# Exploring the stellar rotation of early-type stars in the LAMOST Medium-
Resolution Survey. I. Catalog

Weijia Sun Kavli Institute for Astronomy & Astrophysics and Department of
Astronomy, Peking University, Yi He Yuan Lu 5, Hai Dian District, Beijing
100871, China  Key Laboratory for Optical Astronomy, National Astronomical
Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District,
Beijing 100012, China  Xiao-Wei Duan Kavli Institute for Astronomy &
Astrophysics and Department of Astronomy, Peking University, Yi He Yuan Lu 5,
Hai Dian District, Beijing 100871, China  Key Laboratory for Optical
Astronomy, National Astronomical Observatories, Chinese Academy of Sciences,
20A Datun Road, Chaoyang District, Beijing 100012, China  Licai Deng Key
Laboratory for Optical Astronomy, National Astronomical Observatories, Chinese
Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing 100012, China
School of Astronomy and Space Science, University of the Chinese Academy of
Sciences, Huairou 101408, China  Department of Astronomy, China West Normal
University, Nanchong 637002, China  Richard de Grijs Department of Physics and
Astronomy, Macquarie University, Balaclava Road, Sydney, NSW 2109, Australia
Research Centre for Astronomy, Astrophysics and Astrophotonics, Macquarie
University, Balaclava Road, Sydney, NSW 2109, Australia  Bo Zhang Department
of Astronomy, Beijing Normal University, Beijing 100875, China  Chao Liu Key
Laboratory for Optical Astronomy, National Astronomical Observatories, Chinese
Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing 100012, China

###### Abstract

We derive stellar parameters and abundances (‘stellar labels’) of 40,034
late-B and A-type main-sequence stars extracted from the Large Sky Area Multi-
Object Fiber Spectroscopic Telescope Medium Resolution Survey (LAMOST–MRS).
The primary selection of our early-type sample was obtained from LAMOST Data
Release 7 based on spectral line indices. We employed the Stellar LAbel
Machine (SLAM) to derive their spectroscopic stellar parameters, drawing on
Kurucz spectral synthesis models with
$6000\,\mathrm{K}<T_{\mathrm{eff}}<15,000\,\mathrm{K}$ and
$-1\,\mathrm{dex}<\mathrm{[M/H]}<1\,\mathrm{dex}$. For a signal-to-noise ratio
of $\sim 60$, the cross-validated scatter is $\sim 75\,\mathrm{K}$, 0.06 dex,
0.05 dex, and $\sim 3.5\,\mathrm{km\,s^{-1}}$ for $T_{\mathrm{eff}}$, $\log
g$, [M/H], and $v\sin i$, respectively. A comparison with objects with prior,
known stellar labels shows great consistency for all stellar parameters,
except for $\log g$. Although this is an intrinsic caveat that comes from the
MRS’s narrow wavelength coverage, it only has a minor effect on estimates of
the stellar rotation rates because of the decent spectral resolution and the
profile-fitting method employed. The masses and ages of our early-type sample
stars were inferred from non-rotating stellar evolution models. This paves the
way for reviewing the properties of stellar rotation distributions as a
function of stellar mass and age.

Stellar rotation (1629), Astronomy data analysis (1858), Catalogs (205),
Early-type stars (430), Stellar properties (1624)

††facilities: LAMOST††software: PARSEC (1.2S; Bressan et al., 2012), Astropy
(Astropy Collaboration et al., 2013), Matplotlib (Hunter, 2007), TOPCAT
(Taylor, 2005), dustmaps (Green, 2018)

##  1 Introduction

Early-type stars comprise hot, massive, and luminous stars of spectral types
O, B, A, and early-F. They are short-lived and rare compared with late-type
dwarfs, which are less massive. Most early-type stars are found in dense
interstellar clouds in spiral arms or other dusty regions. As massive stars,
they facilitate the chemical enrichment and reionization of the Universe,
which makes them important contributors to the evolution of their host
galaxies.

Early-type stars are very important for studies of Galactic and stellar
structure. They are the progenitors of various types of supernovae (Poelarends
et al., 2008) and can be sources of gamma-ray bursts (Langer, 2012). During
their lifetimes, they release much ultraviolet radiation, which rapidly
ionizes the surrounding interstellar medium in giant molecular clouds, forming
Hii regions or Strömgren spheres. Massive early-type stars are useful probes
of elemental abundances and tracers for mapping the spiral structure and disk
of the Milky Way (Morgan et al., 1952; Venn, 1995; Carraro et al., 2010, 2017;
Xu et al., 2018).

Most early-type stars have significantly higher rotation rates than solar-type
and low-mass stars (Glebocki et al., 2000), due to their higher initial
angular momenta, shorter contraction timescales to the zero-age main sequence
(ZAMS), lack of deep convective envelopes, and strong magnetic fields (except
for chemically peculiar stars). For instance, Be stars are B-type main-
sequence stars with Balmer-line emission (Rivinius et al., 2013). The latter
is believed to originate from their decretion disks, fed by mass ejected from
the central stars due to rapid rotation (up to $\sim
350\,\mathrm{km\,s^{-1}}$). Binarity is another key parameter that is
different between early-type stars and their late-type counterparts. The
overall multiplicity frequency of main-sequence stars is a steep, increasing,
monotonic function of spectral type from late to early types (Duchêne & Kraus,
2013).

Precise and accurate stellar parameters derived from stellar spectra are
necessary to understand early-type stars. Thanks to rapid improvements in
modern observing facilities, we can now access large numbers of spectra from
large spectroscopic surveys, e.g. the Large Sky Area Multi-Object Fiber
Spectroscopic Telescope survey (LAMOST; Deng et al., 2012), the Sloan Digital
Sky Survey (SDSS; Eisenstein et al., 2011), the Apache Point Observatory
Galactic Evolution Experiment (APOGEE; Majewski et al., 2017), or the Gaia
Radial Velocity Spectrometer (Cropper et al., 2018), which provide
unprecedented opportunities to unravel the stellar population properties of
large stellar samples. Liu et al. (2019) presented 22,901 stellar spectra of
OB stars identified in LAMOST Data Release (DR) 5 based on their distribution
in the space defined by their spectral line indices. A similar approach was
applied by Guo et al. (2021a). These authors reported 10,608 early-type stars
from LAMOST DR7 and estimated the binary fractions of different spectral
types.

To derive stellar ‘labels’ (stellar parameters and abundances), common
practice is to match stellar spectra and model templates using Balmer and
metal lines. In recent years, machine-learning algorithms have been
introduced, which have proved efficient in processing large databases (Ting et
al., 2019; Xiang et al., 2019). Zhang et al. (2020a) reported the
implementation of a data-driven method based on support vector regression
(SVR), known as the Stellar LAbel Machine (SLAM). It can produce stellar
labels for a wide range of spectral types in LAMOST DR5 with high efficiency.

