II. Atmospheric Parameters and Kinematics. The Astrophysical Journal, 2021, 908, 18 pp. 10.3847/1538-4357/abcfc5. insu-03585860

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https://insu.hal.science/insu-03585860v1

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# M-subdwarf Research. II. Atmospheric Parameters and Kinematics

Shuo Zhang<sup>1,2,3,4</sup>①, A-Li Luo<sup>1,2,5,6</sup>①, Georges Comte<sup>7</sup>, Rui Wang<sup>1,2</sup>①, Yin-Bi Li<sup>1</sup>①, Bing Du<sup>1</sup>, Wen Hou<sup>1</sup>, Li Qin<sup>1,5</sup>
John Gizis<sup>6</sup>①, Jian-Jun Chen<sup>1</sup>, Xiang-Lei Chen<sup>1,2</sup>, Yan Lu<sup>1,5</sup>①, Yi-Han Song<sup>1</sup>①, Hua-Wei Zhang<sup>3,4</sup>①, and Fang Zuo<sup>1,2</sup>

<sup>1</sup> CAS Key Laboratory of Optical Astronomy, National Astronomical Observatories, Beijing 100101, People's Republic of China; lal@nao.cas.cn

<sup>2</sup> University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China

<sup>3</sup> Department of Astronomy, School of Physics, Peking University, Beijing 100871, People's Republic of China

<sup>4</sup> Kavli institute of Astronomy and Astrophysics, Peking University, Beijing 100871, People's Republic of China

<sup>5</sup> School of Information Management & Institute for Astronomical Science, Dezhou University, Dezhou 253023, People's Republic of China

<sup>6</sup> Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA

<sup>7</sup> Aix-Marseille Université, CNRS, CNES, LAM, Laboratoire d'Astrophysique de Marseille, Marseille, France; georges.comte@lam.fr

Received 2020 July 8; revised 2020 November 17; accepted 2020 November 19; published 2021 February 18

## Abstract

We applied the revised M subdwarf classification criteria discussed in Zhang et al. to Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) DR7 and combined the result with the M subdwarf sample from Savcheva et al. to construct a new M subdwarf sample for further study. The atmospheric parameters for each object were derived from fitting to the PHOENIX grid, and the sources with available astrometry and photometry from Gaia DR2 were combined for further analysis. The relationship between the gravity and metallicity was explored according to the locus both in the color–absolute magnitude diagram and the reduced proper motion diagram. Objects that have both the largest gravity and the lowest metallicity are located away from the main-sequence cloud and may be considered as the intrinsic M subdwarfs, which can be classified as luminosity class VI. Another group of objects whose spectra show typical M subdwarf characteristics have lower gravity and relatively moderate metal deficiency and occupy part of the ordinary M dwarf region in both diagrams. The Galactic *U*, *V*, *W* space velocity components and their dispersion show that the local Galactic halo population sampled in the solar neighborhood is represented by objects of high gravity and an inconspicuous bimodal metallicity distribution, with a fraction of prograde orbits. The other M subdwarfs seem to belong in part to the thick disk component, with a significant fraction of thin disk, moderately metal-poor objects intricately mixed with them. However, selection effects, especially the favored anticenter direction of investigation in the LAMOST subsample, as well as contamination by multiplicity and parameter coupling, could play important roles and need to be investigated further.

Unified Astronomy Thesaurus concepts: M subdwarf stars (986)

Supporting material: machine-readable table

## 1. Introduction

M subdwarfs are usually recognized as the oldest members of the low-mass stellar populations and as metal-poor counterparts of the late-type M dwarfs. With their extremely long nuclear-burning lifetimes, subdwarfs are supposed to represent early generations of star formation and are therefore potential tracers of Galactic dynamic and chemical evolution history (Savcheva et al. 2014). Despite their scarcity in the solar neighborhood, M subdwarfs are supposed to comprise the majority of stars in the Milky Way stellar halo (Bochanski et al. 2013), while a number of them also populate the thick disk, whose population is supposed to be older than that of the thin disk. Additionally, the cool atmospheres of M subdwarfs provide conditions for studying molecule and dust formation as well as radiative transfer in metal-poor environments (Allard et al. 1997).

In many early investigations, M subdwarfs were considered as metal-poor main-sequence dwarfs (e.g., Lépine et al. 2007; Rajpurohit et al. 2014), with some noteworthy kinematic and spectral properties: red subdwarfs, which exhibit large space velocities relative to the Sun and are kinematically associated with the Galactic halo (Gizis 1997) and thick disk, display shallower TiO absorption bands in the optical spectra than do the ordinary red dwarfs that dominate the Galactic thin disk. Historically, they were usually searched for based on their large proper motions (Sandage 1969; Jones 1972; Hartwick et al. 1984;

Sandage & Kowal 1986; Gizis 1997; Lépine et al. 2003, 2007; Smith et al. 2009; Jao et al. 2011) and characteristic spectral features (Mould 1976; Mould & McElroy 1978; Ake & Greenstein 1980; Lépine & Scholz 2008; Savcheva et al. 2014; Bai et al. 2016; Zhang et al. 2019; Hejazi et al. 2020). The research of metal-poor subdwarfs also has extended to the late M-type and L-type classes in recent years (e.g., Zhang et al. 2017a, 2017b, 2018; Zhang 2019).

However, some studies have suggested that subdwarfs should have a luminosity classification independent of dwarfs —VI—because they are 1 ~ 2 mag less luminous than the main-sequence dwarfs in the H–R diagram, forming an independent sequence, and they more or less show larger surface gravities than the dwarfs (Jao et al. 2008). Results from Kesseli et al. (2019) show that ultra subdwarfs can be as much as five times smaller than their solar-metallicity counterparts for a given temperature. However, subdwarf identification in most of the studies depends much more on the metallicity than on the gravity, and whether gravity constraints for subdwarfs is necessary still remains an open question.

Characterizing M subdwarfs in terms of atmospheric parameters has long been a challenge. Like M dwarfs, the opacity sources are dominated by the molecular absorption bands such as TiO, VO, MgH, FeH, and CaH in the optical, as well as H₂O and CO in the infrared, each of which has millions of spectral lines. These complex band structures leave no
window to access the true continuum and only allow the strongest atomic lines such as Ca I, Na I, and K I to appear at low spectral resolution. In addition, dust clouds form with decreasing temperature, the stellar atmosphere becomes more complicated, and the spectra show the presence of diatomic and triatomic molecules increasing (Rajpurohit et al. 2016). Therefore, the traditional technique of estimating the effective temperature (T<sub>eff</sub>) of a star based on a blackbody approximation and broadband photometry is not applicable to cool M subdwarfs in which the true continuum is covered by a wide variety of molecular absorbers (Allard et al. 1997). It is also difficult to disentangle the effect of reduced metal abundance from that of increasing surface gravity or decreasing temperature because these three parameters affect the pressure structure of the photosphere in a similar way (Jao et al. 2008).

Since accurate metallicities for most M subdwarfs are
difficult to measure, proxies for metallicity have been
introduced. The most widely used metallicity-tracer parameter
ζ, (a parameter derived from CaH2, CaH3, and TiO5 molecular
bandhead indices originally used by Gizis 1997), was
introduced by Lépine et al. (2007) and revised by Dhital
et al. (2012) and Zhang et al. (2019). With the parameter ζ or
the revised definition, two large samples of M subdwarfs were
spectroscopically identified by Savcheva et al. (2014) and
Zhang et al. (2019; hereafter Paper I) using spectra from the
Sloan Digital Sky Survey (SDSS; York et al. 2000) and the
Large Sky Area Multi-Object Fiber Spectroscopic Telescope
(LAMOST; Cui et al. 2012), respectively. According to the
decreasing order of ζ, the M subdwarfs can be divided into
three metallicity subclasses: M subdwarfs (sdM), extreme
metal-poor M subdwarfs (esdM), and ultra metal-poor M
subdwarfs (usdM).

The first model grid based on the PHOENIX radiative transfer code (Allard & Hauschildt 1995) has been used by several authors to compare synthetic spectra to observed ones and to the broadband colors: Dahn et al. (1995), Leggett et al. (1996), and Jones et al. (1996). Gizis (1997) was able to constrain the metallicity scale of subdwarfs from -2 dex for esdM to -1 to -1.5 dex for sdM, while the stars not classified as subdwarfs spanned the range -1 dex to 0 dex. However, this pioneering model grid was far from being optimized because of the lack of theoretical molecular opacities, especially for the very important species CaH.

The NextGen model grid (Hauschildt et al. 1999) brought a number of improvements and was in turn used by, e.g., Woolf & Wallerstein (2005), who demonstrated the α enrichment of halo metal-poor M stars. Several papers using NextGen models to interpret spectra of cool M dwarfs and subdwarfs were subsequently published (e.g., Leggett et al. 2000; Lépine et al. 2004), while Burgasser & Kirkpatrick (2006) compared the performances of NextGen models and AmesCond models on the spectrum of an esdM star. Progress in modeling led the PHOENIX-based computations to the BT-Settl series of grids, the last generation of which proved highly successful in reproducing the features of the observed spectra in detail. Comparisons of a few high-resolution spectra of low-mass stars to synthetic ones show that the latest PHOENIX models have already reached a milestone (Rajpurohit et al. 2014, 2018a, 2018b).

Gaia Data Release 2 (Gaia Collaboration et al. 2018a) has
provided astrometry and photometry for more than one billion
stars. As a result, a large number of subdwarfs that were

beyond the reach of parallax studies now have accurate
trigonometric parallaxes, permitting distance determination and
hence their placement in the Hertzsprung-Russell diagram.
Their 3D kinematics can be studied thanks to high-accuracy
proper motions from Gaia and radial velocities from
spectroscopy.

