11institutetext:  CAS Key Laboratory of Optical Astronomy, National
Astronomical Observatories, Beijing 100101, China.
22institutetext: School of Astronomy and Space Science, University of Chinese
Academy of Sciences, Beijing 100049, China
33institutetext: Graduate Institute of Astronomy, National Central University,
300 Zhongda Road, Zhongli, Taoyuan 32001, Taiwan
44institutetext: Department of Physics, National Central University,300
Zhongda Road, Zhongli, Taoyuan 32001, Taiwan
55institutetext: School of Physics, Astronomy and Mathematics, University of
Hertfordshire, College Lane, Hatfield AL10 9AB, UK
66institutetext: Department of Astronomy, School of Physics, Peking
University, Beijing 100871, China
77institutetext: Kavli institute of Astronomy and Astrophysics, Peking
University, Beijing 100871, China

# Ultracool dwarfs identified using spectra in LAMOST DR7 ††thanks: Tables 1
to 3 are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/

You-Fen Wang 11 A-Li Luo Corresponding Author: A-Li Luo email:
<EMAIL_ADDRESS>2  Wen-Ping Chen Wen-Ping Chen email<EMAIL_ADDRESS>Hugh R. A. Jones 55 Bing Du 11 Yin-Bi Li 11 Shuo Zhang 6677 Zhong-Rui Bai 11
Xiao Kong 11 Yan-Xin Guo 11

(Received September 00, 0000; accepted March 00, 0000)

In this work, we identify 734 ultracool dwarfs with a spectral type of M6 or
later, including one L0. Of this sample, 625 were studied spectroscopically
for the first time. All of these ultracool dwarfs are within 360 pc, with a
Gaia G magnitude brighter than $\sim 19.2$ mag. By studying the spectra and
checking their stellar parameters ($T_{\rm eff}$, log $\it g$, and $\rm[M/H]$)
derived with the LAMOST pipeline, we found their cool red nature and their
metallicity to be consistent with the nature of Galactic thin-disk objects.
Furthermore, 77 of them show lithium absorption lines at 6708 Å, further
indicating their young ages and substellar nature. Kinematics obtained through
LAMOST radial velocities, along with the proper motion and parallax data from
Gaia EDR3, also suggest that the majority of our targets are thin-disk
objects. Kinematic ages were estimated through the relationship between the
velocity dispersion and the average age for a certain population. Moreover, we
identified 35 binaries, with 6 of them reported as binaries for the first
time.

###### Key Words.:

surveys:stars – late-type:stars – low-mass:brown dwarfs – binaries: visual

##  1 Introduction

Ultracool dwarfs (hereafter UCDs) are usually defined as objects with a
spectral type of M7 V or later (Kirkpatrick et al., 1997), comprising very
low-mass stars, brown dwarfs (BDs), and planetary-mass objects. The M7 V
spectral type BDs are almost the highest-mass BDs that are just below the
least mass stellar boundary. While the main-sequence stars, BDs, and
planetary-mass objects are distinguished pedagogically by their masses, the
mass values are not readily measurable. The luminosity and spectral type of a
star, once core hydrogen fusion begins, remain effectively the same (depending
on the mass) for hundreds of thousands to hundreds of million years on the
main sequence. In contrast, for a substellar object, theoretical modeling
indicates that – to use an example from Burrows et al. (1997) – a maximum-mass
BD (about 75 $M_{J}$) has a steady luminosity of $\log L/L_{\odot}\sim-1.3$ to
$\log L/L_{\odot}\sim-2$ and an effective temperature of about $T_{\rm
eff}\sim 3000$ K for the first 10 Myr, then dropping to $\log
L/L_{\odot}\sim-4$ and $T_{\rm eff}\sim 2200$ K by the time the object becomes
1 Gyr old, corresponding to a spectral-type change from about an M6 to an L0.
This age dependence on the spectral type makes it difficult to identify
relatively massive and hot substellar objects. Thus, the class of late M to
mid-L dwarfs represents a mixture of low-mass stars and BDs. Objects with ages
later than mid-L spectral type are certainly BDs.

Brown dwarfs are objects that are not massive enough to sustain core hydrogen
fusion, namely, they are substellar objects with masses of $M\lesssim
75$–80$\leavevmode\nobreak\ M_{J}$ (Marley et al., 2021), where $M_{J}$ is the
Jupiter mass. Theories indicate that the BDs with masses heavier than $\sim
65M_{J}$ (Dantona & Mazzitelli, 1985; Baraffe et al., 2015) have cores hot
enough to fuse lithium – and those above $\sim 13M_{J}$ may ignite deuterium.
Other than these short-lasting fusion reactions, a BD continues to cool and
fades monotonically in terms of brightness. Those with $M\lesssim 13M_{J}$
have no fusion reaction at all and are called “planetary-mass objects” (or
free-floating planets) that are in contrast to exoplanets orbiting hosting
stars. The first M-type BD, an M8, was discovered by Rebolo et al. (1995) in
the nearby cluster the Pleiades. In the same year, another BD of the T type
(T6.5) was found by Nakajima et al. (1995), which is a companion to an M1
dwarf. These discoveries came 30 years after the theoretical prediction of BDs
by Kumar (1963). Because of their intrinsic faintness, any optical
spectroscopic vindication of a BD requires large-aperture telescopes equipped
with sensitive instruments. In spite of thousands of ultracool dwarfs proposed
thus far, the key to true substellar nature by way of spectroscopic
confirmation is possible only among nearby targets and – with dedicated
efforts – in nearby star-forming regions.

Here, we present ultracool dwarfs with spectra types mainly ranging from M6 V
to M9V that have been found with the Large Sky Area Multi-Object Fiber
Spectroscopic Telescope (LAMOST, Luo et al., 2015). Thanks to a 4-m aperture
and a 5-deg field of view to accommodate more than 4000 fibers on the focal
plane, LAMOST is efficient in providing data for spectroscopic sky surveys. In
this work, we examined a set of more than 10,000 spectra for objects with late
M spectral type from the LAMOST DR7111http://dr7.lamost.org (hereafter LDR7)
and excluded the giants, those with low signal-to-noise (S/N) spectra or bad
spectra, and those with earlier spectral types than M6 V. This list of
ultracool dwarfs, while serendipitous in its sky coverage that is set by the
LAMOST survey footprints, have been spectroscopically identified, therefore,
expanding their currently known inventory of the ultracool population in the
solar neighborhood considering the small population of late M dwarfs comparing
with the early ones. This sample represents the low mass stars and bright
brown dwarfs, which is crucial to understanding the physical process at the
stellar and substellar boundary. It is also very useful for exoplanet surveys
since they are much fainter than solar-like stars and, hence, it is easier to
detect the low-mass rocky planets orbiting around them.

This paper is organized as follows. In Sect. 2, we describe the spectral data
set used in this work and the procedure to select the ultracool dwarfs. In
Sect. 3 we present the properties of the sample, such as the positions in the
Gaia color-absolute magnitude diagram (CAMD), to verify their cool and red
atmospheres. In Sect. 4, we diagnose the stellar parameters and compare them
according to literature and we also inspect the possible existence of the
lithium absorption line as an indication of the young age or substellar
nature. In Sect. 5, we perform kinematic analysis using the radial velocity
(RV) provided by LDR7 and the five astrometric parameters from the Gaia Early
Data Release 3 (Gaia Collaboration et al., 2021a, hereafter GEDR3) to infer
their stellar population and kinematical age. In Sect. 6, we report 35
binaries, of which 14 are newly discovered. Finally, we summarize our work in
Sect. 7.

##  2 Data and sample selection

After the first light in 2008, commissioned in 2009–2010, followed by the
Pilot Survey for one year (Luo et al., 2015), LAMOST had completed its five-
year regular survey by June 2017. It is presently undertaking the second five-
year regular survey. The latest data release, LDR7, includes low-resolution
($R\sim\leavevmode\nobreak\ 1800$) spectra from which the stellar parameters
were derived and which form the basis of the work reported here. With a
practical LAMOST limiting sensitivity of Gaia $G\lesssim 19.2$ mag, our
ultracool dwarfs were randomly observed in the footprints of the LAMOST
survey, and the targets are randomly selected in any particular pointing
within 5 square degrees. Information on the fiber assignment can be reviewed
in (Luo et al., 2015). In this paper, we describe in detail on how to identify
ultracool M dwarfs in LDR7 using spectral features.

###  2.1 LAMOST dataset

In order to construct our ultracool dwarf sample, we decided to set the cut at
M6 to account for spectral typing uncertainties introduced in the LAMOST
analysis pipeline (1 - 5 subtype depending S/N ), as well as for spectral type
dependence on age for BDs, so as not to exclude possible young BDs. In LDR7,
11,412 spectra were classified as being M6 or later by the LAMOST
classification pipeline. Among these, about 33% are classified as dwarfs
(listed as “dM” in the official catalogue) and 67% as giants (listed as “gM”
in the official catalogue). In contrast, among early-type M spectra, only
about 4% are found to be giants. The high fraction of giants at late-type M
spectra type is attributed to the selection effect.