Here, we undertake a survey of early-type stars in LAMOST DR7, based on a
sample size that is more than ten times larger than the previously largest
database (Zorec & Royer, 2012). We construct a data-driven model for medium-
resolution spectra based on the SLAM model trained by ATLAS12 atmospheric
models (Kurucz, 2005). We compile a catalog composed of more than 40,000 stars
with effective temperatures of $7000\,\mathrm{K}\leq T_{\mathrm{eff}}\leq
14,500\,\mathrm{K}$ and derive their stellar labels ($T_{\mathrm{eff}}$, $\log
g$, [M/H], and $v\sin i$) and fundamental parameters (masses and ages).

This article is organized as follows. In Section 2, we introduce the primary
selection of our early-type candidates from the LAMOST data. Our application
of the SLAM method to derive stellar labels, as well as the results of our
validation, are presented in Section 3. The final catalog, including estimates
of the fundamental stellar parameters and possible contamination, is described
in Section 4. Finally, conclusions are drawn in Section 5.

##  2 Data

###  2.1 Primary selection

LAMOST is a 4-meter quasi-meridian reflective Schmidt telescope equipped with
4000 fibers across its $5^{\circ}$ field-of-view focal plane (Cui et al.,
2012; Zhao et al., 2012). Following the initial low-spectral-resolution
($R\sim 1800$) survey (LRS), conducted from 2011 to 2018 (LAMOST-I; Luo et
al., 2015), LAMOST has been conducting a medium-resolution survey (MRS),
$R\sim 7500$, with its upgraded spectrographs (LAMOST-II; Liu et al., 2020).
The blue cameras of each spectrograph cover the wavelength range from 4950 Å
to 5350 Å, while the red cameras cover 6300 Å to 6800 Å. With a single
exposure time of 1200 s, the median signal-to-noise ratio (SNR) can reach
values in excess of 5 for stars with Gaia $G$-band magnitudes
$G<14.5\,\mathrm{mag}$. The SNR of co-added spectra composed of three 1200 s
spectra can reach 10 at $G=14.5\,\mathrm{mag}$.

MRS DR7 contains 11,422,346 single-exposure and 2,968,667 co-added spectra
(encompassing both the blue and red bands), which are tabulated in the LAMOST
MRS General Catalog. The LAMOST data reduction pipeline subtracts the sky
background and removes the Earth’s atmospheric telluric absorption in four
bands, including the $B$ band (Zhongrui, 2013). The LAMOST team also released
the LAMOST MRS Parameter Catalog, a subsample of 807,319 spectra whose stellar
parameters and chemical abundances were estimated using various pipelines. The
effective temperatures, surface gravities, and metallicities were determined
by the LAMOST Stellar Parameter pipeline (LASP), whereas the rotational
velocity was measured by matching with ELODIE templates. The elemental
abundances were estimated using a deep-learning method (Wang et al., 2020).

To compile our primary catalog of early-type
($T_{\mathrm{eff}}>7000\,\mathrm{K}$) candidates, we selected the co-added
spectra from the LAMOST MRS General Catalog and cross-matched them with Gaia
early DR3 (EDR3; Gaia Collaboration et al., 2021). Compared with Gaia DR2
(Gaia Collaboration et al., 2018), EDR3 represents a significant improvement
as regards estimates of the parallax systematics, both globally (Lindegren et
al., 2021) and locally (Ren et al., 2021). Lindegren et al. (2021) published
the parallax zero-point based on their analysis of quasars, binary stars, and
the Large Magellanic Cloud. We adopted the photo-geometric distance estimates
of Bailer-Jones et al. (2021)—who inferred distances from EDR3 parallaxes
(corrected for the parallax zero-point) based on a three-dimensional Galactic
model—as the distances of our candidates. We also cross-matched our candidates
with the Two Micron All Sky Survey (2MASS; Skrutskie et al., 2006) for
extinction correction (see Section 4.1). As our preliminary selection
criteria, we rejected those objects with effective temperatures below 6500 K
(in practice below 7000 K to avoid removal of objects with incorrect
temperature estimates) or SNRs less than 15.

Next, we selected those stars with accurate Gaia astrometric and photometric
parameters following Riello et al. (2021). The renormalized unit weight error
(RUWE), introduced after Gaia DR2 (Arenou et al., 2018), was adopted as a
goodness-of-fit indicator ($\texttt{ruwe}<1.4$). Objects with a close
separation on the sky, less than 0.7″(Gaia Collaboration et al., 2021), cannot
yield reliable measurements. Therefore, they were rejected by imposing the
criterion duplicated_source$==$True. We further used the corrected BP and RP
flux excess factor $C^{*}$, introduced by Riello et al. (2021), to quantify
the impact of variations in the local background level. The latter may affect
the $G_{\mathrm{BP}}$ and $G_{\mathrm{RP}}$ integrated photometry. Equation 18
of Riello et al. (2021) was used to select a sample of well-behaved, isolated
stellar sources with good-quality photometry. No saturation correction was
applied, because the bright stars in our sample do not reach the brightness
levels where saturation becomes an issue. As the final step, we rejected
candidates with relative parallax errors larger than 10%.

###  2.2 Line indices

We further used the objects’ spectral line indices to select early-type
candidates. Line indices provide a mapping of the effective temperature
without the caveats associated with extinction correction and flux calibration
(Liu et al., 2015). A line index, in terms of its equivalent width (EW), is
defined as (Worthey et al., 1994)

$\mathrm{EW}=\int\left[1-\frac{f_{\mathrm{line}}(\lambda)}{f_{\mathrm{cont}}(\lambda)}\right]\mathrm{d}\lambda,$
(1)

where $f_{\mathrm{line}}(\lambda)$ and $f_{\mathrm{cont}}(\lambda)$ are the
fluxes of the spectral line and the continuum, respectively, and $\lambda$ is
the rest-frame wavelength.

