11institutetext: INAF - Osservatorio Astrofisico di Catania, via S. Sofia, 78,
95123 Catania, Italy 22institutetext: University of Wrocław, Faculty of
Physics and Astronomy, Astronomical Institute, ul. Kopernika 11, 51-622
Wrocław, Poland 33institutetext: Royal observatory of Belgium, Ringlaan 3,
B-1180 Brussel, Belgium 44institutetext: Department of Astronomy, Beijing
Normal University, Beijing 100875, P. R. China 55institutetext: Key Lab for
Optical Astronomy, National Astronomical Observatories, Chinese Academy of
Sciences, Beijing 100101, P. R. China

# Characterization of Kepler targets based on medium-resolution LAMOST spectra
analyzed with ROTFIT††thanks: Based on observations collected with the Large
Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) located at the
Xinglong observatory, China. ,††thanks: Tables LABEL:Tab:data_red,
LABEL:Tab:data_blue, 2, 3, and 4 are only available at the CDS via anonymous
ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/?/?.

A. Frasca 11 J. Molenda-Żakowicz 22 J. Alonso-Santiago 11 G. Catanzaro 11 P.
De Cat 33 J. N. Fu 44 W. Zong 44 J. X. Wang 44 T. Cang 44 J. T. Wang 4455
<EMAIL_ADDRESS>
(Received 4 February 2022 / Accepted 28 April 2022)

###### Abstract

Aims. In this work we present the results of our analysis of 16 300 medium-
resolution LAMOST spectra of late-type stars in the Kepler field with the aim
of determining the stellar parameters, activity level, lithium atmospheric
content, and binarity.

Methods. We have used a version of the code ROTFIT specifically developed for
the LAMOST medium-resolution spectra to determine stellar parameters via the
adoption of a grid of spectra of real stars. We provide a catalog with the
atmospheric parameters ($T_{\rm eff}$, $\log g$, and [Fe/H]), radial velocity
(RV), and projected rotation velocity ($v\sin i$). For cool stars ($T_{\rm
eff}$$\leq 6500$ K), we also calculated the H$\alpha$ and Li i$\lambda$6708
equivalent width, which are important indicators of chromospheric activity and
evolutionary stage, respectively.

Results. From the sample of 16 300 spectra, we have derived the RV and
atmospheric parameters for 14 300 spectra of 7443 stars. Literature data
(mainly from high- or medium-resolution spectra) were used for a quality
control of the results and to assess the accuracy of the derived parameters.
The $T_{\rm eff}$ and $\log g$ values are in good agreement with the
literature, although their distribution displays some clustering effects,
which may be the result of the nonuniform distribution of the templates in the
parameter space. The most relevant differences are found for [Fe/H], which
appears to be overestimated for metal-poor stars; this overestimation is also
likely due to the template grid. We propose a relation to correct the [Fe/H]
values derived with ROTFIT. We were able to identify interesting objects, such
as double-lined binaries, stars with variable RVs, lithium-rich giants, and
emission-line objects. Based on the H$\alpha$ flux, we found 327 active stars.
We were able to detect the Li i$\lambda$6708 line and measure its equivalent
width for 1657 stars, both giants and stars on the main sequence. Regarding
the latter, we performed a discrete age classification based on the
atmospheric lithium abundance and the upper envelopes of a few open clusters.
Among the giants, we found 195 Li-rich stars, 161 of which are reported here
for the first time. No relationship is found between stellar rotation and
lithium abundance, which allows us to rule out merger scenarios as the
predominant explanation of the enrichment of Li in our sample. The fraction of
Li-rich giants, $\approx$ 4%, is higher than expected.

###### Key Words.:

surveys – techniques: spectroscopic – stars: activity – stars: binaries:
spectroscopic – stars: fundamental parameters – stars: abundances

††offprints: A. Frasca

##  1 Introduction

The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST; Cui et
al. 2012) is a National Major Scientific Project undertaken by the Chinese
Academy of Science. It is a unique instrument, located at the Xinglong station
and situated south of the main peak of the Yanshan mountains in Hebei province
(China). LAMOST combines a large aperture (4-meter telescope) with a wide
field of view (circular region with a diameter of 5 degrees on the sky) that
is covered by 4000 optical fibers. These fibers are connected to 16 multi-
object optical spectrometers with 250 fibers each (Wang et al. 1996; Xing et
al. 1998), making this instrument the ideal tool for obtaining spectroscopic
observations for a large number of targets in an efficient way. The data
acquired with the LAMOST instrument allow multi-fold analyses of the observed
objects to be conducted, including a homogeneous determination of the
atmospheric parameters (APs): the effective temperature $T_{\rm eff}$, surface
gravity $\log g$, metallicity [Fe/H], radial velocity RV, and projected
rotational velocity $v\sin i$.

The LAMOST Extra-GAlactic Survey (LEGAS) and the LAMOST Experiment for
Galactic Understanding and Exploration (LEGUE) were the two initial scientific
driving forces behind the LAMOST project (Zhao et al. 2012). However, it was
soon realized that observations of the field of view of the nominal Kepler
mission with LAMOST would be a scientific gold mine, being a win-win
opportunity for both communities: it would provide the Kepler community with
the data needed for a homogeneous spectroscopic determination of stellar
parameters for objects observed by Kepler while the LAMOST community could
benefit from high-precision results derived from data obtained elsewhere for
Kepler objects to calibrate the LAMOST results. Therefore, the proposal of the
LAMOST-Kepler project (hereafter LK project) was well received in 2010. A
detailed description is given by De Cat et al. (2015, hereafter Paper I). The
first observations for the project were carried out during the test phase of
LAMOST in early 2011. The scientific observations of the pilot survey of
LAMOST began on October 24, 2011, while the first 5-year regular survey
started about one year later, on September 28, 2012. During the first regular
survey of LAMOST, only single-shot low-resolution spectra (LRS) with a
spectral resolution $R\sim 1800$ covering optical wavelengths ranging from 370
to 900 nm were gathered.

The purpose of the observations collected during the LK-LRS project is
multifarious. First, the APs yielded by the LK project complement and can
serve as a test bench for the content of the Kepler Input Catalog (KIC; Brown
et al. 2011). As such, they provide firm bases for asteroseismic and
evolutionary modeling of stars in the Kepler field. Second, the gathered data
enable us to flag interesting objects as they allow us to identify fast-
rotating stars and objects for which the variability in radial velocity (RV)
exceeds $\sim 20$ km s-1; such objects are good candidates for spectroscopic
binaries or pulsating stars. Similarly, stars that show strong emission in
their spectral lines or display other relevant spectral features can be
identified and used for further research that reaches beyond asteroseismic
analysis. The analysis of the LK LRS has been performed by three teams with
different methodologies. Their results have been presented by Ren et al.
(2016) and Zong et al. (2018) for the Asian group, Frasca et al. (2016) for
the European group, and Gray et al. (2016) for the American group.

In 2015, the LK project was extended to include targets within the fields
observed by the K2 space mission (Wang et al. 2020a). Since the start of the
second phase of the regular survey of LAMOST in September 2018, medium-
resolution spectrographs both in single-shot and time-series mode have also
been used. The corresponding medium-resolution spectra (MRS) have a spectral
resolution $R\sim 7500$.

Within the LK-MRS project, time series of MRS LAMOST spectra are being
gathered for 4 footprints in the Kepler field and 16 footprints distributed
within the northern K2 campaigns. Zong et al. (2020) present the first results
of the LK-MRS project based on the analysis of the data up to June 2019, with
the LAMOST stellar parameter pipeline (LASP) adapted to the resolution of the
MRS, $R\sim 7500$ (Luo et al. 2015; Wang et al. 2019).

In this paper we focus on the MRS of objects in the Kepler field that were
gathered during the test phase of the medium-resolution spectrographs in the
year between the end of the first and the start of the second regular survey
of LAMOST (September 2017 – May 2018). They were made available to the general
public in the sixth data release (DR6) of LAMOST on September 30, 2020. We
adapted the code ROTFIT, developed by Frasca et al. (2003, 2006) and discussed
in detail by Molenda-Żakowicz et al. (2013), to MRS LAMOST spectra. Then we
applied it to the spectra collected with plates that intersect with the Kepler
field of view (both from the LK-MRS project and the regular survey), selecting
spectra of sufficient quality to derive the $T_{\rm eff}$, $\log g$, [Fe/H],
RV, and $v\sin i$ of the observed stars. Moreover, we determined the residual
equivalent width of the Balmer H$\alpha$ line $W^{\rm res}_{\rm H\alpha}$ to
search for active stars, and the equivalent width of the Li i $\lambda$6708 Å
absorption line $W_{\rm Li}$ to detect young stars.

This paper is organized as follows. In Sect. 2 we briefly describe the
selection of our sample and the observations. Section 3 presents the methods
of analysis and discusses the accuracy of the data. That section also includes
a brief description of the ROTFIT pipeline, the procedure for the measure of
the activity indicators, and a comparison of the RVs and APs derived in this
work with values from the literature. The results from the chromospheric
activity indicators and the lithium abundance are presented in Sect. 4.1. We
summarize the main findings of this work in Sect. 5.

##  2 Observations and sample selection

The time in between the first (September 2012 – June 2017) and second
(September 2018 – June 2023) phase of the regular survey of LAMOST was used to
test new medium-resolution spectrographs. They have a spectral resolution of
$R\sim 7500$, covering wavelengths of the visible spectrum ranging from 495 to
535 nm and from 630 to 680 nm with a blue and red arm, respectively (Liu et
al. 2019). In this paper, we use MRS retrieved from DR6 that were collected in
the above mentioned test phases from plates that have objects in common with
the Kepler field. This led to an initial sample of 22,629 MRS LAMOST spectra
(Table 1). Their position on the sky is visualized in Fig. 1. Only seven
medium-resolution spectrographs were available for the observations in 2017.
They were fed by fibers positioned as displayed by the dark blue areas in Fig.
1. LAMOST was fully equipped with 16 medium-resolution spectrographs by the
time the observation in 2018 were done (light blue area in Fig. 1). The
results of the LASP pipeline (Luo et al. 2015; Wang et al. 2019) and of the
convolutional neural network method (Wang et al. 2020b) are given in the
LAMOST MRS Parameter Catalog of DR6, which can be downloaded from
http://dr6.lamost.org.

Table 1: Overview of the LK–MRS plates observed in the period September 2017 –
June 2018 that have objects in common with the Kepler field. For each plate,
we give the identifier, the right ascension and declination of the central
star, the seeing during the observations, the exposure times, and the number
of targets.

Plan ID | RA (2000) | Dec. (2000) | Date | Seeing | Exposure | Number of targets
---|---|---|---|---|---|---
| hh:mm:ss.ss | dd:mm:ss.ss | yyyy-mm-dd | (arc sec) | (s) | Total | hot | cool | unclass
HIP9645901 | 19:36:37.98 | +44:41:41.77 | 2017-09-28 | 2.9 | 600$\times$4 | 1337 | 97 | 1023 | 217
HIP9286201 | 18:55:20.10 | +43:56:45.93 | 2017-10-03 | 3.4 | 600$\times$3 | 1320 | 19 | 745 | 556
HIP9737201 | 19:47:26.83 | +47:54:27.24 | 2017-10-03 | 3.3 | 600$\times$3 | 1329 | 78 | 782 | 469
HIP9380801 | 19:06:17.04 | +41:24:49.61 | 2017-10-04 | 2.5 | 600$\times$3 | 1287 | 55 | 965 | 267
HIP9587901 | 19:29:58.91 | +46:56:47.36 | 2017-10-04 | 2.9 | 600$\times$3 | 1288 | 73 | 944 | 271
HIP9448701 | 19:13:53.55 | +48:20:57.43 | 2017-10-05 | 3.3 | 600$\times$3 | 1219 | 36 | 793 | 390
HIP9511901 | 19:21:02.82 | +42:41:13.07 | 2018-05-24 | 2.8 | 900$\times$5 | 2968 | 126 | 1806 | 1036
HIP95119KP01 | 19:21:02.82 | +42:41:13.07 | 2018-05-28 | 3.0 | 900$\times$7 | 2961 | 122 | 1814 | 1025
HIP95119KP01 | 19:21:02.82 | +42:41:13.07 | 2018-05-29 | 2.3 | 600$\times$9 | 2980 | 119 | 1821 | 1040
HIP95119KP01 | 19:21:02.82 | +42:41:13.07 | 2018-05-30 | 2.4 | 900$\times$5 | 2971 | 124 | 1784 | 1063
HIP95119KP01 | 19:21:02.82 | +42:41:13.07 | 2018-05-31 | 2.3 | 1200$\times$4 | 2969 | 127 | 1787 | 1055
TOTAL |  |  |  |  |  | 22629 | 976 | 14264 | 7389

Notes. The identifiers of the plates observed during the regular LAMOST survey
are written in italic.

Figure 1: Selection of the DR6 LK-MRS project data in the Kepler field. The
stars observed on plates that have overlap with the Kepler CCDs are shown as
dots (blue for stars on a Kepler CCD, dark blue for observations in 2017, and
light blue for observations in 2018).

In this paper, we used the ROTFIT code (see Sect. 3) for the determination of
the stellar parameters, radial and projected rotational velocity ($v\sin i$),
chromospheric activity indicators and lithium abundance. We note that APs were
already provided for most targets in other works based on different codes
(e.g., Zong et al. 2020). For this task we used the stacked MRS, which are the
sum of all the individual spectra of the same object acquired in the same
night. We decided to analyze these data with our code with the aim to have
homogeneously determined parameters, using both the blue- and red-arm spectra,
for all the FGKM-type stars for which we derive other parameters of interest,
such as the $v\sin i$, H$\alpha$ emission, and lithium abundance. Since ROTFIT
is optimized for cool stars, we selected the spectra to be analyzed based on
the results of the LASP pipeline. We subdivided the initial sample into a
“hot” sample ($T_{\rm eff}^{\sf LASP}$ $>$ 7000 K), a “cool” sample ($T_{\rm
eff}^{\sf LASP}$ $\leq$ 7000 K), and an “unclass” sample (no $T_{\rm eff}^{\sf
LASP}$ available), which contain 976, 14264, and 7389 spectra, respectively
(see “Number of targets” in Table 1). The spectra in the hot sample are not
considered in the present work and will be included in a forthcoming paper
(Catanzaro et al., in preparation), which will present a customized analysis
based on a spectral-synthesis approach. A quick-look analysis of the spectra
in the cool and unclass samples allowed us to discard bad spectra (e.g.,
missing parts or too many strong spikes) and those with clear signatures of
hot (A-type or earlier) stars. This selection resulted in about 14,250 and
2050 spectra for the cool and unclass sample, respectively. We used a signal-
to-noise ratio (S/N) $\geq$ 10 in at least one arm as a threshold to select
the reliable parameters from the cool sample. The success rate for this sample
of spectra was very high, as we could determine parameters for 13,630 and
13,793 red- and blue-arm spectra, respectively. However, the unclass spectra
with S/N $\geq$ 10 are only a small fraction of the selected sample (about 200
and 1200 spectra for the blue and the red arm, respectively). Therefore, after
a visual scrutiny, we decided to consider also the results from spectra with a
S/N as low as 5 in one of the arms for the unclass sample, because no stellar
parameters are available yet for these data. We ended up with 692 and 618
unclass spectra with APs in the red and blue arm, respectively. The whole
sample selected for a detailed analysis, which includes both cool and unclass,
consists of 16,300 MRS LAMOST spectra. For 14,300 of these spectra we were
able to determine the APs.

The cross-identification with Kepler sources was based on the fiber
coordinates, adopting a radius of 3.7 arcsec (c.f., Zong et al. 2020; Wang et
al. 2020a).

##  3 Data analysis

###  3.1 Radial velocity, projected rotation velocity, and atmospheric
parameters

Figure 2: Example of the continuum-normalized LAMOST spectrum of a slowly
rotating mid-F star (dots) in the blue arm (upper panel) and in the red arm
(lower panel). The best template found by ROTFIT is overplotted with a thin
red line. The difference between the two spectra is shown in the bottom of
each panel with a blue line shifted upward by 0.2.

We measured the RV, the projected rotation velocity, $v\sin i$, and derived
the APs – $T_{\rm eff}$, $\log g$, and [Fe/H] – by applying the code ROTFIT
(e.g., Frasca et al. 2006, 2015), which was purposely modified to fit with the
LAMOST MRS. We adopted, as templates, a grid of high-resolution spectra of
slowly rotating stars ($v\sin i$ $\leq 3$ km s-1) with a low activity level
that were retrieved from the ELODIE archive (R$\simeq$42,000; Moultaka et al.
2004). This is the same grid as that used for the analysis of young stars
within the Gaia-ESO survey by the OACT (Osservatorio Astrofisico di Catania)
node (Frasca et al. 2015). It contains spectra of 388 different stars, which
sufficiently cover the space of the APs, although the density of templates is
not uniform especially in the regime of metal-poor stars.

We prefer real-star spectra over synthetic ones because the former reproduce
the unknown photospheric spectrum better, which can be subtracted from the
target one to leave the chromospheric core contribution and to clean the Li i
line from blended neighbor lines. Some photospheric lines may be missing in
the synthetic spectra, or the depths and widths of some of them may be poorly
reproduced due to uncertain intensity values, Landé factors and broadening
effects.