We cross-matched each of the 11,412 entries with the GEDR3 with a 5″ matching
radius within the LAMOST coordinates (J2000). Firstly, 469 targets that
pipeline classified as late-type M and have Gaia color BP-RP$<1$ were removed
because of a misclassification due to low spectra quality or data reduction.
Secondly, we visually inspected all the spectra and winnowed out giants and
early-type dwarfs via their spectral features, and we also excluded those
having low signal-to-noise ratios. The remaining 734 targets are checked one
by one to ascertain photometric counterparts to avoid mismatch caused by the
multi-to-one problem, judged both by the positions and the colors of the 2MASS
and the LAMOST targets. We further discuss the sample selection and present
some details below.

###  2.2 Spectral features of giants versus dwarfs

A general description of the spectral features of M types in the LAMOST
spectra can be reviewed in the work by Guo et al. (2015). Figure 1 illustrates
the differences in spectral features between a typical dwarf and a giant with
the same spectral type of M6. Prominent features for dwarfs include the K i
doublets near 7688Å and Na i near 8189Å(Gray & Corbally, 2009). The hydride
band of CaH between 6800 and 7000Å is stronger in dwarfs than in giants; the
bands for CrH and FeH around 8700 Å are visible in dwarfs. In comparison,
giants have a more suppressed TiO absorption band to the red side of the Na i
doublets and stronger Ca ii triplets at 8498 Å, 8542 Å, and 8662Å. Moreover,
giants exhibit a gentler slope between 8500 Å and 9000 Å compared to dwarfs
that otherwise have molecular absorption due to TiO, VO, CrH, and FeH.

To select the sample of ultracool dwarfs, we applied visual inspection for all
the 11,412 late M type spectra based on the above features, including both
dwarfs (3764 dMs) and giants (7648 gMs) from the LDR7 official catalogue.
After the inspection of the spectra, we found there are nine “real ultracool
dwarfs” that had been misclassified as giants by the LAMOST pipeline and
released in the giant catalogue; thus, we drew them back to our ultracool
dwarf sample. For the LDR7 released dwarf sample, we excluded spectra with S/N
lower than 2 in the z band, accounting for about four percent, as well as
those of earlier M-type spectra that had been misclassified as late-type by
the LDR7 pipeline. We also removed the spectra that have features between
dwarfs and giants, namely, those with obviously weaker K i and Na i lines than
classical dwarfs, such as YSOs, or those having features other than classical
dwarfs (caused by data reduction, or being the mixture of two or multiple very
close stars). Finally, we got an ultracool dwarf catalog of 734 sources, which
is described in the following subsection. We should note that this sample is
conservative to ensure every source selected is indeed a real dwarf.

Figure 1:  Typical LAMOST spectrum of (a) an M6 III giant (Frasca et al.,
2016), and (b) an M6 dwarf (Newton et al., 2014). Both spectra have S/N
greater than 100 in the $z$ band.

###  2.3 Sample of ultracool dwarfs

The visually identified 734 late-type M dwarfs have spectral type equal to or
later than M6 V, with one L0 included. Figure 2 exhibits typical spectra of
this sample. This sample is by no means complete in terms of sky coverage or
flux but should form a reliable collection of the ultracool dwarf population
in the LAMOST database. The observed spectra in our sample are consistent with
the Hammer M dwarf templates, which have been established using the Sloan
Digital Sky Survey (here after SDSS, Abazajian et al., 2009) optical spectra
(Covey et al., 2007; Yi et al., 2014).

Figure 2:  Typical late-M dwarf LAMOST spectra (solid lines) in comparison to
the Hammer template (blue dashed lines). Numbers given beside each spectral
type corresponds to ID in Table 1. The S/N in SDSS $z$ band for No. 429 $\sim$
70, No. 627 $\sim$ 174, No. 221 $\sim$ 30, No. 456 $\sim$ 33.

Table 1 lists the 734 ultracool dwarfs that we identified using LDR7 spectra,
including 577 of the dM 6 and three gM 6, 128 of the dM 7 and two gM 7 type,
16 of the dM 8 and one gM 8 type, three of the dM 9 and three of the gM 9
type, and one of the L 0 type. Based on a cross-match with SIMBAD, we note
that 625 out of the 734 objects had no spectral type listed in the literature
prior to this work by LAMOST spectral observation.

Table 1: Ultracool dwarfs in the sample

No. | obsid | R.A. | Decl. | SpT1 |  source $\textunderscore$ id |  $\varpi$ |  $\Delta\varpi$ |  $\mu_{\alpha}\cos\delta$ |  $\Delta\mu_{\alpha}\cos\delta$ |  $\mu_{\delta}$ |  $\Delta\mu_{\delta}$ | RUWE |  $G$ |  $G_{BP}$ |  $G_{RP}$ | SpT2
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  | (deg) |  |  | (mas) | (mas/yr) | (mas/yr) |  | (mag) |
1 | 369905116 | 0.29067 | 7.30335 | dM7 | 2745889793400449280 | 25.43 | 0.15 | 135.18 | 0.19 | -78.93 | 0.09 | 1.461 | 16.333 | 18.274 | 14.390 | -
2 | 472904167 | 0.64809 | 17.48399 | dM6 | 2772949702272966144 | - | - | - | - | - | - | - | 16.756 | 18.395 | 14.938 | -
3 | 474610041 | 0.77652 | 39.20759 | dM6 | 2881030840586539264 | 15.91 | 0.06 | 68.35 | 0.04 | -56.65 | 0.04 | 1.009 | 16.574 | 18.716 | 15.222 | -
4 | 592310145 | 1.82317 | 36.46536 | dM6 | 2877146781401666816 | 14.19 | 0.07 | 16.77 | 0.08 | -38.87 | 0.05 | 1.112 | 16.692 | 18.702 | 15.374 | -
5 | 593009044 | 2.23202 | 49.31638 | dM6 | 393621524910343296 | 67.76 | 0.04 | 352.67 | 0.03 | 202.42 | 0.03 | 1.103 | 14.385 | 16.769 | 12.998 | -
6 | 472906086 | 2.45851 | 17.15581 | dM6 | 2772737844422061440 | 28.13 | 0.07 | -6.68 | 0.10 | -77.52 | 0.08 | 1.005 | 16.340 | 18.788 | 14.941 | -
7 | 354310106 | 4.60190 | 36.47204 | dM6 | 2876595273240771840 | 20.78 | 0.05 | 174.36 | 0.04 | -206.20 | 0.05 | 1.003 | 16.127 | 18.178 | 14.791 | -
8 | 284610069 | 5.12607 | 33.08272 | dM7 | 2863419584886542080 | 81.57 | 0.04 | 1075.61 | 0.04 | -863.67 | 0.04 | 1.052 | 13.935 | 16.400 | 12.538 | -
9 | 372110218 | 5.42199 | 36.32373 | dM6 | 378382770487254912 | 10.47 | 0.11 | -73.46 | 0.10 | -26.90 | 0.10 | 1.726 | 16.640 | 18.522 | 15.275 | -
10 | 614109230 | 6.12484 | 36.83748 | dM6 | 378467643336605056 | 30.63 | 0.05 | -132.67 | 0.04 | -14.74 | 0.04 | 1.046 | 15.703 | 17.855 | 14.356 | -
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮

222Column 1: running number. Column 2: LAMOST obsid. Columns 3-4: Right
ascension(RA) and declination(Decl.). Column 5: LAMOST spectral type. Column
6: GEDR3 source$\textunderscore$ id. Columns 7-12: parallax, proper motion in
R.A. and Decl. directions, and the corresponding uncertainty. Columns 13-15:
Gaia G BP and RP magnitudes. Column 16: RUWE from GEDR3. Column 17: SpT from
the literature according to SIMBAD. The electronic version of this table in
entirety is available at http://paperdata.china-vo.org/YFW/aa_table1.csv

The only one L dwarf, listed in Table 1 as No. 556, with the designation
$SDSS\leavevmode\nobreak\ J120430.38+321259.4$, has a SDSS spectral type of L
0e in the optical (West et al., 2008) and M 9.5 in the infrared (Bardalez
Gagliuffi et al., 2014). It was observed in 2012 during the LAMOST pilot
survey but was not included in the release until LAMOST DR6 because of its low
brightness. This L0 dwarf indicates the practical limit of the latest spectral
type in LDR7.