Normalization of the spectra and transformation to the rest frame was done
using the laspec111https://github.com/hypergravity/laspec package (Zhang et
al, 2021). In brief, we normalized our spectra by iteratively fitting a
spectrum three times with a spline function and rejecting pixels deviating by
more than 3$\sigma$ from the median values in 20 Å windows. Following
normalization, the radial velocities, $v_{R}$, were estimated using the cross-
correlation function method with respect to a collection of synthetic spectra
based on the ATLAS9 model atmospheres (Allende Prieto et al., 2018). Because
of the narrow wavelength coverage of both the blue and red spectrographs
($\sim 400\,\mathrm{\AA}$), continuum fluxes may be affected by the non-
uniform spectral response function, especially toward the edges. Therefore, we
calculated the relative flux ratios by normalization of the entire spectrum,
instead of using the pseudo-continuum (e.g. Liu et al., 2015; Guo et al.,
2021a). Note that there might be some offset between the blue and red arms.
Therefore, we applied the cross-correlation technique to both arms and
transformed the red and blue spectra to the rest frame separately. We
discarded those sources with $|v_{R}|>250\,\mathrm{km\,s^{-1}}$ since they are
probably affected by bad pixels suffering from strong cosmic rays or
contaminated by emission lines arising either from their surrounding disks, or
nearby Hii regions.

Figure 1: Normalized sample spectra, in the rest frame, from LAMOST MRS DR7
(blue) and the corresponding best-fitting models (orange) determined by the
SLAM algorithm (see Section 3). Blue and red segments of the same object are
shown in the left and right panels, respectively. The best-fitting effective
temperatures, $T_{\mathrm{eff}}$, and the projected rotational velocities,
$v\sin i$, are listed in the bottom right corners. The red bands correspond to
the spectral regions covering Mg i b (5160.12–5192.62 Å) and H$\alpha$
(6548.0–6578.0 Å).

In Figure 1, we present three sample spectra characterized by different
effective temperatures from LAMOST MRS DR7. Observations of the same object
obtained with the blue and red arms are shown in the left and right panels,
respectively. The wavelength scale was transformed to the rest frame and
fluxes were normalized to the pseudo-continuum, as described above. The best-
fitting models determined by application of the SLAM method are shown as
orange curves. The vertical red bands represent the wavelength ranges covering
Mg i b and H$\alpha$, which were used in our selection of the line indices.
The top and bottom panels represent spectra of two stars with small projected
rotational velocities ($v\sin i<100\,\mathrm{km\,s^{-1}}$), while the middle
panel shows a spectrum that is affected by strong rotational broadening.

Figure 2: Distribution of the H$\alpha$ and Mg i b line indices of the MRS
sample. Regions with high number densities are shown as grayscale contours.
Reference line indices from the ATLAS atmospheric models in the range from
6000 K to 15,000 K are overplotted as colored circles ($\log
g=4.0\,\mathrm{dex}$, [M/H]$=0.0\,\mathrm{dex}$) and triangles ($\log
g=4.0\,\mathrm{dex}$, [M/H]$=-1.0\,\mathrm{dex}$). The large circle at
$\mathrm{EW}_{\mathrm{Mg}}\sim 2\,\mathrm{\AA}$ represents the model for
$T_{\mathrm{eff}}=7000\,\mathrm{K}$. The shadowed area represents the
selection boundary for stars cooler than $7000\,\mathrm{K}$.

Figure 2 shows the stellar loci in the parameter space defined by the line
indices of H$\alpha$ (6548.0–6578.0 Å) and Mg i b (5160.12–5192.62 Å,
reflecting integration over the three main Mg i features at 5167, 5172, and
5183 Å) for the selected MRS sample objects. The contours show the number
densities in dense regions. Line indices from the ATLAS atmospheric models are
overplotted for reference, color-coded by their effective temperature. The
dense cluster at $\mathrm{EW}_{\mathrm{H\alpha}}\sim 4\,\mathrm{\AA}$
represents the low-temperature sample objects
($T_{\mathrm{eff}}<6500\,\mathrm{K}$) remaining following the initial
temperature selection. There is an elongated aggregation at
$\mathrm{EW}_{\mathrm{H\alpha}}\sim 2\,\mathrm{\AA}$, which is mostly composed
of late-type stars with $T_{\mathrm{eff}}<3100\,\mathrm{K}$ that were missed
in the LASP, while another aggregation is located at bottom right around 9400
K. The latter is an artifact caused by a concentration in the line indices
parameter space (see Section 4.1).

To further avoid contamination by late-type stars, we rejected candidates with
$T_{\mathrm{eff}}<7000\,\mathrm{K}$ (the shadowed area in Figure 2). Finally,
we were left with 84,382 early-type candidates with decent SNRs (with median
SNR values in excess of 40). As the next step in our data processing, stellar
labels ($T_{\mathrm{eff}}$, $\log g$, [M/H], and $v\sin i$) of each star in
this reduced sample were extracted. We will outline the adopted method in the
next section.

##  3 Method

SLAM is a data-driven method to estimate precise stellar labels from spectra
based on SVR. Compared with other attempts, also based on SVR (e.g. Li et al.,
2015), SLAM applies a generative model that automatically adjusts the model
complexity and extracts information from the stellar spectra. SLAM’s
performance on application to the LAMOST LRS (Zhang et al., 2020a) and MRS
(Zhang et al., 2020b) spectra has been inspected, and the approach has been
applied to various stellar populations (e.g. Guo et al., 2021b; Li et al.,
2021).

###  3.1 Training

Data-driven methods (e.g. Ness et al., 2015; Ting et al., 2017b) presume that
the stellar labels of the training set are known accurately and precisely.
Ideally, the training set is composed of observed spectra with high SNRs that
have high-fidelity labels, either from a reference set built from well-studied
objects that have been observed in the context of the survey (Hou et al.,
2015) or from a common subset taken from a higher-resolution survey (Ting et
al., 2017b). Unfortunately, such a training set containing a large collection
of early-type stellar labels is not available. Therefore, we used a set of
mock stellar spectra from ATLAS12 atmospheric models to build the training
set.

However, our stellar labels are referenced to the set of model spectra
adopted. For instance, the effective temperatures derived for chemically
peculiar stars—which are prevalent especially among A-type stars (Preston,
1974)—depend on which lines are used (Ca ii K, Balmer H, metallic lines; Gray
& Corbally, 2009). Our sample probably also includes shell stars (e.g.,
Pleione; Gulliver, 1977), which have narrow absorption lines associated with
cooler plasma that originates in a gas disk projected against the stellar
photospheres. In this paper, the results for such objects depend on which
features are covered by the blue and red segments of the observed MRS spectra.
Also note that the adopted ATLAS12 model is a local thermodynamic equilibrium
(LTE) spectral model that does not take into account the presence of non-LTE
(NLTE) effects. The atmospheres of cool stars are well described by LTE model
atmospheres, but stars of spectral types earlier than A require a detailed
treatment of NLTE effects because of the high energy densities of their
radiation fields (Przybilla et al., 2011). Alexeeva et al. (2018) presented
NLTE models for the Mg i b lines, which is of importance in our sample’s
context since neutral magnesium is a minority species. They found that
departures from LTE are essential for stars hotter than $9000\,\mathrm{K}$,
potentially leading to differences in Mg abundance of several tenths of a dex.
Although our method is inevitably limited by the systematic shortcomings
embedded in the theoretical model spectra, this approach can perform well
enough in practice (Ting et al., 2017a).

