M-subdwarf Research. I. Identification, Modified Classification System, and Sample Construction

M-subdwarf stars, as cool stars of a low effective temperature (4000–2400 K, Rajpurohit et al. 2013) have a spectrum dominated by molecular absorption bands, which show considerable overlapping across the whole visible range. The continuum being weak in the blue, the best observing range with standard optical spectrographic instruments is the red and the deep red, where the spectrum is covered by a dense forest of molecular lines, hiding or blending most of the atomic lines used in the usual spectral analysis and diagnostic. At low resolution, molecular absorption bands from metal oxides and hydrides dominate the red range, such as titanium oxide (TiO), vanadium oxide (VO), CaH, and H₂O. Eggen & Greenstein (1965) tried to identify subdwarfs with MgH and TiO bands, then Mould (1976b) proposed a similar method using CaH and TiO bands: because cool subdwarf stars are metal-deficient with respect to normal dwarfs, the metal oxides are depleted with respect to the hydrides at a given effective temperature in their atmosphere, hence the intensity ratio of molecular absorption between an oxide and an hydride should be useful as a separator. The most popular set of indices was defined by Reid et al. (1995) and expanded by Lépine et al. (2003b). We list this classical set of indices in Table 1. Figure 2 shows these wavebands on a template spectrum.

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The value of a spectral index is given by:

$$\begin{eqnarray}&&\mathrm{Index}=\displaystyle \frac{{F}_{\mathrm{fea}}}{{F}_{\mathrm{cont}}},\end{eqnarray} \tag{ 1 }$$

where F_fea is the mean flux in the molecular absorption feature band, and F_cont is a pseudo-continuum flux, i.e., the mean flux in the waveband from λ_Begin to λ_End (for CaH1 index, the pseudo-continuum flux is the average flux of two bands). For example, the CaOH index is measured using the mean flux within fea_CaOH divided by the one within cont_CaOH.

2.2.1. G97 System

The spectroscopic classification system of M subdwarfs was initially defined by G97, from spectra of 79 targets mostly selected from large proper motion catalogs, such as Luyten Half-Second Catalogue (LHS; Luyten 1979) and the Lowell Proper Motion Survey (Giclas et al. 1971). Based on quantitative measures of TiO and CaH features (CaH1, CaH2, CaH3, and TiO5), G97 defined a set of empirical relations on the CaHn–TiO5 (n = 1, 2, 3) diagrams that classified M-dwarf spectra into three subclasses corresponding to increasing metal-poor levels: dwarfs of solar metallicity (dM), normal subdwarfs (sdM), and extreme subdwarfs (esdM).

The initial condition proposed by G97 to identify a spectroscopic subdwarf was the [CaH1, TiO5] relation:

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{CaH}1 & \lt & 0.695\times \mathrm{TiO}{5}^{3}-0.818\times \mathrm{TiO}{5}^{2}\\ & & +\ 0.413\times \mathrm{TiO}5+0.651.\end{array}\end{eqnarray} \tag{ 2 }$$

G97 suggested it was the primary dwarf/subdwarf separator and added a [CaH2, TiO5] relation to separate classic subdwarfs from extreme subdwarfs. Finally, G97 assigned the spectral subclass (linked to the effective temperature) using the CaH3 index. For the coolest stars with TiO5 < 0.49, G97 also suggested that the CaH2 or CaH3 index must be used to avoid inaccuracy caused by the "saturation" of the [CaH1, TiO5] relation.

2.2.2. L07 System

Lépine et al. (2003a) later suggested that the [CaH1, TiO5] relation could be abandoned due to its shorter dynamic range and the lower signal to noise of CaH1 band in very cool stars. They proposed its replacement by a [CaH2+CaH3, TiO5] relation, as producing a result almost equivalent to the former classification for the same stars, according to Lépine et al. (2003b). Along this way, Burgasser & Kirkpatrick (2006) went one step further, defined two separators on the [CaH2+CaH3, TiO5] diagram to differentiate between dM/sdM/esdM:

$$\begin{eqnarray}&&\begin{array}{l}\mathrm{sdM}:(\mathrm{CaH}2+\mathrm{CaH}3)\lt 1.31\times \mathrm{TiO}{5}^{3}\\ \quad -\ 2.37\times \mathrm{TiO}{5}^{2}+2.66\times \mathrm{TiO}5-0.20\end{array}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&\begin{array}{l}\mathrm{esdM}:(\mathrm{CaH}2+\mathrm{CaH}3)\lt 3.54\times \mathrm{TiO}{5}^{3}\\ \quad -\ 5.94\times \mathrm{TiO}{5}^{2}+5.18\times \mathrm{TiO}5-1.03.\end{array}\end{eqnarray} \tag{ 4 }$$