The first step of the analysis performed by ROTFIT is the normalization of the
LAMOST spectra to the local continuum, which was accomplished by the fit of a
low-order polynomial. After the normalization, the RV was measured by cross-
correlating the target spectrum with spectra of four stars of different
spectral type (SpT) selected from the library of ELODIE templates. In
particular, we considered HD117176, HD166620, HD95735, and HD25329, whose SpTs
are G5V, K2V, M2V, and K1 metal-poor, respectively. For measuring RV, we chose
the cross-correlation function (CCF) with the highest peak, which is the one
obtained with the best-matching template. This task was executed both for the
blue and red arm of each spectrum, after excluding the lithium line and the
core of the H$\alpha$ line ($\pm$1 Å around the line center), which would
broaden the CCF peak and could be contaminated by chromospheric activity. To
measure the centroid and full width at half maximum of the CCF peak, we fitted
it with a Gaussian. The RV error, $\sigma_{\rm RV}$, was estimated as the
error of the center of the Gaussian fitted to the CCF peak using the procedure
curvefit (Bevington et al. 1993), taking the CCF noise, $\sigma_{\rm CCF}$,
into account. The CCF noise was evaluated as the standard deviation of the CCF
values in two windows of about 600 km s-1 each at the two sides of the peak.
We adopted the value $w=1/\sigma_{\rm CCF}^{2}$ as the instrumental weight for
all the points of the CCF peak that were considered for the Gaussian fit. For
the spectra with S/N$\geq 50$ we find median RV errors of $\approx$ 0.65 km
s-1 for the blue-arm and $\approx$ 0.70 km s-1 for the red-arm, respectively
(see Fig. 3). Although for a small fraction of sources ($\approx$3%) the RV
error is $\sigma_{\rm RV}>3$ km s-1, the median values reach a maximum of
about 1.3 km s-1 for the spectra with a low S/N (S/N$<$10). The RV errors in
the blue arm display a two-fold behavior, with a larger fraction of them being
similar to those of the red arm and barely visible under the red points in
Fig. 3 and a second branch with larger values. This double-peaked distribution
for the RV errors in the blue arm is clearly visible in the right panel of
Fig. 3, where the histogram displays two distinct peaks at about 0.7 and 1.1
km s-1. The peak with RV errors around 1.1 km s-1 corresponds to stars with
$T_{\rm eff}$$\leq 5500$ K, for which the spectral features included in this
range broaden, giving rise to larger RV errors. We note that the RV errors
evaluated with ROTFIT are in agreement with Liu et al. (2019) and Zhang et al.
(2021), who report typical values of about 1 km s-1 at S/N=20. As a further
check of the RV errors, we used the task fxcor of the IRAF111IRAF is
distributed by the National Optical Astronomy Observatory, which is operated
by the Association of the Universities for Research in Astronomy, inc. (AURA)
under cooperative agreement with the National Science Foundation. package and
a set of synthetic templates for a small subsample of about 100 LAMOST MRS of
FGK-type stars. We find an excellent agreement between the RV values derived
with both codes, both for the blue- and red-arm spectra. The errors calculated
by fxcor on the basis of the CCF peak’s height and the antisymmetric noise
(Tonry & Davis 1979) are, on average, similar to those derived with ROTFIT.

As pointed out by Wang et al. (2019) and Zong et al. (2020), the RV measured
on LAMOST MRS can be affected by systematic offsets in different runs that are
related to the wavelength calibration. The largest offset of about 6.5 km s-1
is found for spectra acquired before May 2018 that were calibrated with Sc
lamps, compared to the following ones for which Th-Ar lamps have been used. To
account for these offsets and correct the RVs, we used a method similar to
that adopted by Zong et al. (2020), which is based on the RV measured by Gaia
for a subset of stars with non-variable RVs enclosed in the LAMOST-MRS plates.
For each plate and observing date, these RV differences display a regular
distribution that can be fitted with a Gaussian, whose center is a measure of
the instrumental offset for the given plate and date (see Figs. 27 and 28 for
some examples). These corrections are reported in Table 8.

The resulting RV and $\sigma_{\rm RV}$ values are given in Cols. 16 and 17 of
Tables LABEL:Tab:data_red and LABEL:Tab:data_blue for the red-arm and blue-arm
spectra, respectively. The RVs corrected for instrumental offsets are reported
in Col. 18 of the same tables.

For some spectra we noted two or three CCF peaks at a level larger than
5$\sigma_{\rm CCF}$ that we considered as significant (see Fig. 18 for an
example). In these cases, we classified the object as a double-lined
spectroscopic binary (SB2) or a triple system (SB3), respectively, and flagged
its spectra accordingly in Tables LABEL:Tab:data_red and LABEL:Tab:data_blue.
For these systems we discarded the RVs and APs from the above tables, even if
they were obtained near the conjunctions, when the lines of the two components
are superimposed. The way the RVs of the components of SB2 systems are derived
is described in Sect. 4.4.

For the determination of APs, the reference spectra were first aligned onto
the target spectrum thanks to the RV measured as described above and were
brought to the resolution of the LAMOST MRS, $R_{\rm MRS}\simeq 7500$, by
convolving them with a Gaussian kernel of width $W=\sqrt{1/R_{\rm
MRS}^{2}-1/R_{\rm ELODIE}^{2}}$. Then, each template was broadened by the
convolution with a rotational profile of increasing $v\sin i$ (in steps of 1
km s-1) until a minimum $\chi^{2}$ was attained.

We point out that the resolution and sampling of the MRS LAMOST spectra do not
allow us to measure $v\sin i$ values smaller than 8 km s-1. This threshold was
found by means of Monte Carlo simulations with artificially broadened spectra
that are described in Appendix A. Therefore, the $v\sin i$ values smaller than
8 km s-1 in Tables LABEL:Tab:data_red and LABEL:Tab:data_blue must be regarded
as “non-detection.” Whenever the mean $v\sin i$ value is smaller than 8 km s-1
in at least one arm, the final $v\sin i$ has been replaced with “$<8$ km s-1”
and flagged as an upper limit in the table containing the average APs (Table
2).

As mentioned above, for each target we applied ROTFIT on both the blue- and
red-arm spectra that were analyzed independently. The templates were sorted in
a decreasing order of $\chi^{2}$, giving the highest score to the best-fitting
template. The MK SpT of the template with the highest score was assigned to
the target star. Two examples of the application of ROTFIT for slowly rotating
stars of mid-F and K0 III SpTs are shown in Figs. 2 and 25, respectively. An
example of the application of ROTFIT for a rapidly rotating ($v\sin i$$\simeq$
110 km s-1) F5 V star is shown in Fig. 26.

Figure 3: Errors of RV, $T_{\rm eff}$, $\log g$, and [Fe/H] (from top to
bottom) as a function of the S/N for the blue-arm and red-arm spectra. The
full cyan and yellow lines in each box are the median of the blue-arm and red-
arm errors, respectively. The blue and red histograms in the right panels
display the distributions of these errors for the blue-arm and red-arm
spectra, respectively.

For each arm, we derived the values of $T_{\rm eff}$, $\log g$, [Fe/H], and
$v\sin i$ as the weighted averages of the parameters of the ten best-matching
templates, using $1/\chi^{2}$ as the weight. As uncertainties of these
parameters we took the standard errors of the weighted means to which we added
in quadrature the average uncertainties of the APs of the templates
($\sigma_{T_{\rm eff}}=\pm$ 50 K, $\sigma_{\log g}=\pm$ 0.1 dex,
$\sigma_{\rm[Fe/H]}=\pm$ 0.1 dex). For the $v\sin i$, we added in quadrature a
value of $\sigma_{v\sin i}=\pm$ 3 km s-1, to take the uncertainty related to
the spectra sampling into account.

As mentioned in Sect. 2, we were able to determine APs and RVs for 97 % of the
blue-arm spectra in the cool sample, while only 30 % of the spectra in the
unclass sample could be successfully analyzed. Regarding the red arm, we could
measure stellar parameters for 96 % of the spectra in the cool sample, and 34
% of the unclass-sample spectra. The S/N ranges from 10 to 900 for the
analyzed spectra in the cool sample and from about 5 to 450 in the unclass
one. However, the median S/N is much smaller in the latter sample, and this
explains the lower success rate in determining the parameters. We remark that
the samples of stars with parameters in the red and blue arm are not the same.
In particular, for the cool and faint stars, the S/N in the red-arm can be
sufficient to derive reliable parameters, while it is too low in the blue arm.

The errors of $v\sin i$, $T_{\rm eff}$, $\log g$, and [Fe/H] are displayed as
a function of S/N in Fig. 3. As shown in this figure, the $v\sin i$ errors
range from about 3 to 10 km s-1, with median values rising to about 4 and 5 km
s-1 for the blue and red arm, respectively, at the lowest S/Ns. The scatter
plot for the percent error of $T_{\rm eff}$ shows values ranging from about 1%
to 9%, with an increasing trend for decreasing S/N. The median values of about
2% and 2.5% for the blue and red arm, respectively, increase slightly with the
decrease of S/N. The errors of $\log g$ are smaller than 0.5 dex for nearly
all the spectra, with median values of about 0.20 and 0.25 dex for the blue
and red arm, respectively. The $\log g$ errors increase slightly with the
decrease of S/N, as shown by the scatter plot and the median, with the red-arm
ones being larger, as also indicated by higher tail of the red histogram.
[Fe/H] values have uncertainties smaller than 0.3 dex for most of the spectra,
with median values of 0.15 dex for both the blue and the red arm. As for
$T_{\rm eff}$ and $\log g$, the [Fe/H] errors increase slightly with the
decrease of S/N; this effect is larger for the red-arm values, as also shown
by the histograms.

We remark that stellar parameters obtained from both arms are consistent for
the vast majority of the stars contained in our sample (see Fig. 4). If we
compare the RVs measured by us in the blue and red arm, which are
simultaneous, we find an offset of about $-0.1$ km s-1 between blue and red
RVs and an rms dispersion of 2.3 km s-1 (see Fig. 29). This can provide us
with a further estimate of the average RV accuracy. If we assume that the
blue- and red-arm RVs have, on average, the same uncertainty, we should divide
this number by $\sqrt{2}$, getting an estimate of about 1.6 km s-1 for the RV
accuracy in both arms. On average, we find differences (blue arm minus red
arm) of: $\Delta\,T_{\rm eff}$ = 65$\pm$175 K, $\Delta\log g$ =
$-$0.08$\pm$0.26, $\Delta$[Fe/H] = 0.00$\pm$0.12 and $\Delta v\sin i$ =
$-$8.7$\pm$9.5 km s-1. For the $v\sin i$, the differences are $\Delta v\sin i$
= $-$3.8$\pm$3.4 km s-1, if we exclude the upper limits. For a better display
of the results, the distribution of these differences for each parameter,
taking the red arm as a reference, is shown in Fig. 5. As seen above for the
$RV$, the difference between the APs in the blue and red arm enables us to
estimate average uncertainties, which turn out to be (dividing by $\sqrt{2}$)
about 120 K, 0.18 dex, 0.09 dex, and 2.5 km s-1for $T_{\rm eff}$, $\log g$,
[Fe/H], and $v\sin i$, respectively. The “zigzag” pattern shown by the $T_{\rm
eff}$ and $\log g$ plots in Fig. 4, which is more evident in Fig. 5, is the
effect of the clustering of the average parameters around those of the best
(minimum $\chi^{2}$) template. This is not surprising, because, unlike other
analysis codes, ROTFIT does not apply any kind of interpolation or
regularization between the parameters of the closest templates. We note the
floor of low $v\sin i$ values for the blue-arm spectra ($v\sin i$BLUE), which
extends up to $v\sin i$${}_{\rm RED}=50-60$ km s-1 and translates into the
tilted strip in Fig. 5. This indicates cases in which the red arm provided a
poor constrain to $v\sin i$ due to the few absorption lines or to the presence
of molecular bands in their red-arm spectra.

Figure 4: Comparison of the parameters obtained from both arms. Typical errors
are displayed in the bottom-right corner of each panel. In the panel
corresponding to the $v\sin i$, the dashed lines show the upper limit at 8 km
s-1.  Figure 5: Differences obtained from both arms (blue and red) for each
parameter. In the panel corresponding to the $v\sin i$, the dashed line shows
the upper limit at 8 km s-1.

The final APs were obtained as the weighted mean of those of the two arms,
whenever measures in both arms were available. As described in Sect. 2, in
total (from the cool and unclass samples) we selected about 16 300 spectra for
our analysis. These spectra, once their coordinates were cross-matched,
correspond to 8268 different stars. For 821 of such sources, it was not
possible to find reliable parameters because of the binary nature of some
sources (see Sect. 4.4) or due to the poor quality of the spectra in other
cases. In total, we provide parameters (see Table 2) for 7443 stars, the vast
majority of which (7146 stars) has been obtained from both arms. Most of the
stars were observed only once (5487) while the rest (1956) have been observed
up to six times.

The final parameters (i.e., the average values for each star obtained from all
its individual measurements) were calculated by employing a S/N-weighted mean,
while the uncertainties were quantified by using the average of individual
errors. For the stars observed once, with both arms we averaged both values,
whereas for those stars with multiple observations we first calculated a
single value per arm and then performed the average of both. We remark that
the average value of the RV for stars with multiple observations can hide a
genuine RV variation ascribable to pulsations or to the presence of an unseen
close companion that would make the source a single-lined spectroscopic binary
(SB1). Therefore, we do not list this value in Table 2, but, for stars with
multiple observations, we calculated the reduced $\chi^{2}$ and the
probability $P(\chi^{2})$ that the RV variations have a random occurrence
(e.g., Press et al. 1992). Whenever $P(\chi^{2})<0.05$ we considered the RV
variation as significant and flagged the corresponding source with “RVvar” in
Table 2. However, the individual values of RV measured in each spectrum can be
found in Tables LABEL:Tab:data_blue and LABEL:Tab:data_red for the blue and
red arm, respectively. In general, the APs derived from different arms or
observations are in good agreement with each other. Just a few outliers have
been detected. In these cases, a visual check of the spectra helped us to
improve the results by leaving out the worst ones (i.e., the noisiest, those
with artifacts, etc.).

Also, $Gaia$ parallaxes have been used to discern the proper values when large
discrepancies in $\log g$-values were found. This was particularly helpful for
low-signal spectra of M-type stars. Typical errors from different arms or
observations are one or two spectral subtypes. Lastly, the final S/N was taken
as the average of individual values. This number is not intended to be an
actual ratio but only an indication of the overall quality of the spectra for
each target. These final values ($T_{\rm eff}$, $\log g$, [Fe/H], $v$ sin $i$,
SpT and S/N) are displayed in Table 2 for the stars in our sample along with
their equatorial coordinates, KIC designation, number of observations (N) and
an indication of the arm(s) with which they have been observed (Arm): blue
(b), red (r) or both (br). The last column (Rem) reports any useful remark,
such as RVvar for stars with variable RV, Li for stars with a detection of the
Li i $\lambda$6708 absorption line, and Haf or Hae for stars with the
H$\alpha$ line filled in by core emission or with a pure H$\alpha$ emission
profile above the local continuum.

Table 2: Final APs of the investigated sources.

RA | Dec. | KIC | N |  $T_{\rm eff}$ | $\log g$ | [Fe/H] | $v\sin i$ | SpT | S/N | Arm | Rem
---|---|---|---|---|---|---|---|---|---|---|---
(J2000) | (J2000) |  |  |  (K) |  |  | (km s-1) |  |  |  |
280.925900 | 42.657299 | KIC07090703 | 1 | 5949 $\pm$ 138 | 4.26 $\pm$ 0.12 | 0.09 $\pm$ 0.11 |  $\leq$8.0 | G1.5 V | 5 | b | …
280.952640 | 42.641399 | KIC07090759 | 1 | 5852 $\pm$ 120 | 4.25 $\pm$ 0.17 | 0.06 $\pm$ 0.15 |  $\leq$8.0 | G2.5 | 30 | br | …
281.054810 | 42.621838 | KIC07090977 | 1 | 6322 $\pm$ 141 | 3.98 $\pm$ 0.15 |  $-$0.07 $\pm$ 0.13 | 18.4 $\pm$ 3.0 | F6I V | 35 | br | …
281.074070 | 42.474880 | KIC06921876 | 1 | 5253 $\pm$ 231 | 3.36 $\pm$ 0.48 |  $-$0.40 $\pm$ 0.16 | 11.5 $\pm$ 3.6 | G8 III | 13 | br | …
281.143590 | 42.475670 | KIC06922004 | 1 | 6915 $\pm$ 221 | 4.11 $\pm$ 0.19 |  $-$0.26 $\pm$ 0.19 | 20.3 $\pm$ 3.7 | A8 Vs | 16 | b | …
281.174930 | 42.476238 | KIC06922059 | 1 | 5829 $\pm$ 70 | 4.31 $\pm$ 0.12 | 0.06 $\pm$ 0.12 | 9.7 $\pm$ 3.7 | G1.5 V | 41 | br | Li
281.212860 | 42.691792 | KIC07091248 | 1 | 5255 $\pm$ 133 | 3.76 $\pm$ 0.40 | 0.01 $\pm$ 0.14 |  $\leq$8.0 | G2.5 IIIb | 17 | br | …
281.235410 | 42.620834 | KIC07091292 | 1 | 5812 $\pm$ 141 | 4.09 $\pm$ 0.18 |  $-$0.22 $\pm$ 0.14 | 28.0 $\pm$ 3.9 | G3 V | 85 | br | Li
281.258420 | 42.605980 | KIC07091357 | 1 | 5701 $\pm$ 114 | 4.43 $\pm$ 0.12 |  $-$0.05 $\pm$ 0.16 |  $\leq$8.0 | G1.5 V | 11 | b | …
281.260650 | 42.478771 | KIC06922204 | 1 | 5843 $\pm$ 140 | 4.21 $\pm$ 0.20 |  $-$0.13 $\pm$ 0.15 | 10.8 $\pm$ 3.9 | G3 V | 45 | br | Li
… | … | … | … | … | … | … | … | … | … | … | …

Notes. The full table is only available in electronic form.