The training process involves two different SLAM models. The first model is
used to convert high-resolution spectra from the model grid
($T_{\mathrm{eff}}$, $\log g$, $[\mathrm{Fe}/\mathrm{H}]$) to yield random
values for these parameters within predefined ranges. The second one is used
to construct mock spectra resembling the MRS spectra using synthetic spectra
convolved with the rotational profile ($v\sin i$) and instrumental broadening.

Note that the specific intensity profiles pertaining to the stellar atmosphere
vary from center to limb. The convolution approach is an approximate
representation of the rotation profile under the assumption that center-to-
limb variations are negligible compared to rotation effects (Gray, 2005). This
approximation will cease to hold for rapid rotation, which induces temperature
and gravity inhomogeneities, leading to differences that depend on the spin
axis orientation with respect to the line of sight. Such gravitational
darkening effects, most notable in Be—B-type stars exhibiting Balmer-line
emission (Townsend et al., 2004)—will result in an underestimation of the
rotation velocities. Nevertheless, for the majority of our sample objects this
effect is minor and only a small fraction of rapid rotators suffer from this
systematic error. As for the limb darkening law, we adopted a fixed value for
the linear limb-darkening coefficient, $\epsilon=0.6$, a value typical for the
range of temperatures found among our sample (Royer et al., 2002a). Wade &
Rucinski (1985) pointed out that the coefficient depends on the effective
temperature and the wavelength, and Díaz et al. (2011) estimated that
neglecting these variations may produce an error of $\sim 2$% in $v\sin i$;
therefore, adoption of a more adequate limb darkening law would be a potential
improvement.

First, we used synthetic stellar spectra from the Pollux database (Palacios et
al., 2010) to generate the training set. The model grid covered
$T_{\mathrm{eff}}$ from 6000 K to 15,000 K in steps of 100 K, $\log g$ from
3.5 dex to 4.5 dex in steps of 0.5 dex, and $[\mathrm{Fe}/\mathrm{H}]$ from
$-1.0\,\mathrm{dex}$ to $1.0\,\mathrm{dex}$ in steps of 0.5 dex. Spectra were
computed based on the plane-parallel ATLAS12 model atmospheres in LTE (Kurucz,
2005). The microturbulent velocity was fixed at $2\,\mathrm{km\,s^{-1}}$. We
used this original set of ATLAS12 model spectra to train the first SLAM model
and then applied this SLAM model to generate 10,000 synthetic spectra covering
a uniform distribution in $\log(T_{\mathrm{eff}})$, $\log g$, and
$[\mathrm{Fe}/\mathrm{H}]$.

In the second step, the synthetic spectra were convolved with the rotational
broadening and downgraded to a resolution of $R\sim 7500$ to resemble the MRS
spectra from both the blue and red arms. We normalized these mock spectra
using the same procedure as used for the MRS spectra and re-sampled them to a
wavelength step of 0.2 Å, approximately the sampling step of $\lambda/3R$.
Gaussian noise resulting in $\mathrm{SNR}=40$ was added to the spectra to
simulate the practical conditions pertaining to the observed spectra.

We adopted a grid of SLAM hyperparameters (parameters used to control the
learning process) defined by $\epsilon=0.05$, $C=[0.1,1,10]$, and
$\gamma=[0.1,1,10]$, where $\epsilon$ and $C$ represent the tube radius and
penalty level in the SVR algorithm, respectively, and $\gamma$ represents the
width of the kernel of the radial basis function. These hyperparameters define
the complexity of the SVR model, which is automatically determined by the
training set through the mean-squared error. The best-fitting hyperparameters
were found through five-fold cross-validation, i.e. by partitioning the entire
training sample into five equal-sized subsets and adopting a single subsample
as validation data to test the model trained by the other four subsamples.
This cross-validation was repeated five times, iterating through all five
subsamples.

Figure 3: Model spectra for $T_{\mathrm{eff}}=8000\,\mathrm{K}$ (bottom),
10000 K (middle), and 13000 K (top). Each group is further offset by $v\sin
i=0\,\mathrm{km\,s^{-1}}$ (blue), $150\,\mathrm{km\,s^{-1}}$ (green), and
$300\,\mathrm{km\,s^{-1}}$ (orange). Observations of the same object obtained
with the blue and red arms are shown in the left and right panels,
respectively. The model spectra have been broadened to the MRS resolving
power, $R=7500$, and resampled to the MRS wavelength coverage.  Figure 4: As
Figure 3, but for different metallicities, i.e.,
$\mathrm{[M/H]}=0.0\,\mathrm{dex}$ (blue) and $-1.0\,\mathrm{dex}$ (green).
Figure 5: As Figure 3, but for different surface gravities, i.e., $\log
g=4.0\,\mathrm{dex}$ (blue) and $3.5\,\mathrm{dex}$ (green). The red curve
represents the flux ratio of the $\log g=4.0\,\mathrm{dex}$ and $\log
g=3.5\,\mathrm{dex}$ models, $F_{\log g=4.0}/F_{\log g=3.5}$.

The predicted performance of the SLAM method fundamentally depends on how the
spectral-line features vary as a function of the adopted labels. As one of the
first applications to early-type stars, we present Figures 3, 4, and 5 to
illustrate these variations as functions of $v\sin i$, [M/H], and $\log g$,
respectively. Three groups of model spectra for different temperatures are
shown at the top (13,000 K), middle (10,000 K), and bottom (8000 K). The left
(right) panels show the blue (red) segments of the MRS spectral range. The
model spectra were broadened to the MRS resolving power, $R=7500$, and
resampled to the MRS wavelength coverage. The default parameter set includes
solar metallicity $\mathrm{[M/H]}=0$, $\log g=4.0\,\mathrm{dex}$, and $v\sin
i=0\,\mathrm{km\,s^{-1}}$.

Figure 3 and 4 show clear evidence that the model spectra are strongly
dependent on the values of $v\sin i$ and [M/H]. As the rotation velocity
increases, the absorption lines become blended and only strong lines remain
visible. The effects of rotational broadening on the spectra can be
differentiated easily from the impact of other stellar labels
($T_{\mathrm{eff}}$, [M/H], and $\log g$). This enables us to unequivocally
probe the effects of stellar rotation. All metal line depths decrease with
decreasing metallicity, although the H$\alpha$ profile is largely unchanged
(as is He i 6678 for hotter B-type stars). Thus, the potential degeneracy
between higher temperature and lower metallicity could be alleviated by the
strength of the H$\alpha$ profile. Moreover, the equivalent widths of the
Balmer lines are maximal around 9000 K due to the relatively high excitation
energy of the Balmer series (10.2 eV) (Gray, 2005). The presence of He i
and/or Si ii, which only appear at higher temperatures, could help to resolve
this degeneracy.