From a much larger published sample of M-type spectra selected from the high proper motion catalog Lepine and Shara Proper Motion (LSPM)-north (Lépine & Shara 2005), L07 proposed an update of this classification system based on an empirical calibration of the TiO/CaH ratio for stars of near-solar metallicities. For this, they introduced a parameter ζ_TiO/CaH., which quantifies the weakening of the TiO band-strength due to the metallicity effect, with values ranging from ζ = 1 for stars of near-solar metallicities to ζ = 0 for the most metal-poor (and TiO depleted) subdwarfs. The ζ parameter is defined as

$$\begin{eqnarray}&&{\zeta }_{\mathrm{CaH}/\mathrm{TiO}}=\displaystyle \frac{1-\mathrm{TiO}5}{1-{[\mathrm{TiO}5]}_{{Z}_{\odot }}};\end{eqnarray} \tag{ 5 }$$

the ${[\mathrm{TiO}5]}_{{Z}_{\odot }}$ is a third order polynomial fit of the TiO5 spectral index as a function of the CaH2+CaH3 index. In L07, these indices are measured in spectra of a kinematical selection of local disk dwarfs of roughly the solar metallicity, giving

$$\begin{eqnarray}\begin{array}{rcl}{[\mathrm{TiO}5]}_{{Z}_{\odot }} & = & -0.05\\ & & -0.118\times (\mathrm{CaH}2+\mathrm{CaH}3)\\ & & +0.670\times {\left(\mathrm{CaH}2+\mathrm{CaH}3\right)}^{2}\\ & & -0.164\times {\left(\mathrm{CaH}2+\mathrm{CaH}3\right)}^{3}.\end{array}\end{eqnarray} \tag{ 6 }$$

L07 suggested that the separation between subdwarfs and ordinary dwarfs could be effective when applying the single condition: ζ < 0.825. L07 also refined the scheme by introducing an additional class of usdM corresponding to the most metal-poor ones.

Since then, L07 system has been widely used in the identification, classification, and subtype determination of the cool subdwarf spectra (e.g., Lépine & Scholz 2008; Bochanski et al. 2013; Savcheva et al. 2014; Bai et al. 2016; Zhang et al. 2017).

2.2.3. ζ and the Metallicity

2.3.1. Specific Problems with S14 Sample Selection

To search for subdwarfs, S14 adopted the L07 system as a filter to select candidates from M-type spectra in SDSS DR7 and finally identified 3517 M subdwarfs with optical spectra. However, two problems may be identified in this subdwarf sample:

(1) As shown in Figure 3, a large fraction (1447) of objects in the sample do not seem to satisfy Equation (2), which means the L07 system is not identical to the original G97 system. In fact, these targets do not exhibit classical "subdwarf" characteristics, such as large proper motions. This leads to the suspect that there is a group of stellar objects that have subdwarf-like [CaH2+CaH3] TiO5 relationship but which might not be classified as genuine "subdwarfs." Hence, neglecting the primary condition defined by G97—the CaH1 feature—leads to the misclassification results of some stellar objects when using only the L07 system.

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(2) In the work of S14, the online catalog provided CaH, TiO indices and ζ values for the M-subdwarf sample, a large part of which were directly taken from West et al. (2011). These measurements were performed on spectra reduced to the rest frame using RV measurements by cross-correlation with M-dwarf templates. As mentioned above, S14 adopted ζ < 0.825 as the subdwarf selection criterion. However, S14 also provided a value of RV for each target derived from cross-correlation with a set of M-subdwarf template spectra built by the authors. We have recomputed the CaH, TiO spectral indices and the ζ index using these last RV values: the results plotted in Figure 4 show that there are 744 objects with ζ > 0.825, which should be classified as dwarfs rather than subdwarfs according to this selection criterion.

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These discrepancies clearly arise from the accuracy of the rest-frame reduction of spectra used to measure indices. The whole process is highly sensitive to the template spectra used in the cross-correlation. Therefore, a method independent of templates to measure RVs of the candidates is mandatory for us to ensure the accuracy of the final sample, since the LAMOST pipeline does not contain subdwarf templates.