###  3.2 Comparison with the literature

Figure 6: Comparison with the APOGEE RVs. Upper-left panel: Comparison between
the RV measured on the blue-arm LAMOST MRS (Table LABEL:Tab:data_blue) and
APOGEE values (Jönsson et al. 2020). Filled symbols represent the stars with
multiple spectra. The one-to-one relation is shown by the continuous line. The
RV differences between LAMOST and APOGEE, $\Delta$RV, are displayed in the
lower box and show an average value of $0.0$ km s-1 (dashed line) and a
standard deviation of 6.1 km s-1 (dotted lines). Upper-right panel: Same as
the upper-left panel but for the red-arm RVs listed in Table
LABEL:Tab:data_red. The purple squares in both panels enclose the more
discrepant points (more than four times the rms). The distributions of the RV
differences are shown by the histograms in the lower panels. The Gaussian fits
are overplotted with black lines, and the center ($\mu$) and dispersion
($\sigma$) of the Gaussians are also marked in these boxes.

The uncertainties evaluated by ROTFIT (Sect. 3.1) are internal to the
procedure and do not give an account of the real accuracy of the parameters.
To this aim we compared the parameters that were derived in the present work
with those available in the literature. As regards the RV, we compared the
values measured in the blue-arm and red-arm spectra (Fig. 6), corrected for
the systematic offsets, with those measured by the Apache Point Observatory
Galactic Evolution Experiment (APOGEE) and reported in the DR16 catalog
(Jönsson et al. 2020). We note an almost zero average offset between our
corrected RVs and APOGEE, both for the blue and red arm. The rms of the data
dispersion around the mean is 6.1 km s-1 for both arms, which can be
considered as an upper limit for the data accuracy. Indeed, some stars can
have variable RVs because of pulsations or due to the presence of an unseen
companion. The points that are more discrepant in Fig. 6 refer to 18 stars
(KIC 5268955, 5527172, 5609753, 5688032, 6425135, 6777016, 6924881, 7119181,
7879399, 8022670, 8223328, 8687869, 9099927, 9651996, 10294429, 10987439,
11044668, and 11554998) that are known to be variable in RV in previous
studies (see Frasca et al. 2016; Luo et al. 2016, 2018; Wang et al. 2019,
2020b; Jönsson et al. 2020; Tian et al. 2020) or show a significant RV spread
in the MRS analyzed in this work. If we discard these data the rms scatter
decreases to 3.4 km s-1. Another way to see the effect of stars with variable
RV and to take it into account, is to investigate the distributions of the RV
differences between LAMOST and APOGEE, which we have plotted in the lower
panels of Fig. 6. The distributions, both for the red and the blue arm, are
regular and symmetrical in their central part, which has been fitted with a
Gaussian. The excesses with respect to the Gaussian in the wings of the
distributions are most likely due to objects with variable RV. The Gaussian
fits suggest an accuracy of the RV measurement of about 1.3 km s-1 or better.

Figure 7: Comparison of $T_{\rm eff}$ values. (a) Comparison between the
values of effective temperature in our database of LAMOST spectra and in the
literature. Filled symbols represent dwarfs ($\log g_{\rm ROTFIT}\geq 3.5$),
open symbols represent giants ($\log g_{\rm ROTFIT}<3.5$). Different colors
have been used for different literature sources, as indicated in the main
text. The comparison with the APOGEE and LASP $T_{\rm eff}$ is shown in the
middle (b) and bottom (c) panels, respectively. The dotted lines in the top
box of each panel represent one-to-one relationships. The solid lines are
linear fits to the data. The differences between ROTFIT and literature
parameters are shown in the lower parts of each panel along with their average
values and standard deviations. Stars indicated with arrows are discussed in
the text.

Figure 8: Comparison of $\log g$ values derived in the present work with those
from the literature (a), APOGEE (b), and LASP (c). The meaning of lines and
symbols is as in Fig. 7.

Figure 9: Comparison of [Fe/H] values derived in the present work with those
from the literature (a), APOGEE (b), and LASP (c). The meaning of lines and
symbols is as in Fig. 7. The sources enclosed in the yellow rectangle in box
(c) are discussed in Appendix B.

The results of the comparison of the APs derived from MRS in the present work
with those found in the literature are shown in Figs. 7, 8, and 9 for $T_{\rm
eff}$, $\log g$, and [Fe/H], respectively. The majority of the literature
parameters that are used for those comparisons were derived with the APOGEE
Stellar Parameter and Chemical Abundance Pipeline (ASPCAP) for 2486 stars from
the APOGEE DR16 catalog (Jönsson et al. 2020) and with LASP adapted to the MRS
(see Zong et al. 2020, and references therein) for 2408 stars. The values of
the APs determined by us are plotted versus the APOGEE ones in the middle
panels of Figs. 7, 8, and 9, while the comparison with the LASP ones is shown
in the bottom panels of the same figures. The remaining literature
determinations, which are compared with our values in Figs. 7a, 8a, and 9a,
were derived from high-resolution optical or, in two cases, low-resolution
infrared spectra by Brewer & Fischer (2018, 48 stars, navy blue circles),
Brewer et al. (2016, 19 stars, green diamonds), Furlan et al. (2018, 127
stars, green circles), Grieves et al. (2018, 34 stars, red circles), Guo et
al. (2017, 63 stars, azure circles), Huber et al. (2014, 86 stars, orange
circles), Lomaeva et al. (2019, 7 stars, yellow squares), Niemczura et al.
(2015, 2 stars, yellow triangles), Niemczura et al. (2017, 2 stars, yellow
triangles), Notsu et al. (2015, 1 star, yellow triangle), Petigura et al.
(2017, 51 stars, yellow circles), Sarmento et al. (2020, 62 stars, black
pentagons), or Tkachenko et al. (2013, 1 star, yellow triangle).

Those 5397 determinations concern 4018 individual stars. For 2892 stars from
that sample, the literature values of APs were provided only in one paper, for
980 stars in two papers, for 90 stars in three papers, for 30 stars in four
papers, for 12 stars in five papers, for seven stars in six papers, for three
stars in seven papers, and for four stars in eight papers. Since the above
mentioned works do not provide information on all the three APs, the numbers
of individual stars for which we found the literature values of $T_{\rm eff}$,
$\log g$ and [Fe/H] are, respectively, 5220, 3994, and 5179.

In order to find a linear relation between our determinations of the APs and
the literature values, for each star we either used the literature values of
the APs and their errors (stars with single literature determinations) or
computed the weighted means of the APs and their errors (stars with two or
more literature determinations). We note the overall good agreement between
our $T_{\rm eff}$ values and those from the literature, with an average offset
of only $5$ K and an rms of 160 K. Indeed, a linear regression (full line in
Fig. 7a) gives a slope $b$=0.89, which is smaller than one-to-one relation
(dotted line in the same plot). A similar slope is seen in Fig. 7c in which we
compare our $T_{\rm eff}$ values with those derived with the LASP pipeline.
However, the agreement with the APOGEE temperatures, shown in the middle
panel, looks better and the linear regression has a slope nearly equal to 1
($b$=0.98). The dispersion of the $T_{\rm eff}$ differences around the mean is
of about 160 K, which is an estimate of the accuracy of our $T_{\rm eff}$
determinations. In Fig. 7c, there are two $T_{\rm eff}$ outliers, which we
discuss in more detail in Appendix B.

The values of $\log g$ display also a good agreement with the literature with
a small offset of only 0.01 dex and a scatter of about 0.31 dex (Fig. 8 a).
The comparison of our values of $\log g$ with those from APOGEE and LASP
catalogs (Fig. 8 b and c, respectively) displays an overall good agreement,
with an rms dispersion of $\approx$ 0.3. We note only very few discrepant
sources that are labeled with their KIC identifiers and discussed in Appendix
B.

The agreement of $\log g$ with the literature is better than that found in
Frasca et al. (2016, hereafter Paper II), where we found most of the $\log g$
values derived from low-resolution LAMOST spectra to be clustered around the
gravity typical for red giants ($\log g$ $\approx 2.5$) and main-sequence (MS)
stars ($\log g$ $\approx 4.5$). The clustering effect, which is mostly the
result of the nonuniform density of templates in the space of parameters, is
less pronounced in this case, likely due to the higher sensitivity to $\log g$
of spectra with a higher resolution. That effect is still visible for the data
in the present work, especially for the stars with low gravity for which the
ROTFIT values tend to cluster around $\log g$ = 1.5, which is very likely
caused by the small number of templates with a very low gravity. However, the
comparison presented in this paper shows that the $\log g$ values are accurate
enough to distinguish between giant and MS stars, which, together with an
accurate $T_{\rm eff}$ determination unaffected by interstellar extinction,
was one of the main purposes of our analysis. The knowledge of these
parameters is, in fact, necessary for the spectral subtraction and flux
calibration that we use to measure the chromospheric emission in the H$\alpha$
core (see Sects. 3.3 and 4.1) and the lithium equivalent width and abundance
(Sect. 4.2).

The agreement of [Fe/H] values with the literature is much poorer than of the
previous parameters (Fig. 9). We found a very small slope for the linear
regression of the data ($b$=0.54 in Fig. 9a or $b$=0.39 in Fig. 9b), which
indicates that we are getting correct [Fe/H] values only around the solar one
([Fe/H]=0) and we are systematically overestimating the metallicity for metal-
poor stars ([Fe/H]$<-0.3$) and underestimating it for metal-rich stars
([Fe/H]$>+0.2$). We think that this effect, already seen in the results based
on the low-resolution data of Paper II, is due to the relative scarcity of
metal-poor and super metal-rich stars among our templates that generates a
sort of “smoothing” of the final [Fe/H] values. Indeed, the handful of stars
with the lowest metallicity in Fig. 9 a and b lie close to the one-to-one
relation. For these stars, the templates with a higher metallicity have a
spectrum so different that they have not played any role in the [Fe/H]
determination.

We thus propose a correction relation for the LAMOST metallicity, based on the
linear fit shown in Fig. 9 b, which can be expressed as

${\rm[Fe/H}]_{\rm corr}=2.57\cdot{\rm[Fe/H]}-0.01,$ (1)

applicable in the range

${\rm[Fe/H]}>-1.0.$

Additionally, in Fig. 9c we find a group of 27 stars, which have been enclosed
in a yellow rectangle. All those stars are cool ($T_{\rm eff}$$\lesssim$ 4500
K) giants for which the LASP [Fe/H] values are very low while the ROTFIT
[Fe/H] values are close to zero. Those stars we discuss in more detail in
Appendix B.

###  3.3 Balmer H$\alpha$ and lithium equivalent width

The most sensitive diagnostics of magnetic activity in the range covered by
the LAMOST MRS is the Balmer H$\alpha$ line. We therefore identified objects
with H$\alpha$ emission, which can be produced by various physical mechanisms
in addition to the presence of an active chromosphere, such as magnetospheric
accretion in the youngest evolutionary phases of low- and intermediate-mass
stars, or circumstellar (or circumbinary) matter. As the chromospheric
emission can only show up as a small to moderate filling of the line core,
depending on the activity level and on the photospheric flux of the star, the
removal of the photospheric spectrum is crucial to emphasize the H$\alpha$
core emission. To this aim, we subtracted the non-active template that best
matches the final APs from each LAMOST red-arm spectrum. This template has
been aligned to the target RV, rotationally broadened at the $v\sin i$ of the
target and resampled on its spectral points. The “emission” H$\alpha$
equivalent width, $W^{\rm res}_{\rm H\alpha}$, was interactively measured by
integrating the residual emission profile (see Fig. 10, upper panel).

Figure 10: Example of the subtraction of the best non-active, lithium-poor
template (red line) from the spectrum of KIC 8095028 (black dots), which
reveals the chromospheric emission in the H$\alpha$ core (blue line in the top
panel) and emphasizes the Li i $\lambda$6708 Å absorption line, with the
nearby blended lines removed (bottom panel).

To speed up this procedure and to reduce spurious detections, we firstly made
the measurements of $W^{\rm res}_{\rm H\alpha}$ only on the spectra with a S/N
$\geq$ 20\. Moreover, among these spectra, we selected a subsample of likely
active stars as those for which an automatic procedure, which measure the
H$\alpha$ equivalent width in a fixed wavelength range of 3 Å around the line
center, gave rise to a value larger than 0.1 Å. Then, to pick up low-signal (6
$<$ S/N $<$ 20) spectra with a relevant filling or a pure H$\alpha$ emission
above the continuum, we added the spectra with S/N $<$ 20 for which the
“initial” automatic measure of $W^{\rm res}_{\rm H\alpha}$ was larger than 0.5
Å in the same integration range. For all these spectra, the $W^{\rm res}_{\rm
H\alpha}$ was measured interactively, as described above, and the error was
calculated as the product of the integration range times the error in the
placement of the continuum, which was evaluated as the rms of the values of
the subtracted spectra in two regions at the two sides of the H$\alpha$ line.
We end up with a total of 546+31 (cool,+ unclass) spectra of 334 stars
displaying H$\alpha$ in emission or filled in by a minimum amount as defined
above. The maximum value, $W^{\rm res}_{\rm H\alpha}$ $=10.98$ Å, was found
for KIC 8749284, an active star already discovered by us in Paper II as an
object with H$\alpha$ emission above the continuum.

The values of $W^{\rm res}_{\rm H\alpha}$, along with their errors, are quoted
in Table 3. We also report whether the line is observed as a pure emission
feature and whether the measure is uncertain as a result of the low S/N or
other possible spectral issues.

The subtraction of the photospheric template also allowed us to measure the
equivalent width of the Li i $\lambda$ 6707.8 Å line by removing the nearby
lines (basically Fe i $\lambda$ 6707.4 Å), which are blended with the lithium
line in the observed spectrum. We used a similar approach to that used for
H$\alpha$ to select the spectra on which we measure the lithium equivalent
width, $W_{\rm Li}$. We fixed a threshold of 0.05 Å (50 mÅ) from an automatic
measurement of the lithium absorption in the residual spectrum integrating it
in a range of 6 Å centered on the Li i $\lambda$ 6707.8 Å line for the spectra
with an S/N larger than 20 and 150 mÅ for the low-signal spectra. We detected
a $W_{\rm Li}$ above the given thresholds for 2763 spectra, corresponding to
1657 different stars. For stars with multiple visits, we calculated the
weighted average of the values of $W_{\rm Li}$ measured in different epochs,
adopting a weight $w=1/\sigma_{W_{\rm Li}}^{2}$, where $\sigma_{W_{\rm
Li}}^{2}$ is the error on the individual measure. We took the maximum of the
weighted standard deviation and the standard error of the weighted mean as the
final uncertainty.

The highest value of lithium equivalent width, $W_{\rm Li}$ = 626 mÅ, was
found for KIC 11657857 (= IRAS 19170+4937), which is also one of the coldest
lithium-rich giants ever discovered.

##  4 Results

###  4.1 Chromospheric activity

Late-type stars, which have convective envelopes, rotation and differential
rotation able to produce strong magnetic fields by a dynamo action, display a
complex of phenomena known as magnetic activity. These include, radio and/or
X-ray coronal emission, UV and optical emission lines produced in a
chromosphere, fast energy releases (in the continuum and/or in spectral lines)
known as flares, and rotational modulation of brightness produced by cool
spots. For stars with a SpT later than mid-F ($T_{\rm eff}$$\leq 6500$ K) the
H$\alpha$ line is an efficient diagnostic of magnetic activity, especially for
the cooler ones with a moderate to high level of activity, if we subtract the
underlying photospheric spectrum, as we have explained in Sect. 3.3.

The equivalent width of an emission line formed in a chromospheric layer can
be used to quantify the activity level, when it is converted into energetic
units. Therefore, more accurate indicators of chromospheric activity are the
line flux in units of stellar surface, $F$, and the ratio between the line
luminosity and bolometric luminosity, $R^{\prime}$, which can be calculated,
for the H$\alpha$, as

$\displaystyle F_{\rm H\alpha}$ $\displaystyle=$ $\displaystyle F_{6563}W^{\rm
res}_{\rm H\alpha}$ (2) $\displaystyle R^{\prime}_{\rm H\alpha}$
$\displaystyle=$ $\displaystyle L_{\rm H\alpha}/L_{\rm bol}=F_{\rm
H\alpha}/(\sigma T_{\rm eff}^{4}),$ (3)

where $F_{6563}$ is the continuum surface flux at the H$\alpha$ center, which
we evaluated from the BT-Settl synthetic spectra (Allard et al. 2012) at the
stellar temperature and surface gravity of the target. The flux error includes
both the error of the equivalent width and the uncertainty in the continuum
flux at the line center, which is obtained by propagating the $T_{\rm eff}$
and $\log g$ errors.