M subdwarfs have been found both at high Galactic latitudes, as expected for halo-population members, and at much lower latitudes in fields located toward the Galactic anticenter, which suggests that one could use them to study the mix of various populations in the solar neighborhood. Therefore, it becomes especially interesting to explore the links between their atmospheric parameters, especially gravity and metallicity, and their kinematic properties. For this, we need a reasonably accurate estimation of the atmospheric parameters of a large sample of subdwarfs for which we have accurate photometry and astrometry and the same data on a control sample of ordinary M dwarfs. The present work, based only on low-resolution spectroscopy, has its limitations and must be considered as a preliminary step toward this goal.

The paper is organized as follows. In Section 2, we briefly summarize the observational material that will be used in Sections 4 and 5. In Section 3, we analyze the properties of the PHOENIX-based BT-Settl CIFIST model grid to evaluate its performance by comparing spectral indices of BT-Settl synthetic spectra to those measured on real-world template spectra of M dwarfs and subdwarfs. Then, we fit the template spectra with the synthetic grid to get the atmospheric parameter ranges for each template spectrum. In Section 4, we derive the atmospheric parameters for spectra of a sample of M dwarfs and subdwarfs from the best-fit PHOENIX BT-Settl synthetic spectra. This leads to the construction of a cleaned, genuine subdwarf sample, a normal dwarf sample, and a third population whose properties point, not to subdwarfs, but to metal-deficient dwarfs. In Section 5, we explore the links between the distribution of the atmospheric parameters of the stars belonging to these three samples and their photometric and kinematic properties as provided by the Gaia Data Release 2, using a color-absolute magnitude diagram, a reduced proper motion diagram, and 3D Galactic motion distributions. Finally, the conclusions and summary are provided in Section 6.

## 2. Observational Data

The low-resolution spectra of M dwarfs and subdwarfs are
from LAMOST DR7 and SDSS DR7, and the astrometric data
is from Gaia DR2.

LAMOST is a reflecting Schmidt telescope located at the Xinglong Station of the National Astronomical Observatory, China (40°N, 105°E), with a mean aperture of 4.3 m and a field of view of 5°. The observable sky area extends from -10° to +90° decl. A total of 4000 optical fibers positioned on the focal plane yield a high spectrum acquisition rate per night. Until 2020 March, DR7 published more than 10 million low-resolution spectra (R ~ 1800) covering 3800-9000 Å (Luo et al. 2015) and 2.17 million medium resolution spectra (R ~ 7500) covering 3700-5900 Å and 5700-9000 Å (Liu et al. 2020).

The SDSS began regular survey operations in 2000, and
has progressed through several phases until now: SDSS-I
(2000–2005), SDSS-II (2005–2008), SDSS-III (2008–2014),
and SDSS-IV (2014–2020). The SDSS DR7 contains over 1.6
million low-resolution spectra in total, including 930,000
<figure><img src="image_3.png" /><figcaption>Figure 1. The “canonical” diagram classically used to identify subdwarfs from dwarfs: spectral composite index CaH2+CaH3 vs. TiO5. Models are plotted with the following codes: continuous lines, log g = 4.5 models; dashed lines, log g = 5.0 models; and dotted lines, log g = 5.5 models. Black: solar metallicity; blue: -1.0 dex; and magenta: -2.0 dex. The small 2-digit labels indicate T<sub>eff</sub> points (e.g., “32” means 3200 K). Observed template spectra: black dots represent normal main-sequence dwarfs; subdwarf templates colored in blue are for the “sdM” subclass, green for “esdM”, and magenta for “usdM” subclass. The M0V to M7V “standard dwarf” spectral type sequence is labeled on all graphs.</figcaption></figure>

spectroscopically separate the subdwarfs from the normal dwarfs. The spectral indices were defined initially by Reid et al. (1995). The boundaries of the d/sd/esd/usd metallicity classification scheme are also plotted. This diagram may represent more or less a metallicity–gravity diagram, since TiO5 is a metallicity (and alpha) indicator, while CaH2+CaH3 is a gravity indicator, and both are naturally strongly T<sub>eff</sub> dependent. The subdwarfs are expected to lie in order along temperature sequences, while the fan shape of their distribution reflects their atmospheric metal deficiencies.

The normal dwarf template sequence is well ordered and fits quite well with the model family {log g = 4.5, [Fe/H] = 0.0} track, although with the coolest types (M6 ~ M7) being a bit offset, as would be expected from an insufficient value of the model gravity. This is an important point and needs to be discussed further. All late-type M dwarfs are expected to have higher surface gravities than early M dwarfs due to the near 1-to-1 mass–radius relation for low-mass stars. Note that between metallicities of 0.0 and −1.0, the displacement of the model track is quite small even at the lowest T<sub>eff</sub>, making the estimates of moderate metal deficiencies rather difficult on this diagram.

The subdwarf templates also draw quite well defined and well separated sequences with increasing slopes from sd to usd, the latter one being almost vertical at a constant TiO5 index of almost null absorption. The coolest types of dwarfs and sd are somehow confused; this questions the validity of the templates themselves, which are built from spectra that are either insufficient in number or too noisy to be really representative of the genuine subtype definition.

The metallicity of the sd subclass is not consistent with a −1.0 value; it must be more deficient, or affected by a higher gravity, or both. The model family {log g = 5.0, [Fe/H] = −2.0} could provide a reasonable fit for usdM0 ~ 3, but the track moves toward significant values of the TiO5 opacity for later subtypes, and therefore the real stars must be more deficient. The model family {log g = 5.5, [Fe/H] = −2.0} track yields more or less an outer envelope for the subdwarfs, implying that most of the right-hand distribution

of their representative points is driven more by large metal deficiencies than by high gravity.

### 3.3. Fitting the dM and sdM Templates with the Model

Using template spectra rather than hundreds of individual spectra to compare with the models enables us to smooth accidental differences due to noise and uncertainties in individual classification, and in principle gives access to high signal-to-noise ratio data. However, the final quality of a template depends on the number of individual spectra co-added to build it. We shall hereafter use the COMPLETE collection of templates of Zhong et al. (2015), i.e., the interpolated 221 spectra in total spanning 12 subclasses (from dMr to usdMp) and 18 subtypes (from M0 to M8.5).

The parameter grid of the synthetic spectra is shown in Table 1. Note that the grid is not uniform: the value log g = 6.0 only pertains for T<sub>eff</sub> ≥ 3000 K, and the [α/M] ratio is dependent on the metallicity.

The spectral fitting region extends from 6000 Å to 8800 Å with a step size of 1 Å, which covers most prominent spectral features used for classification. Before the fitting process, the synthetic spectra were smoothed to the resolution of the observed spectra.

In the fitting process, we set the spectral flux as a function of T<sub>eff</sub>, log g, and [M/H], and assume:

$$F_{o,\lambda} = F_{m,\lambda} \times P_{n,\lambda} + \epsilon_{\lambda}, \quad (1)$$

where F<sub>o,λ</sub> is the flux of the observed spectrum at wavelength λ, F<sub>m,λ</sub> is the flux of the synthetic spectrum generated by the PHOENIX model wavelength λ, P<sub>n,λ</sub> is an n-order polynomial factor used to correct the inaccuracies of the continuum of the observed spectrum (here, we set n = 4 based on the optimal experimental results), and ε<sub>λ</sub> is the difference between the synthetic spectrum and the observed spectrum.

The equation above can be solved by minimizing the loss function L = Σ<sup>N</sup><sub>λ=1</sub>(F<sub>m,λ</sub> × P<sub>n,λ</sub> − F<sub>o,λ</sub>)<sup>2</sup> using the least-squares method to obtain the coefficient matrix solution of P<sub>n,λ</sub>. Then, we obtain the best-fit synthetic spectrum by minimizing
<figure><img src="image_4.png" /><figcaption>Figure 2. Template spectra of subtype dM0, sdM2, esdM4, and usdM6, with their corresponding synthetic spectra and fitting residuals.</figcaption></figure>

the $\chi^2$ distance,

$$\chi^2 = \frac{\sum_{i=1}^{N} [(F_{o_i} - F'_{m_i})^2 / \epsilon_i^2]}{N}, \quad (2)$$

where $F'_{m_i}$ is the flux of the ith pixel of the synthetic spectrum corrected by polynomial, $\epsilon_i$, the error of flux of the ith pixel, and N is the number of pixels involved in the calculation.

For each given template spectrum, we calculate the $\chi^2$ values when matching all of the synthetic spectra in the grid and then interpolate between the parameters by synthesizing linear combinations of the top-five best-fit synthetic spectra, as done by Yee et al. (2017).

The fitting results of four template spectra of different spectral subtypes and metallicity subclasses (dM0, sdM2, esdM4, and usdM6), with their corresponding estimated parameters, are shown in Figure 2 as examples. The shape of the residual spectra indicate that the errors mainly come from the region of 6000-7000 Å, where there remains some incompleteness in line lists and/or missing or incomplete opacities for some molecules used in the modeling (CaOH, CN, CaH, etc.). In addition, the far-red region of the observed spectra could be contaminated by telluric absorption.

Figure 3 shows the residual levels of the fitting results of all of the templates. The residual level of the fitting results gradually increases from ~5% for early-type M stars to 10% for the late types: both the spectral quality and the number of objects for template building decrease dramatically for the latest types.

Finally, the distributions of the estimated results of log g and [Fe/H] of the templates above are shown in Figure 4. The dispersions are large for both parameters, with the basic trend

<figure><img src="image_5.png" /><figcaption>Figure 3. Residuals between template spectra of different spectral subtypes and their best-fit synthetic spectra. Black, blue, purple, and red represent subclass dM, sdM, esdM, and usdM, respectively. The error bar is the standard deviation of the difference between the flux of the template spectrum and the flux of the synthetic spectrum. The number beside each node represents the number of spectra used to construct the template spectrum.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 4. Distributions of estimated atmospheric parameters of the template spectra of different subclasses. The colors represent the same subclasses as in Figure 3.</figcaption></figure>

being a clear decrease of the average metallicity from sd to usd, accompanied by a more confused increase in gravity. Note that when using the complete set of templates (221 in total), we can meet spectra of slightly atypical characteristics, as illustrated in the top panel of Figure 2, in which a dM0 is metal-poor and 100 K cooler than a standard dM0 of solar metallicity.