Any variations caused by variations in $\log g$ are small, as shown in Figure
5. To provide to a clearer picture of the latter effect, the flux ratios of
the $\log g=4.0\,\mathrm{dex}$ and $\log g=3.5\,\mathrm{dex}$ models, $F_{\log
g=4.0}/F_{\log g=3.5}$, are overplotted as red curves. Generally, the
dependence on $\log g$ is weak. In the blue arm, mostly only the Mg i b lines
exhibit some changes for cooler models. As for H$\alpha$ in the red arms, its
wings are merely influenced by Stark broadening for the hotter models with
lower gravity, and only the line cores show some dependence on $\log g$. This
suggests a poor capability for predicting the surface gravity, particularly
for cooler stars.

###  3.2 Uncertainties

We will discuss two types of uncertainties, internal errors associated with
the SLAM method itself and external uncertainties associated with the observed
spectra.

The internal uncertainty pertaining to the optimization method could be
represented by the SLAM errors, as converted from the Hessian matrix. The
diagonal elements of the covariance matrix were used as the formal errors. We
also estimated the precision of the model based on the cross-validated scatter
($\sigma_{\mathrm{CV}}$), which is the standard deviation of the difference
between the predicted and true values:

$\sigma_{\mathrm{CV}}=\frac{1}{m}\sqrt{\sum_{i=1}^{m}\left(\theta_{i,\mathrm{SLAM}}-\theta_{i}\right)^{2}},$
(2)

where $\theta_{i}$ and $\theta_{i,\mathrm{SLAM}}$ are the true and predicted
stellar labels, respectively. The cross-validated scatter was calculated based
on a subset composed of one-tenth of the full training sample. This subset was
randomly selected to ensure uniformity across the parameter ranges.

Figure 6: Uncertainties in the stellar labels ($T_{\mathrm{eff}}$, $\log g$,
[M/H], and $v\sin i$) versus SNR. Blue squares, cyan circles, and green
triangles represent the cross-validated scatter, $\sigma_{\mathrm{CV}}$, SLAM
error, and bias, respectively. The $\sigma_{\mathrm{CV}}$ values of
$T_{\mathrm{eff}}$, $\log g$, [M/H], and $v\sin i$ mostly converge at $\sim
75\,\mathrm{K}$, 0.06 dex, 0.05 dex, and $\sim 3.5\,\mathrm{km\,s^{-1}}$,
respectively, for $\mathrm{SNR}>60$. In each panel, the $\sigma_{\mathrm{CV}}$
values of the corresponding label for two different subsamples, split by their
temperatures, are shown as dashed ($T_{\mathrm{eff}}<10,000\,\mathrm{K}$) and
dotted ($T_{\mathrm{eff}}>10,000\,\mathrm{K}$) lines.

Figure 6 shows the uncertainties in the stellar labels for different SNRs,
from 20 to 100. For objects with $\mathrm{SNR}>60$, the $\sigma_{\mathrm{CV}}$
values for $T_{\mathrm{eff}}$, $\log g$, [M/H], and $v\sin i$ are $\sim
75\,\mathrm{K}$, 0.06 dex, 0.05 dex, and $\sim 3.5\,\mathrm{km\,s^{-1}}$,
respectively. Both $\sigma_{\mathrm{CV}}$ and the SLAM error converge for
$\mathrm{SNR}>60$, but $\sigma_{\mathrm{CV}}$ is much larger than the SLAM
error. This is due to the unconsidered errors in the stellar labels in both
the training and validation processes. Thus, following Zhang et al. (2020a),
we recommend the cross-validated scatter as a more reliable estimate to
evaluate the performance of the SLAM model. The cross-validated test also
yields the biases (see the triangles in Figure 6), which contribute less than
10% to the overall uncertainties.

Note that the uncertainties just discussed represent the average behavior of
the SLAM model. Its performance will vary across a wide range of the relevant
parameter space, especially for $T_{\mathrm{eff}}$. The top left panel of
Figure 6 shows $\sigma_{\mathrm{CV}}$ for two different subsamples, divided by
their temperatures, $T_{\mathrm{eff}}<10,000\,\mathrm{K}$ (dashed line) and
$T_{\mathrm{eff}}>10,000\,\mathrm{K}$ (dotted line). The performance of the
hotter subsample is much worse than that of the cooler stars. The same trend
with effective temperature is seen for [M/H] and $v\sin i$. Figure 3 shows
that the available metallic absorption features become weaker as the
temperature increases, particularly for the blue arm. This lack of information
leads to larger uncertainties in estimates of the stellar labels for hotter
stars, which also holds for lower metallicities. The exception is $\log g$
(top right), where there is no significant difference between the
$\sigma_{\mathrm{CV}}$ values for the hotter and cooler subsamples. This could
be due to our use of both the blue and red segments of the MRS spectra, which
broadly offsets the spectral dependence on effective temperature.

###  3.3 Validation

Figure 7: Comparison of stellar labels from SLAM and literature results (Huang
& Gies, 2006a, b; Huang et al., 2010; Zorec & Royer, 2012; Soubiran et al.,
2016). (Top left) $T_{\mathrm{eff}}$ shows great consistency for
$T_{\mathrm{eff}}<15,000\,\mathrm{K}$, the upper limit from the training
model. The vertical error bars are on the order of or smaller than the data
points. (Top right) $\log g$ from SLAM marginally agrees with the literature
values, with significant scatter. (Bottom left) [M/H] from SLAM follows the
one-to-one correlation with the literature results. (Bottom right) Our
estimates of $v\sin i$ are consistent with the one-to-one relation with the
literature values. The $v\sin i$ values from Huang & Gies (2006a) and Huang et
al. (2010) were calibrated based on high-precision measurements. The error
bars for our estimates (horizontal axis) come from the cross-validated scatter
($\sigma_{\mathrm{CV}}$).

A comparison of the stellar labels derived from SLAM and those collected from
the literature is shown in Figure 7. The validation sample comes from Huang &
Gies (2006a, b), Huang et al. (2010), Zorec & Royer (2012), and Soubiran et
al. (2016). Soubiran et al. (2016) is a bibliographical catalog containing
determinations of stellar atmospheric parameters. Its stellar parameters
($T_{\mathrm{eff}}$, $\log g$, and [M/H]) were collected from the literature
based on high-resolution ($R\geqslant 25,000$) and high SNR (SNR $>50$)
spectra. Although these parameters were not derived homogeneously, the median
value of the standard deviation of the values from different measures is
0.76%. The main sources of rotational velocities are Huang & Gies (2006b) and
Huang et al. (2010). Those authors conducted a survey of B-type stars based on
moderate-resolution ($R\sim 2000$–4000) spectra from the WIYN 3.5 m and CTIO 4
m telescopes.