Table 3: Activity indicators.

DESIG | KIC | RA | Dec. | $T_{\rm eff}$ | err | $\log g$ | err | $W^{\rm res}_{\rm H\alpha}$ | err | $F_{\rm H\alpha}$ | err | $R^{\prime}_{\rm H\alpha}$
---|---|---|---|---|---|---|---|---|---|---|---|---
|  | $\degr$ | $\degr$ | (K) | (dex) | (Å) |  (erg cm-2s-1) |
J184805.69+415751.8 | KIC06497820 | 282.023712 | 41.964409 | 5164 | 101 | 4.44 | 0.26 | 0.779 | 0.163 | 3.632e+06 | 8.214e+05 | -4.045
J184847.43+421316.2 | KIC06752578 | 282.197632 | 42.221169 | 3536 | 90 | 4.77 | 0.13 | 1.478 | 0.152 | 7.400e+05 | 1.557e+05 | -4.078
J184942.18+435303.5 | KIC08008128 | 282.425781 | 43.884331 | 5920 | 177 | 4.02 | 0.15 | 0.095 | 0.061 | 7.637e+05 | 4.982e+05 | -4.960
J184951.21+431802.6 | KIC07661598 | 282.463379 | 43.300739 | 5834 | 136 | 4.29 | 0.16 | 0.036 | 0.034 | 2.736e+05 | 2.596e+05 | -5.380
J185114.02+451313.2 | KIC08932950 | 282.808441 | 45.220352 | 5829 | 99 | 4.33 | 0.12 | 0.107 | 0.032 | 8.102e+05 | 2.482e+05 | -4.907
J185236.87+451902.5 | KIC09002183 | 283.153656 | 45.317371 | 5309 | 135 | 4.49 | 0.14 | 0.113 | 0.069 | 5.934e+05 | 3.677e+05 | -4.880
J185336.19+444900.1 | KIC08671812 | 283.400818 | 44.816711 | 4980 | 103 | 3.09 | 0.27 | 0.375 | 0.057 | 1.436e+06 | 2.569e+05 | -4.385
J185342.86+450847.1 | KIC08866716 | 283.428589 | 45.146439 | 4927 | 132 | 2.93 | 0.27 | 0.197 | 0.080 | 7.184e+05 | 3.052e+05 | -4.668
J185441.45+451133.4 | KIC08867218 | 283.672729 | 45.192612 | 4944 | 132 | 4.55 | 0.11 | 0.121 | 0.028 | 4.640e+05 | 1.215e+05 | -4.863
J185450.75+401409.3 | KIC05077994 | 283.711487 | 40.235920 | 5608 | 97 | 4.19 | 0.27 | 0.244 | 0.091 | 1.584e+06 | 6.004e+05 | -4.549
J185501.45+445803.9 | KIC08736810 | 283.756073 | 4.967758 | 5874 | 166 | 4.08 | 0.15 | 0.672 | 0.245 | 5.241e+06 | 1.995e+06 | -4.110
J185519.56+445212.3 | KIC08672632 | 283.831512 | 44.870090 | 4730 | 124 | 4.58 | 0.11 | 0.268 | 0.170 | 8.305e+05 | 5.382e+05 | -4.534
J185633.42+451348.1 | KIC08935655 | 284.139252 | 45.230042 | 3575 | 106 | 4.71 | 0.12 | 4.820 | 0.276 | 2.359e+06 | 5.429e+05 | -3.594
J185637.96+443001.1 | KIC08479165 | 284.158173 | 44.500309 | 6076 | 130 | 4.09 | 0.17 | 0.073 | 0.044 | 6.490e+05 | 3.944e+05 | -5.076
… | … | … | … | … | … | … | … | … | … | … | … | …

Notes. The full table is only available in electronic form at the CDS.

Figure 11: Activity indicators. Left panel: H$\alpha$ flux versus $T_{\rm
eff}$ (open circles for giants, purple dots for MS stars). Right panel:
$R^{\prime}_{\rm H\alpha}$ versus $T_{\rm eff}$ (same symbols). The straight
dashed line in each panel is the boundary between chromospheric emission
(below) and accretion as derived by Frasca et al. (2015). The objects with a
flux close to this boundary are labeled with integer numbers and are discussed
briefly in the text.

The H$\alpha$ fluxes and $R^{\prime}_{\rm H\alpha}$ of our targets are plotted
as a function of the effective temperature in Fig. 11 using different symbols
for giant (open circles) and MS stars (dots). This plot also shows the
boundary between young stars with mass accretion and chromospherically active
stars. The latter lie below this line, which is also close to a “saturated”
activity regime for MS stars (see, e.g., Frasca et al. 2015).

We note that only two stars lie higher (or right over) the dividing line (3
and 4 in Fig. 11), but we classified them with ROTFIT as giant stars. Their
high H$\alpha$ flux is likely the fingerprint of an extremely high activity
level due to an enhanced rotation rate, which could be the result of a
particular evolutionary phase or of spin-orbit synchronization for an
unresolved binary or an SB1 system in which the companion of the cool giant is
overwhelmed by its flux (similar to many long-period RS CVn binaries). We
cannot exclude the contribution of other processes, such as circumstellar
matter or shells, as the cause for the strong H$\alpha$ emission (see also
their H$\alpha$ profiles in Fig. 30).

The stars with the highest H$\alpha$ flux, which lie above or close to the
dividing line between accretors and chromospherically active stars, are
indicated with progressive numbers (with decreasing $T_{\rm eff}$) in Fig. 11.
In the following we report a few notes on these sources.

KIC 9720659 (#1) is the star with the earliest SpT (F0 V, $T_{\rm eff}$ = 6785
K) in our sample of H$\alpha$ emitters. According to the H$\alpha$ profile, it
could be a Herbig star, with broad wings typical of an A- or F-type star with
an emission core, similar to CQ~Tau (e.g., Alcalá et al. 2021, and references
therein). We did not detect any other emission line in its spectrum. However,
a moderate infrared excess, indicative of circumstellar matter or a
protoplanetary disk is visible in its spectral energy distribution (SED; Fig.
33).

KIC 8022670 = V2279 Cyg (#2) is mentioned in the SIMBAD astronomical database
as an “eruptive variable star.” It has been reported as a periodic variable
(Cepheid?) by Schmidt et al. (2007) and Pigulski et al. (2009) with a period
of about 4.12 d and an amplitude of 0.30 mag. Schmidt et al. (2011) included
this star in their study of type II Cepheid candidates and related stars from
the Robotic Optical Transient Search Experiment 1 (ROTSE-1), which was based
on LRS. They report $T_{\rm eff}$ in the range 4905–4957 K, $\log g$ = 4.1,
and a solar metallicity. They also report H$\alpha$ emission (c.f. their Fig.
1) with a Lick-IDS (Lick Observatory Image Dissector Scanner) index of about
$-2.29$. We find nearly the same effective temperature, $T_{\rm eff}$ =
4985$\pm$110 K, but a different $\log g$= 2.64$\pm$0.41 dex. The latter is in
better agreement with other literature values, such as $\log g$ = 2.68
(Christiansen et al. 2012) or $\log g$ = 2.82 (Ho et al. 2017) that indicate
this star as a giant. It was subsequently reported as an active flaring star
by Davenport (2016) and Oláh et al. (2021) on the basis of Kepler photometry.
In particular, Oláh et al. (2021) classify it as a flaring giant with a radius
of 3.3 $R_{\sun}$ for which 55 flares have been detected by Kepler.

KIC 8749284 (#3) is reported in SIMBAD as a “rotationally variable star” with
a period $P_{\rm rot}\simeq 3.22$ d (Debosscher et al. 2011). It is also
classified as an active giant, based on Kepler light photometry (see Gaulme et
al. 2020), which displays intense flare activity (Oláh et al. 2021), with 88
flares detected during Kepler observations. We find $T_{\rm eff}$=5048$\pm$112
K and $\log g$ = 3.20$\pm$0.30, which indicates an evolved star, as only a
weak lithium absorption line ($W_{\rm Li}$ $\simeq 40$ mÅ), which is not
compatible with a pre-main-sequence (PMS) object, has been detected. This is
in agreement with the $T_{\rm eff}$=5089 K and the radius of 4.6 $R_{\sun}$
reported by Oláh et al. (2021). The SED of this object reveals a strong
infrared excess that begins from the $H$ band, which is likely due to cold
circumstellar matter. We note that this star was already included in the LK-
LRS project and we already detected the H$\alpha$ emission in the low-
resolution LAMOST spectra as well as the infrared excess in its SED (Frasca et
al. 2016).

KIC 6201369 (#4) is not present in SIMBAD. In the Gaia early third data
release (EDR3) there is a nearby source at about 6″ that is about 6 mag
fainter. No spectroscopic observations can be found in the literature for this
object. We find $T_{\rm eff}$ = 4731$\pm$118 K and $\log g$ = 2.76$\pm$0.27,
meaning that it is likely another active giant with a very strong and
redshifted H$\alpha$ emission. The Li i$\lambda$6708 line is not detected in
the MRS spectrum of this source. There is no information in the literature
about brightness variations; this source, although in its field of view, was
not observed by Kepler.

KIC 8095028 (#5) is a young (strong lithium) fast-rotating ($P_{\rm
rot}=0.397$ d, McQuillan et al. 2014) and flaring star (see Davenport 2016 and
Goodarzi et al. 2019). An MRS spectrum of this target is displayed in Fig.10.
We classified it as a K3.5 V star with $T_{\rm eff}$=4858$\pm$126 K and $\log
g$=4.58$\pm$0.15, to be compared with the values of $T_{\rm eff}$ = 4464 K and
$\log g$ = 4.49 reported by McQuillan et al. (2014). The lithium equivalent
width of $W_{\rm Li}$ = 272 mÅ places this star just below the Pleiades upper
envelope in Fig. 12 (i.e., it is the MS star with the highest $W_{\rm Li}$ in
our sample; see Sect. 4.2).

KIC 10063343 (#6) is an ultrafast rotator ($P_{\rm rot}=0.337$ d, McQuillan et
al. 2014), which shows several flare episodes in the Kepler light curves (see,
e.g., Davenport 2016; Yang & Liu 2019). We confirm it as a K5 V star ($T_{\rm
eff}$ = 4579$\pm$105, $\log g$ = 4.65$\pm$0.11) rotating at $v\sin i$ = 104 km
s-1. The Li i$\lambda$6708 line is not visible in the low-signal MRS spectrum
of this source.

KIC 8935655 (#7) is a dMe flaring star (see Yang et al. 2017; Davenport 2016).
Hardegree-Ullman et al. (2019) report an M4 V SpT and $T_{\rm eff}$ = 3241 K;
we find this star slightly earlier (M1.5 V) and hotter ($T_{\rm eff}$ =
3575$\pm$102 K) and confirm it as a slowing rotating ($v\sin i$$<8$ km s-1)
dMe star. Our temperature is instead in very good agreement with that based on
APOGEE spectra, $T_{\rm eff}$ = 3554$\pm$69 K (Jönsson et al. 2020). The Li
i$\lambda$6708 line is not visible in the MRS spectrum of this source.

###  4.2 Lithium abundance and age

Table 4: Lithium equivalent widths and abundances.

DESIG | KIC | RA | Dec. | $T_{\rm eff}$ | $\log g$ |  $A$(Li) | $W_{\rm Li}$ | Class
---|---|---|---|---|---|---|---|---
|  | $\degr$ | $\degr$ | (K) | (dex) | (dex) | (mÅ) |
J184441.98+422834.4 | KIC06922059 | 281.174930 | 42.476238 |  5829$\pm$ 70 |  4.31$\pm$0.12 |  2.32${}^{+0.20}_{-0.27}$ |  45$\pm$17 | Hya
J184456.49+423715.0 | KIC07091292 | 281.235410 | 42.620834 |  5812$\pm$141 |  4.09$\pm$0.18 |  2.52${}^{+0.16}_{-0.18}$ |  68$\pm$11 | UMa
J184502.55+422843.5 | KIC06922204 | 281.260650 | 42.478771 |  5843$\pm$140 |  4.21$\pm$0.20 |  2.50${}^{+0.22}_{-0.24}$ |  64$\pm$18 | Hya
J184529.95+422421.2 | KIC06922382 | 281.374820 | 42.405910 |  5894$\pm$ 97 |  4.04$\pm$0.15 |  2.14${}^{+0.40}_{-2.44}$ |  28$\pm$28 | Hya
J184613.19+421535.2 | KIC06751420 | 281.554960 | 42.259800 |  4688$\pm$112 |  2.56$\pm$0.25 |  1.20${}^{+0.45}_{-1.30}$ |  26$\pm$26 | …
J184700.25+440107.3 | KIC08144149 | 281.751070 | 44.018719 |  5728$\pm$117 |  4.34$\pm$0.19 |  2.05${}^{+0.41}_{-2.32}$ |  29$\pm$29 | Hya
J184713.75+435409.1 | KIC08075941 | 281.807310 | 43.902538 |  5400$\pm$241 |  3.93$\pm$0.43 |  2.09${}^{+0.36}_{-0.49}$ |  51$\pm$24 | UMa
J184715.22+421233.3 | KIC06751838 | 281.813420 | 42.209251 |  4625$\pm$121 |  2.51$\pm$0.22 |  1.01${}^{+0.46}_{-1.10}$ |  20$\pm$20 | …
J184732.37+435138.3 | KIC08007262 | 281.884890 | 43.860657 |  6821$\pm$ 73 |  4.18$\pm$0.11 |  3.03${}^{+0.16}_{-0.20}$ |  56$\pm$16 | …
J184741.36+442038.4 | KIC08344972 | 281.922360 | 44.344002 |  5739$\pm$147 |  4.28$\pm$0.18 |  2.08${}^{+0.20}_{-0.23}$ |  30$\pm$ 7 | Hya
J184753.87+435727.6 | KIC08076240 | 281.974460 | 43.957680 |  5660$\pm$132 |  4.20$\pm$0.21 |  2.11${}^{+0.29}_{-0.43}$ |  37$\pm$19 | Hya
J184805.84+440407.9 | KIC08144580 | 282.024350 | 44.068871 |  4883$\pm$126 |  3.03$\pm$0.32 |  1.69${}^{+0.39}_{-0.73}$ |  48$\pm$35 | …
J184805.93+424448.3 | KIC07175400 | 282.024720 | 42.746750 |  6015$\pm$156 |  4.08$\pm$0.14 |  2.51${}^{+0.29}_{-0.40}$ |  52$\pm$25 | …
J184814.26+423130.9 | KIC07009054 | 282.059450 | 42.525253 |  6633$\pm$130 |  4.09$\pm$0.16 |  3.10${}^{+0.15}_{-0.17}$ |  81$\pm$14 | …
J184826.05+434740.2 | KIC07938762 | 282.108550 | 43.794521 |  5571$\pm$147 |  4.43$\pm$0.17 |  2.56${}^{+0.28}_{-0.34}$ |  102$\pm$38 | UMa
… | … | … | … | … | … | … | … | …

Notes. The full table is only available in electronic form at the CDS.

Lithium is burned in stellar interiors at temperatures of about
$2.5\,\times\,10^{6}$ K. Therefore, it is progressively depleted from the
stellar atmospheres of late-type stars with deep enough convective envelopes.
The degree of depletion depends on the internal structure of the star and
therefore, for the MS stars, on the mass. Thus, its abundance can be used as
an empirical indicator of age for MS stars cooler than about 6500 K. A simple
and effective way to get an age estimate is a diagram showing the equivalent
width of lithium as a function of effective temperature (or a color index)
together with the upper envelopes of young open clusters that can be used as
boundaries to separate the star sample in age classes (Fig. 12).

We adopted the upper envelopes of the Hyades (Soderblom et al. 1990), the
Pleiades (Soderblom et al. 1993a; Neuhaeuser et al. 1997), and IC 2602 (Montes
et al. 2001), whose ages are of about 650 (White et al. 2007), 125 (White et
al. 2007), and 30 Myr (Stauffer et al. 1997), respectively. The lower envelope
of the Pleiades corresponds to the upper boundary for the members of the Ursa
Major (UMa) cluster ($age\approx$ 300 Myr; Soderblom et al. 1993b). The
boundaries are remarkably close to each other for temperatures higher than
6000 K and therefore, also taking into account the errors on $W_{\rm Li}$, we
preferred to restrict the age classification to objects with $T_{\rm eff}$
$\leq$ 6000 K. In line with what done by Guillout et al. (2009) and Frasca et
al. (2018), we have defined four age classes for the MS stars: (i) “PMS-like”
encompasses objects that lie above the Pleiades upper boundary; (ii)
“Pleaides-like” comprises stars that fall between the upper and lower Pleiades
envelopes; (iii) “UMa-like” stars are those located between the lower Pleiades
boundary (corresponding to the UMa upper envelope) and the Hyades envelope;
and (iv) “Hyades-like” stars are those with $W_{\rm Li}$$>20$ mÅ that lie
below the Hyades upper envelope.