## 4. Sample Construction and Atmospheric Parameter Estimates

To estimate the atmospheric parameters $T_{eff}$, log g, and [M/H] of M subdwarfs from low-resolution spectra and investigate the trends of these parameters with the kinematic properties of the stars, we need a sufficiently large sample of subdwarfs spanning the broadest possible range of parameters.

In Paper I, we had explored LAMOST DR4 in which 2791 M subdwarfs were identified. Extending the search to LAMOST DR7, a total of 4767 visually selected candidates are retrieved, including the previously obtained DR4 ones. Combining this sample with SDSS objects published by Savcheva et al. (2014), we submitted these spectra to a least-squares based fitting process with PHOENIX synthetic spectra. The determination of atmospheric parameters is not always possible with a reasonable accuracy because the error budget of the fitting process depends on the signal-to-noise ratio (S/N) of the spectra. Thus, the final combined LAMOST + SDSS
sample of stars with known atmospheric parameters will be reduced with respect to the initial numbers.

## 4.1. Sample Construction and Individual Spectra Fitting

Because of magnitude limitations, most M dwarfs in the LAMOST sample range in spectral type below M3, and only a few cooler and fainter spectra of low S/N are available. The data of SDSS DR7 cover a more extended parameter space, with cooler and lower metallicity objects. The two surveys point to different fields, with the SDSS observing high Galactic latitudes, favoring the detection of halo and thick disk objects, and the LAMOST survey targeting regions of the Galactic anticenter. Therefore, in this study, we combine the subdwarfs from SDSS DR7 (SEGUE-I/II) and LAMOST DR7 to construct a consistent sample of M subdwarfs that is more representative of the total population of these stars.

First, it is useful to discuss three points on which the processing of the LAMOST and SDSS spectra sets will differ: (1) selecting criteria, (2) spectroscopic resolution, and (3) spectral data reduction.

(1) Selecting criteria. Several works have been conducted to identify M subdwarfs from SDSS and LAMOST low-resolution spectral data sets (West et al. 2004; Lépine & Scholz 2008; Bochanski et al. 2013; Savcheva et al. 2014; Zhang et al. 2016; Bai et al. 2016; Paper I), and the two largest samples published were from Savcheva et al. (2014) and Paper I, respectively.

The selecting conditions differ for these two samples. The principal separator used is the standard parameter $\zeta$, initially introduced by Lépine et al. (2007) based on a combination of CaH2, CaH3, and TiO5 spectral indices:

$$ \zeta_{\text{CaH/TiO}} = \frac{1 - \text{TiO5}}{1 - [\text{TiO5}]_{\text{Z}_{\odot}}}, \quad (3) $$

in which the $[\text{TiO5}]_{\odot}$ is a third-order polynomial fit of the TiO5 spectral index as a function of the CaH2+CaH3 index as

$$ [\text{TiO5}]_{\odot} = a + b \times (\text{CaH2} + \text{CaH3}) + c \times (\text{CaH2} + \text{CaH3})^2 + d \times (\text{CaH2} + \text{CaH3})^3, \quad (4) $$

so that $\zeta = 1$ for solar metallicity and $\zeta = 0$ for the most metal-poor objects where TiO5 absorption becomes undetectable. The coefficients $a, b, c$, and $d$ derived for SDSS objects by Lépine et al. (2007) led to the calibration $\zeta_{L07}$, which was later revised by Lépine et al. (2013; hereafter $\zeta_{L13}$). The condition for a star to belong to the subdwarf population was set as $\zeta_{L07} < 0.825$ and $\zeta_{L13} < 0.825$.

Since $\zeta$ was found to be dependent on the M dwarfs reference sample, instrumental set-up and various factors influential in the reduction process (Lépine et al. 2013), we proposed a new calibration adapted to LAMOST spectra in Paper I (hereafter $\zeta_{Z19}$), and we suggested the condition for LAMOST subdwarfs being set as $\zeta_{Z19} < 0.75$, with an additional screening condition based on the CaH1 index.

(2) Spectroscopic resolution. Along the wavelength of a spectrum from SDSS or LAMOST, the physical resolution (depending on the grating × focal length of the camera × pixel size of the detector) varies in a complicated way. For LAMOST, when spectra are extracted and rebinned in constant

log-wavelength steps by the 1D pipeline, this variation is +/- "dissolved" into another variation. Additionally, although in theory, all spectra obtained from the same instrument are supposed to have an identical resolving power, in practice for a large-scale survey project, the resolution changes slightly at different observation dates, due to imperfect instrument stability.

In the actual calculation, assuming a Gaussian instrumental profile, the resolution $R$ of a spectrum at wavelength $\lambda$ can be derived from $\lambda/\Delta\lambda$, where $\Delta\lambda$ is the full width at half maximum (FWHM) of the spectral line broadening at that wavelength. The Gaussian kernel $\sigma = \text{FWHM}/2.355$ used to convolve the synthetic spectrum is derived from $\sqrt{\sigma_0^2 - \sigma_m^2}$, where $\sigma_m$ corresponds to the synthetic spectrum, and $\sigma_0$ corresponds to the observed spectrum. Since the resolution of the synthetic spectra is extremely high, we set $\sigma_m$ as 0 here.

Prior to the fitting process, the observed spectra are shifted to the rest frame based on the measured radial velocities. The fitting range was set to 6000-8800 Å, in which the pixels marked by "bad" flags and the spectral intervals heavily contaminated by telluric absorption (7210-7350 Å, 7560-7720 Å, and 8105-8240 Å) were masked. We divided the region 6000-8800 Å into seven bands evenly and used a dedicated convolution kernel for each 400 Å band.

For SDSS and LAMOST spectra, we adopted different convolution kernels calculated as follows. For an SDSS spectrum, we computed the mean value of the $\sigma$ in each band by the "dispersion" value of each pixel stored in the fits file. For a LAMOST spectrum, we calculated the mean value of the FWHM of the arc-lamp spectrum in each band, obtained on the same day for wavelength calibration purposes.

(3) Data reduction. In the fitting process described above, we first correct the continuum of an observed spectrum using a fourth-order polynomial and then choose the best-fit synthetic spectrum based on the chi-squared minimum principle. We find that the continuum slopes of some observed LAMOST spectra differ largely from their corresponding corrected spectra. This deformation is mainly caused by flux calibration problems (Du et al. 2016) and would affect the accuracy of the spectral indices. To control this unwanted bias, we measure the spectral indices of each polynomial-corrected observed spectrum, and calculate the difference between them and the original indices measured on the uncorrected spectrum. We then construct the distribution of each index difference, as shown in Figure 5. Although the offset of a single index is generally small, the error on the $\zeta$ parameter composed of multiple indices may be considerably enlarged. Hence, targets with at least one spectral index difference beyond $3\sigma$ of the corresponding difference distribution are removed from the final subdwarf sample.

We summarize the specific solution to build the combined LAMOST + SDSS subdwarf sample in seven steps as follows:

(1) Select 4767 visually inspected subdwarfs from LAMOST DR7.

(2) Recalculate the indices of the SDSS subdwarfs from Savcheva et al. (2014) with the radial velocities recorded in the catalog (see Paper I for more comments).

(3) Calculate the resolution of each spectrum using the profile of a corresponding arc-lamp spectrum (LAMOST) or the "dispersion" value stored in the fits file (SDSS) and get the Gaussian convolution kernels.

(4) Smooth the synthetic spectra to fit every observed spectrum and estimate the atmospheric parameters.
<figure><img src="image_7.png" /></figure>

**Figure 5.** Each subdiagram shows a spectral index error distribution for the LAMOST subdwarfs. The errors are the differences between the values measured from the original spectra minus the values measured from the continuum-corrected spectra. They reflect the deformation level of the local pseudocontinuum, due to imperfect flux calibration. The bottom right panel shows the distribution of the derived parameter $\zeta$ values with a scatter of 0.133, although the scatters of each of the indices (CaH2, CaH3, and TiO5) used to calculate $\zeta$ are quite smaller.

Figure 6 shows the fitting result of a LAMOST extreme subdwarf in the upper panel and an SDSS subdwarf spectrum showing H$\alpha$ emission in the lower panel. The spectral bands contaminated by telluric absorptions are masked.

(5) For each index, measure its value on each observed spectrum and on its corresponding continuum-corrected spectrum, and get their difference.

(6) Exclude the objects with one or more spectral index differences beyond $3\sigma$ of the corresponding difference distribution.

(7) Combine the two samples above, and apply the selecting cuts by removing the objects of $\zeta_{L07} \ge 0.825$, $\zeta_{L13} \ge 0.825$, and $\zeta_{Z19} \ge 0.75$.

Finally, a sample of 3131 subdwarfs is assembled, 1722 of which have reliable kinematic properties. To provide better understanding, we summarize in Table 3 the various sub-samples used in this work.

We must underline that we have not used the CaH1 index as a filter until now. For comparison, we also estimate the atmospheric parameters of an M dwarf sample that contains around 70,000 visually inspected spectra from LAMOST (Zhang et al. 2019). Figure 7 shows the combined LAMOST +SDSS sample of subdwarfs together with the comparison sample of LAMOST M dwarfs. The LAMOST sample contains a large number of early-type and medium metal-poor stars, while the SDSS sample covers a broader range of spectral types and metal abundances.

## 4.2. Results of Parameter Estimation

### 4.2.1. Signal-to-noise Ratio Impact on Quality

Statistically, the fit residuals between the observed spectra and the synthetic spectra vary with S/N. Figure 8 shows the distribution of fitting residuals for subdwarfs from the two surveys. The left panel shows the LAMOST subdwarfs mainly covering M0–M3, while the SDSS subdwarfs on the right panel cover M0 to M8. The residual levels stabilize below 10% after the S/N becomes larger than ~30. The later-type subdwarfs

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

**Figure 6.** Upper panel: a LAMOST extreme subdwarf spectrum and its best-fit synthetic spectrum. The spectral bands contaminated by telluric absorptions are masked. Lower panel: an SDSS subdwarf spectrum showing H$\alpha$ emission and its best-fit synthetic spectrum.

from both samples show higher residual levels because of an average lower spectrum quality.