2.3.2. The Need to Recalibrate ζ_TiO/CaH

2.3.3. Difficulties in Using LAMOST Spectra

Taking factors above into account, we conclude that a reliable M-dwarf sample and a carefully verified M-subdwarf sample from LAMOST data must first be built in order to define the separators between subdwarfs and dwarfs. An accurate rest-frame reduction, based on an RV measurement method independent of template spectra is necessary to get correct spectral indices. The dwarfs can be used to calibrate the ζ parameter, and the CaH1 index should be taken into consideration. In addition, the CaOH index is much closer to CaH1 (∼150 Å) than TiO5, and its comparison with CaH1 is as useful as TiO5 in separating subdwarfs from dwarfs. Then, combining revised G97 and L07 schemes, an automated search for subdwarf candidates in the entire LAMOST DR4 can be made. Finally, visual inspection will be adopted as the ultimate tool for confirmation of subdwarf identification.

LAMOST is an all-reflective Schmidt-type telescope located in the Xinglong Station of the National Astronomical Observatory, China (105° E, 40° N). It has a 6.67 m spherical primary mirror, which, combined with the corrector, provides an effective aperture of 4 m. It offers both a large field of view (5°) and a large aperture ratio. Feeding 16 double channel spectrographs are 4000 fibers mounted on the focal plane, which allow a high spectral acquisition rate (Cui et al. 2012). As it is dedicated to a spectral survey of celestial objects over the entire available northern sky, both Galactic and extragalactic surveys are conducted. The Galactic one, the LAMOST Experiment for Galactic Understanding and Exploration (LEGUE), focuses on the Galactic anti-center direction, the disk at selected longitudes away from the Galactic anti-center, and the halo (Luo et al. 2015).

Standard techniques are used in the analysis of the spectra. On the original charged coupled device (CCD) image, 4000 pixels are used to record blue and red wavelength regions across 3700–5900 Å and 5700–9000 Å, respectively. The blue and red channels are combined, and each spectrum is rebinned to calculate the RV. A combined spectrum is resampled at a scale of 69 km s⁻¹ per pixel, i.e., the difference between two adjacent points in the wavelength is Δlog(λ) = 0.0001. The raw CCD data are reduced by the LAMOST data reduction software named LAMOST 2D pipeline. The 2D pipeline performs the tasks of subtraction of dark and bias, correction of flat field, extraction of spectra, subtraction of skylight, calibration of the wavelength, merging of subexposures with cosmic-ray elimination, and combination of blue and red wavelength ranges (Luo et al. 2015).

The DR4 of the LAMOST regular survey contains 7620,612 spectra, covering the entire optical band (∼3700–9000 Å) at resolution R ∼ 1800, including 6944,971 stellar spectra, 153,348 extragalactic spectra (galaxies and quasi-stellar objects (QSO)), and 522,293 spectra classified as unknown (most of the latter because of insufficient signal to noise).

The heliocentric RV is the projection of the star's 3D velocity along the line of sight and can be measured from the Doppler shift of spectral lines. A conventional and accurate way to determine RV is by cross-correlating the target spectrum with a rest-frame template spectrum of a similar type (Tonry & Davis 1979). The LAMOST 1D pipeline provides a redshift measurement "z" for each object by matching it with a template spectrum. However, up until now, M-subdwarf templates were not yet available for the 1D pipeline, and thus the RVs measured using ordinary M-dwarf templates for subdwarf candidates would be of insufficient accuracy.

To overcome this problem, we have adopted an alternate RV determination method independent of templates. The natural way is to fit single Gaussian profiles to a set of absorption lines of neutral metals (Savcheva et al. 2014; Bai et al. 2016). However, M subdwarfs are basically faint red objects whose spectra often have a low or very low signal-to-noise ratio (S/N), and the useful metal lines at low resolution often do not exhibit nice Gaussian profiles. In many cases, the profiles are constructed by only 3–5 flux points and are not even symmetric. Therefore, we designed the following process to estimate RV from the Doppler shift of eight prominent absorption lines listed in Table 2. The method is based on the fact that the wavelengths of the eight lines would shift simultaneously due to the Doppler effect caused by radial motion, hence the offsets of the line centers would be identical in the logarithmic wavelength. The details of this method are described below:

• 1.  
  The wavelengths of a LAMOST spectrum are recorded in an exponential form in the fits file header as

  $$\begin{eqnarray*}&&\lambda ={10}^{(\mathrm{head}+n\ast \mathrm{step})},\end{eqnarray*}$$

  where the head corresponds to the COEFF0 field, which records the decimal logarithm of the central wavelength of the first pixel, (usually around 3.5682), n = 0, 1, 2, 3, ..., and step ≡ 0.0001. Therefore the observational accuracy of the RV when the shift of a line is defined to 1 step unit, i.e., when Δn = ±1, is $c\ast (1-{10}^{\mathrm{head}+{\rm{\Delta }}n\ast 0.0001})\,\approx \pm 69$ km s⁻¹. We recall that this corresponds to the sampling step of the pipeline reconstructed spectrum: the actual physical spectral resolution (somewhat variable along the spectral range) is of the order of 2.5 sampling steps, but naturally, RV measurement methods actually allow final accuracies of a fraction of a spectrum pixel.
• 2.  
  Since the LAMOST subdwarfs are within 1 kpc of the Sun (from apparent magnitude considerations), the Sun's escape velocity—550 km s⁻¹ (Kafle et al. 2014)—can be used as a proxy for the escape velocity of the entire sample. When Δn = ±10, the corresponding RV is ±690 km s⁻¹, hence we suppose that the shift of a line would be less than 10 step units.
• 3.  
  Without any prior knowledge of the type of spectrum (late-K star, M star, QSO, or unknown), for each line in Table 3, we get the wavelength step index n₀ in the spectrum corresponding to its rest-frame wavelength, and then find the Δn of the lowest flux point in the range $[{\lambda }_{{n}_{0}-10},{\lambda }_{{n}_{0}+10}]$. We insist that this is an entirely automated process that could provide positions of "true" absorption lines, as well as simple accidental deeps in the object's continuum, but its virtue is that the "line" profiles themselves are not required to be Gaussian.
• 4.  
  We count the number of "lines" affected by each Δn ∈ [−10, 10]. The Δn corresponding to the largest number of lines is adopted as our target Δn∗. Note that the number of lines should be at least three to avoid a large random error; otherwise we will flag the target as unable to be measured. At a later visual inspection stage of the selection process, we also filter out the objects with more than three "lines," which are merely local flux minima instead of real absorption lines.
• 5.  
  The "lines" affected by the shift Δn∗ are then used to measure the RV: this is achieved on an interpolated spectrum with artificially 15 times increased resolution to acquire a better precision (Bochanski et al. 2007). The mean value of the RVs obtained from these lines is our final RV, and the standard deviation is the error.

Our RV measurements have a median achieved typical uncertainty of 13.9 km s⁻¹. In Figure 5, we compare the RVs of 1926 M dwarfs from our M-dwarf sample (see Section 4.1 below) with the RVs provided by Gaia DR2 on the same stars. Our measurements show a fair agreement with Gaia RVs with a offset of 5.50 km s⁻¹ and a dispersion of 13.5 km s⁻¹. Similar systematic offsets are also found in other comparisons: 4.54 km s⁻¹ between LAMOST and APOGEE (Anguiano et al. 2018), and 3.8 km s⁻¹ between LAMOST and MMT+Hectospec (Huang et al. 2015). Note that four of the eight absorption lines (the K i doublet and the Na i doublet) are located within telluric absorption bands and sometimes the line centers are altered by insufficiently corrected telluric absorption by O₂ and H₂O. To solve this problem, we assign a same weight to each of the eight lines of Table 3 and impose that three "lines" at least must be detected to provide a valuable result. In addition, we also inspect the 7000–9000 Å range of each spectrum in our final subdwarf sample and remove the objects that do not show identifiable absorption lines by eye-check to improve the reliability of the final results.

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The initial step consists in assembling two reference samples from LAMOST data: one of ordinary M dwarfs, the other of carefully validated M subdwarfs. These allow the revision of the various selection and classification tools of G97 and L07 in order to apply them to LAMOST spectra. Since the existing standard M-subdwarf spectral templates are not perfectly appropriate for LAMOST spectra, we choose the most reliable identification/confirmation method underlined in all the former works—visual inspection—as our first identification tool to assemble a reliable subdwarf sample from LAMOST data. Although Bai et al. (2016) provided 108 verified M subdwarfs from LAMOST DR2, the candidates submitted to visual inspection were provided by screening through the G97/L07 systems. Therefore, to obtain a larger subdwarf sample, and while we select a comparison sample of purely ordinary M dwarfs, the visual inspection was targeted at the entire M-type spectra data set (auto-classified by LAMOST 1D pipeline) from the fourth year of the LAMOST regular survey, containing nearly 100,000 spectra. In this process, potential contaminant,s such as M giants, double stars, and unrecognizable objects, can be removed, and the spectral subtype of each M-dwarf spectrum can also be verified based on the eye-check result.