The top left panel of Figure 7 presents a comparison of the effective
temperatures. Because Zorec & Royer (2012) estimated their temperatures based
on Strömgren photometric color indices, which is inconsistent with the
spectroscopic method used for our sample and other literature sources, we did
not include their estimates. There is great consistency between our results
and the literature results up to $T_{\mathrm{eff}}=15,000\,\mathrm{K}$. This
is the temperature limit inherited from the training model, where the upper
limit is set by the parameter grid of the atmospheric models. Thus, we
disregard $T_{\mathrm{eff}}$ comparisons beyond this limit.

As for $\log g$ (see the top right panel of Figure 7), it demonstrates the
worst performance among the four stellar labels: $\log g$ from SLAM roughly
agrees with the literature values, although with significant scatter. This
poor performance of $\log g$ has been investigated by Zhang et al. (2020b),
who used the Coefficient of Dependence (COD) to quantify the global spectral
information content. They found that the COD of $\log g$ remains low for dwarf
stars. This means that the spectral information content in $\log g$ is not
well carried in the MRS spectra. This is, however, not a major issue for our
analysis as the resulting $v\sin i$ values are not significantly affected by
this poor performance (as demonstrated in the bottom right panel of Figure 7).
Our analysis of the bolometric luminosities (see Section 4.1) and, thus, the
stellar masses (see Section 4.2) depends only weakly on this stellar label.

[M/H] from SLAM follows the one-to-one correlation with the literature
results. However, there might be an offset of 0.08 dex toward higher
metallicity. This might be due to the intrinsic error in the training model.
However, the linear correlation with a slope close to unity ensures the
reliability of our estimates.

The bottom right panel of Figure 7 presents a comparison of $v\sin i$ values.
Despite their low resolution ($R\sim 2000$–4000), Huang & Gies (2006a) and
Huang et al. (2010) achieved sufficient SNR ($>50$) to ensure the reliability
of their measurements. Their results have been validated by Zorec & Royer
(2012), yielding an almost one-to-one correlation (with a slope of $0.971\pm
0.04$) with the results from high-resolution ($R>20,000$) spectra. For the
$v\sin i$ comparison, we used the calibration function derived by Zorec &
Royer (2012, their Equation 3) to correct their values. Zorec & Royer (2012)
compiled the current-largest catalog of 2014 A-type field stars, which
includes Royer et al. (2002a, b)’s results. However, because our sample is on
average $\sim 4\,\mathrm{mag}$ fainter than theirs, there are only six matches
(included in Figure 7). Linear regression yields,

$v\sin i_{\mathrm{SLAM}}=1.05_{\pm 0.04}v\sin i_{\mathrm{Lit}}-4.97_{\pm
8.37},$ (3)

which is a remarkable consistency in measures of $v\sin i$. The offset is not
significant compared with its uncertainty, which could be associated with the
variable instrumental broadening. The actual spectral resolution of a fiber
depends on its location on the observation plate, which may generate slightly
different broadening values. The wavelength coverage of a given spectrum is
also affected by the fiber positioning, leading to variations in the
information retained in the data. Both effects introduce possible biases in
estimates of stellar rotation, but they are well-constrained in the slow
rotation regime.

Ideally, rotation measurements should be linked to surface gravity
measurements, in the sense that the surface gravity determines the steepness
of the pressure gradient, which in turn generates the pressure broadening, a
second broadening mechanism in addition to the rotational instrumental
broadening. The uncertainties in estimating $\log g$ should therefore affect
the $v\sin i$ derivation. In our case, this effect could be mediated in one of
three ways. First, pressure broadening strongly affects predominantly the
Balmer lines rather than the narrow lines (e.g. Mg i b); rotational
information is well preserved if one were to use narrow-line absorption.
Second, the median-resolution spectrograph enables us to resolve the different
broadened rotation and pressure profiles. Using a method similar to profile
fitting rather than calculating the full width at half maximum, we can
disentangle these two mechanisms. Third, the vast majority of our sample
objects are dwarf stars. They span a relatively small range in $\log g$,
around 4.0 dex, compared with the giant stars. Thus, the impact of large
uncertainties in $\log g$ can be controlled adequately.

Moreover, the consistency between our estimates and the literature results can
extend to lower $v\sin i$, even below the detection limit for MRS resolution,
suggesting that our estimates can potentially apply also to very slow
rotators. Since the offset (if any) is minor, we used the results from the
SLAM model without adjustments. For further use of complementary samples, we
recommend using the inverse function of Equation 3 for calibration.

##  4 Results

Here we discuss our procedures to derive the fundamental parameters
(bolometric luminosity, mass, and age) from the SLAM stellar labels, including
the extinction and bolometric corrections (Section 4.1), and the use of the
stellar evolutionary diagram (Section 4.2). We further demonstrate the impact
of our selection criteria on these fundamental parameters, as well as the
stellar labels, allowing us to derive the final catalog.

###  4.1 Bolometric luminosities

Since the majority of our sample is embedded in the Galactic disk, we use the
high-precision photometry from Gaia, combined with 2MASS photometry given that
it is only marginally affected by extinction, to estimate the bolometric
luminosities. We infer the extinction toward each star based on the difference
between the observed Gaia and the intrinsic color indices. The intrinsic color
index, $\left(G_{\mathrm{BP}}-G_{\mathrm{RP}}\right)_{0}$, was derived from
the PARSEC 1.2S (Bressan et al., 2012) evolutionary tracks by interpolating
the model grid defined by $\log T_{\mathrm{eff}}$, $\log g$, and
$[\mathrm{M}/\mathrm{H}]$ (assuming no $\alpha$ enhancement) to the
corresponding values derived from SLAM.

Figure 8: Distribution of the difference in $E(B-V)$ estimated in this paper
and by Green et al. (2019). The comparisons are for stars with
$E(B-V)>0.5\,\mathrm{mag}$ (blue) and
$0.25\,\mathrm{mag}<E(B-V)<0.5\,\mathrm{mag}$ (orange). The mean values of the
differences ($\mu$) and the dispersions ($\sigma$) are also shown.