### 4.2.2. Comparison with Literature Results

In order to estimate the accuracy of the derived parameters, we cross-match the entire sample of LAMOST DR7 M-type stars with objects having known parameters from literature. As a result, we find a total of 269 observations for 167 stars studied with high or medium spectral resolution in nine papers, and the comparison is shown in Figure 9. Although a systematic bias in the effective temperature appears from around 3700K to the cool end, it generally follows a 1-to-1 trend with the literature values. The metallicity also seems to follow a 1-to-1 trend, while the gravity values show a larger range than the literature ones. Note that we have masked several telluric absorption bands where gravity-sensitive K and Na lines are located in the fitting process, and so the accuracy of our estimated gravity values is therefore affected somehow. The distributions of the differences (measurements from this work versus literature values) for the three parameters are shown in Figure 9. The bias and scatter are 165 K and 170 K for $T_{\text{eff}}$, 0.03 dex and 0.32 dex for log g, and -0.17 dex and 0.41 dex for [Fe/H], respectively.

## 5. Sample Properties Analysis

In this section, we analyze the properties of the subdwarf sample by comparing it with the dwarf sample on spectral index diagrams and the Gaia DR2 H-R diagram, and provide a preliminary account of their kinematic properties from the reduced proper motion diagram and in the 3D galactic motion system.

In Paper I, we suggested a screening condition associated with the CaH1 index be combined with the classical $\zeta$ condition to identify a subdwarf via its low-resolution spectrum. To show
<table><caption>**Table 3**
The Stellar Samples Used in This Work</caption><thead><tr><th></th><th>LAMOST M<br>Dwarfs<br>(1)</th><th>LAMOST M Sub-<br>dwarfs Initial Sample<br>(2)</th><th>SDSS M Subdwarfs<br>Initial Sample<br>(3)</th><th>LAMOST+SDSS Combined Subdwarf<br>Sample with Atmospheric Param. before<br>CaOH/CaH1 Cut</th><th>LAMOST+SDSS Green-<br>marked “Subdwarfs”</th><th>LAMOST+SDSS “Genuine”<br>Subdwarfs after CaOH/<br>CaH1 Cut<br>(4)</th><th>LAMOST M<br>Giants<br>(5)</th></tr></thead><tbody><tr><td>N</td><td>~70,000</td><td>4767</td><td>2780</td><td>3131 (LAMOST: 1852); (SDSS: 1279)</td><td>855</td><td>2276</td><td>7200</td></tr><tr><td>N<sub>Gaia</sub></td><td>35,382</td><td>...</td><td>...</td><td>1722 (LAMOST: 1160); (SDSS: 562)</td><td>526</td><td>1196</td><td>...</td></tr></tbody></table>

**Note.**

(1) The numbers corresponding to $N_{Gaia}$ means the objects (N) have available data from Gaia DR2 and can be used for kinematic analysis. The flag is set as 1 if all of the following conditions are true: a. phot_bp_mean_flux_over_error > 10, b. phot RP_mean_flux_over_error > 10, c. phot g_mean_flux_over_error > 10, d. ResFlag = 1 & ModFlag = 1 (from Bailer-Jones et al. 2018), e. astrometric_excess_noise_sig ≤ 2, and f. ruwe ≤ 1.4. (2) A visually identified sample from Zhang et al. (2019) for comparison. (3) Savcheva et al. (2014), the spectral indices are recalculated using the radial velocities published in the catalog. (4) i.e., using the Equation (5) in the present paper. (5) A visually identified sample from Zhang et al. (2019) for comparison.
<figure><img src="image_9.png" /><figcaption>**Figure 7.** M subdwarf sample constructed in this work, combining the low-resolution spectra from SDSS (blue dots) and LAMOST (red dots) data sets. The M dwarfs used for comparison (black dots) are visually confirmed from LAMOST data (Zhang et al. 2019). The bottom right internal subdiagram shows the spectral type distributions of the two subsamples.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 8.** Spectral fitting residual of subdwarfs as a function of the signal-to-noise ratio in the *i* band. Left panel: LAMOST subdwarfs; right panel: SDSS subdwarfs.</figcaption></figure>

the importance of gravity and a gravity-dependent index—CaH1—for identifying a “genuine” subdwarf, we divide the subdwarf sample selected above into two groups by the separator curve (Equation (9) in Paper I) on the [CaOH, CaH1] index diagram:

$$CaH1 < 0.4562 \times CaOH^3 - 0.1977 \times CaOH^2 - 0.01899 \times CaOH - 0.7631. \quad (5)$$

The objects that do not meet Equation (5) are marked in green in the following figures.

For further analysis, we retrieve proper motions and photometric magnitudes in *G*, *BP*, and *RP* bands of these stars from Gaia Data Release 2, and estimated distances from Bailer-Jones et al. (2018). To ensure reliability, we set a series of filter conditions as listed in the notes to Table 3, and finally 1722 objects among the 3131 selected in Section 4 meet the conditions, 526 of which are green-marked “subdwarfs.”

## 5.1. Spectral Index Diagram

As shown in Figure 10, the upper left panel shows the green-marked “subdwarfs.” According to the $\zeta$ values, we also divide the remaining subdwarfs into sdM/esdM/usdM subclasses on the [TiO5, CaH2+CaH3] diagram, as can be seen in the upper right panel, and the objects in the three subclasses are plotted as blue, purple, and magenta points, respectively. Most of the green-marked “subdwarfs” appear located in the “sdM” region, which is colored in blue. Therefore, we compare the gravity and metallicity of the two groups and display those distributions in the bottom left and middle panels. As shown in the bottom middle panel, the green objects share similar metal

abundance distribution with the blue labeled ones, however, their gravities are systematically lower than the latter ones by some 0.2 dex.

With the available proper motions of these targets from Gaia DR2, we also compare the total proper motions of the two groups in the bottom right panel of Figure 10. The proper motions of green-marked “subdwarfs” are overall smaller than those of the sdMs. Generally speaking, a large proper motion is a classical property of subdwarfs, though some objects may have relatively small proper motions due to the 3D motion direction. Proper motions of esdMs and usdMs are larger than those of sdMs (not shown in the figure), which means that the green ones do behave more like dwarfs than subdwarfs.

The gravity differences can be seen more clearly in Figure 11, in which we add the LAMOST M dwarfs and a new sample of M giants onto the [CaOH, CaH1] index diagram. The giants were also spectroscopically identified by visual inspection (Zhang et al. 2019). Giants, and dwarfs and subdwarfs are classified as luminosity class III, and V, respectively, and Jao et al. (2008) have proposed that subdwarfs be classified as VI, this sequence tracing the gravity variation trend. Therefore, Figure 11 clearly illustrates the gravity segregation between the luminosity classes of giants/dwarfs/subdwarfs thanks to the sensitivity of the CaH1 index to log g, especially when compared to CaOH index. The entire catalog can be accessed online and each column of the data is described in Table 4.

## 5.2. H-R Diagram

Using estimated distances from Bailer-Jones et al. (2018), we derive the absolute magnitudes $M_G$, $M_{BP}$, and $M_{RP}$ of the dwarfs and subdwarfs. Since most of the M-type stars we analyze here are located within 1 kpc, we choose to ignore the effect of extinction in the calculation. Figure 12 shows the stars on Gaia color–absolute magnitude diagram [BP–RP, $M_{RP}$]. On this diagram, which is an observational Hertzsprung–Russell diagram, the gray dots represent the dwarf sample, the green dots represent the “subdwarfs” that do not meet Equation (5), and the red dots represent the remaining subdwarfs (all subclasses together). The green-marked “subdwarfs” fall almost completely in the dwarf region, and thus once again verify the conclusion that they behave more like dwarfs than subdwarfs.

Besides, we find that a number of Equation (5) selected subdwarfs (red dots) also overlap with dwarfs on this diagram. This point will be developed below.

Figure 13 shows the metal abundance and gravity variation of these stars on the Gaia color–magnitude diagram. The subdwarfs falling in the dwarf region are the ones with the highest metal abundances or the smallest surface gravities. In other words, stars that are away from the main sequence have both large gravity and low metal abundance, and they should be the “genuine” subdwarfs.

## 5.3. Kinematics

### 5.3.1. Reduced Proper Motion diagram

Aside from the H-R diagram, another useful tool for effectively separating different stellar populations is the reduced proper motion (RPM; Jones 1972) diagram (e.g., Salim & Gould 2002; Subasavage et al. 2005; Lépine et al. 2007; Faherty et al. 2009), which uses photometric information
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Upper panels show the comparison of atmospheric parameters of 167 M stars estimated from 269 LAMOST spectra (including multi-observations) with the ones compiled from literature. Parameter values from different literature are shown in different colors as listed in the legend. Error estimates provided are shown as corresponding error bars. The uncertainties for the values from LAMOST spectra are the upper values of internal errors determined from signal-to-noise ratio and $\sqrt{\chi^2}$. The bottom panels show the distribution of differences along with the corresponding mean value and standard deviation.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 10.** The gravity and metallicity distributions of the green-marked "subdwarfs" vs. the other sdMs. The two upper panels show the distribution of spectral indices of four groups of subdwarfs: green-marked "subdwarfs" (the subdwarfs that do not meet Equation (5)), sdMs, esdMs, and usdMs (the remaining subdwarfs classified into categories according to the $\zeta$ values). The sdMs, esdMs, and usdMs are colored in blue, purple, and magenta, respectively. The bottom left and middle panels show the comparison of green-marked "subdwarfs" with the sdMs. The bottom right panel compares the total proper-motion distribution of the green-marked "subdwarfs" with that of the other sdMs.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>Figure 11. M-type stars with different gravity values shown on the spectral index diagram CaH1 vs. CaOH. Color coding is the same as in the upper left panel of Figure 10. To illustrate the sensitivity to gravity of this diagram, an M giant sample (7200 objects visually identified from Zhang et al. 2019 and colored in yellow) and the M dwarf sample are added.</figcaption></figure>

(color) and proper motions of the stars. Even without knowledge of the distance to the stars, the RPM diagram can be used to constrain kinematic properties of large stellar samples, because a given stellar population whose members are orbiting in the Galactic potential has a characteristic space velocity distribution reflected in a combination of luminosity and transverse motion. The definition of the reduced proper motion H is

$$H = m + 5 \log \mu + 5 = M + 5 \log T, \quad (6)$$

where m is the apparent magnitude of a star in a given photometric band, μ is the annual total proper motion (in arcsec yr⁻¹), M is the absolute magnitude, and T is the tangential velocity (in au yr⁻¹).