Figure 3 shows the sky distribution of the ultracool dwarfs(light purple solid
circles) and the 11,412 LDR7 released late M type spectra(in green crosses),
the background grey circles are the footprints(consist of more than 4900
plates each plate covers 5 square degrees) of the LDR7, covering about 20000
square degrees of the northern sky. In order to test the completeness and
ratio of the red faint objects observed, we downloaded the data from GEDR3 in
the sky area of LDR7 and obtained about 130 million Gaia sources. We then
empirically estimated the number of the late-type M dwarfs by the color cut of
Gaia $BP-RP>3$ and apparent magnitude cut of $G<19$, which result in 458
thousand objects. Using the absolute magnitudes of $G>9$, we got 143 thousand
candidates, accounting for 0.11% of the total. While for the approximately 10
million of the Gaia sources observed by LAMOST DR7, the pipeline classified
3,764 as late-type dMs, accounting for 0.03%, which means the very low portion
of late dMs due to telescope magnitude limits. Although most of the LDR7
released late-type M dwarfs are correctly classified as real M type, many have
low signal-to-noise ratio spectra or have fake spectral features. To avoid
missing late dMs, we carefully check the spectral features for LAMOST released
late dMs and gMs, and identified 734 relatively high S/N ultracool dwarfs
later than M6, which ranging $5>BP-RP>2.63$ and absolute G magnitude between
8.94 and 16.71(with relative parallax error smaller than 20%). Since our
ultracool dwarf sample is composed of good quality spectra and populated
primarily with solar metallicity single stars, we can obtain more reliable
atmosphere parameters and use them to update LAMOST classification templates.

Figure 3:  Sky distribution of LAMOST DR7 released 11,412 late M stars are
shown in green crosses), while the identified ultracool dwarfs are in light
purple solid circles. The footprints for the LDR7 are plotted as grey big
circles in the background.

##  3 GEDR3 photometry

The 11,412 late M spectra from LDR7 were cross-matched with the GEDR3 data
within 5 arcsec as the previous section mentioned. In this section, we study
the distribution of heliocentric distance and magnitude, $BP-RP$ versus $G-RP$
two-color diagram and CAMD diagram. Our ultracool dwarfs are very faint and
red objects and represent the faintest stellar or substellar objects that
LAMOST has ever observed. The heliocentric distance and Gaia magnitude
distribution show the practical limitation of the LAMOST.

To plot diagrams in this section, We restricted to objects with parallax that
has relative uncertainty is smaller than 20% (Lutz & Kelker, 1973; Luri et
al., 2018), and that all Gaia $G,BP$, and $RP$ values are greater than zero.
The parallaxes of these ultracool dwarfs are large and hence expected to be
nearby, we, therefore, adopted the reciprocal of the GEDR3 parallax as the
distance of each source and thus determined their absolute magnitudes.

###  3.1 Gaia magnitudes and distance distribution

There are 677 of the ultracool dwarfs that meet the above mentioned
requirements. The distance distribution is shown in Figure 4(a), with the
ultracool dwarf sample in black solid lines. Figure 4 (b) shows their Gaia $G$
magnitude distribution.

Figure 4(a) indicates that the ultracool dwarfs are all within 360 pc. We
notice that most of the ultracool dwarfs are within 100 pc ($\sim$ 83%). The G
magnitude range is from $\sim$ 12 to $\sim$ 19.134 mag, the peak is at around
$\sim$ 16 mag – mean value of 16.206, corresponding to a spectral S/N measured
in the equivalent SDSS $z$ band S/N of 2 to 432 with a median of 61. We note
that our sample has spectra of good quality and is relatively convenient for
model fitting or use as optical spectra templates.

Figure 4:  Histograms of distance (panel a, reciprocal of the GEDR3 parallax,
$binsize=20$ pc), Gaia $G$ magnitude (panel b,$binsize=0.5$ mag).

###  3.2 Testing the sample with colors and absolute magnitude

Figure 5 (a) exhibits the CAMD of $G$ absolute magnitude versus $BP-RP$, and
(b) shows the two-color diagram of $G-RP$ versus $BP-RP$. For both (a) and (b)
panels, the sources in Table 1 are in black solid circles, and the 11,412 LDR7
released late-type M from LDR7 are in cyan dots.

In Figure 5 (a), the main sequence, giant and white dwarf loci are obvious for
the 11,412 late M from the LDR7. Our ultracool dwarf samples are all located
in the bottom right corner – the loci of the reddest and coldest objects with
$BP-RP$ between 2.63 and 5.00, G absolute magnitude between 8.94 and 16.71. It
is reassuring to see that our ultracool dwarfs behave as expected, namely,
they are consistent with being cool dwarfs. Although there seem to be white
dwarfs below the upper main sequence among the 11412 released late M objects,
the case is not always true. There are eight sources located at the loci of
the white dwarf, but after checking their spectra, only three are DA white
dwarfs and M dwarf binaries; whereas the other five do not show any obvious
features of a white dwarf.

In panel (b), our ultracool dwarfs(black solid circles) locate at the top
right – the red and cold loci as well, consistent with the Reylé (2018) on
$G-RP$ color. However, the $G-RP$ color has greater uncertainties than the
$BP-RP$ colors, presumably due to the relatively shorter color baseline of the
$G-RP$ Gaia data. There are 49 sources with $G-RP$ greater than 1.5 when $BP-
RP$ between 3 and 4.2, which is a fainter sub-sample with a mean G band
magnitude of 16.825. They usually have RUWE (listed in table 1) value bigger
than 1: the mean value is 3.28 and the median is 2.10. Greater RUWE values,
that is, more than 1.4, indicates a significant possibility that there is an
unresolved binary involved (Belokurov et al., 2020). The binary could be the
cause of the peculiar $G-RP$ color. In Section 6.2, we show the $G-RP$ color
for binaries in this paper. It is noteworthy that there are several high
proper motion and wide separation binaries, which could lead to complexity and
possible errors in the cross-matching process.

Our $BP-RP$ color appeared as expected, with normal distribution and without
the problem Gaia Collaboration et al. (2021b) remarked for the case of UCDs (
which have greater scatter on $BP-RP$ color caused by bigger uncertainty on
$BP$ magnitude due to their red and faint nature) since our sample is
restricted to brighter sources. There are 533 of the ultracool sample reported
in the work of Gaia Collaboration et al. (2021b), where they reported the
nearby stars within 100 pc selected by the Gaia photometry and astrometry, and
we report their spectral type in this work. Besides, our sample reported
fourteen M6V to M8V which are predicted by Reylé (2018) using Gaia DR2 and
2MASS data. Skrzypek et al. (2016) and Ahmed & Warren (2019) reported 40,000
late-type M select by photometry, but only three objects in this sample
overlap with our sample; this is probably because their samples are much
fainter.

Figure 5:  (a) $G$ absolute magnitude versus $BP-RP$ diagram. $G$ absolute
magnitude computed from the inverse of the parallax with no correction of
extinction. The entire LAMOST DR7 late M sample is plotted in cyan dots,
whereas the ultracool dwarfs are in black solid circles. (b)Gaia $G-RP$ versus
$BP-RP$ color-color diagram. Symbols are the same as in the top panel.

##  4 Spectroscopic analysis

Mass or age is needed to ascertain their sub-stellar nature and neither
quantity is readily available. We hence relied on other criteria such as the
$T_{\rm eff}$, log $\it g$, $\rm[M/H]$ and strength of the lithium line, all
available in the catalog and spectra of LDR7, as proxies of mass and age.

###  4.1 Atmospheric parameters

Stellar atmosphere parameters $T_{\rm eff}$ , log $\it g$, and $\rm[M/H]$ for
M type objects in LDR7 are provided by LAMOST Stellar Parameter Pipeline for M
stars (hereafter LASPM, Du et al., 2021). It minimizes $\chi^{2}$ between the
observed low-resolution spectra and a linear combination of five best-matching
grids in the wavelength range of 6000 to 8800 Å with some specific
contamination of the earth atmosphere masked (Du et al., 2021) to derive the
stellar parameters. The LASPM does not provide stellar parameters for spectra
with S/N in the SDSS $i$ band bellow 5. The grids are from BT-Settle
CIFIST2011 grids (Allard et al., 2011, 2012). The CIFIST2011 model is
calculated from the radiative transfer code named “PHOENIX” with the solar
abundance from Caffau et al. (2011), considering dust formation, gravitational
settling, and convection. The line lists used are introduced briefly in Du et
al. (2021). The coverage of $T_{\rm eff}$, log $\it g$ and $\rm[M/H]$are 300
to 8000K, 0.0 to 0.6 dex, and -2.5 to 0.5 dex with steps of 100 K, 0.5 dex,
and 0.5, respectively.

The measured stellar parameters of the ultracool dwarfs are listed in Table 2.
Letters “H, M, and L” in column 10 refer the first letter of ”high,” ”medium,”
and “low,” indicating the strength of the lithium line, with “H” the strongest
and “L” the weakest, based on visual checking of the lithium line. The label
“N” indicates the absence of the lithium line. We did calculate the equivalent
width, but it is a weak feature and the flux near 6708 Å is often rather
noisy, so we do not report the value here.

Table 2: Radial velocity and atmosphere parameters in LDR7.