The typical uncertainty in $E(G_{\mathrm{BP}}-G_{\mathrm{RP}})$ should be on
the order of 0.1 mag (e.g. Green et al., 2019). Figure 8 shows a comparison of
$E(B-V)$ values estimated in this paper and by Green et al. (2019). The
transformation from measured $E(G_{\mathrm{BP}}-G_{\mathrm{RP}})$ to $E(B-V)$
was calculated based on the Cardelli et al. (1989) and O’Donnell (1994)
extinction law with $R_{\mathrm{V}}=3.1$. The extinction from Green et al.
(2019) was queried based on dust maps (Green, 2018) and converted to
$E(B-V)_{\mathrm{Green}}$ using Table 6 of Schlafly & Finkbeiner (2011).

Since our sample stars are mostly embedded in the Galactic disk, we selected
two subsamples affected by significant reddening, i.e.
$E(B-V)>0.5\,\mathrm{mag}$ and $0.25\,\mathrm{mag}<E(B-V)<0.5\,\mathrm{mag}$.
Comparison with the Green et al. (2019) reddening map for high extinction
suggests a typical uncertainty of $\sim 0.1\,\mathrm{mag}$ in $E(B-V)$. There
is great consistency between both estimates, although our results might be
biased toward lower extinction by $\sim 0.01\,\mathrm{mag}$.

The bolometric correction (BC) was adopted from Chen et al. (2019), who
considered the effects of spectral type and non-linearities. The bolometric
luminosities were calculated as

$M_{\mathrm{bol}}=m_{K_{\mathrm{S}}}+BC_{K_{\mathrm{S}}}-\mathrm{DM}-\frac{A_{K_{\mathrm{S}}}}{E({G_{\mathrm{BP}}}-{G_{\mathrm{RP}}})}E(G_{\mathrm{BP}}-G_{\mathrm{RP}}),$
(4)

where $\mathrm{DM}$ is the distance modulus calculated from the Gaia EDR3
parallaxes (Bailer-Jones et al., 2021) and $A_{i}$ is the extinction
coefficient for a given passband, $i$, based on O’Donnell (1994). We adopted
the 2MASS $K_{\mathrm{s}}$ band to mitigate the influence of extinction in the
Galactic plane. Since the photometric precision of the 2MASS $K_{\mathrm{s}}$
band is better than 0.03 mag for our sample (Skrutskie et al., 2006) and
infrared bands are less affected by extinction
($\frac{A_{K_{\mathrm{s}}}}{E({G_{\mathrm{BP}}}-{G_{\mathrm{RP}}})}=0.26$),
the choice of $K_{\mathrm{s}}$ leads to better estimates of
$M_{\mathrm{bol}}$. The bolometric luminosities were derived by adopting
$M_{\mathrm{\odot,bol}}=4.74\,\mathrm{mag}$. The corresponding error was
estimated by bootstrap sampling of all determinations using Equation 4,
including the stellar labels. The median value of the uncertainties in the
bolometric luminosities is $\Delta\log(L/L_{\odot})=0.02$.

Figure 9: Hertzsprung–Russell diagram of single, normal stars. Evolutionary
tracks of $1.5,1.7,2.0,2.4,2.8,3.6,5\,\mathrm{M_{\odot}}$ are shown as gray
curves. Black reference lines outline the selection boundary for stars of
solar metallicity. The colors represent the logarithm of the stellar numbers
in each bin.

We show the Hertzsprung–Russell diagram of our sample objects in Figure 9. The
majority of the sample have effective temperatures between 6500 K and 15,000
K. The lower boundary reflects the rejection of stars with
$T_{\mathrm{eff}}<6500\,\mathrm{K}$—$\log(T_{\mathrm{eff}}/\mathrm{K})<3.81$—in
Section 2.1, whereas the upper boundary is limited by the hottest stars in the
ATLAS atmospheric models. Note that there is an abnormal concentration close
to the 15,000 K boundary. This is an artifact caused by the temperature limit
in the training process. Thus, we reject all stars with
$T_{\mathrm{eff}}>14,500\,\mathrm{K}$—$\log(T_{\mathrm{eff}}/\mathrm{K})>4.16$—(black
vertical line) from further analysis. The aggregation around 9400
K—$\log(T_{\mathrm{eff}}/\mathrm{K})\sim 3.97$—shown in Figure 2 no longer
exists, suggesting that it does not reflect any real physical property.

In addition to a temperature cut, we also limited our selection to those stars
that are still on the main sequence. As stars evolve off the core-hydrogen-
burning phase, their rotation velocities decelerate significantly owing to the
conservation of angular momentum during the evolutionary expansion of
subgiant-branch stars (e.g., Wu et al., 2016). Because these evolved stars may
have $\log g$ beyond our model grids, we cannot confirm the accuracy of any
resulting estimates. Our selection boundary also includes some stars in the
small contraction phase before they move toward the red giant branch. This
phase is a rapid transition from core to shell hydrogen burning. Therefore,
any contamination associated with this phase will be of minor importance.

###  4.2 Stellar masses and ages

Figure 10: Mass and age ($t/t_{\mathrm{MS}}$) distributions of selected
single, normal stars. Typical errors are indicated by the error bar at top
left.

We used PARSEC 1.2S evolutionary tracks in the $\log T_{\mathrm{eff}}$–$\log
L$ space to estimate individual stellar masses and ages for a given
metallicity, [M/H]. Following Zorec & Royer (2012), we represent the stellar
age by $t$, for the age in years, as well as by $t/t_{\mathrm{MS}}$, for the
life span from the ZAMS to the terminal-age main sequence (TAMS). The
corresponding error was estimated by resampling of $\log T_{\mathrm{eff}}$ and
$\log L$. Figure 9 shows that parts of the evolutionary tracks of the shell
H-burning phase reside within our selection boundary for main-sequence stars,
generating a degeneracy between mass and age. In order to test its influence
on our approach, we performed the same analysis on a mock data set, extracted
from theoretical evolutionary tracks. We verified that the degeneracy is only
important for objects at the very end of the evolutionary phase
($t/t_{\mathrm{MS}}>0.95$). The corresponding error is smaller than 2% for
both the resulting mass and age estimates.

In Figure 10, we present the distribution in the $t/t_{\mathrm{MS}}$–$M$ plane
of the single, normal stars selected within the boundary defined in Figure 9.
The general distribution of our sample in the mass–age diagram displays a
similar profile as that of Zorec & Royer (2012). The trend toward larger
$t/t_{\mathrm{MS}}$ with increasing mass reflects the temperature cut at
$T_{\mathrm{eff}}=14500\,\mathrm{K}$ (the vertical line in Figure 9). However,
our sample fills the lack of objects observed for the lower mass regime (their
Figure 4).