Since the dwarfs belong to the thin disk population and the subdwarfs are claimed to belong to the thick disk and halo populations, the comparison between blue to red or optical to near-infrared colors and the reduced proper motions can in principle relatively clearly distinguish the Population I dwarfs and Population II subdwarfs: (1) given an absolute magnitude, subdwarfs are bluer in color; (2) subdwarfs being members of a population spanning a spatial volume more extended out of the Galactic plane with more eccentric orbits, they have higher average tangential velocities (Salim & Gould 2002; Lépine et al. 2007). The RPM diagram combines these two features so that the subdwarfs and main-sequence stars fall into two separate regions. This method has long been used to separate high-velocity subdwarfs from dwarfs (Jones 1972; Yong & Lambert 2003a, 2003b).

Figure 14 shows the RPM diagram for our stars, using Gaia DR2 color and proper motions. A clear similarity with the information contained in the H-R diagram of Figure 14 can be noted. Although the selection biases of the combined LAMOST+SDSS subdwarf sample are poorly known (a mix of pointing directions, different limiting survey depths, velocity ellipsoid sampling, density distribution sampling, spatial inhomogeneities, etc.), basic trends can be outlined. First, the subdwarfs falling below the region occupied by the main-sequence dwarfs have low metal abundances and higher gravities. Second, remaining subdwarfs appear clearly divided in two clouds (noted A and B in the following) with a quite

clean separation: Cloud A is not distinct from the lower part of the main-sequence dwarf cloud, while Cloud B is centered around a half magnitude below the center of Cloud A. The fact that Cloud A and B are especially distinct in the RPM diagram imply that these two clouds sample two distinct populations whose kinematic behaviors are different.

### 5.3.2. Galactic Velocity Components

Using the usual textbook transformation formula, we compute the three-dimensional space velocity components U, V, and W in the right-handed Galactic frame: the U and V are contained in the Galactic plane; U points toward the Galactic center, while V is the velocity component in the direction of the solar motion. The W component is perpendicular to the Galactic plane and points toward the North Galactic pole. U, V, and W for our targets are determined using the radial velocities, coordinates, proper motions, and distances derived from the parallaxes. The components are reduced to the local standard of rest (LSR; Fuchs et al. 2009) by correcting from the solar motion assumed to be (U⊙, V⊙, W⊙) = [11.1, 12.24, 7.25] km s⁻¹ (Schönrich et al. 2010).

In Figures 15 and 16, we divide our remaining subdwarfs into different gravity and metallicity groups and compare them with the green-marked “subdwarfs” and dwarfs. Each dwarf bin contains 7000 objects and each subdwarf bin contains 100 objects. As expected, the green-marked “subdwarfs” behave mostly like field dwarfs with only a slightly larger dispersion in all of the velocity components. In addition, the yellow bins in Figure 15 representing the subdwarf group with the lowest gravity and the light blue bins in Figure 16 representing the subdwarf group with the highest metallicity have nearly the same behaviors in V as the dwarfs and the green-marked “subdwarfs.”

To further explore the kinematic behavior of the full subsamples, we draw several histograms in Figure 17, in which the dwarfs, green-marked “subdwarfs,” and Cloud A and Cloud B subdwarfs are plotted separately. The mean values and standard deviations are also shown on each panel, except for |z|, the absolute value of the distance to the Galactic plane, for which the quartiles are computed. The separation between Cloud A and Cloud B objects is defined by the fiducial line drawn on Figure 14. Several points emerge:

(a) The gravities increase systematically from dwarfs (mean close to 5.0, in agreement with the results from Section 3) to Cloud B subdwarfs (mean around 5.2).

(b) Metallicity decreases systematically from dwarfs (mean around −0.4 dex) to Cloud B subdwarfs. The metallicity of the dwarfs, quite surprisingly, appears systematically poorer than solar, with a distribution tail down to −1. dex. Although the error assessment and control is difficult in the spectral fitting process, we recall that the comparison in Section 4.2 with the sample of 167 stars having a metallicity measurement in the literature did not reveal any major systematic deviation.

(c) As shown in Figure 18, the halo candidates in Cloud B subdwarfs exhibit an inconspicuous bimodal distribution of metallicity, with two subpopulations, one around [Fe/H] = −1 dex and the other around −1.5 dex.

(d) The mean values and dispersions of the U, V, and W components agree quite well with the dwarf sample belonging to the thin disk, with a velocity lag of
<table><caption>**Table 4**

Data Description of the Subdwarf Catalog</caption><thead><tr><th>Column Name</th><th>Unit</th><th>Description</th></tr></thead><tbody><tr><td>ID</td><td>...</td><td>SpecObjID for SDSS objects and obsid for LAMOST objects</td></tr><tr><td>specname</td><td>...</td><td>Name of spectrum</td></tr><tr><td>ra</td><td>deg</td><td>R.A. (J2000)</td></tr><tr><td>dec</td><td>deg</td><td>Decl. (J2000)</td></tr><tr><td>l</td><td>deg</td><td>Galactic longitude</td></tr><tr><td>b</td><td>deg</td><td>Galactic latitude</td></tr><tr><td>rv</td><td>km s<sup>-1</sup></td><td>Heliocentric radial velocity</td></tr><tr><td>Teff</td><td>K</td><td>Estimated effective temperature</td></tr><tr><td>logg</td><td>dex</td><td>Estimated surface gravity</td></tr><tr><td>FeH</td><td>dex</td><td>Estimated overall metallicity</td></tr><tr><td>snri</td><td>...</td><td>Average spectrum signal-to-noise ratio in i band</td></tr><tr><td>spt</td><td>...</td><td>Spectral subtype</td></tr><tr><td>CaOH</td><td>...</td><td>Spectral index of CaOH band</td></tr><tr><td>CaH1</td><td>...</td><td>Spectral index of CaH1 band</td></tr><tr><td>CaH2</td><td>...</td><td>Spectral index of CaH2 band</td></tr><tr><td>CaH3</td><td>...</td><td>Spectral index of CaH3 band</td></tr><tr><td>TiO5</td><td>...</td><td>Spectral index of TiO5 band</td></tr><tr><td>ZetaL07</td><td>...</td><td>The value of ζ parameter calibrated by Lépine et al. (2007)</td></tr><tr><td>ZetaD12</td><td>...</td><td>The value of ζ parameter calibrated by Dhital et al. (2012)</td></tr><tr><td>ZetaL13</td><td>...</td><td>The value of ζ parameter calibrated by Lépine et al. (2013)</td></tr><tr><td>ZetaZ19</td><td>...</td><td>The value of ζ parameter calibrated by Zhang et al. (2019)</td></tr><tr><td>source</td><td>...</td><td>The source of spectrum (LAMOST/SDSS)</td></tr><tr><td>parallax</td><td>mas</td><td>Gaia DR2 parallax</td></tr><tr><td>parallax_error</td><td>mas</td><td>Standard error of Gaia DR2 parallax</td></tr><tr><td>pmra</td><td>mas yr<sup>-1</sup></td><td>Gaia DR2 proper motion in R.A. direction</td></tr><tr><td>pmra_error</td><td>mas yr<sup>-1</sup></td><td>Standard error of Gaia DR2 proper motion in R.A. direction</td></tr><tr><td>pmdec</td><td>mas yr<sup>-1</sup></td><td>Gaia DR2 proper motion in decl. direction</td></tr><tr><td>pmdec_error</td><td>mas yr<sup>-1</sup></td><td>Standard error of Gaia DR2 proper motion in decl. direction</td></tr><tr><td>astrometric_gof_al</td><td>...</td><td>Goodness of fit statistic of model with respect to along-scan observations</td></tr><tr><td>astrometric_excess_noise_sig</td><td>...</td><td>Significance of excess noise</td></tr><tr><td>phot_g_mean_flux_over_error</td><td>...</td><td>G-band mean flux divided by its error</td></tr><tr><td>phot_g_mean_mag</td><td>mag</td><td>Gaia DR2 G-band mean magnitude</td></tr><tr><td>phot_bmeanaimag</td><td>...</td><td>Integrated BP mean flux divided by its error</td></tr><tr><td>phot_bmean_mag</td><td>mag</td><td>Gaia DR2 integrated BP mean magnitude</td></tr><tr><td>phot_rp_mean_flux_over_error</td><td>...</td><td>Integrated RP mean flux divided by its error</td></tr><tr><td>phot_rp_mean_mag</td><td>mag</td><td>Gaia DR2 integrated RP mean magnitude</td></tr><tr><td>bp RP</td><td>mag</td><td>Gaia DR2 BP-RP color</td></tr><tr><td>ruwe</td><td>...</td><td>Renormalized Unit Weight Error associated to each Gaia source</td></tr><tr><td>rest</td><td>pc</td><td>Estimated distance from Bailer-Jones et al. (2018), based on Gaia DR2</td></tr><tr><td>ResFlag</td><td>...</td><td>The Result Flag from Bailer-Jones et al. (2018)</td></tr><tr><td>ModFlag</td><td>...</td><td>The Modality Flag from Bailer-Jones et al. (2018)</td></tr><tr><td>flag</td><td>...</td><td>Set as 1 for the final sample used in kinematic part, see Table 3 for details</td></tr><tr><td>V<sub>total</sub></td><td>km s<sup>-1</sup></td><td>Total spatial velocity</td></tr><tr><td>Z</td><td>pc</td><td>Vertical distance away from Galactic plane</td></tr><tr><td>U</td><td>km s<sup>-1</sup></td><td>Velocity component points toward the galactic center</td></tr><tr><td>V</td><td>km s<sup>-1</sup></td><td>The tangential velocity component rotating around galactic center</td></tr><tr><td>W</td><td>km s<sup>-1</sup></td><td>Velocity component points toward the north galactic pole</td></tr></tbody></table>

Note. The complete catalog can be accessed online in the China-VO PaperData repository: doi:10.12149/101043.