R.A. | Decl. | RV | $T_{\rm eff}$ | $eT_{eff}$ | log $\it g$ |  elog $\it g$ | $\rm[M/H]$ |  e$\rm[M/H]$ | Li |  S/N $i$ |  S/N $z$
---|---|---|---|---|---|---|---|---|---|---|---
(deg) |  (km s-1) | (K) | (dex) | (dex) |  |  |
0.29067 | 0.29067 | 11.85 | 2960 | 87 | 4.80 | 0.14 | -0.20 | 0.10 | N | 80 | 106
0.64809 | 0.64809 | -20.56 | 3045 | 87 | 4.21 | 0.15 | -0.27 | 0.10 | N | 69 | 95
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮
15.77892 | 15.77892 | 22.22 | 3053 | 108 | 4.61 | 0.17 | -0.23 | 0.12 | N | 13 | 19
15.88307 | 15.88307 | -25.09 | 3063 | 97 | 4.88 | 0.16 | -0.18 | 0.11 | N | 78 | 97
15.93150 | 15.93150 | 3.06 | 3091 | 75 | 4.30 | 0.13 | -0.23 | 0.09 | N | 84 | 110
15.93207 | 15.93207 | 3.51 | 3081 | 100 | 4.72 | 0.17 | -0.09 | 0.12 | N | 63 | 79
16.16718 | 16.16718 | -0.17 | 3004 | 105 | 4.87 | 0.17 | -0.25 | 0.12 | L | 57 | 82
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮
333The parameters in LDR7. Columns 1-2: Position from LDR7 in epoch J2000.
Column 3: RV. Column: 4-9: effective temperature, surface gravity, and
metallicity, each parameter with their uncertainty followed. Column 10 label
indicates if there is a lithium absorption line at 6708 $\AA$ by “H/M/L’
’(with the strength of the lithium at “H” as the highest level, “M” the
medium, and ”L” the weakest) or “N”(indicating no obvious lithium line).
Columns 11 and 12: S/N in the SDSS $i$ and $z$ band. Here we show only a
portion of this table, and it is published in its entirety in the online
machine-readable format at http://paperdata.china-vo.org/YFW/aa _table2.csv

We present the atmospheric parameters in Table 2. The effective temperature
spread is from 2600 K to 3300 K, while the mean temperatures for each SpT are:
M6 $\sim$ 3018 K, M7 $\sim$ 2917 K, M8 $\sim$ 2775 K, and M9 $\sim$ 2675 K.
The mean temperatures cool down as the spectral type gets latter from M6 V to
M9 V, and are roughly consistent with the literature that adopts atmospheric
grid fitting with low or mid to high-resolution spectra (Rajpurohit et al.,
2013; López-Valdivia et al., 2019) within 200K, but they are usually higher
than the literature. We note there are only a few M8 and M9 dwarfs in both
literature and our sample which makes the comparison difficult. If we make a
comparison with the results of Reid & Hawley (2005) or Kaltenegger & Traub
(2009), our mean temperatures are higher by about 350 K for each same SpT for
late M dwarfs. One reason for this bias might be caused by the saturation of
TIO absorption band in spectra later than M6. The TiO band is sensitive to
temperature and weak for high temperatures, and then starts to saturate to the
cool end (Passegger et al., 2016). This TiO behavior was not properly
described in earlier versions of the PHOENIX models. The surface gravity
varies from 3.5 to 5.5 dex with a mean of 4.43 dex. The measurement of surface
gravity from the LASPM is broadly consistent with our expectations. And the
metallicity varies from -0.99 to +0.38. The mean metallicity is
$<\hbox{$\rm[M/H]$}>\leavevmode\nobreak\ =-0.33$, consistent with Galactic
disk dwarfs according to Wyse & Gilmore
($<\hbox{$\rm[M/H]$}>\leavevmode\nobreak\ =-0.4$, 1995).

Thus, we give several cautions for our derived stellar parameters.

Firstly, the LASPM assumed the giants(with a spectral type of “gM”) have a
surface gravity between 0 and 4.00 dex, while the dwarfs (with a spectral type
of “dM” ) have between 3.5 and 5.5. If a dwarf is misclassified as a “gM” it
is likely this dwarf will have log $\it g$ value that is smaller than 3.5. In
our ultracool dwarf sample, there are 16 objects that have a surface gravity
smaller than 3.5, but we checked their spectra and we know that they have
prominent K i doublets near 7688Å, and Na i near 8189Å. So, for these objects,
we set their surface gravity at -9999.99.

Next, we know that LASPM assumed the giants (with spectral type of “gM”) have
surface gravity between 0 and 4.00 dex, while the dwarfs (with a spectral type
of “dM” ) between 3.5 and 5.5. If a dwarf is misclassified as “gM,” it is
likely this dwarf will have log $\it g$ smaller than 3.5. In our ultracool
dwarf sample, there are 16 objects that have surface gravity smaller than 3.5,
but we checked their spectra and we know that they have prominent K i doublets
near 7688Å, and Na i near 8189Å. So, for these objects, we set their surface
gravity at -9999.99.

Lastly, although the values for the stellar parameters are statically
consistent with the expectations, it is better to check the spectra before
adopting the parameters because LASPM, which is a pipeline aimed at compute
parameters for a large number of objects, does not guarantee the accuracy of
parameters for each individual object. In Table 2, the last two columns list
the S/N for consideration.

###  4.2 Lithium diagnosis

Given the uncertainty in $T_{\rm eff}$, log $\it g$ and $\rm[M/H]$, we did not
attempt to estimate the mass of each of our ultracool dwarfs by connecting the
atmospheric model to evolutionary ones. Instead, we can use a more direct
proxy by looking for the presence of the lithium absorption line at 6708 Å.
Given the low dispersion of the LAMOST DR7 spectra, we did not measure the
equivalent width. Generally, the lithium test for BDs, including analysis of
the equivalent width, requires an 8 to 10-meter telescope and mid-to-high
dispersion spectroscopy (Rebolo et al., 1995; Martín et al., 1999; Kirkpatrick
et al., 2008).

The lithium line for our ultracool dwarfs was checked. Figure 6 compares an
ultracool dwarf showing the lithium line and another one without the lithium
line, each with an inset zooming into the wavelength range about the lithium
line at 6708 Å. In Table 2, as mentioned in the previous subsection, the 10th
column labels “H/M/L” for the targets showing the lithium line, indicating the
strength of high, medium, or weak, whereas “N” marks those with no detection
of the line. There are 77 out of the 734 ultracool dwarfs with a prominent
lithium absorption line at 6708 Å. We further explored the lithium line using
the LAMOST single exposure spectra to exclude the impact of one bad single
spectrum and to make sure that none of the above-mentioned lithium lines is
caused by noise.

Figure 6:  Comparison of two spectra based on their 6708 Å lithium lines: One
with the lithium line and another without. Panel (a) shows an M6 spectrum with
a lithium absorption line. An M6 spectrum without lithium is shown in panel
(b) for comparison. The small windows in each panel zoom in on the region that
containing the 6708 Ålithium line. The atmosphere parameters from the LAMOST
1D pipeline are labeled.

There is roughly 10% of our ultracool dwarf sample exhibiting the lithium
feature, which is consistent with the study from Reiners & Basri (2009). The
presence of a lithium line in a cool M dwarf with an age older than a few
hundred Myr is firm evidence of mass below 65 $M_{J}$, namely, below the
hydrogen-burning limit; therefore, it is a brown dwarf (Reiners & Basri,
2009). However, lithium depletion is expected to take about 100 Myr to reach
completion. Definitive inference from the presence of lithium requires that
reliable ages are established for all objects, which is not available
especially for the field objects. Thus, it is safe to say that these 77
ultracool dwarfs are very probably brown dwarfs and that these lithium
detections represent the first automated survey mode discoveries of lithium,
establishing a significant new sample of lithium detections.

##  5 Kinematic diagnosis

Our ultracool dwarfs are all within 360 pc, namely, they are in the solar
neighborhood and likely to be Galactic disk members. However, there is a
possibility that they may have a halo origin and will have a relatively high
space velocity.

In this section, we study their kinematics. We calculate the $UVW$ space
motion and Galactic position using the RV (listed in Table 2) from LDR7 1D
pipeline and the astrometric data from GEDR3. The position, namely, the
Galacticocentric distance and Galactic height, suggests that they are disk
objects. With their LSR-corrected $UVW$ velocity, we plotted our ultracool
dwarfs on the Toomre diagram. In addition, we calculate the probability ratios
of the thin-disk-to-thick-disk as well as that of the thick-disk-to-halo. In
short, we conclude most of them are thin-disk objects. Using the thin-disk
objects, we calculate the mean and scatter of the $UVW$ velocities to infer
their kinematic ages.

###  5.1 Space position and velocity

To ensure that the data we used are reliable, we excluded the data with
relative uncertainty on parallax greater than 20%. Considering the RV, because
of the typically broad spectral features and relatively poor S/N for M type
spectra (especially for late M types) the RVs from low-resolution spectra
provided by LDR7 for our ultracool dwarfs are potentially not reliable and we
should exclude the unreliable RVs.