Fast rotators ($v\sin i>300\,\mathrm{km\,s^{-1}}$) will change their surface
temperatures and luminosities significantly compared with their non-rotating
counterparts. This is mainly due to (1) the notion that the centrifugal
support results in a decrease in the surface temperature and luminosity by
decreasing the effective gravity (Meynet & Maeder, 1997); and (2) the
orientation of a star with respect to the line of sight determines the
observed fraction of the stellar surface (Collins & Smith, 1985). Such
mechanisms are not included in the Bressan et al. (2012) non-rotating
evolutionary tracks and might introduce additional biases and uncertainties
into estimates of fundamental stellar parameters. This caveat could be
alleviated by employing detailed asteroseismic modeling (e.g. Corsaro et al.,
2017; Li et al., 2019). Unfortunately, such information is not available for
our sample. Nevertheless, parameters based on non-rotating models are slightly
influenced by rotation effects. Zorec & Royer (2012) compared the masses and
ages determined based on non-rotating evolutionary tracks with those resulting
from rotation (Meynet & Maeder, 2000; Ekström et al., 2008; Brott et al.,
2011; Ekström et al., 2012). They found that differences are smaller than or
around 10% if the rotation is not close to the critical rotation rate
($\Omega/\Omega_{\mathrm{crit}}$, where $\Omega$ is the angular rotation
velocity). Since only a fraction of our sample objects are rapid rotators, our
implementation of non-rotating evolutionary tracks is reasonable.

As our final selection step, we discarded any star with large errors in either
mass or relative age ($\sigma_{M}\geq 0.1\,\mathrm{M_{\odot}}$,
$\sigma_{t/t_{\mathrm{MS}}}\geq 0.15$). To ensure the accuracy of our $v\sin
i$ estimates, we also made a selection based on the associated SLAM error
($\sigma_{v\sin i}/v\sin i<0.05$). Combined with our temperature selection
(Section 4.1), the final catalog contains 40,034 stars. All stellar labels and
fundamental parameters are listed in Table 1.

Table 1: Contents of the Catalog

Num | Column | Unit | Description
---|---|---|---
1 | ID |  |  Gaia DR3 source ID
2 | obsid |  |  LAMOST MRS observation ID
3 | RA | ° |  Right Ascension (J2000)
4 | Dec | ° |  Declination (J2000)
5, 6 |  $\mathrm{EW}_{\mathrm{H\alpha}}$, $\mathrm{EW}_{\mathrm{Mg}}$ | Å |  Line indices of H$\alpha$ and Mg i b EW
7, 8 |  $v_{\mathrm{R,b}}$, $v_{\mathrm{R,r}}$ | $\mathrm{km\,s^{-1}}$ |  Radial velocities, blue and red arms
9 | $T_{\mathrm{eff}}$ | K |  Effective temperature from SLAM
10 | $\sigma_{T_{\mathrm{eff}}}$ | K |  Uncertainty in $T_{\mathrm{eff}}$ (SLAM error)
11 | $\log g$ | dex |  Surface gravity from SLAM
12 | $\sigma_{\log g}$ | dex |  Uncertainty in $\log g$ (SLAM error)
13 | [M/H] | dex |  Metallicity from SLAM
14 | $\sigma_{\mathrm{[M/H]}}$ | dex |  Uncertainty in [M/H] (SLAM error)
15 | $v\sin i$ | $\mathrm{km\,s^{-1}}$ |  Projected rotation velocity from SLAM
16 | $\sigma_{v\sin i}$ | $\mathrm{km\,s^{-1}}$ |  Uncertainty in $v\sin i$ (SLAM error)
17 | $\log L/L_{\odot}$ |  |  Logarithmic luminosity
18 | $\sigma_{\log L}$ |  |  Uncertainty in $\log L/L_{\odot}$
19 | $M$ | $M_{\odot}$ |  Stellar mass
20 | $\sigma_{M}$ | $M_{\odot}$ |  Uncertainty in $M$
21 | $t/t_{\mathrm{MS}}$ |  |  Life span from the ZAMS to the TAMS
22 | $\sigma_{t/t_{\mathrm{MS}}}$ |  |  Uncertainty in $t/t_{\mathrm{MS}}$
23, 24 |  $\mathrm{SNR_{b}}$, $\mathrm{SNR_{r}}$ |  |  Signal-to-noise ratio for blue and red arms
25, 26 |  $\chi^{2}_{\mathrm{b}}$, $\chi^{2}_{\mathrm{r}}$ |  |  $\chi^{2}$ estimates of the best fit of the blue and red arms

††footnotetext: (Only a portion of this table is shown here to demonstrate its
form and content. This table is available in its entirety in machine-readable
form in the online journal.)

##  5 Conclusions

We have compiled a spectroscopic catalog of stellar parameters for 40,034
early-type stars with $7000\,\mathrm{K}\leq T_{\mathrm{eff}}\leq
14,500\,\mathrm{K}$. The primary selection of the LAMOST DR7 MRS spectra was
carried out by considering the line indices of H$\alpha$ and Mg i b. We used a
synthetic atmospheric model library to build the training set for a data-
driven model to estimate the stellar labels. The precisions of our estimates
are $\sim 75\,\mathrm{K}$, 0.06 dex, 0.05 dex, and $\sim
3.5\,\mathrm{km^{-1}}$ for $T_{\mathrm{eff}}$, $\log g$, [M/H], and $v\sin i$,
respectively, for $\mathrm{SNR}>60$.

As the first in a series of papers aimed at exploring stellar rotation, we
have illustrated the large volume of our sample and the capability of MRS
spectra to sample stellar projected rotation velocities as small as a few
$\mathrm{km\,s^{-1}}$. This will help answer fundamental questions regarding
the origins and characteristics of their angular momentum. Note that the
rotation behavior of our sample might be subject to external effects, e.g.
binary and chemically peculiar stars. Cluster members may have a different
rotation distribution compared with the field (Huang & Gies, 2006b; Sun et
al., 2019). These extenuating factors might influence analyses of stellar
rotation. We will address this issue in Paper II, where we discuss our
sample’s statistical properties. Further studies should quantitatively
investigate rotation as a function of stellar mass, age, metallicity, etc.
Finally, a better theoretical characterization of the angular momentum of
early-type stars in our sample would be beneficial to better understand how to
recover the rotation distribution.

L. D. acknowledges research support from the National Natural Science
Foundation of China through grants 11633005, 11473037, and U1631102. The
Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic
Telescope; LAMOST) is a National Major Scientific Project built by the Chinese
Academy of Sciences. Funding for the project has been provided by the National
Development and Reform Commission. LAMOST is operated and managed by the
National Astronomical Observatories, Chinese Academy of Sciences. This work
has made use of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC;
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

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