(This table is available in its entirety in machine-readable form.)

$V = -10 \text{ km s}^{-1}$. The green-marked and Cloud A objects have greater velocity dispersions, suggesting possible membership to the thick disk, but their mean $V$ value significantly deviates from the usually adopted $-60 \text{ km s}^{-1}$. Cloud B objects are obviously dominated by halo members, with a mean $V$ largely retrograde and with considerable dispersion.

(e) The quartiles of the $|z|$ distributions show that the dwarf sample is the one which is the most concentrated around the Galactic plane, while Cloud B contains the most diffuse population out of this plane. These histograms

also show that the LAMOST+SDSS surveys sample the M-dwarf population inside the scale height of the thin disk above the Galactic plane (600 pc; Jurić et al. 2008), while the subdwarf one is sampled only up to less than 1 kpc (one scale height of the thick disk or less; Gilmore & Reid 1983; Veltz et al. 2008; Carollo et al. 2010).

(f) The striking similarity of all of the indicators (except for a marginal difference in log $g$) between the green-marked objects and the Cloud A ones imply that they are members of the same stellar population as defined kinematically, only differing by the CaH1 and CaOH
<figure><img src="image_14.png" /><figcaption>**Figure 12.** All of the subdwarfs and dwarfs on the Gaia color-magnitude diagram. The absolute magnitudes in RP band are derived from the Gaia DR2 apparent magnitudes and estimated distances from Bailer-Jones et al. (2018). Most of the green-marked “subdwarfs” fall into the main-sequence region populated by the M dwarfs (gray dots), and the remaining subdwarfs (red dots) lie in part below the main sequence with a large dispersion, but some are also distributed across the main-sequence region.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Figure 13.** After the removal of the green-marked “subdwarfs,” the remaining samples are shown on the Gaia color–absolute magnitude diagram again. On the left panel, subdwarfs are color coded for different metallicities, while the same ones on the right panel are color coded for different gravities. Note that the subdwarfs with log g > 5.5 or log g < 4.5 (38 objects in total) are not plotted on the right panel to make the color bar more tight.</figcaption></figure>

indices. In the following, these two groups will be considered as a unique subsample that will be designated as Extended Cloud A.

### 5.3.3. The Toomre Diagram

Trying to push forward the analysis, we have plotted in Figure 19 the Toomre diagram for all our stars.

The dwarf cloud appears slightly asymmetric, with an extension toward negative V velocity component. This is not unexpected since two- or three-component disk (thin, thick, and intermediate) model populations (Schönrich & Binney 2009, and references therein) predict such an asymmetry. The Extended Cloud A group seems to be more or less coincident with the dwarf cloud, while Cloud B objects are scattered across a large area of the diagram.

1. Halo objects: To select halo objects, a stringent condition on their total velocity (Bonaca et al. 2017), which would avoid pollution by possibly numerous thick disk stragglers (Smith et al. 2009), is:

$$ |V - V_{\text{LSR}}| \ge 220 \text{ km s}^{-1}, \qquad (7) $$

<figure><img src="image_16.png" /><figcaption>**Figure 14.** After the removal of the green-marked “subdwarfs,” the remaining samples are shown on the reduced proper motion diagram. The color coding is the same as in Figure 12. The fiducial separation line between Cloud A and Cloud B objects is drawn (see text).</figcaption></figure>

which translates, with the adopted velocity components of the LSR ($U = 0, V = 220, W = 0 \text{ km s}^{-1}$), into:

$$ v_{\text{tot}} = \sqrt{U^2 + V^2 + W^2} \ge 220 \text{ km s}^{-1}, \qquad (8) $$

where $v_{\text{tot}}$ is the total space velocity with respect to the LSR.

This selection provides a kinematic sample of the local halo haunting the solar neighborhood, which essentially contains stars from Cloud B, (220 objects), with a handful from Extended Cloud A, (9 objects), accompanied by targets considered as outliers from the dwarf cloud (71 objects; see below). Its kinematic characteristics are in fair agreement with those of already identified halo-population stars selected across more widely extended volumes and using more luminous targets (Smith et al. 2009; Bond et al. 2010; Bochanski et al. 2013): $\langle U \rangle = 5 \text{ km s}^{-1}$ and $\sigma_U = 173 \text{ km s}^{-1}$, $\langle V \rangle = -248 \text{ km s}^{-1}$ and $\sigma_V = 77 \text{ km s}^{-1}$, and $\langle W \rangle = 6 \text{ km s}^{-1}$ and $\sigma_W = 89 \text{ km s}^{-1}$. With the adopted value of the LSR velocity, the fiducial line at $V = -220 \text{ km s}^{-1}$ separates the stars that have retrograde orbits from those that have prograde ones. A striking fact is the quite large fraction of prograde objects (258 stars or 40%) observed in the present local halo sample; therefore, the strongly negative value of $\langle V \rangle$ quoted above does not account completely for a complex orbital distribution.

The metallicity of this halo sample, in spite of the kinematic cut applied, remains bimodal. Previous studies, based mostly on F–G–K stars in which metallicity is derived from atomic lines, have already found a substantial metal-rich component in the halo population (and the metallicity distribution of globular clusters is one historic and well-documented example; see, e.g., Zinn 1985; Harris 1996), but the metal-rich peak is generally found around $[\text{Fe/H}] = -0.6 \text{ dex}$ (Bonaca et al. 2017). The prograde objects are also reputedly more metal rich than the retrograde ones, implying that they could belong to different subpopulations. The metal-rich one contains inner halo objects, while the metal-poor one is made of outer halo objects, and these two subpopulations have different formation histories and different space distributions. In the present local halo sample, we do not find such a segregation, the number of prograde metal-poor objects remaining important, while many higher metallicity stars are on obviously retrograde orbits, as shown in the right panel of Figure 19.
<figure><img src="image_17.png" /><figcaption>**Figure 15.** Velocity component distribution of dwarfs and subdwarfs with different gravities in the Galactic 3D motion system (U, V, W). From left to right, the abscissa represents the velocity component of U, V, and W, respectively. The ordinate represents the distance from Galactic plane. Except for the green-marked "subdwarfs," the remaining subdwarfs are divided into groups with different gravities and distinguished by different colors. Each dwarf bin contains 7000 stars and each subdwarf bin contains 100 stars. The node and the error bar show the mean value and the standard deviation of each bin, respectively.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**Figure 16.** Velocity component distribution of dwarfs and subdwarfs with different metallicities in the Galactic 3D motion system (U, V, W). Except for the green-marked "subdwarfs," the remaining subdwarfs are divided into groups with different metallicities and distinguished by different colors. The meaning of the axes and the number of stars contained in each bin are the same as in Figure 15.</figcaption></figure>

2. Thin disk dwarfs: Since some spectroscopically identified dwarfs are found to kinematically belong to the local halo, we could expect some continuity in the dwarf high-velocity distribution tail, and therefore a number of them would also be kinematically mixed with the Extended Cloud A population and need to be disentangled.

To select thin disk dwarfs, a condition of type $v_{tot}$ = constant is not completely satisfactory because of the asymmetry of the dwarf cloud in the Toomre diagram. A correct way to proceed would be to compute for each star its probability of membership to one of the three populations—halo, thick disk, and thin disk, as proposed
<figure><img src="image_19.png" /><figcaption>**Figure 17.** Histograms of some characteristics for the various subpopulations of dwarfs and subdwarfs for which Gaia astrometry is available. From left to right, log g, [Fe/H], *U*, *V*, *W* space velocity components, and |z|. From top to bottom: (a) all spectroscopically identified M dwarfs, (b) green-marked "subdwarfs," (c) Cloud A subdwarfs (see Figure 14 for definition), (d) Cloud B subdwarfs, (e) Extended Cloud A (see text for definition), and (f) disk outliers (spectroscopically identified M dwarfs whose total space velocity with respect to the LSR is larger than that of 99% of the population; see Figure 19 for their location on Toomre diagram). The μ and σ on each panel indicate the mean value and standard deviation, respectively. For the |z| distributions, the quartiles are indicated.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Figure 18.** Bimodal distribution of metallicity of the halo candidates, which are selected from Cloud B subdwarfs with $v_{\text{tot}} \ge 220$ km s⁻¹. The mean values and standard deviations of each Gaussian fit are also shown on the diagram.</figcaption></figure>

by, e.g., Bensby et al. (2003)—but we prefer to postpone such a calculation because the selection effects in the present sample are not correctly assessed. We choose a simplified and empirical procedure as follows: we assume that the distribution of the dwarf stars in the Toomre diagram is consistent with an incomplete ellipse, and that the isodensity contours of this ellipse trace a constant probability level of a star to belong to its parent population. We select the isodensity contour containing 99% of the dwarf cloud and fit an ellipse to this contour. All stars found outside are considered as “outliers” from the thin disk dwarf population.