Thus, we measured the RV based on cross-correlation with M type spectral
templates from Zhong et al. (2015) for comparison with the RVs that come from
LDR7. Our RV measurements are called $RV_{CM}$ hereafter. Then we applied an
iterative three-sigma clip to residuals of the two sets of RV to cut out
unreliable RVs. Figure 7 shows the final RV comparison after iteration with a
three-sigma clip. The x-axis is from LDR7 and the y-axis is from our
$RV_{CM}$(in black solid circles) the standard deviation is 9.96 km s-1. We
adopted the LDR7 RV and 10% of RV for uncertainty, which is a relatively
conservative value for uncertainty. The final adopted RV from LDR7 is
consistent within three sigmas of $RV_{CM}$ but the two RVs have an offset of
about 3.0 km s-1. After the exclusion of all unreliable measurements, there
are 541 sources left in our sample.

Figure 7:  Comparison of the LDR7 RV versus $RV_{CM}$ after a 3 sigma clip on
the residuals of the two sets of RVs. The x-axis is the LDR7 RV and y-axis
$RV_{CM}$. The ultracool dwarfs in our sample are shown in black solid
circles.

Using the five GEDR3 astrometric parameters (R.A., Decl., proper motion, and
parallax) and the LDR7 RV, the $UVW$ space motion, then Galactocentric
distance ($R$) and Galactic height ($Z$) are computed based on the following
assumptions: 1) space motion with the U positive towards the Galactic center,
V positive toward the Galactic rotation, and W positive to the Galactic north
pole; 2) the distance between the earth and Galactic center is
$R_{\bigodot}=8.2$ kpc (Bland-Hawthorn & Gerhard, 2016); 3) the motion of the
local standard of rest (hereafter LSR) is 238 km s-1, and velocity of the sun
with respect to the LSR is
$[U_{\bigodot},V_{\bigodot},W_{\bigodot}]=[14.0,12.24,7.25]$ km s-1(Schönrich
et al., 2010; Schönrich, 2012; Bland-Hawthorn & Gerhard, 2016); and 4) the
distribution of equatorial coordinates, proper motion, and parallax is a
multivariate Gaussian(Marchetti et al., 2019; Li et al., 2021). The derived
$UVW$, Galactocentric distance($R$) and Galactic height($Z$) are listed in
Table 3.

Table 3: Kinematic parameters.

R.A. | Decl. | $U$ | V | W | Z | R | TD/D | TD/H
---|---|---|---|---|---|---|---|---
(deg) |  (km s-1) | (pc) |
0.29067 | 0.29067 | $-16.47^{+0.17}_{-0.17}$ | $-14.41^{+0.69}_{-0.70}$ | $-22.55^{+0.87}_{-0.98}$ | $-6.58^{+0.19}_{-0.19}$ | $8204.83^{+0.08}_{-0.09}$ | 0.01 | 5157
1.82317 | 1.82317 | $12.80^{+1.34}_{-1.33}$ | $-37.79^{+3.13}_{-3.08}$ | $3.72^{+1.59}_{-1.64}$ | $-5.34^{+0.15}_{-0.16}$ | $8225.22^{+0.13}_{-0.13}$ | 0.01 | 4663
2.23202 | 2.23202 | $-21.07^{+0.36}_{-0.41}$ | $-17.74^{+0.83}_{-0.76}$ | $11.62^{+0.19}_{-0.22}$ | $21.71^{+0.01}_{-0.01}$ | $8206.28^{+0.00}_{-0.00}$ | 0.01 | 4965
2.45851 | 2.45851 | $8.02^{+0.14}_{-0.14}$ | $-10.95^{+0.41}_{-0.40}$ | $-4.75^{+0.43}_{-0.43}$ | $0.07^{+0.06}_{-0.06}$ | $8208.28^{+0.04}_{-0.04}$ | 0.01 | 5259
5.12607 | 5.12607 | $-32.29^{+0.54}_{-0.52}$ | $-60.11^{+1.06}_{-1.12}$ | $-44.20^{+0.71}_{-0.67}$ | $19.01^{+0.00}_{-0.00}$ | $8204.61^{+0.01}_{-0.01}$ | 0.28 | 2186
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮
444The kinematic parameters. Columns 1-2 show the position from LDR7 in J2000,
columns 3-5 are space motion U V W with a unit of km s-1. Columns 6-7 show the
Galactic z and distance R with units in pc. The last two columns list the
probability of Galactic membership, TD/D is the probability ratio of the thick
disk to the thin disk, while TD/H indicates the probability ratio of the thick
disk to the halo. Here is only a portion of this table, this table is
published in its entirety in the online machine-readable format at
http://paperdata.china-vo.org/YFW/aa _table3.csv

###  5.2 Galactic population analysis

Figure 8:  Galactic R versus Z diagram (a). Toomre diagram for our objects
(b). For both plots (a) and (b), our ultracool dwarfs are in black solid
circles. The blue squares are objects in binary systems, The green dashed
curve shows the thick-thin disk limit (Venn et al., 2004) of total velocity.
The blue and yellow dashed curve indicates the thick and halo limit from
Nissen & Schuster (2010) or Bonaca et al. (2017).

We show in Figure 8 the derived $UVW$ velocities relative to the LSR and the
Galactic position $R$ and $Z$. The black solid circles indicate the objects in
our sample, in panel (b), the blue squares show objects in binary systems. The
Galactocentric distance and Galactic height are shown in plot (a). From this
figure, their Galactic heights are between $\sim$ -289 and +229 pc and the
Galactic distances are between 8.1 and 8.5 kpc, which means they are the
nearby local sample dominated by thin-disk objects. Further, we judge their
Galactic membership using the Toomre diagram in plot (b) of Figure 8. The
dashed lines in different colors are the total velocity limits between disk
and halo from the literature. The green line indicates the thick-thin disk
limit(Venn et al., 2004), the yellow and red are the thick disk-halo limit
from Nissen & Schuster (2010) and Bonaca et al. (2017), respectively. Adopting
either Nissen & Schuster (2010) or Bonaca et al. (2017), we see that the
ultracool dwarfs are disk members in our sample and most of our sources are
located within the thick-thin disk limit. There are 46 out of the 541 single
objects located beyond the thin-thick disk limit but within the thick disk-
halo limit; they are thick-disk objects, leaving 495 as thin-disk objects. The
blue squares in Figure 8 panel (b) remind us of the binaries that we need to
consider when doing further analysis in Section 5.3.

We studied the Galactic membership through thick-disk-to-thin-disk (hereafter
TD/D) and thick-disk-to-halo (hereafter TD/H) probability ratios, which are
calculated considering the distribution of thin-thick-halo components in
velocity as well as the observed fractions of each population in the solar
neighborhood following Bensby et al. (2003). The probability for each object
is listed in Table 3. Two of our objects have the TD/H probability of 0.06 and
0.09 (less than 0.1), but according to their Galactic position (Figure 8), we
conclude they are disk objects. Adopting a TD/D probability smaller than 0.1,
491 of the 541 objects are within the thin disk. In principle, the velocities
of the objects in binary (as shown in Fig. 8) or multiple systems will be
affected by their companions, so we did not include them in the following
kinematic study. In Section 6, we further discuss these binaries.

We conclude that most of our ultracool dwarfs are thin-disk objects, while a
small portion of them are thick-disk objects that are consistent with the
metallicity analysis (see Section 4.1). In the next sub-section, we compute
the $UVW$ average value with respect to the Sun and the dispersion for our
ultracool dwarfs, so as to estimate the kinematic age. For further study, we
require the thin-disk objects to be judged as thin-disk stars by both the
Toomre diagram and the probability ratio according to Bensby et al. (2003)
method. There are 477 single thin-disk objects that meet our requirements.
Correspondingly, there are 70 single thick-disk objects.

###  5.3 Velocity distribution and kinematic ages

Figure 9 shows the distribution of the $UVW$ velocities for the thin-disk
objects over-plotted with a Gaussian fit (in black ) and the thick-disk ones
(in dotted cyan bins). The binaries are not included in this figure to ensure
that the objects shown are all singles to the best of our knowledge. We find
that the velocities of the thin-disk objects in our sample have a prominent
Gaussian profile and the velocity dispersion is very small. While for the
thick disk components, the $W$ velocity shows a prominent Gaussian peak in
Figure 9 panel (c), but the distribution of $U$ and $W$ velocity does not look
like a Gaussian distribution. This may be caused by the relatively small
number of only 70 plotted. Hence, we did not carry out further kinematic
analyses for the thick-disk objects in the following sections.