We adopted a lower threshold of 20 mÅ for the Hyades-like stars, because the
typical error of $W_{\rm Li}$ is 20 mÅ, and lower values of $W_{\rm Li}$ are
normally associated with stars older than the Hyades. Therefore, the stars
with $W_{\rm Li}$ $<$ 20 mÅ and those for which no Li i absorption has been
detected are not classified. The stars that belong to the four age classes
defined above are labeled as PMS, Ple, UMa, and Hya, respectively, in Table 4.
The MS star with the highest value of $W_{\rm Li}$ is KIC 8095028, which is
close to the upper envelope of the Pleiades stars. In the end, only three MS
stars were classified as PMS-like, but all of them lie very close to the
Pleiades upper envelope and therefore their PMS nature is questionable; they
should be broadly considered as very young stars. We find 19 Pleiades-like
(1.6%), 247 UMa-like (21%), and 343 Hyades-like stars (30%) in our sample of
MS stars ($\log g$$>$3.7) with a detection of the lithium line (1184 stars).

Figure 12: Equivalent width of the Li i $\lambda$6707.8 line ($W_{\rm Li}$)
plotted as a function of $T_{\rm eff}$ (open circles for giants, purple dots
for MS stars). The lines show the upper boundaries for Hyades (dash-dotted
blue), Pleiades (solid red for both the lower and upper boundary), and IC 2602
(dashed orange) clusters. Most of the stars with a strong lithium absorption
are lithium-rich giants.  Figure 13: Lithium abundance as a function of
$T_{\rm eff}$. The upper envelopes of $A$(Li) for IC 2602, Pleiades, NGC 6475
($age\approx$ 300 Myr), and Hyades clusters adapted from Sestito & Randich
(2005) are overplotted. The meaning of the symbols is the same as in Fig. 12.

We calculated the lithium abundance, $A$(Li), from our values of $T_{\rm
eff}$, $\log g$, and $W_{\rm Li}$ by interpolating the curves of growth of
Lind et al. (2009), which span the $T_{\rm eff}$ range 4000–8000 K and log
from 1.0 to 5.0 and include nonlocal thermal equilibrium corrections. We note
that for the few stars with $T_{\rm eff}$$<4000$ K the lithium abundance is
extrapolated and could be less accurate. The errors of $A$(Li) take into
account both the $T_{\rm eff}$ and $W_{\rm Li}$ errors222We did not consider
the errors of $\log g$ for the evaluation of $A$(Li) errors because an error
$\sigma_{\log g}$ = 0.5 dex translates into an uncertainty of only a 0.1 or
0.2 dex, at most, in $A$(Li), in the $T_{\rm eff}$ range of our targets. . In
Fig. 13 we show the lithium abundance as a function of $T_{\rm eff}$ along
with the upper envelopes of the distributions of some young open clusters
shown by Sestito & Randich (2005). We note that the age of NGC 6475 of about
300 Myr is close to the UMa cluster, and its upper envelope corresponds to the
lower envelope of the Pleiades in Fig. 12. This plot shows that the age
classification made on the basis of the $W_{\rm Li}$ diagram and upper
envelopes of open clusters is confirmed by the $A(Li)$ diagram.

The object with the highest lithium abundance, $A$(Li) = 3.97$\pm$0.26, is KIC
11657857 (= IRAS 19170+4937), which is also the coolest lithium-rich giant.
The SED (see Sect. 4.3) of this source (Fig. 31) displays infrared excess
starting from about 10 $\mu$m, which is clearly revealed by IRAS (Abrahamyan
et al. 2015), AKARI (Ishihara et al. 2010), and WISE (Cutri et al. 2021) data.
Another object with a very large value of lithium abundance
($A$(Li)=2.98$\pm$0.15) is KIC 8363443, which is a lithium-rich giant already
known from the literature. No infrared excess is visible in the SED of this
source (Fig. 32).

###  4.3 Lithium-rich giants

As mentioned in Sect. 4.2, lithium is a fragile element, which is
progressively destroyed by nuclear reactions at temperatures much lower than
those of H-burning cores. As such, it is very sensitive to stellar evolution.
Canonical models (Iben 1967a, b; Soderblom et al. 1993a) predict Li depletion
as a direct consequence of the first dredge-up (FDU) once stars reach the red
giant branch (RGB). According to this, we do not expect to find abundances of
Li above 1.5 dex in red giants (Charbonnel & Balachandran 2000). Observations
confirm this theoretical scenario (Bonsack 1959; Gratton et al. 2004).
However, a few giants with Li abundances larger than this value, the so-called
Li-rich giants, have been discovered since several decades (e.g., Wallerstein
& Sneden 1982; Luck 1982). A large number of such stars have recently been
found in the field (Casey et al. 2016a; Smiljanic et al. 2018a; Gao et al.
2019; Martell et al. 2021), globular clusters (Kirby et al. 2016) as well as
open clusters (Monaco et al. 2014; Alonso-Santiago et al. 2017, 2019; Magrini
et al. 2021) representing a fraction around 1$\%$ of all known giants. These
stars have from early-F to A-type progenitors on the MS
($M_{\ast}=1.5-2.5\,M_{\sun}$).

As noted above, we find 1657 stars with a detectable amount of lithium in our
sample of 7443 stars, representing about 21% of the total. Excluding 1184
stars with $\log g$$>$3.7, which we classified as MS stars, we are left with
473 evolved stars with a detectable Li i $\lambda$6708 line. Among them there
are the Li-rich giants ($A$(Li)$\geq$1.5), including those that exhibit an
abundance above the primordial value (i.e., $A$(Li)$\geq$2.7). We refer to
this subset as super Li-rich stars. In order to determine their fraction, we
first need to know the total number of giants in our sample. To identify them,
we plotted the Kiel ($T_{\rm eff}$–$\log g$) diagram and examined the
distribution of the stars in it. In the left panel of Fig. 14 giants clearly
stand out from MS stars. As seen, their maximum density is centered at $T_{\rm
eff}$ $\approx$ 4800 K and $\log g$$\,\approx$ 2.6. Moving down in the diagram
toward the point of maximum density of MS stars, we set the giants boundary at
a place approximately equidistant from both points. In this way, stars with
$T_{\rm eff}$ $\leq$ 5750 K and $\log g$ $\leq$ 3.6 will be considered as
giants. By taking this criterion into account, we found 3276 giants in our
sample, out of which 195 have $A$(Li)$\geq$1.5, which implies a fraction of
Li-rich giants of 6.0%. This number is practically not affected by minor
changes to the selection criterion. Surprisingly, this fraction is much higher
than $\approx$1.3%, which is the result obtained by the most recent surveys
(Gao et al. 2019; Martell et al. 2021) after analyzing stellar samples much
larger than ours. Among the 195 Li-rich giants detected, 34 were already
observed by Gao et al. (2019) while the remaining 161 are reported here for
the first time.

Figure 14: Kiel ($T_{\rm eff}$–$\log g$) diagram for the final sample of the
stars observed in this work. The left panel shows the stellar density and the
right one highlights the position of the Li-rich (1.5 $\leq$ $A$(Li) $<$ 2.7)
and super Li-rich giants ($A$(Li) $\geq$ 2.7). The dashed lines delimit the
area populated by giants according to our selection criteria, as explained in
the text.

In order to understand the evolutionary status of these Li-rich giants, we
placed them on the Hertzsprung-Russell (HR) diagram. For this task, we first
calculated their luminosity from the analysis of the SED, as explained in
Appendix D. Then, we added the PARSEC evolutionary tracks (Bressan et al.
2012) for a solar metallicity (Z = 0.017) and finally, we marked the base of
the RGB and the RGB bump on them. The resulting HR diagram of these sources is
shown in Fig. 15. As inferred from their position on the diagram, the vast
majority of our sources are low-mass stars with masses in the range 1$-$3 M☉.

According to their position in the HR diagram and the loci indicated in Fig.
15, three evolutionary stages can be distinguished. The first one corresponds
to the stars located to the left of the green strip. These objects could have
not yet reached the RGB333Although these stars were selected as giants, they
could actually be at the end of the subgiant phase according to the HR diagram
in Fig. 15. Regardless of this group, the fraction of Li-rich giants is still
very high, 5.5%. Even when considering the stars over the strip or those that
have already passed it but whose positions, within the errors, might be
indicating that they are still over or slightly before the strip ($\approx$ 45
stars), the fraction of Li-rich giants would be around 4.2%, still much higher
than the 1.3% found by other authors. and their initial lithium is still
observable in their atmospheres. Those stars in the diagram placed between
both strips are classified as RGBs. Approximately in the middle of this phase,
the FDU takes place and drastically depletes the amount of the photospheric
Li. As commented before, $A$(Li)$>$1.5 should not be observed in these stars.
Some of them, the closest to the green strip, could not yet have undergone the
FDU, and therefore, their lithium abundance is explained as in the previous
case. Nevertheless, with regard to the remaining stars, the existence of these
Li-rich giants implies the additional contribution of a mechanism capable of
enhancing the atmospheric lithium content. This is also valid for those stars
found after the RGB bump, to the right of the orange strip.

Figure 15: Hertzsprung-Russell diagram for all the Li-rich giants. The symbols
are color coded by the lithium abundance $A$(Li). The PARSEC post-MS
evolutionary tracks (Bressan et al. 2012) for a metallicity Z = 0.017 are
plotted with black lines. The green and orange strips mark the base of the RGB
and the RGB bump, respectively.

However, a single universal mechanism that can explain this phenomenon as a
whole does not seem to exist; there is more likely a mixture of various
processes at work. External pollution is one of the scenarios most often
claimed to explain it. The extra contribution of Li could be due to both the
engulfment of a substellar companion (Siess & Livio 1999; Aguilera-Gómez et
al. 2016) and the enrichment of the local interstellar medium caused by the
explosion of a nearby supernova (Woosley & Weaver 1995). On the other hand,
the internal production via the Cameron-Fowler mechanism (CFM; Cameron &
Fowler 1971) would allow these stars to create new Li. However, an extra-
mixing process after the FDU is absolutely required in this case. Binarity has
also been invoked to solve the Li puzzle, either as an external or internal
mechanism. In the first case, the Li-rich giant would be the consequence of
the merge of a white dwarf with a red giant in a binary system (Zhang et al.
2020) while in the second one, the tidal spin-up from a binary companion would
provide the internal extra-mixing necessary to start the CFM (Casey et al.
2019).

We tested some of these hypotheses by taking advantage of our observations.
Firstly, binarity is unlikely to explain the Li enhancement, as no binaries
have been found among our sample of Li-rich giants. The scenario of engulfment
of a substellar companion or a white dwarf does not match what is observed
either. According to it, we would expect enhanced rotational velocities among
the Li-rich stars, as a natural consequence of the transfer of angular
momentum (Aguilera-Gómez et al. 2016; Privitera et al. 2016). However, in our
sample, no significant differences are found with regards to the fraction of
fast rotators (as well as the metallicity distribution) between Li-rich and
Li-normal giants (Table 5). Additionally, fast rotators444In line with other
works (e.g., Carlberg et al. 2012; Martell et al. 2021), we considered 10 km
s-1 an adequate value to separate fast from slow rotators since the typical
$v$ sin$i$ among giants is around 3–5 km s-1 and the macroturbulence velocity
$\approx$7 km s-1 (Carney et al. 2008). ($v$ sin$i$ $\geq$10 km s-1) show an
average $A$(Li)=2.0$\pm$0.5, a value fully consistent with that of stars with
$v$ sin$i<$10 km s-1, $A$(Li)=1.9$\pm$0.4, and a correlation between lithium
abundance and stellar rotation is not observed (see Fig. 16), as also found in
previous works (e.g., Martell et al. 2021). However, the occurrence of fast
rotators seems to be higher among the super Li-rich giants (42.9%) than in the
Li-rich sample (29.9%), although the sample is not so large as to have good
statistical significance.

Table 5: Percentages of fast rotators ($v\sin i$$\geq$10 km s-1) and stars with a solar metallicity (i.e., $-$0.2$\leq$[Fe/H]$\leq$+0.2) among the Li-normal and Li-rich giants. N is the number of stars in each sample. Sample | N | Fast rotators | Solar stars
---|---|---|---
Li-normal | 3081 | 31.1 | 91.4
Li-rich | 195 | 31.3 | 90.3
Figure 16: Abundance of Li as a function of the $v\sin i$ among our Li-rich
giant sample. The vertical line shows the limit between slow and fast
rotators, while the horizontal one represents the boundary between Li-rich and
super Li-rich giants.

Despite the fact that Li-rich giants are observed throughout the entire RGB
phase, recent studies (Smiljanic et al. 2018a; Deepak & Reddy 2019; Singh et
al. 2019; Casey et al. 2019; Kumar & Reddy 2020; Martell et al. 2021) show
that their frequency is significantly higher at the red clump. A higher
occurrence in a particular evolutionary phase (i.e., during the He-core
burning) would therefore imply an internal origin (likely related to the He
flash, Kumar & Reddy 2020) as the main responsible for the Li observed. The
accurate classification of the Li-rich giants in the different evolutionary
stages is beyond the scope of this work. Only for a merely indicative purpose,
we assume that the region in the Kiel diagram (right panel in Fig. 14) with
the highest density of stars (the sequence with 2.3$\leq$$\log g$$\leq$3.0)
corresponds to the red clump. Then, in line with other works (e.g., Martell et
al. 2021) super Li-rich giants are more concentrated in this part of the
diagram than Li-rich giants (71.4% versus 51.1%, respectively).

Finally, as commented above, KIC 11657857 is the object that exhibits the
highest Li abundance, $A$(Li)=3.97, in our sample (see Fig.17). It is a super
Li-rich M-type star (see, e.g., Alcalá et al. 2011a, for another example),
which also shows an infrared excess. According to its location in the HR
diagram (the brightest and the coolest), KIC 11657857 is most likely to be an
asymptotic giant branch (AGB) star, the only one in our Li-rich sample. High-
resolution spectroscopic observations would be necessary to properly
characterize this interesting object.

Figure 17: Spectrum of KIC 11657857 (black line and dots), the star with the
highest abundance of Li in our sample, versus that of a Li-normal giant with
similar stellar parameters (red line) around the Li line at 6708 Å, whose
center is marked with a vertical dashed line.

###  4.4 Spectroscopic binaries

The resolution of the LAMOST MRS is sufficient to detect binary and multiple
systems and to study their RV curves for deriving the orbital elements and the
physical parameters of the components of these systems (see, e.g., Pan et al.
2020; Wang et al. 2021).

As anticipated in Sect. 3, in some spectra (more than 250) we noted two or
three peaks in the CCF that resulted to be significant in comparison with the
CCF noise. These objects are SB2 or SB3 systems, respectively. In these cases,
the analysis with ROTFIT is meaningless, so we do not report any parameter in
Tables LABEL:Tab:data_red and LABEL:Tab:data_blue and flag them as SB2 or SB3.
In some cases the binary nature is questionable, because the CCF displays only
an asymmetric peak (i.e., no clear valley between the peaks is visible) that
can be due to both an unresolved SB2 system or starspots. For these spectra we
kept the APs in Tables LABEL:Tab:data_blue and LABEL:Tab:data_red, whenever we
considered them as reliable, and flagged them as “SB2?.” In total, we found 27
spectra corresponding to 7 different sources, which display three peaks in the
CCF (SB3) and more than 230 spectra corresponding to 98 sources with two peaks
in the CCF (SB2). The SB3 and SB2 binaries in our sample of MRS are listed in
Table 11.

For the spectra with multiple peaks in the CCF that are sufficiently resolved,
we derived the RV of the individual components by fitting the CCF with
multiple Gaussians with an approach similar to that used for single-lined
objects. An example of the fitting procedure for an SB2 system is shown in
Fig. 18. The RV values for the individual components of the SB3 and SB2
systems listed in Table 11 are not reported in this paper and will be
published in forthcoming works dedicated to the double and multiple systems in
our sample.

Figure 18: Cross-correlation function (black line) for a double-lined
spectroscopic binary (SB2) in the blue arm (upper panel) and in the red arm
(lower panel). The two-Gaussian fit of CCF is displayed with a green line, and
the centers of the primary (more luminous) and secondary components are
indicated with vertical dotted blue and red lines, respectively.

Whenever an SB2 system is observed near the conjunctions, only one peak is
visible in the CCF and the RV, measured with a single Gaussian fit, has to be
considered as a “blended” value of the RVs of the two components, which is
close to the velocity of the barycenter of the system.

In the following, we show the case of a few systems for which we could build
an RV curve, including also data from a few spectra acquired in 2019 (DR7). We
used the weighted average of the corrected RVs measured in the red and the
blue arm, with a weight inversely proportional to the squares of their errors.
We used the stacked spectra to maximize the S/N for binary systems with a
period longer than a few days, while the individual spectra acquired during
each night have been used for binaries with a short or unknown period. We
mention here the cases of the eclipsing binaries KIC 8301013 and KIC 5359678,
whose RV curves based on LAMOST MRS data have been studied by Pan et al.
(2020) and Wang et al. (2021), respectively. They also presented an in-depth
analysis of their Kepler light curves.