The kinematically “purified” dwarf sample shows typical velocity component values of the thin disk population (Edvardsson et al. 1993; Reddy et al. 2003): $\langle U \rangle = 0$ km s⁻¹ and $\sigma_U = 44$ km s⁻¹, $\langle V \rangle = -13$ km s⁻¹ and $\sigma_V = 30$ km s⁻¹, and $\langle W \rangle = 0$ km s⁻¹ and $\sigma_W = 26$ km s⁻¹, and its stars have exclusively prograde orbits, as expected. The metallicity, as outlined above, is on
<figure><img src="image_21.png" /><figcaption>**Figure 19.** Left panel: Toomre diagram for all stars in the present study. Black points: all spectroscopically identified M dwarfs; green circles: the green-marked "subdwarfs"; blue circles: Cloud A subdwarfs; red circles: Cloud B subdwarfs. The black dashed curve encloses 99% of the M dwarf population: all black points outside of this curve are considered as representative of "outliers." The dashed red circle is our adopted limit $v_{\text{tot}} = 220 \text{ km s}^{-1}$ for halo-population assignment. The dashed magenta vertical line separates retrograde orbits on its left from prograde orbits on its right. Right panel: the M dwarfs with thin disk kinematics have been removed. The green-marked "subdwarfs" and Cloud A subdwarfs are merged into a single group, Extended Cloud A. The M dwarf outliers have been separated based on their total space velocity $v_{\text{tot}}$ with respect to the LSR. The Cloud B subdwarfs are color coded in four categories based on their metallicity and $v_{\text{tot}}$.</figcaption></figure>

average slightly deficient, the histogram showing three peaks, one solar or slightly supersolar, the principal one around −0.4 dex and the third one around −1 dex. Since the selection effects are not under control, we doubt that this three-component would be significant.

3. Thick disk population and its elusive limits: The Extended Cloud A occupies a large area, somewhat fan shaped vertically, in the Toomre diagram, broadly covering the dwarf cloud and merging beyond it into the halo region, with practically all orbits prograde. The shape of the $|z|$ histogram, with its peak displaced from that of the thin disk dwarfs and its quartiles systematically larger shows that this population is clearly thicker in z. The average metal content is poorer than that of the thin disk dwarfs at [Fe/H] = −0.74 dex with an [Fe/H] distribution having a long metal-poor tail extending to −2.5 dex. We suspect that the Extended Cloud A population is an intricate mix of objects really belonging to a thick disk component with pollution by an important contribution of thin disk “mild” subdwarfs very difficult to disentangle, with unknown selection effects playing a role in the background. A possible way to separate these contributions is the detailed computation of individual orbits and the study of the $z_{\text{max}}$ and eccentricities, but such a work is far beyond the scope of the present study.

In the Toomre diagram, the Extended Cloud A population is mixed with a fraction of the Cloud B population, corresponding to stars that preferentially belong to the high metallicity peak of the bimodal [Fe/H] distribution of Cloud B in Figure 17. These stars likely belong in part to the halo, because our halo selection kinematic cut is very stringent, and in part to the thick

disk, but their assignments to the two components would probably also need a detailed orbital calculation.

The [Fe/H] distribution of the outliers from the dwarf cloud show that they span the same broad metallicity range as the principal dwarf population, peaking at −0.6 dex, only slightly more metal poor than the ordinary disk dwarfs. Their distribution in $|z|$ is clearly more extended, making them probable members of the thick disk. Their velocity dispersions $\sigma_U = 119 \text{ km s}^{-1}$, $\sigma_V = 90 \text{ km s}^{-1}$, and $\sigma_W = 75 \text{ km s}^{-1}$ suggest that they contain a majority of objects belonging to the thick disk, with some pollution by an inner halo fraction.

To conclude, the combined subdwarf sample extracted from LAMOST DR7 and SDSS DR7 contains a mix of objects belonging to various components: clear halo members with an implicit bimodal metallicity and considerable orbital mixing between retrograde and prograde cases, and an important thick disk fraction merging both into the halo and thin disk. The spectroscopically selected M dwarfs themselves, who almost totality belong to the standard thin disk, contain a small fraction (less than 1% of the total) of outliers belonging both to the thick disk and the halo. It is quite unclear if the present situation is dependent or not on the selection effects, especially the favored directions of investigation toward the Galactic anticenter in the LAMOST survey.

## 6. Summary and Conclusion

In the most widely used classification system, M-type main-sequence stars are classified into dM/sdM/esdM/usdM subclasses corresponding to different metal abundances
according to the CaH2, CaH3, and TiO5 molecular bands in the low-resolution spectrum. The metal-poor subclasses are named as subdwarfs, which have typical kinematic characteristics of thick disk and halo populations. However, in the present work, we suggest the “genuine” subdwarfs belonging to population II be classified as luminosity class VI on the H–R diagram. For these stellar objects, having larger surface gravity is a necessary condition as important as “being metal deficient,” and the three spectral indices in classical classification systems cannot be fully competent at selecting these subdwarfs. This conclusion is drawn from a series of experiments including the comparison of synthetic spectra with the templates, measuring atmospheric parameters for a subdwarf sample, and combining with a kinematics analysis, etc. According to the spectral index CaOH–CaH1 relationship and the empirical relationship on RPM diagram, we divide a spectroscopically identified sample of subdwarfs into multiple groups and analyze the multi-population properties in this sample from their multi-dimensional parameters.

The sample including subdwarfs from both LAMOST and SDSS was combined with a control group of dwarfs selected from LAMOST, and their atmospheric parameters were estimated based on fits to the PHOENIX grid. The technical details of the whole fitting procedure of individual spectra are developed, including the use of different convolution kernels to smooth the synthetic spectra and the pseudocontinuum flux correction specifically implemented for the LAMOST data. The residuals of the fitting procedure can be used to determine the precision, which depends on the S/N of the observed spectra. The accuracy of the process is evaluated using 167 M-type stars with measured atmospheric parameters from the literature that have LAMOST spectra; the bias and scatter of the comparison of parameters are 165 ± 170 K for T<sub>eff</sub>, 0.03 ± 0.32 dex for gravity, and −0.17 ± 0.41 dex for metallicity. A systematic bias in effective temperature exists for T<sub>eff</sub> lower than 3700 K, while the gravity and metallicity both appear in fair agreement. The effective temperature scale produced by these detailed fits is reasonably consistent with those published by Rajpurohit et al. (2014) for the subdwarfs and Rajpurohit et al. (2018a) for the dwarfs. The following analysis is mainly dependent on the latter two atmospheric parameters.

For the sample of subdwarfs and dwarfs, apparent magnitudes, broadband colors, and proper motions are obtained from cross-matching these two sets with Gaia DR2, and the distances are from Bailer-Jones et al. (2018). The objects are selected so as to have acceptable quality flags in photometry, distance, and accuracy. The spectroscopic “subdwarfs” do not entirely lie below the main sequence, but rather are distributed in an extended region that overlaps the one occupied by the M dwarfs in the color–absolute magnitude diagram, while the objects that lie away (and below) from the main sequence are the ones with both larger gravity and lower metal abundance. They are the “genuine” subdwarfs, for which the luminosity class VI (Jao et al. 2008) is justified. Alternatively, some “subdwarfs” with gravity similar to that of the dwarfs or only slightly higher also behave like dwarfs in many respects, although they are medium metal-deficient based on the definition using the CaH and TiO spectral indices. We have been able to sort out a significant subsample of objects which, in spite of having a low metallicity on average, appear intricately mixed with the ordinary main-sequence dwarfs and

also share their location in a reduced proper motion diagram. These “subdwarfs” should perhaps be better classified as “metal-poor dwarfs.”

A provisional kinematic analysis of these samples show that the sdM population lying below the main-sequence cloud is dominated by halo stars, in which an implicit bimodal metallicity distribution appears, with a peak around −1.0 dex and a second peak around −1.5 dex. This group, which samples the Galactic halo only in a very local volume (typically less than 1 kpc in radius), contains a mix of objects of prograde and retrograde orbits, as revealed by their location in the Toomre diagram, without a clear trend with metallicity. The other subdwarfs, including those that we prefer to consider as “metal-poor dwarfs” appear as a mixed population of thick disk and thin disk members. If “lying below the main sequence” and “associated with halo kinematics” (with a large negative V component and large dispersions in *U*, *V*, and *W*) define intrinsic features of the genuine subdwarfs belonging to Population II stars, then both a large gravity (average log g = 5.2–5.4) and low metal abundance should be essential attributes of them. The fact that the two properties must exist simultaneously needs to be underlined: we have only found a handful of halo objects among the other subdwarfs, even those that have a metallicity lower than −1.0 dex.

The vast majority of ordinary dwarfs populate the Galactic thin disk, as expected, with an average metallicity slightly lower than solar. A small fraction (less than 1%) form a set of kinematic outliers, halo and thick disk probable members. Finally, the CaH1 index is a good indicator of gravity experimentally, and behaves better in separating subdwarfs from dwarfs than the composite index CaH2+CaH3 (the CaH2 index is defined in a region of a CaH band that also overlaps a major TiO band extending redward from 6700 Å).

Though contamination by a low ratio of multiplicity (12.5% ± 1.9%: Ziegler et al. 2015) and the parameter coupling effect would influence the accuracy of parameter measurements, a preliminary conclusion can still be drawn from the analysis results above. Besides, the accurate discrimination of subdwarfs has to be revisited with more information, such as high-resolution spectra and multiband data, and the estimates of parameters also need a more complete model grid (an independent alpha enrichment, such as in the analysis of Hejazi et al. 2020, more complete opacity and line lists, etc.). The subpopulation membership assessment of the subdwarfs found in numbers in the large-area spectroscopic surveys, in turn, needs careful control of selection effects and detailed orbital calculations.

We thank the anonymous referee for helpful comments and suggestions. Z.S. thanks Dr. Yan. H.L. for the thoughtful discussion about smoothing the synthetic spectra, and Dr. Allard, F. for her helpful private communication about PHOENIX models. This work is supported by the National Key R&D Program of China (No. 2019YFA040550), and the National Science Foundation of China (No. U1931209). Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, LAMOST) is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences.
*Software:* astropy (Astropy Collaboration et al. 2013), matplotlib (Barrett et al. 2005), pandas (McKinney 2010), numpy (Oliphant 2007), scipy (Virtanen et al. 2020).

## ORCID iDs

Shuo Zhang https://orcid.org/0000-0003-1454-1636

A-Li Luo https://orcid.org/0000-0001-7865-2648

Rui Wang https://orcid.org/0000-0001-6767-2395

Yin-Bi Li https://orcid.org/0000-0001-7607-2666

John Gizis https://orcid.org/0000-0002-8916-1972

Yan Lu https://orcid.org/0000-0001-7846-3652

Yi-Han Song https://orcid.org/0000-0001-7255-5003

Hua-Wei Zhang https://orcid.org/0000-0002-7727-1699

## References

Ake, T. B., & Greenstein, J. L. 1980, ApJ, 240, 859

Allard, F. 2016, in SF2A-2016: Proc. Annual Meeting of the French Society of Astronomy and Astrophysics, ed. C. Reylé et al. (Lyon: Centre de Recherche Astrophysique de Lyon), 223

Allard, F., & Hauschildt, P. H. 1995, ApJ, 445, 433

Allard, F., Hauschildt, P. H., Alexander, D. R., & Starrfield, S. 1997, ARA&A, 35, 137

Allard, F., Hauschildt, P. H., Alexander, D. R., Tamanai, A., & Schweitzer, A. 2001, ApJ, 556, 357

Allard, F., Homeier, D., & Freytag, B. 2011, in ASP Conf. Ser. 448, Model Atmospheres From Very Low Mass Stars to Brown Dwarfs, ed. C. Johns-Krull, M. K. Browning, & A. A. West (San Francisco, CA: ASP), 91

Allard, F., Homeier, D., & Freytag, B. 2012, RSPTA, 370, 2765

Allard, F., Homeier, D., & Freytag, B. 2013, MmSAI, 84, 1053

Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481

Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33

Bai, Y., Luo, A. L., Comte, G., et al. 2016, RAA, 16, 107

Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Mantelet, G., & Andrae, R. 2018, AJ, 156, 58

Baraffe, I., Homeier, D., Allard, F., & Chabrier, G. 2015, A&A, 577, A42

Barrett, P., Hunter, J., Miller, J. T., Hsu, J. C., & Greenfield, P. 2005, in ASP Conf. Ser. 347, Matplotlib—A Portable Python Plotting Package, ed. P. Shopbell, M. Britton, & R. Ebert (San Francisco, CA: ASP), 91

Bensby, T., Feltzing, S., & Lundström, I. 2003, A&A, 410, 527

Bochanski, J. J., Savcheva, A., West, A. A., & Hawley, S. L. 2013, AJ, 145, 40

Bonaca, A., Conroy, C., Wetzel, A., Hopkins, P. F., & Kereš, D. 2017, ApJ, 845, 101

Bond, N. A., Ivezić, Ž., Sesar, B., et al. 2010, ApJ, 716, 1

Burgasser, A. J., & Kirkpatrick, J. D. 2006, ApJ, 645, 1485

Caffau, E., Ludwig, H. G., Steffen, M., Freytag, B., & Bonifacio, P. 2011, SoPh, 268, 255

Carollo, D., Beers, T. C., Chiba, M., et al. 2010, ApJ, 712, 692

Castelli, F., & Kurucz, R. L. 2004, A&A, 419, 725

Cui, X.-Q., Zhao, Y.-H., Chu, Y.-Q., et al. 2012, RAA, 12, 1197

Dahn, C. C., Liebert, J., Harris, H. C., & Guetter, H. H. 1995, in Proc. of ESO Workshop The Bottom of the Main Sequence—and Beyond, ed. C. G. Tinney (Berlin: Springer), 239

Dhital, S., West, A. A., Stassun, K. G., et al. 2012, AJ, 143, 67

Du, B., Luo, A. L., Kong, X., et al. 2016, ApJS, 227, 27

Edvardsson, B., Andersen, J., Gustafsson, B., et al. 1993, A&A, 500, 391

Faherty, J. K., Burgasser, A. J., Cruz, K. L., et al. 2009, AJ, 137, 1

Fuchs, B., Dettbarn, C., Rix, H.-W., et al. 2009, AJ, 137, 4149

Gaia Collaboration, Babusiaux, C., van Leeuwen, F., et al. 2018b, A&A, 616, A10

Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018a, A&A, 616, A1

Gilmore, G., & Reid, N. 1983, MNRAS, 202, 1025

Gizis, J. E. 1997, AJ, 113, 806

Gunn, J. E., Carr, M., Rockosi, C., et al. 1998, AJ, 116, 3040

Gunn, J. E., Siegmund, W. A., MANNERY, E. J., et al. 2006, AJ, 131, 2332

Gustafsson, B., Bell, R. A., Eriksson, K., & Nordlund, A. 1975, A&A, 500, 67

Gustafsson, B., Edvardsson, B., Eriksson, K., et al. 2008, A&A, 486, 951
Harris, W. E. 1996, AJ, 112, 1487

Hartwick, F. D. A., Cowley, A. P., & Mould, J. R. 1984, ApJ, 286, 269

Hauschildt, P. H., Allard, F., & Baron, E. 1999, ApJ, 512, 377

Hejazi, N., Lépine, S., Homeier, D., Rich, R. M., & Shara, M. M. 2020, AJ, 159, 30

Jao, W.-C., Henry, T. J., Beaulieu, T. D., & Subasavage, J. P. 2008, AJ, 136, 840

Jao, W.-C., Henry, T. J., Subasavage, J. P., et al. 2011, AJ, 141, 117

Jones, E. M. 1972, ApJ, 173, 671

Jones, H. R. A., Longmore, A. J., Allard, F., & Hauschildt, P. H. 1996, MNRAS, 280, 77

Jurić, M., Ivezić, Ž., Brooks, A., et al. 2008, ApJ, 673, 864

Katz, D., Sartoretti, P., Cropper, M., et al. 2019, A&A, 622, A205

Kesseli, A. Y., Kirkpatrick, J. D., Fajardo-Acosta, S. B., et al. 2019, AJ, 157, 63

Kurucz, R. L. 1973, PhD thesis, Harvard Univ.

Leggett, S. K., Allard, F., Berriman, G., Dahn, C. C., & Hauschildt, P. H. 1996, ApJS, 104, 117

Leggett, S. K., Allard, F., Dahn, C., et al. 2000, ApJ, 535, 965

Lépine, S., Hilton, E. J., Mann, A. W., et al. 2013, AJ, 145, 102

Lépine, S., Rich, R. M., & Shara, M. M. 2003, AJ, 125, 1598

Lépine, S., Rich, R. M., & Shara, M. M. 2007, ApJ, 669, 1235

Lépine, S., & Scholz, R.-D. 2008, ApJL, 681, L33

Lépine, S., Shara, M. M., & Rich, R. M. 2004, ApJL, 602, L125

Lindegren, L., Hernández, J., Bombrun, A., et al. 2018, A&A, 616, A2

Liu, C., Fu, J., Shi, J., et al. 2020, arXiv:2005.07210

Luo, A.-L., Zhao, Y.-H., Zhao, G., et al. 2015, RAA, 15, 1095

Luri, X., Brown, A. G. A., Sarro, L. M., et al. 2018, A&A, 616, A9

McKinney, W. 2010, in Proc. 9th Python in Science Conf. 445, ed. S. van der Walt & J. Millman (Austin, TX), 51

Mould, J. R. 1976, ApJ, 210, 402

Mould, J. R., & McElroy, D. B. 1978, ApJ, 220, 935

Oliphant, T. E. 2007, CSE, 9, 10

Rajpurohit, A. S., Allard, F., Rajpurohit, S., et al. 2018a, A&A, 620, A180

Rajpurohit, A. S., Allard, F., Teixeira, G. D. C., et al. 2018b, A&A, 610, A19

Rajpurohit, A. S., Reylé, C., Allard, F., et al. 2014, A&A, 564, A90

Rajpurohit, A. S., Reylé, C., Allard, F., et al. 2016, A&A, 596, A33

Reddy, B. E., Tomkin, J., Lambert, D. L., & Allende Prieto, C. 2003, MNRAS, 340, 304

Reid, I. N., Hawley, S. L., & Gizis, J. E. 1995, AJ, 110, 1838

Salim, S., & Gould, A. 2002, ApJL, 575, L83

Sandage, A. 1969, ApJ, 158, 1115

Sandage, A., & Kowal, C. 1986, AJ, 91, 1140

Savcheva, A. S., West, A. A., & Bochanski, J. J. 2014, ApJ, 794, 145

Schönrich, R., & Binney, J. 2009, MNRAS, 399, 1145

Schönrich, R., Binney, J., & Dehnen, W. 2010, MNRAS, 403, 1829

Smith, M. C., Evans, N. W., Belokurov, V., et al. 2009, MNRAS, 399, 1223

Subasavage, J. P., Henry, T. J., Hambly, N. C., et al. 2005, AJ, 130, 1658

Veltz, L., Bienaymé, O., Freeman, K. C., et al. 2008, A&A, 480, 753

Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, NatMe, 17, 261

West, A. A., Hawley, S. L., Walkowicz, L. M., et al. 2004, AJ, 128, 426

Woolf, V. M., & Wallerstein, G. 2005, MNRAS, 356, 963

Yee, S. W., Petigura, E. A., & von Braun, K. 2017, ApJ, 836, 77

Yong, D., & Lambert, D. L. 2003a, PASP, 115, 22

Yong, D., & Lambert, D. L. 2003b, PASP, 115, 796

York, D. G., Adelman, J., Anderson, J. E. J., et al. 2000, AJ, 120, 1579

Zhang, L., Pi, Q., Han, X. L., et al. 2016, NewA, 44, 66

Zhang, S., Luo, A. L., Comte, G., et al. 2019, ApJS, 240, 31

Zhang, Z. 2019, MNRAS, 489, 1423

Zhang, Z. H., Galvez-Ortiz, M. C., Pinfield, D. J., et al. 2018, MNRAS, 480, 5447

Zhang, Z. H., Homeier, D., Pinfield, D. J., et al. 2017a, MNRAS, 468, 261

Zhang, Z. H., Pinfield, D. J., Gálvez-Ortiz, M. C., et al. 2017b, MNRAS, 464, 3040

Zhong, J., Lépine, S., Hou, J., et al. 2015, AJ, 150, 42

Ziegler, C., Law, N. M., Baranec, C., Riddle, R. L., & Fuchs, J. T. 2015, ApJ, 804, 30

Zinn, R. 1985, ApJ, 293, 424