The mean and sigma of the $UVW$ for singles(477 thin-disk objects) are
presented below in Table 4. Our velocity data in this sub-section are
heliocentric, so the average value of the sample reflects the anti-motion of
the solar system relative to these dwarfs. Using our objects for reference, we
find
$(U,V,W)_{\bigodot}=[14.02^{+1.20}_{-1.21},17.60^{+0.71}_{-0.71},6.19^{+1.21}_{-1.20}]$
km s-1; these average velocities agree within 3$\sigma$ of previous literature
results for the solar motion; for instance, Wang et al. (2018) studied the
$UVW$ velocity of about 200 L and T dwarfs, and found the solar motion of
$(U,V,W)_{\bigodot}=[7.9\pm 1.7,13.2\pm 1.2,7.2\pm 1.0]$ km s-1 . The $U$ and
$W$ velocity of LSR we derived are consistent within 3 $\sigma$ with the
adapted values in section 5.1: $(U,V,W)_{\bigodot}=[14.0,12.24,7.25]$km
s-1(Schönrich et al., 2010), while the $V$ velocity is slightly bigger. The
$V_{\bigodot}$ is subject to controversies with the value varying from 1 to 21
km s-1(Bovy et al., 2012; Robin et al., 2017; Gaia Collaboration et al.,
2021b).

Table 4: Velocity distributions of thin-disk objects and their kinematic ages.

| $<v>$ | low err | high err | $\sigma_{v}$ | low err | high err | Age | low err | high err
---|---|---|---|---|---|---|---|---|---
|  (km s-1) |  (km s-1) | (Gyr)
$U$ | -14.03 | 1.20 | 1.20 |
$V$ | -17.60 | 0.71 | 0.71 |
$W$ | -6.19 | 1.21 | 1.20 |
$\sigma_{U}$ |  | 25.71 | 1.17 | 1.18 |
$\sigma_{V}$ |  | 18.53 | 0.89 | 0.89 |
$\sigma_{W}$ |  | 18.60 | 1.43 | 1.37 |
$\sigma_{tot}$ |  | 36.75 | 4.21 | 4.07 |
Age |  | 2.97 | 0.90 | 1.06
555Distribution of the $UVW$ velocity and their kinematic age.

The standard
deviation:$[\sigma_{U},\sigma_{V},\sigma_{W}]=[25.71^{+1.17}_{-1.18},18.53^{+0.89}_{-0.89},18.60^{+1.43}_{-1.37}]$
and total standard deviation: $\sigma_{v}=36.75^{+4.21}_{-4.07}$ are all
listed in Table 4. Our velocity dispersion is consistent with literature
results that focus on BD samples, for instance, (23.0, 15.8, 12.2) from Wang
et al. (2018), (25, 23, 20) km s-1from Schmidt et al. (2010) and (30.2, 16.5,
15.8) km s-1from Zapatero Osorio et al. (2007).

Our objects spend their time in a galactic potential which will vary and lead
to dynamical evolution. A monotonic increase of velocity dispersion with age
is seen for a given stellar population. We studied the kinematic age following
the relationship between velocity dispersion and age given in Binney &
Tremaine (2008):

$\sigma_{v}(\tau)=v_{10}\left(\frac{\tau+\tau_{1}}{10{\rm
Gyr}+\tau_{1}}\right)^{\beta},$ (1)

where $\sigma_{v}$ is the unweighted total velocity dispersion, and we used
all six best-fit parameter sets of $v_{10}$, $\tau_{1}$ and $\beta$ in Table 2
of Aumer & Binney (2009) to provide an average age in ($\tau$). With
$\sigma_{v}=36.75^{+4.21}_{-4.07}$ km s-1, we find $\tau=2.97^{+0.90}_{-1.06}$
Gyr (listed in Table 4). This value is similar to the value of 3.1 Gyr for a
sample of 63 late M dwarfs(Reiners & Basri, 2009), but older than 1.7 Gyr for
a sample of nearby L and T dwarfs (Wang et al., 2018) – consistent within
3$\sigma$ for both values.

Figure 9:  Histograms of $UVW$ velocities for the ultracool dwarfs. Objects in
binary systems are deleted. Black solid histograms over-plotted with the
fitted Gaussian curve for the 477 thin-disk objects. Cyan dotted bars show the
70 thick-disk objects. Bin size is 10 km s-1 for all three panels.

##  6 Binaries in our sample

Among the sources in Table 1, one particular group deserves special attention:
objects in binary systems. We study them using the GEDR3 and Pan-STARRS DR1
(here after PS1, Chambers et al., 2016) data. In this subsection, we report 35
“co-moving” binaries. The following subsections describe how we selected the
binaries and carried out our analysis using the CAMD diagram, along with our
literature search for previously reported binaries.

###  6.1 Identification of the binaries

Every source in Table 1 has been queried in GEDR3 for possible companions
within an angular radius of 16″. We then selected the systems with components
comparable in proper motion and parallax; these are “common proper motion”
binaries. We checked all images in PS1, but in Figure 10, we only present the
PS1 images of six newly discovered binaries in this work and the eight newly
discovered ones by Gaia Collaboration et al. (2021b). Table LABEL:tab:cpm
summarizes the properties of all our binaries. In this table, the first column
is the identification number, with component “$a$” being the entry in Table 1,
namely, having a LAMOST spectrum. Component “$b$” is the co-moving object in
the system, with no implication of apparent brightness or mass relative to the
component “$a$.” Column 2 lists the GEDR3 source_id, with columns 3 and 4
being the coordinates in J2000 epoch computed the GEDR3 epoch J2016.0; Columns
5 to 10 list the GEDR3 $G$-band magnitude, parallax, proper motion, RUWE, and
the angular separation (calculated using the positions in columns 3 and 4.
Column 11 lists the references.

We note that the diameter of the LAMOST fiber is 3.3 arcsec and due to fiber
packing, it is not feasible to target each component in a very close binary or
multiple systems. We note that in this sample, every LAMOST object in Table 1
and its “companion” from the GEDR3 are resolved by GEDR3. But only the LAMOST
“a” component in the pair was targeted by LAMOST, so its spectral type is
known as listed in Table 1.

Figure 10:  PS1 y/i/g band combined images for the 14 newly discovered
binaries. The first two rows of images (labeled 5, 12, 15, 16, 18, and 19)
show the binaries discovered directly in this work and the last two rows of
images show those found by Gaia Collaboration et al. (2021b).

With north at top south at the bottom, west at right, and east at left. Their
number IDs in Table LABEL:tab:cpm are labeled in each frame. The scale is 20
arcsec for all these binary frames. The component “$a$” is always at the
center of each image. The positions for the two components are labeled out in
two frames(for those that have a wider separation).

###  6.2 Positions in the CAMD

Figure 11:  CAMDin the Gaia photometry system for binary components. The
x-axis is $G-G_{RP}$ and the y axis is absolute $G$ magnitude. The legends at
the top right describe the meaning of each symbol.

There are 35 binaries in total and 6 of them are newly discovered in this
work, with images presented in Figure 10. Below, we show the positions for all
of these binaries in the CAMD. With the magnitudes and parallaxes from the
GEDR3, we studied the binaries in the CAMD. To plot the CAMD, we require the
objects have relative uncertainty on a parallax better than 20$\%$ and Gaia
$G$ and $G_{RP}$ magnitudes greater than zero.

In Figure 11, the black solid dots indicate the whole sample. While the blue
squares indicate the LAMOST ”a” components; the red triangles indicate the
GEDR3 ”b” components. The “a” and “b” components are connected using the
dotted lines: there are 21 lines. The left 14 binaries have at least one
component lacking a parallax or magnitude measurements from GEDR3, leading
that only one component appears on this figure without lines connecting the
two components. The dotted lines are largely parallel to the main sequence,
which proves that they are coeval binaries, though some lines are far from the
main sequence. There is one “b” component at the white dwarf loci: “26b”. The
“26ab” is a known white dwarf-main-sequence binary reported by Tian et al.
(2020). There are several lines not parallel to the main-sequence, which
indicate that the components with significantly different colors might have
different metallicities and ages. Besides, objects with redder colors and
brighter magnitudes than the main sequence might be unresolved binaries.

###  6.3 Previously known systems

To search for known binaries, we first looked into the WDS catalog, the
successor to the Index Catalogue of Visual Double Star, maintained by the
United States Naval Observatory. The catalog provides parameters for double
and multiple systems. There are 16 systems in Table LABEL:tab:cpm, already
listed in the WDS catalog. Another binary catalog that we cross-matched with
is the “Catalog of ultrawide binary stars from Gaia DR2” (Tian et al., 2020),
in which we found seven of our binaries. The third catalog we queried is the
“SUPERWIDE Catalog” by Hartman & Lépine (2020), in which six of our binaries
are listed. In the fourth catalog, we searched in Table 3 from Gaia
Collaboration et al. (2021b), and found 19 of our binaries. In the literature,
these are known as a “binary” that is worthy of attention for its particular
properties.