Another eclipsing binary with a period $P_{\rm orb}\simeq$ 24.24 days and a
very eccentric orbit ($e\simeq$0.680) is KIC 7821010. An orbital solution,
based on the Kepler light curve and RVs derived from high-resolution HIDES
spectra, has been presented by Hełminiak et al. (2019). Our RVs of KIC 7821010
are displayed in Fig. 19. We note the very good agreement with the RVs and the
orbital solution of Hełminiak et al. (2019), which are also displayed in Fig.
19.

Figure 19: Radial velocity curve of KIC 7821010. The RV data from Hełminiak et
al. (2019) are shown with blue and red squares and the orbital solution with
dotted blue and red lines for the primary and secondary component,
respectively. The LAMOST MRS RVs derived in this work are overplotted with
filled black circles for the primary and open circles for the secondary
component, respectively. The green x symbols display the RV values measured by
us near the conjunctions, where a single peak is visible in the CCF.

We also measured the RVs of the eclipsing binary system KIC 6206751, which has
a much smaller orbital period, $P_{\rm orb}=1.2453$ days, and a circular orbit
(Lee & Park 2018). We note that the RVs of the primary component are in very
good agreement with those from Matson et al. (2017), while for the secondary
component, which is much less luminous than the primary, the agreement is less
good (Fig. 20), but our values are still compatible within the errors.

Figure 20: Radial velocity curve of KIC 6206751. The RV data from Matson et
al. (2017) are displayed with blue and red squares and the orbital solution
with dotted blue and red lines for the primary and secondary component,
respectively. The LAMOST MRS RVs derived in this work are overplotted with
filled black circles for the primary and open black circles for the secondary
component. The green x symbols display the RV values measured by us near the
conjunctions, where a single peak is visible in the CCF.

As a further example, we show the case of KIC 10274200, a non-eclipsing SB2,
for which we determined the period and the orbital parameters from our data
only (see Fig. 21). We searched for the best orbital period by applying the
periodogram analysis (Scargle 1982) to the RVs of the primary and secondary
components. Then, we fitted the observed RV curve with the curvefit routine
(Bevington et al. 1993) to determine the orbital parameters and their standard
errors, which are listed in Table 6. We remark that these are very preliminary
estimates and new data are needed to refine the orbital solution. As mentioned
above, a more in-depth study of the RVs of binary and multiple systems will be
the subject of future works.

Table 6: Orbital parameters of KIC 10274200.

Parameter | Value
---|---
HJD0a | 58020.45$\pm$0.05
$P_{\rm orb}$ ($d$) | 4.278$\pm$0.001
$e$ | 0.04$\pm$0.04
$\omega$ (∘) | 20.0$\pm$0.5
$\gamma$ (km s-1) |  $-11\pm$3
$K_{1}$ (km s-1) | 80$\pm$1
$K_{2}$ (km s-1) | 93$\pm$3
$M_{1}\sin^{3}i$ ($M_{\sun}$) | 1.23$\pm$0.08
$M_{2}\sin^{3}i$ ($M_{\sun}$) | 1.06$\pm$0.05
$M_{2}$/$M_{1}$ | 0.86$\pm$0.03
$a\sin i$ ($R_{\sun}$) | 14.6$\pm$0.2

  * a

Heliocentric Julian date (HJD-2,400,000) of the periastron passage.

Figure 21: Radial velocity curve of KIC 10274200. The LAMOST MRS RVs derived
in this work are plotted with filled circles for the primary and open circles
for the secondary component. The green x symbols display the RV values
measured near the conjunctions, where a single peak is visible in the CCF. The
orbital solution is displayed with a dotted blue and red line for the primary
and secondary component, respectively.

##  5 Summary

We have presented the results of the analysis of about 16,300 LAMOST MRS of
cool (FGKM-type) stars in the field of the Kepler space telescope performed
with the code ROTFIT. We were able to determine the APs ($T_{\rm eff}$, $\log
g$, and [Fe/H]), the RV, and the projected rotational velocity ($v\sin i$) for
about 14 300 spectra corresponding to 7443 different stars. The average
uncertainties of these parameters are about 0.7 km s-1, 2.5 %, 0.25 dex, and
0.15 dex for the RV, $T_{\rm eff}$, $\log g$, and [Fe/H], respectively. We
were able to measure $v\sin i$ values larger than 8 km s-1, which is the lower
threshold for this measure resulting from the resolution and sampling of the
MRS, as found from Monte Carlo simulations. The typical uncertainty for $v\sin
i$ measures is 3–4 km s-1. The comparison of our determinations of $T_{\rm
eff}$ and $\log g$ with literature values derived from spectroscopic analyses
shows an overall good agreement with very few outliers. The case is different
for [Fe/H], which is clearly overestimated for metal-poor stars by our
analysis method. This is likely the result of the nonuniform distribution of
the grid of templates in the space of parameters, which is more important in
the low-metallicity domain. We propose a calibration relation to correct the
metallicity values.

The resolution $R\sim 7500$ and the spectral coverage of the MRS were adequate
to discover and study very interesting objects, such as spectroscopic
binaries, chromospherically active stars, young stars, and lithium-rich
giants. Based on the emission or filling of the H$\alpha$ line core, we
discovered 327 active stars that are young MS stars or more evolved stars that
rotate faster than usual due to tidal spin-orbit synchronization or to
evolutionary effects. We detected the Li i$\lambda$6708 Å line and measured
its equivalent width, $W_{\rm Li}$, in 1657 stars, both giants and MS stars.
We also calculated the lithium abundance $A$(Li) from $W_{\rm Li}$ and the
APs, thanks to suitable curves of growth. Regarding the MS stars, we carried
out a discrete age classification based on the $W_{\rm Li}$ and $A$(Li) and
the upper envelopes of the $W_{\rm Li}$–$T_{\rm eff}$ diagrams of young open
clusters. We found, among the 1184 MS stars where the lithium line was
detected, only 3 stars above (but very close to) the Pleiades upper envelope,
19 stars with an age comparable to the Pleiades ($age\approx$ 125 Myr), 247
UMa-like stars whose age should be similar to that of the UMa cluster
($age\approx 300$ Myr), and 343 Hyades-like stars ($age\approx 600$ Myr).

We have also found 195 Li-rich giants, out of which 161 are reported here for
the first time. The super Li-rich giant KIC 11657857, with $A$(LI)$\approx$4,
stands out among them. It is an IRAS source that shows infrared excess and,
according to its position in the HR diagram, is an AGB star. The fraction of
Li-rich giants found in this work, around 4%, is considerably higher than that
observed in other works. The lack of enhanced rotational velocities among the
Li-rich giants allows us to exclude external mechanisms (mergers) as the most
likely explanation for the observed enrichment of Li in our sample. We find
that fast rotators are more recurrent among the super Li-rich giants than
among the Li-rich giants. Additionally, the former seem to occur more
frequently at the red clump with respect to the latter, which appear to be
more evenly distributed over the entire RGB phase.

Moreover, we have found 98 double-lined spectroscopic binaries (SB2) and 7
triple systems (SB3) from the shape of the CCF, which displays two and three
significant peaks for SB2 and SB3 systems, respectively. For three SB2 systems
with MRS taken at different epochs, we have also presented the RV curves.

###### Acknowledgements.

We are grateful to the anonymous referee for a careful reading of the
manuscript and very useful suggestions that helped us to improve our work.
Guoshoujing Telescope (the Large Sky Area Multi-Object Fibre 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. LAMOSTis operated and managed by the
National Astronomical Observatories, Chinese Academy of Sciences. Support from
the Italian Ministero dell’Istruzione, Università e Ricerca (MIUR) is also
acknowledged. JM-Ż acknowledges the Wrocław Centre for Networking and
Supercomputing grant no. 224. JNF and WZ acknowledge the support of the Joint
Fund of Astronomy of National Natural Science Foundation of China (NSFC) and
Chinese Academy of Sciences through the Grants 11833002, 12090040, 12090042
and 11903005. This research made use of SIMBAD and VIZIER databases, operated
at the CDS, Strasbourg, France. This publication makes use of data products
from the Two Micron All Sky Survey, which is a joint project of the University
of Massachusetts and the Infrared Processing and Analysis Center/California
Institute of Technology, funded by the National Aeronautics and Space
Administration and the National Science Foundation. This publication makes use
of data products from the Wide-field Infrared Survey Explorer, which is a
joint project of the University of California, Los Angeles, and the Jet
Propulsion Laboratory/California Institute of Technology, funded by the
National Aeronautics and Space Administration.