To achieve this arduous task, we use the manual "eyecheck" mode of the Hammer spectral typing facility (Covey et al. 2007), an IDL code that uses the relative strength of a series of spectral features in the range of 4000–9100 Å for classifying stellar spectra (Lee et al. 2008; West et al. 2011; Dhital et al. 2012; Savcheva et al. 2014). Yi et al. (2014) have modified the Hammer code to better adapt it to LAMOST M spectra. The manual mode of Hammer allows the user to compare a target spectrum with a collection of M-dwarf template spectra and to assign a label to each target.

Referring to the aspect of single subdwarf spectra and/or templates provided in previous works, such as G97, L07, Jao et al. (2008), S14, and Bai et al. (2016), we base our initial assignment of a target spectrum into the "giant," "dwarf," or "subdwarf" category on the following basic recipes:

(1) The K i doublet around 7700 Å and Na i doublet around 8200 Å are highly gravity-sensitive, thus they are almost invisible in giants, but are prominent both in dwarfs and subdwarfs. Compared with dwarfs, the CaH1 absorption band of an M-giant spectrum of the same spectral type is almost invisible, as is the CaH3 band, while its TiO5 minimum is as deep as the CaH2 minimum.

(2) The most obvious differences between M subdwarfs and dwarfs are the features around 6200–6400 and 6800–7200 Å. CaH1 absorption band is much more prominent in subdwarf spectra than in dwarfs, which is almost as deep as CaOH and even deeper, respectively, for esdM and usdM. Regarding subdwarfs, the TiO5 minimum is less deep than the CaH2 minimum for sdM, is even less deep than the CaH3 minimum for esdM, and the entire TiO absorption band is almost invisible for usdM.

Note that the reddest part of TiO5 is blended with a strong atomic line 7148 Å of Ca i, which is very close to the third (and deepest in normal conditions) "tooth"-like absorption of the TiO, which makes it easy to misidentify the minimum of TiO5 on low-resolution noisy spectra.

In this step, we label each target with a spectral subtype (M0, M1, ...M9) and a type information, such as "dwarf," "giant," "subdwarf," "double star," or "odd." As a result, 325 subdwarfs are selected and validated. Combined with the 108 M subdwarfs from Bai et al. (2016), we now have a "labeled" subdwarf sample that includes 433 visually identified spectra in total.

Besides, 90,018 ordinary M dwarfs are identified, of which 83,213 have measurable RVs: these define our M-dwarf comparison sample. This comparison sample is also used for the calibration of ζ.

We measure the spectral indices defined in Section 2.1 and Table 1 on all spectra of the "labeled" subdwarf sample and on all spectra of the M-dwarf comparison sample. The M-dwarf results are used to build the TiO5–[CaH2+CaH3] diagram shown in Figure 6. The barycentric line across the data cloud directly provides the recalibration of the ζ_TiO/CaH = 1 curve for average solar metallicity objects. We get:

$$\begin{eqnarray}\begin{array}{rcl}{[\mathrm{TiO}5]}_{{Z}_{\odot }} & = & -1.326\\ & & +\ 2.417\times (\mathrm{CaH}2+\mathrm{CaH}3)\\ & & -\ 1.083\times {\left(\mathrm{CaH}2+\mathrm{CaH}3\right)}^{2}\\ & & +\ 0.2465\times {\left(\mathrm{CaH}2+\mathrm{CaH}3\right)}^{3}.\end{array}\end{eqnarray} \tag{ 7 }$$

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Based on this updated calibration of ζ, we find that the optimal separator curve used to select subdwarfs from dwarfs in the [TiO5, [CaH2+CaH3]] space can be defined as ζ < 0.75, as shown in Figure 7: it exactly separates almost all our subdwarfs belonging to the "labeled" subsample. Furthermore, ζ < 0.75 excludes a sufficient fraction, in a statistical sense, of ordinary dwarfs (98%). This ζ value is smaller than the canonical 0.825 recommended by L07, Dhital et al. (2012), and Lépine et al. (2013), which reflects the differences in the instrumental response to the real spectra between LAMOST and other setups. The separators between sdM/esdM/usdM are still adopted as ζ < 0.5 and ζ < 0.2. Figure 7 shows the comparison between these several systems.

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The characteristic of prominent CaH1 absorption in subdwarfs can be clearly seen on Figure 8, where we compare the index values of M-dwarf and M-subdwarf templates built by Bochanski et al. (2007) and S14, respectively. The result shows excellent discrimination between dwarfs and subdwarfs across the entire spectral sequence when plotting on the [CaH1, TiO5] diagram. Therefore, we suggest that the CaH1 feature should be taken into consideration to select spectroscopic subdwarfs, especially for early-M-type subdwarfs of moderate metal deficiency in which TiO5 absorption is not very strong and ζ loses efficiency as a separator.

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In addition, as the middle diagram of Figure 8 shows, the CaOH index and the TiO5 index show similar monotonic trend along the effective temperature sequence. The result is to be expected, because the CaOH band depth, as well as the TiO5 one, heavily relies on the atmospheric abundance of the alpha element O. Due to the CaOH feature being much closer to the CaH1 band than the TiO5 feature, the ratio of the CaOH index to the CaH1 index maybe less affected by errors arising from the distortion of continuum affected by various instrumental factors or flux calibration problems (Du et al. 2016).

Using the visually identified dwarfs and "labeled" subdwarfs, we derive two equations to define separator curves on the CaH1 versus TiO5 index diagram and CaH1 versus CaOH index diagram, respectively, yielding:

$$\begin{eqnarray}&&\mathrm{CaH}1\lt 0.6522\times \mathrm{TiO}{5}^{2}-0.577\times \mathrm{TiO}5+0.8937\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{CaH}1 & \lt & 0.4562\times {\mathrm{CaOH}}^{3}-0.1977\times {\mathrm{CaOH}}^{2}\\ & & -\ 0.01899\times \mathrm{CaOH}-0.7631.\end{array}\end{eqnarray} \tag{ 9 }$$

Equation (8) is shown in the left panel of Figure 9 with a comparison with the original one from G97, i.e., Equation (2). Equation (9) is shown in the right panel of Figure 9.

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The determination of spectral subtypes (SpT) for cool subdwarfs can be made by several methods, such as using the depth of the CaH molecular bands (G97; L07) or the shape of the relatively opacity-free region within 8200–9000 Å (Jao et al. 2008). In this work, we follow the definition in L07 in which the "metallicity" subclass assignment is dependent on the combined value of the CaH2 and CaH3 indices, given as:

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{Sp} & = & 1.4\times {\left(\mathrm{CaH}2+\mathrm{CaH}3\right)}^{2}-10\\ & & \times \,(\mathrm{CaH}2+\mathrm{CaH}3)+12.4.\end{array}\end{eqnarray} \tag{ 10 }$$

It will thus be easy to compare our sample with previous works on the spectral sequence. The derived value of SpT is rounded up to the nearest integer, giving the spectral subtype value from 0 for M0 to 7 for M7.

To build the final sample, we search by automatic processing LAMOST DR4 using the constraints detailed above. A spectrum is adopted as a candidate if it meets the following three conditions:

• (1)  
  It has an available RV measurement.
• (2)  
  ζ < 0.75.
• (3)  
  It satisfies Equations (8) or (9).

Ultimately, visual examination of the spectrum is utilized to confirm (or not) the nature of the candidate.

To avoid missing targets as much as possible, we search for candidate subdwarfs among late-K-type stars, M-type stars, QSOs, and unknowns (as classified by LAMOST 1D automated pipeline), including 1271,426 spectra in total. Adding QSOs to the sample to be explored was decided because of strong molecular absorption by TiO (and VO in the coolest objects) gives a very choppy appearance to the spectra of late-type dwarf stars, quite similar to continuum breaks exhibited by QSOs in specific redshift ranges. As a matter of fact, cool M-type stars and QSO are often contaminating each other in surveys dedicated to each class (Kirkpatrick et al. 1997).

Our final subdwarf sample is constructed via visual inspection of each candidate spectrum. It consists of 2791 objects and covers the spectral sequence from M0 to M7, in which 291 objects had been investigated by previous researches. Figure 10 summarizes the distribution of their spectral subtypes. Most objects are earlier than M4, a result not unexpected since the metal deficiency has a tendency to decrease atmospheric opacity and to move the spectral types toward higher effective temperatures, on one hand. On the other hand, instrumental selection by the red channel spectrograph performance of LAMOST also plays against detection of very cool faint objects. According to our newly recalibrated ζ parameter, the present sample can also be divided into the sdM/esdM/usdM classes with ζ < 0.75, ζ < 0.5, and ζ < 0.2, respectively. There are 2386 sdMs, 295 esdMs, and 110 usdMs in total.

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We provide an M-subdwarf catalog containing 2791 objects, the spectra of which can be accessed from the LAMOST Data Release web portal⁶ and the catalog can be obtained online as well as by contacting the corresponding author. We give the values and errors of each spectral index (CaOH, CaH1, CaH2, CaH3, and TiO5), compute the ζ value, and provide an Hα activity indicator for each target. The radial velocities are measured with the method described in Section 3.2. The spectral subtypes for subdwarfs are computed based on Equation (10) (Lépine et al. 2007).

Additional data from external sources are compiled in this catalog: photometric magnitudes measured in various bandpasses; five optical and near-infrared bands (g, r, i, z, and y; Tonry et al. 2012) from the Pan-STARRS1 (PS1) 3π survey (Kaiser et al. 2010), which is a systematic imaging survey of 3/4 of the sky north of −30°; the near-infrared J (1.25 μm), H (1.65 μm), and Ks (2.16 μm) bands from the Two Micron All Sky Survey (2MASS); and W1, W2, W3, and W4 bands centered at wavelengths of 3.4, 4.6, 12, and 22 μm, respectively, are provided by the AllWISE Data Release (Cutri et al. 2014), which has produced a new Source Catalog and Image Atlas with enhanced sensitivity and accuracy compared with earlier Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) data releases (Kirkpatrick et al. 2014, 2016). G, BP, and RP magnitudes in the new Gaia photometric system (Gaia Collaboration et al. 2018) are also provided.

The astrometric parameters from Gaia DR2 are also provided: proper motions and parallaxes (Gaia Collaboration et al. 2018). We also give estimated distances recorded in the catalog from Bailer-Jones et al. (2018). An important point must be underlined: the distances provided by Bailer-Jones et al. (2018) are probabilistic estimates based on an elaborate statistical processing of Gaia DR2 data, using specific prior modeling (in particular, stellar density distribution along Galactic lines of sight) to avoid physical errors resulting from "blind" simple inversions of measured parallaxes, as discussed in e.g., Luri et al. (2018).

Table 4 gives the description of each column of the catalog. A partial catalog extract is also shown in Table 5. The complete catalog is available in CSV format online.⁷

Chromospheric activity is common among ordinary M dwarfs and has been largely studied by several authors, in particular, from the large spectroscopic database of the SDSS (see e.g., West et al. 2004, 2011) and it has also been found in many M subdwarfs (Bochanski et al. 2007; Savcheva et al. 2014). At the spectral resolution of survey instruments like the SDSS combination or LAMOST, the brightest and most easily detectable emission line is Hα, accompanied in the most active objects by Ca ii emission (both in H and K lines and in the far-red triplet), and sometimes by higher Balmer series lines. According to the criteria for designating a star as active as defined by West et al. (2011), we measure the equivalent widths of an Hα emission line for each object and remove the unreliable ones via visual inspection. Finally, a total of 141 active subdwarfs with prominent Hα emission lines are found, including 120 sdMs, 18 esdMs, and 3 usdMs, amounting to more than 5% of the total sample. The Hα activity flag for each object is listed in the catalog. The flag is set as 1 for the active ones, 0 for the ones without emission features, and −9999 for the ones with S/N < 3 in the r or i band.

As Figure 10 shows, the activity fraction of M dwarfs is increasing in later types, a result consistent with former studies (see e.g., West et al. 2011). Unfortunately, due to the observational selection against subdwarfs cooler than M3–M4 in our sample, it is difficult to derive a reliable estimate of the fraction of active subdwarfs. Previous studies have shown that among M subdwarfs, chromospheric activity is significantly less frequent than among ordinary M dwarfs, but the spectral type at which the maximum rate of activity observed does not appear to differ. This reduction is claimed to be an argument to confirm that the chromospheric activity is a proxy for the age of the subdwarfs, whose bulk of observationally selected population that are associated with the Galactic halo and thick disk should be of substantially older formation than that of the disk dwarfs.