System No. 21, known as $LP\,213-67$ and $LP\,213-68$, has a rich record in
the literature and might prove to be a quadruple system (Dupuy & Liu, 2017).
It was first discovered by Luyten & Hughes (1980) as a pair of ultracool dwarf
(M6.5 for $LP\,213-67$ and M8 for $LP\,213-68$), and later investigated by
Close et al. (2003) using the AO system on Gemini to resolve the LP 213-68
666Originally in Close et al. (2003), they reported an observation of
$LP\,213-67$ but Dupuy & Liu (2017) found that the separation and position
angle derived by Close et al. (2003) is much closer with their study on
$LP\leavevmode\nobreak\ 213-68$ rather than the result of
$LP\leavevmode\nobreak\ 213-67$ by Konopacky et al. (2010). Dupuy & Liu
(2017), with a decade-long astrometric monitoring image from Keck Observatory,
Hubble Space Telescope, and CFHT/WIRCam, suggested that $LP\,213-68$ may be a
system with a main-sequence star having mass $\sim 97$ MJup plus a BD $\sim
80$ MJup with a $\sim 2397$-day period. On the other hand, Konopacky et al.
(2010) tried to use the Keck II 10 m telescope with the LGS AO system to
derive the orbit and period for $LP\,213-67$, but failed with insufficient
epoch coverage. They provide a separation of 0$\aas@@fstack{\prime\prime}$032
$\pm$ 0$\aas@@fstack{\prime\prime}$002 and position angle of $\sim$
126.77$\degr$ on 2006 Jun 21. A more detailed summary on $LP\,213-67$ and
$LP\,213-68$ can be found in Dupuy & Liu (2017). We note that the ”b”
component of this binary system has a red color and brighter absolute G
magnitude; furthermore, the RUWEs of the two components is greater than 1.4.
The above color, absolute magnitude, and RUWE information could be indications
of an unresolved binary for each individual component for other wide binary
systems.

##  7 Summary

LAMOST DR7 released 11,412 spectra with the SpT equal to or later than M6,
with both giants and dwarfs included. We visually inspected individual spectra
according to spectral features and selected 734 ultracool dwarfs by excluding
giants, misclassified early-type M dwarfs, and low S/N spectra. Based on the
SIMBAD database, about 82% of the ultracool dwarfs have not been measured
their spectral type before LAMOST.

We cross-matched all these 11,412 entries with the GEDR3 within 5 arcsec and
obtained their position on the CAMD with magnitudes and parallax of Gaia. We
found that these samples show their correct locus as cool dwarfs on both the
CAMD and the $BP-RP$ versus $G-RP$ diagram. The ultracool dwarfs are within
360 pc(83% of our ultracool dwarf sample are within 100pc) and brighter than
19.2 in Gaia G magnitude. The mean value of G band magnitude is around 16 mag.

We analyzed the stellar parameter measurements from LDR7. Effective
temperature, surface gravity, and metallicity exhibit trends that are
consistent with the literature expectation. Since these parameters are not
calibrated for lacking sufficient external parameter estimation, it is
important that individual spectra are checked before adopting the parameters.
We did not estimate the mass for the ultracool dwarfs using stellar parameters
and evolutionary tracks, but we checked the lithium line at 6708 Åusing the
LAMOST low-resolution spectra. Overall, 10% of our ultracool dwarfs show a
lithium absorption line, which is an indication of the young and substellar
nature of ultracool dwarfs.

With the RV from LDR7 and astrometric data from GEDR3, we studied the Galactic
membership of these ultracool dwarfs. From the Galactic position, Toomre
diagram, and the probability ratio of thick-disk-to-thin-disk (TD/D) and
thick-disk-to-halo (TD/H), we drew the same conclusion: they are all disk
objects and most of them belong to the thin disk. This is consistent with the
distances and metallicity distribution of LDR7. Using 477 thin-disk objects,
we studied their $UVW$ distribution. The mean and dispersion of the velocities
are derived as
$(U,V,W)_{\bigodot}=[14.02^{+1.20}_{-1.21},17.60^{+0.71}_{-0.71},6.19^{+1.21}_{-1.20}]$
km s-1and
$[\sigma_{U},\sigma_{V},\sigma_{W}]=[25.71^{+1.17}_{-1.18},18.53^{+0.89}_{-0.89},18.60^{+1.43}_{-1.37}]$.
The total standard deviation in velocity is $\sigma_{v}=36.75^{+4.21}_{-4.07}$
km s-1, corresponding to a kinematic age of $\tau=2.97^{+0.90}_{-1.06}$ Gyr.

We found 35 common proper motion binaries and 6 of them are newly discovered
binaries. Those with both parallax and magnitudes are shown on the CAMD: one
literature source is known ultracool dwarf-white dwarf binary and its location
is as expected. Furthermore, several binaries are shown to be coeval binaries
and several of them appear to exhibit a peculiar color.

###### Acknowledgements.

We thank Mr. Shih-Yun Tang for the idea of binarity study and help with Gaia
data usage. We thank Dr. Richard L. Smart for a very useful discussion on the
kinematic study of nearby cool objects. This work is supported by the National
Key R&D Program of China(No. 2019YFA0405502), National Science Foundation of
China (No U1931209), Chinese Space Station Telescope(CSST) pre-research
projects of Key Problems in Binaries and Chemical Evolution of the Milky Way
and its Nearby Galaxies. WPC acknowledges the financial support from the grant
MOST 106-2112-M-008-005-MY3. HRAJ acknowledges support from a CAS PIFI Grant
No. 2020VMA0033 and UK STFC grant ST/R006598/1. YXG acknowledges the National
Science Foundation of China (Nos U2031137). YBL acknowledges the science
research grants from the China Manned Space Project with NO.CMS-
CSST-2021-A10,NO.CMS-CSST-2021-A08 and NO.CMS-csst-2021-B05. 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.

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##  Appendix A Binaries

Table 5:  Binaries in the sample. No. |  source $\textunderscore$ id | R.A. | Decl. | $G$ | $\varpi$ | $\mu_{\alpha}\cos\delta$ | $\mu_{\delta}$ | RUWE | Sepa | LAMOST | REF
---|---|---|---|---|---|---|---|---|---|---|---
|  | (deg) | (mag) | (mas) |  (mas yr-1) |  | (arcsec) | (SpTy) |
1a | 374266821724115840 | 14.60929 | 40.96502 | 16.563 | 10.562 | 65.447 | -30.010 | 1.055 | 1.30 | dM6 | 4
1b | 374266821723253120 | 14.60905 | 40.96529 | 17.154 | 10.640 | 69.022 | -29.769 | 0.866 | - | - | 4
2a | 402667207072027008 | 16.21190 | 49.46696 | 16.265 | 10.983 | -72.543 | -48.021 | 1.121 | 1.50 | dM6 | 4
2b | 402667202774679808 | 16.21172 | 49.46733 | 17.297 | 10.916 | -68.486 | -48.482 | 0.948 | - | - | 4
3a | 321982840504952448 | 19.87751 | 38.24850 | 17.648 | 11.075 | 0.015 | -47.740 | 0.893 | 5.87 | dM6 | 2;4
3b | 321982844799985536 | 19.87646 | 38.24974 | 17.630 | 11.045 | 0.255 | -48.071 | 1.011 | - | - | 2;4
4a | 289697678714664320 | 20.60659 | 22.07549 | 16.098 | 18.790 | -21.133 | -11.048 | 1.209 | 7.33 | dM6 | 3
4b | 289697678714664192 | 20.60783 | 22.07711 | 14.670 | 18.848 | -21.140 | -12.270 | 1.026 | - | - | 3
5a | 316277788200150400 | 24.21901 | 33.36533 | 17.688 | 7.123 | 46.367 | -0.923 | 1.171 | 1.09 | dM6 | -
5b | 316277788200960128 | 24.21876 | 33.36516 | 19.207 | 7.158 | 45.694 | -1.860 | 1.022 | - | - | -
6a | 96492285755736448 | 25.81853 | 20.82407 | 16.421 | 17.828 | 144.663 | -18.064 | 1.188 | 1.86 | dM6 | 4
6b | 96492285755202688 | 25.81801 | 20.82404 | 16.580 | 18.012 | 146.567 | -14.172 | 0.883 | - | - | 4
7a | 342530930417172224 | 29.08084 | 37.48177 | 15.929 | 22.216 | 203.994 | -50.869 | 0.966 | 7.36 | dM7 | 1;4
7b | 342530930417172096 | 29.07952 | 37.48021 | 15.747 | 22.257 | 205.307 | -49.469 | 1.166 | - | - | 1;4
8a | 345777204139584384 | 29.50488 | 41.38132 | 15.137 | 30.660 | -35.967 | 20.361 | 1.047 | 3.03 | dM6 | 1
8b | 345765453109062784 | 29.50516 | 41.38053 | 15.274 | 30.592 | -34.291 | 23.813 | 1.209 | - | - | 1
9a | 126144258931133568 | 39.74078 | 25.22135 | 14.728 | 30.488 | 208.525 | -51.629 | 1.179 | 2.82 | dM7 | 1;4
9b | 126144258931133440 | 39.74023 | 25.22191 | 17.014 | 30.398 | 211.976 | -49.911 | 1.156 | - | - | 1;4
10a | 433763835445730944 | 42.96403 | 44.56884 | 14.782 | - | - | - | - | 8.63 | dM6 | 1
10b | 433763831149781376 | 42.96188 | 44.56989 | 15.413 | 32.648 | 145.710 | -90.795 | 1.207 | - | - | 1
11a | 3262741489171756160 | 50.45314 | -0.86917 | 17.287 | 12.074 | 71.038 | -109.761 | 0.971 | 1.55 | dM6 | 4
11b | 3262741489172243328 | 50.45300 | -0.86876 | 16.806 | 12.117 | 74.970 | -108.469 | 0.986 | - | - | 4
12a | 216686773736734336 | 55.75914 | 32.12439 | 17.342 | 3.451 | 4.907 | -6.991 | 1.033 | 1.24 | gM9 | -
12b | 216686773735019264 | 55.75880 | 32.12433 | 17.324 | 3.262 | 4.859 | -7.500 | 0.843 | - | - | -
13a | 3313784735944668544 | 66.91222 | 17.30882 | 15.627 | 9.768 | 19.060 | -34.859 | 1.197 | 14.16 | gM9 | 3
13b | 3313784735944668032 | 66.91387 | 17.31239 | 13.162 | 9.561 | 19.384 | -34.017 | 1.111 | - | - | 3
14a | 3406246551375179392 | 71.25115 | 17.27227 | 16.194 | 16.229 | 69.710 | -24.550 | 1.079 | 1.01 | dM6 | 4
14b | 3406246551373367168 | 71.25095 | 17.27208 | 16.225 | 16.471 | 70.797 | -22.375 | 1.000 | - | - | 4
15a | 3390528895217011712 | 79.88052 | 14.72899 | 16.591 | 5.100 | -1.850 | -8.109 | 1.164 | 8.74 | dM6 | -
15b | 3390528890920404736 | 79.88102 | 14.72661 | 18.416 | 5.480 | -1.689 | -7.719 | 1.007 | - | - | -
16a | 3446362851590055808 | 82.80520 | 30.94254 | 16.556 | 6.561 | 3.024 | -28.840 | 0.990 | 11.60 | dM6 | -
16b | 3446362916013895552 | 82.80219 | 30.94369 | 12.644 | 7.148 | 5.606 | -26.952 | 4.962 | - | - | -
17a | 3349802297332186496 | 89.32967 | 17.14099 | 15.428 | 48.737 | 233.929 | -263.654 | 1.044 | 7.26 | dM6 | 1;2;3;4
17b | 3349805247975323392 | 89.32774 | 17.14157 | 12.785 | 48.804 | 242.615 | -260.695 | 1.241 | - | - | 1;2;3;4
18a | 884269552193012096 | 105.63858 | 27.68727 | 17.734 | 9.054 | -34.352 | -37.865 | 0.860 | 1.27 | dM6 | -
18b | 884269552190985344 | 105.63892 | 27.68717 | 18.312 | 8.646 | -34.871 | -39.144 | 1.005 | - | - | -
19a | 3141512047219196672 | 113.14261 | 6.11010 | 16.784 | 14.341 | -50.159 | -33.730 | 1.037 | 0.75 | dM6 | -
19b | 3141512051515263872 | 113.14247 | 6.10994 | 16.613 | 14.031 | -46.712 | -33.758 | 2.795 | - | - | -
20a | 660597997696173440 | 134.56281 | 19.76340 | 11.966 | 194.144 | -767.060 | -100.176 | 2.574 | 2.66 | dM6 | 3
20b | 660597997697274752 | 134.56311 | 19.76273 | 12.486 | 196.262 | -937.133 | -34.559 | 3.539 | - | - | 3
21a | 779689606794219136 | 161.80254 | 40.44548 | 15.159 | 40.432 | -298.288 | -33.258 | 1.498 | 18.37 | dM7 | 1;4
21b | 779689533779300736 | 161.80740 | 40.44702 | 17.023 | 39.475 | -301.661 | -33.982 | 2.785 | - | - | 1;4
22a | 3809562019331072384 | 162.94824 | 2.89455 | 15.647 | 35.030 | -350.031 | -56.090 | 1.011 | 3.53 | dM7 | 1;4
22b | 3809562019330343040 | 162.94878 | 2.89537 | 15.867 | 34.915 | -342.425 | -55.518 | 1.027 | - | - | 1;4
23a | 729808234575686912 | 163.62886 | 25.96367 | 15.645 | 25.827 | -85.038 | -114.002 | 1.012 | 2.26 | dM6 | 2;4
23b | 729808230280106752 | 163.62946 | 25.96346 | 15.800 | 25.828 | -90.340 | -117.304 | 0.975 | - | - | 2;4
24a | 3699132156679086720 | 181.09290 | 0.88691 | 16.980 | 13.642 | 93.048 | -64.666 | 1.176 | 1.90 | dM6 | 4
24b | 3699132156679086848 | 181.09238 | 0.88680 | 16.624 | 13.189 | 93.822 | -66.237 | 1.092 | - | - | 4
25a | 4015042738059517440 | 185.36273 | 30.64324 | 13.383 | 83.504 | -209.779 | -267.270 | 0.926 | 5.32 | dM6 | 1;2
25b | 4015042738059517568 | 185.36136 | 30.64379 | 13.436 | 83.463 | -191.036 | -253.760 | 1.167 | - | - | 1;2
26a | 4010091053083980032 | 186.44945 | 28.60449 | 17.268 | 12.288 | -85.753 | -259.333 | 1.057 | 17.51 | dM6 | 3;4
26b | 4010090670831602432 | 186.44531 | 28.60193 | 18.565 | 12.500 | -87.315 | -258.321 | 0.879 | - | - | 3;4
27a | 4011353223713622528 | 189.36063 | 29.87850 | 16.547 | 20.354 | -156.452 | -102.041 | 1.000 | 10.98 | dM6 | 1;2;3;4
27b | 4011353223713630592 | 189.36366 | 29.87879 | 12.594 | 20.291 | -156.509 | -98.555 | 1.384 | - | - | 1;2;3;4
28a | 1466583795164173184 | 198.02211 | 32.22596 | 16.053 | 18.687 | 113.194 | -88.446 | 1.360 | 1.00 | dM6 | 1;4
28b | 1466583795162485120 | 198.02190 | 32.22578 | 16.073 | 18.623 | 112.014 | -87.261 | 1.093 | - | - | 1;4
29a | 3664079485466748288 | 207.56108 | 1.50458 | 16.384 | 13.764 | 57.639 | -40.418 | 2.049 | 1.01 | dM6 | 4
29b | 3664079519825981056 | 207.56099 | 1.50484 | 17.223 | 13.431 | 54.726 | -41.720 | 0.833 | - | - | 4
30a | 3674243817630610304 | 212.46527 | 7.40705 | 15.128 | 35.534 | -210.456 | -36.320 | 0.704 | 1.38 | dM6 | 1
30b | 3674243817629910016 | 212.46545 | 7.40739 | 15.282 | 35.373 | -222.378 | -47.723 | 0.764 | - | - | 1
31a | 1477762323724646272 | 214.94243 | 31.61928 | 15.442 | 52.662 | 104.455 | -21.802 | 1.125 | 9.87 | dM7 | 3
31b | 1477762319428998400 | 214.94467 | 31.61770 | 12.962 | 52.747 | 99.281 | -25.453 | 1.320 | - | - | 3
32a | 1267909667590644992 | 225.58881 | 25.43186 | 18.204 | 15.332 | -124.062 | -54.785 | 1.128 | 9.02 | dM7 | 2 ;4
32b | 1267909671886228224 | 225.58885 | 25.43437 | 20.059 | 15.745 | -123.180 | -54.482 | 1.081 | - | - | 2;4
33a | 1271532528341730176 | 228.43425 | 27.39515 | 15.559 | 14.194 | -54.379 | 19.133 | 5.421 | 1.31 | dM6 | 4
33b | 1271532528339403648 | 228.43417 | 27.39480 | 16.390 | 14.219 | -59.596 | 23.552 | 0.983 | - | - | 4
34a | 1221808523727348480 | 232.99323 | 24.75628 | 17.206 | 7.709 | -71.250 | 30.714 | 0.978 | 3.34 | dM6 | 1;2
34b | 1221808519429702784 | 232.99400 | 24.75679 | 19.335 | 7.591 | -71.475 | 30.192 | 1.081 | - | - | 1;2
35a | 2079073928612821760 | 298.47977 | 44.41504 | 11.908 | 214.574 | 349.363 | -480.322 | 1.611 | 9.75 | dM7 | 1
35b | 2079074130463898624 | 298.47977 | 44.41233 | 11.535 | - | - | - | - | - | - | 1
777Column 1 the identification(ID) number of the binaries, arranged in the
order R.A. rising. Column 2: GEDR3 source$\textunderscore$ id. Columns 3-4:
R.A. and Decl. in J2000(transferred from the GEDR3 epoch J2016.0). Columns
5-9: Gaia G band magnitude, parallax, proper motion, and RUWE from GEDR3.
Column 10: Eeparation of the two components calculated using the position in
columns 3 and 4. Column 11: References from 1-4: Mason et al. (2001); Hartman
& Lépine (2020); Tian et al. (2020); Gaia Collaboration et al. (2021b). The
six objects without a reference are newly discovered.