## References

  * Abrahamyan et al. (2015) Abrahamyan, H. V., Mickaelian, A. M., & Knyazyan, A. V. 2015, Astronomy and Computing, 10, 99
  * Abt et al. (2002) Abt, H. A., Levato, H., & Grosso, M. 2002, ApJ, 573, 359
  * Abt & Morrell (1995) Abt, H. A. & Morrell, N. I. 1995, ApJS, 99, 135
  * Aguilera-Gómez et al. (2016) Aguilera-Gómez, C., Chanamé, J., Pinsonneault, M. H., & Carlberg, J. K. 2016, ApJ, 829, 127
  * Alcalá et al. (2011a) Alcalá, J. M., Biazzo, K., Covino, E., Frasca, A., & Bedin, L. R. 2011a, A&A, 531, L12
  * Alcalá et al. (2011b) Alcalá, J. M., Biazzo, K., Covino, E., Frasca, A., & Bedin, L. R. 2011b, A&A, 531, L12
  * Alcalá et al. (2021) Alcalá, J. M., Gangi, M., Biazzo, K., et al. 2021, A&A, 652, A72
  * Allard (2014) Allard, F. 2014, in Exploring the Formation and Evolution of Planetary Systems, ed. M. Booth, B. C. Matthews, & J. R. Graham, Vol. 299, 271–272
  * Allard et al. (2012) Allard, F., Homeier, D., & Freytag, B. 2012, Philosophical Transactions of the Royal Society of London Series A, 370, 2765
  * Allende Prieto et al. (2008) Allende Prieto, C., Majewski, S. R., Schiavon, R., et al. 2008, Astronomische Nachrichten, 329, 1018
  * Alonso-Santiago et al. (2017) Alonso-Santiago, J., Negueruela, I., Marco, A., et al. 2017, MNRAS, 469, 1330
  * Alonso-Santiago et al. (2019) Alonso-Santiago, J., Negueruela, I., Marco, A., et al. 2019, A&A, 631, A124
  * Anders et al. (2019) Anders, F., Khalatyan, A., Chiappini, C., et al. 2019, A&A, 628, A94
  * Balona et al. (2011) Balona, L. A., Pigulski, A., De Cat, P., et al. 2011, MNRAS, 413, 2403
  * Bastien et al. (2016) Bastien, F. A., Stassun, K. G., Basri, G., & Pepper, J. 2016, ApJ, 818, 43
  * Batalha et al. (2013) Batalha, N. M., Rowe, J. F., Bryson, S. T., et al. 2013, ApJS, 204, 24
  * Berger et al. (2018) Berger, T. A., Huber, D., Gaidos, E., & van Saders, J. L. 2018, ApJ, 866, 99
  * Bevington et al. (1993) Bevington, P. R., Robinson, D. K., Blair, J. M., Mallinckrodt, A. J., & McKay, S. 1993, Computers in Physics, 7, 415
  * Bonsack (1959) Bonsack, W. K. 1959, ApJ, 130, 843
  * Bressan et al. (2012) Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127
  * Brewer & Fischer (2018) Brewer, J. M. & Fischer, D. A. 2018, ApJS, 237, 38
  * Brewer et al. (2016) Brewer, J. M., Fischer, D. A., Valenti, J. A., & Piskunov, N. 2016, ApJS, 225, 32
  * Brown et al. (2011) Brown, T. M., Latham, D. W., Everett, M. E., & Esquerdo, G. A. 2011, AJ, 142, 112
  * Bruntt et al. (2012) Bruntt, H., Basu, S., Smalley, B., et al. 2012, MNRAS, 423, 122
  * Bruntt et al. (2011) Bruntt, H., Frandsen, S., & Thygesen, A. O. 2011, A&A, 528, A121
  * Buchhave et al. (2012) Buchhave, L. A., Latham, D. W., Johansen, A., et al. 2012, Nature, 486, 375
  * Cameron & Fowler (1971) Cameron, A. G. W. & Fowler, W. A. 1971, ApJ, 164, 111
  * Cardini & Cassatella (2007) Cardini, D. & Cassatella, A. 2007, ApJ, 666, 393
  * Carlberg et al. (2012) Carlberg, J. K., Cunha, K., Smith, V. V., & Majewski, S. R. 2012, ApJ, 757, 109
  * Carney et al. (2008) Carney, B. W., Gray, D. F., Yong, D., et al. 2008, AJ, 135, 892
  * Casagrande et al. (2011) Casagrande, L., Schönrich, R., Asplund, M., et al. 2011, A&A, 530, A138
  * Casagrande et al. (2016) Casagrande, L., Silva Aguirre, V., Schlesinger, K. J., et al. 2016, MNRAS, 455, 987
  * Casagrande et al. (2014) Casagrande, L., Silva Aguirre, V., Stello, D., et al. 2014, ApJ, 787, 110
  * Casey et al. (2019) Casey, A. R., Ho, A. Y. Q., Ness, M., et al. 2019, ApJ, 880, 125
  * Casey et al. (2016a) Casey, A. R., Ruchti, G., Masseron, T., et al. 2016a, MNRAS, 461, 3336
  * Casey et al. (2016b) Casey, A. R., Ruchti, G., Masseron, T., et al. 2016b, MNRAS, 461, 3336
  * Catanzaro et al. (2010) Catanzaro, G., Frasca, A., Molenda-Żakowicz, J., & Marilli, E. 2010, A&A, 517, A3
  * Catanzaro et al. (2011) Catanzaro, G., Ripepi, V., Bernabei, S., et al. 2011, MNRAS, 411, 1167
  * Charbonnel & Balachandran (2000) Charbonnel, C. & Balachandran, S. C. 2000, A&A, 359, 563
  * Christiansen et al. (2012) Christiansen, J. L., Jenkins, J. M., Caldwell, D. A., et al. 2012, PASP, 124, 1279
  * Cui et al. (2012) Cui, X.-Q., Zhao, Y.-H., Chu, Y.-Q., et al. 2012, Research in Astronomy and Astrophysics, 12, 1197
  * Cutri et al. (2021) Cutri, R. M., Wright, E. L., Conrow, T., et al. 2021, VizieR Online Data Catalog, II/328
  * Davenport (2016) Davenport, J. R. A. 2016, ApJ, 829, 23
  * De Cat et al. (2015) De Cat, P., Fu, J. N., Ren, A. B., et al. 2015, ApJS, 220, 19 (Paper I)
  * de Medeiros & Mayor (1999) de Medeiros, J. R. & Mayor, M. 1999, A&AS, 139, 433
  * Debosscher et al. (2011) Debosscher, J., Blomme, J., Aerts, C., & De Ridder, J. 2011, A&A, 529, A89
  * Deepak & Reddy (2019) Deepak & Reddy, B. E. 2019, MNRAS, 484, 2000
  * Delfosse et al. (1998) Delfosse, X., Forveille, T., Perrier, C., & Mayor, M. 1998, A&A, 331, 581
  * Deshpande et al. (2013) Deshpande, R., Blake, C. H., Bender, C. F., et al. 2013, AJ, 146, 156
  * Dong et al. (2014) Dong, S., Zheng, Z., Zhu, Z., et al. 2014, ApJ, 789, L3
  * Famaey et al. (2005) Famaey, B., Jorissen, A., Luri, X., et al. 2005, A&A, 430, 165
  * Fehrenbach et al. (1997) Fehrenbach, C., Duflot, M., Mannone, C., Burnage, R., & Genty, V. 1997, A&AS, 124, 255
  * Fekel (1997) Fekel, F. C. 1997, PASP, 109, 514
  * Frasca et al. (2003) Frasca, A., Alcalá, J. M., Covino, E., et al. 2003, A&A, 405, 149
  * Frasca et al. (2017) Frasca, A., Biazzo, K., Alcalá, J. M., et al. 2017, A&A, 602, A33
  * Frasca et al. (2015) Frasca, A., Biazzo, K., Lanzafame, A. C., et al. 2015, A&A, 575, A4
  * Frasca & Catalano (1994) Frasca, A. & Catalano, S. 1994, A&A, 284, 883
  * Frasca et al. (2011) Frasca, A., Fröhlich, H. E., Bonanno, A., et al. 2011, A&A, 532, A81
  * Frasca et al. (2018) Frasca, A., Guillout, P., Klutsch, A., et al. 2018, A&A, 612, A96
  * Frasca et al. (2006) Frasca, A., Guillout, P., Marilli, E., et al. 2006, A&A, 454, 301
  * Frasca et al. (2016) Frasca, A., Molenda-Żakowicz, J., De Cat, P., et al. 2016, A&A, 594, A39
  * Frinchaboy & Majewski (2008) Frinchaboy, P. M. & Majewski, S. R. 2008, AJ, 136, 118
  * Fröhlich et al. (2012) Fröhlich, H. E., Frasca, A., Catanzaro, G., et al. 2012, A&A, 543, A146
  * Fukugita et al. (1996) Fukugita, M., Ichikawa, T., Gunn, J. E., et al. 1996, AJ, 111, 1748
  * Furlan et al. (2018) Furlan, E., Ciardi, D. R., Cochran, W. D., et al. 2018, ApJ, 861, 149
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1
  * Gao et al. (2019) Gao, Q., Shi, J.-R., Yan, H.-L., et al. 2019, ApJS, 245, 33
  * Gaulme et al. (2020) Gaulme, P., Jackiewicz, J., Spada, F., et al. 2020, A&A, 639, A63
  * Gilmore et al. (2012) Gilmore, G., Randich, S., Asplund, M., et al. 2012, The Messenger, 147, 25
  * Gontcharov (2006) Gontcharov, G. A. 2006, Astronomy Letters, 32, 759
  * Goodarzi et al. (2019) Goodarzi, H., Mehrabi, A., Khosroshahi, H. G., & He, H. 2019, ApJS, 244, 37
  * Gorlova et al. (2012) Gorlova, N., Van Winckel, H., & Jorissen, A. 2012, Baltic Astronomy, 21, 165
  * Gratton et al. (2004) Gratton, R., Sneden, C., & Carretta, E. 2004, ARA&A, 42, 385
  * Gray & Toner (1987) Gray, D. F. & Toner, C. G. 1987, ApJ, 322, 360
  * Gray et al. (2016) Gray, R. O., Corbally, C. J., De Cat, P., et al. 2016, AJ, 151, 13
  * Grenier et al. (1999) Grenier, S., Baylac, M. O., Rolland, L., et al. 1999, A&AS, 137, 451
  * Grieves et al. (2018) Grieves, N., Ge, J., Thomas, N., et al. 2018, MNRAS, 481, 3244
  * Guillout et al. (2009) Guillout, P., Klutsch, A., Frasca, A., et al. 2009, A&A, 504, 829
  * Guo et al. (2017) Guo, X., Johnson, J. A., Mann, A. W., et al. 2017, ApJ, 838, 25
  * Handler & Shobbrook (2002) Handler, G. & Shobbrook, R. R. 2002, MNRAS, 333, 251
  * Hardegree-Ullman et al. (2019) Hardegree-Ullman, K. K., Cushing, M. C., Muirhead, P. S., & Christiansen, J. L. 2019, AJ, 158, 75
  * Hauck & Mermilliod (1998) Hauck, B. & Mermilliod, M. 1998, A&AS, 129, 431
  * Hauschildt et al. (1999) Hauschildt, P. H., Allard, F., & Baron, E. 1999, ApJ, 512, 377
  * Hełminiak et al. (2019) Hełminiak, K. G., Konacki, M., Maehara, H., et al. 2019, MNRAS, 484, 451
  * Henden et al. (2016) Henden, A. A., Templeton, M., Terrell, D., et al. 2016, VizieR Online Data Catalog, II/336
  * Hillenbrand et al. (2013) Hillenbrand, L. A., Hoffer, A. S., & Herczeg, G. J. 2013, AJ, 146, 85
  * Ho et al. (2017) Ho, A. Y. Q., Ness, M. K., Hogg, D. W., et al. 2017, ApJ, 836, 5
  * Holanda et al. (2020a) Holanda, N., Drake, N. A., & Pereira, C. B. 2020a, AJ, 159, 9
  * Holanda et al. (2020b) Holanda, N., Drake, N. A., & Pereira, C. B. 2020b, MNRAS, 498, 77
  * Howarth et al. (1997) Howarth, I. D., Siebert, K. W., Hussain, G. A. J., & Prinja, R. K. 1997, MNRAS, 284, 265
  * Hubble (1942) Hubble, E. 1942, Science, 95, 212
  * Huber et al. (2013) Huber, D., Chaplin, W. J., Christensen-Dalsgaard, J., et al. 2013, ApJ, 767, 127
  * Huber et al. (2014) Huber, D., Silva Aguirre, V., Matthews, J. M., et al. 2014, ApJS, 211, 2
  * Iben (1967a) Iben, Jr., I. 1967a, ApJ, 147, 650
  * Iben (1967b) Iben, Jr., I. 1967b, ApJ, 147, 624
  * Ishihara et al. (2010) Ishihara, D., Onaka, T., Kataza, H., et al. 2010, A&A, 514, A1
  * Jackson et al. (2015) Jackson, R. J., Jeffries, R. D., Lewis, J., et al. 2015, A&A, 580, A75
  * Jönsson et al. (2020) Jönsson, H., Holtzman, J. A., Allende Prieto, C., et al. 2020, AJ, 160, 120
  * Kepler Mission Team (2009) Kepler Mission Team. 2009, VizieR Online Data Catalog, V/133
  * Kharchenko et al. (2007) Kharchenko, N. V., Scholz, R. D., Piskunov, A. E., Röser, S., & Schilbach, E. 2007, Astronomische Nachrichten, 328, 889
  * Kirby et al. (2016) Kirby, E. N., Guhathakurta, P., Zhang, A. J., et al. 2016, ApJ, 819, 135
  * Koenig et al. (2012) Koenig, X. P., Leisawitz, D. T., Benford, D. J., et al. 2012, ApJ, 744, 130
  * Küker et al. (2019) Küker, M., Rüdiger, G., Olah, K., & Strassmeier, K. G. 2019, A&A, 622, A40
  * Kumar & Reddy (2020) Kumar, Y. B. & Reddy, B. E. 2020, Journal of Astrophysics and Astronomy, 41, 49
  * Lambert & Ries (1981) Lambert, D. L. & Ries, L. M. 1981, ApJ, 248, 228
  * Lee & Park (2018) Lee, J. W. & Park, J.-H. 2018, MNRAS, 480, 4693
  * Lehmann et al. (2011) Lehmann, H., Tkachenko, A., Semaan, T., et al. 2011, A&A, 526, A124
  * Lind et al. (2009) Lind, K., Asplund, M., & Barklem, P. S. 2009, A&A, 503, 541
  * Lindegren et al. (2018) Lindegren, L., Hernández, J., Bombrun, A., et al. 2018, A&A, 616, A2
  * Linsky et al. (1979) Linsky, J. L., Hunten, D. M., Sowell, R., Glackin, D. L., & Kelch, W. L. 1979, ApJS, 41, 481
  * Liu et al. (2019) Liu, N., Fu, J.-N., Zong, W., et al. 2019, Research in Astronomy and Astrophysics, 19, 075
  * Lomaeva et al. (2019) Lomaeva, M., Jönsson, H., Ryde, N., Schultheis, M., & Thorsbro, B. 2019, A&A, 625, A141
  * Lucey et al. (2020) Lucey, M., Ting, Y.-S., Ramachandra, N. S., & Hawkins, K. 2020, MNRAS, 495, 3087
  * Luck (1982) Luck, R. E. 1982, PASP, 94, 811
  * Luo et al. (2012) Luo, A. L., Zhang, H.-T., Zhao, Y.-H., et al. 2012, Research in Astronomy and Astrophysics, 12, 1243
  * Luo et al. (2015) Luo, A. L., Zhao, Y.-H., Zhao, G., et al. 2015, Research in Astronomy and Astrophysics, 15, 1095
  * Luo et al. (2016) Luo, A. L., Zhao, Y. H., Zhao, G., et al. 2016, VizieR Online Data Catalog, V/149
  * Luo et al. (2018) Luo, A. L., Zhao, Y. H., Zhao, G., & et al. 2018, VizieR Online Data Catalog, V/153
  * Magrini et al. (2021) Magrini, L., Smiljanic, R., Franciosini, E., et al. 2021, arXiv e-prints, arXiv:2108.11677
  * Mann et al. (2012) Mann, A. W., Gaidos, E., Lépine, S., & Hilton, E. J. 2012, ApJ, 753, 90
  * Marcy et al. (2014) Marcy, G. W., Isaacson, H., Howard, A. W., et al. 2014, ApJS, 210, 20
  * Martell et al. (2021) Martell, S. L., Simpson, J. D., Balasubramaniam, A. G., et al. 2021, MNRAS, 505, 5340
  * Martínez-Arnáiz et al. (2011) Martínez-Arnáiz, R., López-Santiago, J., Crespo-Chacón, I., & Montes, D. 2011, MNRAS, 414, 2629
  * Mathur et al. (2017) Mathur, S., Huber, D., Batalha, N. M., et al. 2017, ApJS, 229, 30
  * Matson et al. (2017) Matson, R. A., Gies, D. R., Guo, Z., & Williams, S. J. 2017, AJ, 154, 216
  * Mazeh et al. (2015) Mazeh, T., Perets, H. B., McQuillan, A., & Goldstein, E. S. 2015, ApJ, 801, 3
  * McNamara et al. (2012) McNamara, B. J., Jackiewicz, J., & McKeever, J. 2012, AJ, 143, 101
  * McQuillan et al. (2013) McQuillan, A., Mazeh, T., & Aigrain, S. 2013, ApJ, 775, L11
  * McQuillan et al. (2014) McQuillan, A., Mazeh, T., & Aigrain, S. 2014, ApJS, 211, 24
  * Mermilliod et al. (2008) Mermilliod, J. C., Mayor, M., & Udry, S. 2008, A&A, 485, 303
  * Mészáros et al. (2013) Mészáros, S., Holtzman, J., García Pérez, A. E., et al. 2013, AJ, 146, 133
  * Molenda-Żakowicz et al. (2014) Molenda-Żakowicz, J., Brogaard, K., Niemczura, E., et al. 2014, MNRAS, 445, 2446
  * Molenda-Żakowicz et al. (2008) Molenda-Żakowicz, J., Frasca, A., & Latham, D. W. 2008, Acta Astron., 58, 419
  * Molenda-Zakowicz et al. (2007) Molenda-Zakowicz, J., Frasca, A., Latham, D. W., & Jerzykiewicz, M. 2007, Acta Astron., 57, 301
  * Molenda-Żakowicz et al. (2011) Molenda-Żakowicz, J., Latham, D. W., Catanzaro, G., Frasca, A., & Quinn, S. N. 2011, MNRAS, 412, 1210
  * Molenda-Żakowicz et al. (2013) Molenda-Żakowicz, J., Sousa, S. G., Frasca, A., et al. 2013, MNRAS, 434, 1422
  * Monaco et al. (2014) Monaco, L., Boffin, H. M. J., Bonifacio, P., et al. 2014, A&A, 564, L6
  * Montes et al. (1995) Montes, D., Fernandez-Figueroa, M. J., de Castro, E., & Cornide, M. 1995, A&A, 294, 165
  * Montes et al. (2001) Montes, D., López-Santiago, J., Fernández-Figueroa, M. J., & Gálvez, M. C. 2001, A&A, 379, 976
  * Moultaka et al. (2004) Moultaka, J., Ilovaisky, S. A., Prugniel, P., & Soubiran, C. 2004, PASP, 116, 693
  * Neuhaeuser et al. (1997) Neuhaeuser, R., Torres, G., Sterzik, M. F., & Randich, S. 1997, A&A, 325, 647
  * Nidever et al. (2002) Nidever, D. L., Marcy, G. W., Butler, R. P., Fischer, D. A., & Vogt, S. S. 2002, ApJS, 141, 503
  * Nielsen et al. (2015) Nielsen, M. B., Schunker, H., Gizon, L., & Ball, W. H. 2015, A&A, 582, A10
  * Niemczura et al. (2015) Niemczura, E., Murphy, S. J., Smalley, B., et al. 2015, MNRAS, 450, 2764
  * Niemczura et al. (2017) Niemczura, E., Polińska, M., Murphy, S. J., et al. 2017, MNRAS, 470, 2870
  * Nordström et al. (2004) Nordström, B., Mayor, M., Andersen, J., et al. 2004, A&A, 418, 989
  * Notsu et al. (2015) Notsu, Y., Honda, S., Maehara, H., et al. 2015, PASJ, 67, 32
  * O’Dell et al. (2003) O’Dell, C. R., Peimbert, M., & Peimbert, A. 2003, AJ, 125, 2590
  * Oláh et al. (2021) Oláh, K., Kővári, Z., Günther, M. N., et al. 2021, A&A, 647, A62
  * Olney et al. (2020) Olney, R., Kounkel, M., Schillinger, C., et al. 2020, AJ, 159, 182
  * Pakhomov et al. (2009) Pakhomov, Y. V., Antipova, L. I., Boyarchuk, A. A., Zhao, G., & Liang, Y. 2009, Astronomy Reports, 53, 685
  * Pan et al. (2020) Pan, Y., Fu, J.-N., Zong, W., et al. 2020, ApJ, 905, 67
  * Pérez et al. (2016) Pérez, A. E. G., Prieto, C. A., Holtzman, J. A., et al. 2016, The Astronomical Journal, 151, 144
  * Petigura et al. (2017) Petigura, E. A., Howard, A. W., Marcy, G. W., et al. 2017, AJ, 154, 107
  * Petigura et al. (2013) Petigura, E. A., Marcy, G. W., & Howard, A. W. 2013, ApJ, 770, 69
  * Pigulski et al. (2009) Pigulski, A., Pojmański, G., Pilecki, B., & Szczygieł, D. M. 2009, Acta Astron., 59, 33
  * Pinsonneault et al. (2012) Pinsonneault, M. H., An, D., Molenda-Żakowicz, J., et al. 2012, ApJS, 199, 30
  * Pinsonneault et al. (2014) Pinsonneault, M. H., Elsworth, Y., Epstein, C., et al. 2014, ApJS, 215, 19
  * Pizzolato et al. (2003) Pizzolato, N., Maggio, A., Micela, G., Sciortino, S., & Ventura, P. 2003, A&A, 397, 147
  * Pojmanski (1997) Pojmanski, G. 1997, Acta Astron., 47, 467
  * Press et al. (1992) Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 1992, Numerical recipes in FORTRAN. The art of scientific computing
  * Privitera et al. (2016) Privitera, G., Meynet, G., Eggenberger, P., et al. 2016, A&A, 593, A128
  * Queloz et al. (1998) Queloz, D., Allain, S., Mermilliod, J. C., Bouvier, J., & Mayor, M. 1998, A&A, 335, 183
  * Ramsay et al. (2020) Ramsay, G., Doyle, J. G., & Doyle, L. 2020, MNRAS, 497, 2320
  * Reiners et al. (2014) Reiners, A., Schüssler, M., & Passegger, V. M. 2014, ApJ, 794, 144
  * Reinhold et al. (2013) Reinhold, T., Reiners, A., & Basri, G. 2013, A&A, 560, A4
  * Ren et al. (2016) Ren, A., Fu, J., De Cat, P., et al. 2016, ApJS, 225, 28
  * Roberts et al. (1987) Roberts, D. H., Lehar, J., & Dreher, J. W. 1987, AJ, 93, 968
  * Rodríguez & Breger (2001) Rodríguez, E. & Breger, M. 2001, A&A, 366, 178
  * Royer et al. (2002) Royer, F., Grenier, S., Baylac, M. O., Gómez, A. E., & Zorec, J. 2002, A&A, 393, 897
  * Saar & Osten (1997) Saar, S. H. & Osten, R. A. 1997, MNRAS, 284, 803
  * Sarmento et al. (2020) Sarmento, P., Delgado Mena, E., Rojas-Ayala, B., & Blanco-Cuaresma, S. 2020, A&A, 636, A85
  * Scargle (1982) Scargle, J. D. 1982, ApJ, 263, 835
  * Schmidt et al. (2007) Schmidt, E. G., Langan, S., Rogalla, D., & Thacker-Lynn, L. 2007, AJ, 133, 665
  * Schmidt et al. (2011) Schmidt, E. G., Rogalla, D., & Thacker-Lynn, L. 2011, AJ, 141, 53
  * Sestito & Randich (2005) Sestito, P. & Randich, S. 2005, A&A, 442, 615
  * Siess & Livio (1999) Siess, L. & Livio, M. 1999, MNRAS, 308, 1133
  * Singh et al. (2019) Singh, R., Reddy, B. E., Bharat Kumar, Y., & Antia, H. M. 2019, ApJ, 878, L21
  * Skrutskie et al. (2006) Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163
  * Smiljanic et al. (2018a) Smiljanic, R., Franciosini, E., Bragaglia, A., et al. 2018a, A&A, 617, A4
  * Smiljanic et al. (2018b) Smiljanic, R., Franciosini, E., Bragaglia, A., et al. 2018b, A&A, 617, A4
  * Soderblom et al. (1993a) Soderblom, D. R., Jones, B. F., Balachandran, S., et al. 1993a, AJ, 106, 1059
  * Soderblom et al. (1990) Soderblom, D. R., Oey, M. S., Johnson, D. R. H., & Stone, R. P. S. 1990, AJ, 99, 595
  * Soderblom et al. (1993b) Soderblom, D. R., Pilachowski, C. A., Fedele, S. B., & Jones, B. F. 1993b, AJ, 105, 2299
  * Stauffer et al. (1997) Stauffer, J. R., Hartmann, L. W., Prosser, C. F., et al. 1997, ApJ, 479, 776
  * Steinmetz et al. (2006) Steinmetz, M., Zwitter, T., Siebert, A., et al. 2006, AJ, 132, 1645
  * Thygesen et al. (2012) Thygesen, A. O., Frandsen, S., Bruntt, H., et al. 2012, A&A, 543, A160
  * Tian et al. (2020) Tian, H.-J., El-Badry, K., Rix, H.-W., & Gould, A. 2020, ApJS, 246, 4
  * Tkachenko et al. (2013) Tkachenko, A., Aerts, C., Yakushechkin, A., et al. 2013, A&A, 556, A52
  * Tkachenko et al. (2012) Tkachenko, A., Lehmann, H., Smalley, B., Debosscher, J., & Aerts, C. 2012, MNRAS, 422, 2960
  * Tonry & Davis (1979) Tonry, J. & Davis, M. 1979, AJ, 84, 1511
  * Torres et al. (2012) Torres, G., Fischer, D. A., Sozzetti, A., et al. 2012, ApJ, 757, 161
  * Tucker et al. (2006) Tucker, D. L., Kent, S., Richmond, M. W., et al. 2006, Astronomische Nachrichten, 327, 821
  * Udalski et al. (1992) Udalski, A., Szymanski, M., Kaluzny, J., Kubiak, M., & Mateo, M. 1992, Acta Astron., 42, 253
  * Uytterhoeven et al. (2010) Uytterhoeven, K., Briquet, M., Bruntt, H., et al. 2010, Astronomische Nachrichten, 331, 993
  * Uytterhoeven et al. (2011) Uytterhoeven, K., Moya, A., Grigahcène, A., et al. 2011, A&A, 534, A125
  * Valdes et al. (2004) Valdes, F., Gupta, R., Rose, J. A., Singh, H. P., & Bell, D. J. 2004, ApJS, 152, 251
  * Walkowicz et al. (2011) Walkowicz, L. M., Basri, G., Batalha, N., et al. 2011, AJ, 141, 50
  * Wallerstein & Sneden (1982) Wallerstein, G. & Sneden, C. 1982, ApJ, 255, 577
  * Wang et al. (2013) Wang, J., Fischer, D. A., Barclay, T., et al. 2013, ApJ, 776, 10
  * Wang et al. (2021) Wang, J., Fu, J., Niu, H., et al. 2021, MNRAS, 504, 4302
  * Wang et al. (2020a) Wang, J., Fu, J.-N., Zong, W., et al. 2020a, ApJS, 251, 27
  * Wang et al. (2019) Wang, R., Luo, A. L., Chen, J. J., et al. 2019, ApJS, 244, 27
  * Wang et al. (2020b) Wang, R., Luo, A. L., Chen, J.-J., et al. 2020b, ApJ, 891, 23
  * Wang et al. (1996) Wang, S.-G., Su, D.-Q., Chu, Y.-Q., Cui, X., & Wang, Y.-N. 1996, Appl. Opt., 35, 5155
  * White et al. (2007) White, R. J., Gabor, J. M., & Hillenbrand, L. A. 2007, AJ, 133, 2524
  * Wilson (1953) Wilson, R. E. 1953, Carnegie Institute Washington D.C. Publication, 0
  * Woosley & Weaver (1995) Woosley, S. E. & Weaver, T. A. 1995, ApJS, 101, 181
  * Wu et al. (2014) Wu, Y., Du, B., Luo, A., Zhao, Y., & Yuan, H. 2014, in Statistical Challenges in 21st Century Cosmology, ed. A. Heavens, J.-L. Starck, & A. Krone-Martins, Vol. 306, 340–342
  * Wu et al. (2011) Wu, Y., Singh, H. P., Prugniel, P., Gupta, R., & Koleva, M. 2011, A&A, 525, A71
  * Xiang et al. (2019) Xiang, M., Ting, Y.-S., Rix, H.-W., et al. 2019, ApJS, 245, 34
  * Xing et al. (1998) Xing, X., Zhai, C., Du, H., et al. 1998, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 3352, Advanced Technology Optical/IR Telescopes VI, ed. L. M. Stepp, 839–849
  * Yang & Liu (2019) Yang, H. & Liu, J. 2019, ApJS, 241, 29
  * Yang et al. (2017) Yang, H., Liu, J., Gao, Q., et al. 2017, ApJ, 849, 36
  * Yanny et al. (2009) Yanny, B., Rockosi, C., Newberg, H. J., et al. 2009, AJ, 137, 4377
  * York et al. (2000) York, D. G., Adelman, J., Anderson, John E., J., et al. 2000, AJ, 120, 1579
  * Zhang et al. (2021) Zhang, B., Li, J., Yang, F., et al. 2021, ApJS, 256, 14
  * Zhang et al. (2020) Zhang, X., Jeffery, C. S., Li, Y., & Bi, S. 2020, ApJ, 889, 33
  * Zhao et al. (2006) Zhao, G., Chen, Y.-Q., Shi, J.-R., et al. 2006, Chinese J. Astron. Astrophys., 6, 265
  * Zhao et al. (2012) Zhao, G., Zhao, Y.-H., Chu, Y.-Q., Jing, Y.-P., & Deng, L.-C. 2012, Research in Astronomy and Astrophysics, 12, 723
  * Zheng et al. (2020) Zheng, Z.-P., Qiu, B., Luo, A. L., & Li, Y.-B. 2020, PASP, 132, 024504
  * Zong et al. (2018) Zong, W., Fu, J.-N., De Cat, P., et al. 2018, ApJS, 238, 30
  * Zong et al. (2020) Zong, W., Fu, J.-N., De Cat, P., et al. 2020, ApJS, 251, 15

##  Appendix A Monte Carlo simulations for $v\sin i$

We run a Monte Carlo simulation to evaluate the resolution in $v\sin i$ that
can be reached with the LAMOST MRS data and the ROTFIT code. To this aim, we
used synthetic BT-Settl spectra (Allard et al. 2012) with $\log g$=4.5 and
$T_{\rm eff}$ = 4000, 5000, and 6000 K. We brought these spectra to the
resolution of LAMOST MRS by the convolution with a Gaussian kernel of the
proper width (see Sect. 3.1) and resampled them on the LAMOST MRS points. Then
we rotationally broadened these spectra from 0 to 30 km s-1 in steps of 1 km
s-1 and made 200 simulations per each $v\sin i$, adding a random noise
corresponding to signal-to-noise ratios S/N=50 and 100. We applied the code
ROTFIT to each simulated spectrum, analogously to what we did with the target
spectra, to determine the $v\sin i$ both for the red- and the blue-arm
spectral ranges.

In Figs. 22 and 23, we show some examples of the results of these simulations
for the red- and blue-arm spectra, respectively. As apparent from these plots,
we are not able to resolve $v\sin i$’s lower than about 8 km s-1, for which
the measured values, $v\sin i$MEAS, stay at a nearly constant level.
Thereafter, the measured $v\sin i$ starts to grow with the simulated $v\sin i$
and smoothly follows the one-to-one line (dashed blue line in the plots).
Therefore, we adopted 8 km s-1 as the upper limit for the $v\sin i$ measures
on the LAMOST MRS. We point out that this limit is related to the sampling and
resolution of the LAMOST MRS and it is not the result of inaccuracies in the
analysis code. These simulations provide also us with another estimate of the
$v\sin i$ accuracy. The $v\sin i$ errors measured with ROTFIT on the target
spectra were in most cases comparable with those inferred by the
aforementioned Monte Carlo simulations, which are in the range 3–4 km s-1 for
spectra with S/N=50.

Figure 22: Results of the Monte Carlo simulations on $v\sin i$ for red-arm
LAMOST MRS. BT-Settl synthetic spectra with $\log g$=4.5 and three different
$T_{\rm eff}$ values, as indicated in the title of each box, have been
adopted. The S/N=50. The average $v\sin i$ values measured with our procedure
(dots) are plotted against the “theoretical” $v\sin i$ to which the spectra
have been broadened. The error bars represent the standard deviations of the
200 simulations at each $v\sin i$. The 1:1 relation is plotted with a dashed
blue line.

Figure 23: Results of the Monte Carlo simulations on $v\sin i$ for blue-arm
LAMOST MRS. The $T_{\rm eff}$, $\log g$, and S/N are indicated in the top
title of each box. The meaning of the symbols is the same as in Fig. 22.

##  Appendix B Stars with discrepant values of stellar parameters compared to
the literature

We discuss in this section the stars whose $T_{\rm eff}$, $\log g$, or [Fe/H]
values appear as outliers in Figs. 7, 8, or 9 where we compare our APs
determinations with those from the literature.

As regards the effective temperature, we note two stars, KIC 7612547 and KIC
8750025, with very discrepant values ($\Delta$$T_{\rm eff}$$>$1300 K) that are
marked with their KIC identifiers in Fig. 7c. Furthermore, we measure a lower
temperature for the very few objects with $T_{\rm eff}$$>$ 7500 K in the
APOGEE or LASP samples. This is obviously due to the template grid used by
ROTFIT, which is optimized for FGKM stars and does not contain a sufficient
number of hot stars.

As regards the gravity, we found three stars with discrepant $\log g$ values
($\Delta$$\log g$$>$2.0 dex): KIC 8494839, KIC 8750025, and KIC 10526137.
Those stars are marked in Figs. 8a, b, or c with their KIC identifiers.

Finally, as regards the metallicity, we notice a group of 27 stars (KIC
5949422, 5957774, 6127083, 6685477, 6849670, 6852771, 6862553, 6864450,
6938848, 6949847, 7039688, 7186646, 7287513, 7360068, 7532435, 7603295,
7691709, 7820467, 7880048, 7880839, 7949214, 8036035, 8169032, 8686000,
8950928, 9026866, and 9099050) for which the LASP pipeline produces very low
values of [Fe/H] but which in the same time are found in this paper to be of
solar metallicity. Those stars fall into a yellow rectangle in Fig. 9c and are
discussed at the bottom of this section.

In Table 7, we provide the APs derived from the LAMOST MRS spectroscopy in
this paper for four stars indicated with their KIC numbers in Figs. 7 or 8.
That table provides also the APs derived from the LAMOST MRS data by Zong et
al. (2020) who used the LASP pipeline (two stars) or by Wang et al. (2020b)
who used the Stellar Parameters and Chemical Abundances Network (SPCANet)
neural network (two stars, we provide the mean values and their standard
errors calculated from individual AP measurements), high-resolution
spectroscopy by Jönsson et al. (2020) (two stars), Dartmouth stellar
isochrones by Huber et al. (2014) (one star), the LAMOST low-resolution
spectroscopy by Xiang et al. (2019) (two stars, for KIC 10526137 we provide
the mean values and their standard errors calculated from two individual AP
measurements), or the Bayesian stellar parameters derived from the Gaia DR2
parallaxes and optical photometry by Anders et al. (2019) (four stars). We
note that not for all the literature values of APs listed in Table 7 the
$1\sigma$ uncertainties have been provided.

Since the APs of stars listed in Table 7 show noticeable scatter, our general
conclusion is that the APs derived by means of methods other than analysis of
high-resolution spectroscopy should be taken with care, and the respective
stars should be observed again, possibly with high-resolution spectroscopy.

Table 7: Atmospheric parameters of stars marked in Figs. 7 or 8.

$T_{\rm eff}$ | $\log g$ | [Fe/H] | Reference
---|---|---|---
(K) | (dex) | (dex) |
KIC 7612547
4969$\pm$246 | 2.02$\pm$0.39 |  $-$1.54$\pm$0.24 | this paper
5029$\pm$110 | 2.03$\pm$0.09 |  $-$1.39$\pm$0.02 | J20
6301$\pm$705 | 2.82$\pm$0.99 |  $-$2.20$\pm$0.26 | Z20
5056$\pm$53 | 2.53$\pm$0.12 |  $-$1.45$\pm$0.05 | W20 (mean)
5038$\pm$33 | 1.88$\pm$0.06 |  $-$1.42$\pm$0.05 | X19
5093 | 2.47 |  $-$0.65 | A19
KIC 8494839
5046$\pm$162 | 2.93$\pm$0.47 |  $-$0.44$\pm$0.17 | this paper
4188$\pm$80 | 0.50$\pm$0.07 |  $-$1.23$\pm$0.01 | J20
4278 | 1.29 |  $-$0.69 | A19
KIC 8750025
6239$\pm$129 | 4.01$\pm$0.14 |  $-$0.02$\pm$0.14 | this paper
4226$\pm$634 | 1.91$\pm$0.51 |  $-$0.75$\pm$0.20 | Z20
4791$\pm$673 | 2.38$\pm$0.89 |  $-$0.56$\pm$0.24 | W20 (mean)
4009 | 1.13 |  $-$0.33 | A19
KIC 10526137
3337$\pm$79 | 0.65$\pm$0.34 |  $-$0.12$\pm$0.11 | this paper
3161 | 0.19 | 0.25 | A19
5857$\pm$404 | 5.30$\pm$0.45 |  $-$1.15$\pm$0.22 | X19 (mean)
3492$\pm$92 | 4.85$\pm$0.09 | 0.06$\pm$0.18 | H14

A19 = Anders et al. (2019); H14 = Huber et al. (2014); J20 = Jönsson et al.
(2020); W20 = Wang et al. (2020b); X19 = Xiang et al. (2019); Z20 = Zong et
al. (2020).

Figure 24: Comparison of the [Fe/H] values derived by Zong et al. (2020) with
the values reported in the literature. Different colors and symbols are used
for different literature sources, as indicated in the text. The solid line is
a linear fit to the data. The dotted line represents the one-to-one
relationship.

For KIC 7612547, which is marked in Fig. 7c, we found a very large discrepancy
($\simeq 1330$ K) between our $T_{\rm eff}$ value and the one derived with the
LASP pipeline on the same spectra. However, the APs reported in the present
work are in excellent agreement with those from the literature, as can be seen
in Table 7. Therefore, we conclude that our APs are fully reliable and the
LASP values are affected by issues, as also apparent from their very large
errors.

For KIC 8494839, which is marked in Figs. 8b and c, the $\log g$ value derived
in this paper is significantly higher than the $\log g$ reported by Jönsson et
al. (2020). We note, however, that this value was flagged by Jönsson et al.
(2020) as possibly falling in an unreliable range of calibration
determination. The $\log g$ value derived by Anders et al. (2019) falls in
between the determinations reported in this paper and by Jönsson et al.
(2020).

The APs of KIC 8750025, which is marked in Figs. 7c and 8c, are very different
from the literature determination listed in Table 7. Also, Gaia Collaboration
et al. (2018), Kepler Mission Team (2009) or Pinsonneault et al. (2012)
consistently point to a cool star of $T_{\rm eff}$ between 4000 and 4500 K. In
this paper, we analyzed ten LAMOST MRS measured in 2018 while Wang et al.
(2020b) derived APs from two spectra measured in 2019 and one, in 2018. The
APs derived by Wang et al. (2020b) from the spectrum acquired on May, 24,
2018, which was also analyzed in this paper, yielded $T_{\rm eff}$ =
6135$\pm$119 K, $\log g$ = 4.16$\pm$0.17 dex, and [Fe/H] = $-$0.09$\pm$0.12
dex (thus the large standard errors of the means listed in Table 7), which
agree with the APs we derived within the respective $1\sigma$ error bars.
Since the reason for the discrepancy in the APs of KIC 8750025 derived from
the LAMOST MRS measured in different seasons is not clear, we suggest using
them with care.

According to our AP determinations, KIC 10526137, which is marked in Fig. 7a,
is a late-type giant of metallicity slightly lower than solar. For that star,
the APs reported in the literature show high dispersion (see Table 7). In
particular, the $\log g$ determinations range from 0.19 dex (Anders et al.
2019) to 5.30 dex (Xiang et al. 2019). Berger et al. (2018) who used the
parallaxes from the Gaia DR 2 (Gaia Collaboration et al. 2018; Lindegren et
al. 2018) and the DR25 Kepler Stellar Properties Catalog (Mathur et al. 2017)
computed that radius of this star, $R=146.830\,\rm{R_{\odot}}$, and classified
it as a red giant. We find the analyses based on the Gaia parallaxes carried
out by Anders et al. (2019) and Berger et al. (2018) to be conclusive and the
APs of KIC 10526137 derived in this paper to be fully reliable.

Figure 24 shows the comparison of the [Fe/H] values derived from the MRS
LAMOST spectra by Zong et al. (2020) and the literature values for the 27
stars that fall into the yellow rectangle in Fig. 9c. The [Fe/H] values
derived in this paper are indicated with black open circles. Those derived
from high-resolution APOGEE spectra by Jönsson et al. (2020) or Olney et al.
(2020) are indicated with large purple dots. The [Fe/H] values derived from
the MRS LAMOST spectra by Wang et al. (2020b) are indicated with green squares
and those derived from the LRS LAMOST spectra by Xiang et al. (2019) are
indicated with blue triangles. The linear fit to the data is plotted with a
solid line. The linear regression gives a slope $b=0.96$ and intercept
$a=0.83$.

Both this paper and Zong et al. (2020) find those 27 stars to be late-type
giants cooler than $\sim$4500 K. The discrepancies in [Fe/H] shown in Fig. 24
highlight the necessity of using high-resolution spectroscopic analyses for
deriving precise and accurate values of APs; they also show that in the
discussed range of the APs neither LASP nor ROTFIT provide results that are
fully reliable.

##  Appendix C Online figures and tables

Figure 25: Same as Fig. 2 but for a K0 III star.  Figure 26: Same as Fig. 2
but for a mid-F star rotating at about 110 km s-1.  Figure 27: Radial velocity
difference of LK–MRS to Gaia (black histograms) for two plates calibrated with
different lamps in the blue arm (top: 58267-HIPP95119KP01; bottom: