# Stellar Parameters and Chemical Abundances Estimated from LAMOST-ii@ DR8 MRS
based on Cycle-StarNet

Rui Wang Key Laboratory of Optical Astronomy, National Astronomical
Observatories, Chinese Academy of Sciences, Beijing 100012, China  A-Li Luo
Key Laboratory of Optical Astronomy, National Astronomical Observatories,
Chinese Academy of Sciences, Beijing 100012, China  University of Chinese
Academy of Sciences, Beijing 100049, China  Shuo Zhang Department of
Astronomy, Peking University, Beijing 100871, China  Kavli institute of
Astronomy and Astrophysics, Peking University, Beijing 100871, China  Yuan-Sen
Ting Research School of Astronomy $\&$ Astrophysics, Australian National
University, Cotter Rd, Weston, ACT 2611, Australia  School of Computing,
Australian National University, Acton, ACT 2601, Australia  Teaghan O’Briain
Department of Physics and Astronomy, University of Victoria, Victoria, BC V9E
2E7, Canada  LAMOST MRS Collaboration  Department of Astronomy, Beijing Normal
University, Beijing 100875, China  Key Laboratory of Optical Astronomy,
National Astronomical Observatories, Chinese Academy of Sciences, Beijing
100012, China  Yunnan Observatories, Chinese Academy of Sciences, Kunming
650216, China  Kavli Institute for Astronomy and Astrophysics, Peking
University, Beijing 100871, China  School of Astronomy and Space Science,
Nanjing University, Nanjing 210093, China  Department of Physics, Hebei Normal
University, Shijiazhuang 050024, China  Department of Astronomy and Institute
of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005,
China A-Li Luo<EMAIL_ADDRESS>&<EMAIL_ADDRESS>
###### Abstract

Deriving stellar atmospheric parameters and chemical abundances from stellar
spectra is crucial for understanding the evolution of the Milky Way. By
performing a fitting with MARCS model atmospheric theoretical synthetic
spectra combined with a domain-adaptation method, we estimate the fundamental
stellar parameters (Teff, log g, [Fe/H], $v_{mic}$ and $v_{mac}$) and 11
chemical abundances for 1.38 million FGKM-type stars of the Medium-Resolution
Spectroscopic Survey (MRS) from LAMOST-ii@ DR8. The domain-adaptation method,
cycle-starnet, is employed to reduce the gap between observed and synthetic
spectra, and the L-BFGS algorithm is used to search the best-fit synthetic
spectra. By combining the 2MASS photometric survey data, Gaia EDR3 parallax,
and MIST isochrones, the surface gravities of the stars are constrained after
estimating their bolometric luminosities. The accuracy of Teff, log g, and
$[\text{Fe}/\text{H}]$ can reach 150 K, 0.11 dex and 0.15 dex, evaluated by
the PASTEL catalog, asteroseismic samples, and other spectroscopic surveys.
The precision of these parameters and elemental abundances ([C/Fe], [Na/Fe],
[Mg/Fe], [Si/Fe], [Ca/Fe], [Ti/Fe], [Cr/Fe], [Mn/Fe], [Co/Fe], [Ni/Fe], and
[Cu/Fe]) is assessed by repeated observations and validated by cluster
members. For spectra with signal-to-noise (S/N) ratios greater than 10, the
precision of the three stellar parameters and elemental abundances can achieve
76 K, 0.014 dex, 0.096 dex, and 0.04-0.15 dex. For spectra with S/N ratios
higher than 100, the precision stabilizes at 22 K, 0.006 dex, 0.043 dex, and
0.01-0.06 dex. The full LAMOST MRS stellar properties catalog is available on-
line.

stars: atmospheres – methods: data analysis – techniques: spectroscopic

††software:  Numpy (Oliphant, 2006), Scipy (Jones et al., 2001–), Matplotlib
(Hunter, 2007), Pandas (McKinney, 2011), Astropy (Price-Whelan et al., 2018),
PyTorch (Paszke et al., 2017), iSpec (Blanco-Cuaresma et al., 2014a; Blanco-
Cuaresma, 2019), Apache Spark (Zaharia et al., 2016), Topcat (Taylor, 2005)

##  1 Introduction

The atmospheric parameters and chemical abundances of the stars play a pivotal
role in elucidating their evolutionary stages, and offer valuable information
on revealing the formation history of the Milky Way. Accuracy and precision of
these parameters are important statistical criteria in measurement work, and
improving both of them is always the goal pursued (Jofré et al., 2019). So
far, it is generally considered that high-resolution (R $\geq$ 40,000)
spectroscopy project, such as Gaia-ESO (Gilmore et al., 2012), is suitable for
the observation and measurement tasks of the standard benchmark stars because
their fine spectral characteristics can well constrain theoretical models to
provide accurate star parameters and chemical abundances. However, limited by
the observation condition and exposure time, obtaining a huge collection of
high-quality high-resolution spectra is very expensive. In recent years, Rix
et al. (2016), Ting et al. (2017), Xiang et al. (2019) have shown that stellar
parameters and 10-20 chemical elements (with precisions of 0.01 dex to 0.1
dex) can be extracted from low-resolution (R $\leq$ 6000) high-quality (S/N
$>$ 100) spectra based on data-driven methods, which provide theoretical and
technical support for analysis of low-/medium-resolution (R from 1800 to
20000) spectra of multiple objects spectroscopic survey such as LAMOST (Luo et
al., 2015; Liu et al., 2020), Subaru PFS (Takada et al., 2014), 4MOST (de Jong
et al., 2019). These surveys can greatly expand the distribution range of the
atmospheric parameters and chemical abundances, and reveal the formation
history of the Milky Way by combining astrometric information (Xiang & Rix,
2022).

The spectral fitting techniques are mostly used to derive stellar parameters
by synthesizing the most similar theoretical spectra to transfer theoretical
stellar labels to the observed spectra. The industrial measurement process
often relies on meticulous spectral reduction, accurate theoretical spectral
grids, and efficient fitting algorithms. Besides, the most important materials
are the construction of the model spectra. The choice of theoretical
atmosphere model (1D/LTE or 3D/N-LTE), the atomic and molecular line lists,
the solar abundances composition, isotope ratio, and the parameter sampling
space should be made to produce synthetic spectra according to the source
selection strategies and the characteristics of the observations. The fitting
techniques need to be specially designed based on spectral characteristics.
The theoretical spectra and the observed spectra often show separate
distributions in the high-dimensional flux space, due to the imperfection of
the theoretical spectra and the observed errors caused by the observation
conditions and various instrument effects. O’Briain et al. (2021, 2020)
proposed a method, cycle-starnet, based on domain adaptation to reduce the gap
between the synthetic and the observed spectra, which combines the data
consistency of data-driven methods and the physical interpretability of model-
driven methods.

The data-driven methods promoted cooperation between the international
spectroscopic surveys, which improved the development of the measurement of
the stellar parameters for low- and medium-resolution spectra. Xiang et al.
(2019) estimated the stellar parameters and chemical abundances of 1.6 million
LAMOST low-resolution spectra by transferring APOGEE and GALAH stellar labels.
Wheeler et al. (2020) analyzed millions of the low-resolution spectra to
obtain several chemical elements of 5 channels using the Cannon (Ness et al.,
2015) and revealed the distribution of the Milky Way from the perspective of
chemical kinematics. Xiang et al. (2021a, b) also predicted the atmospheric
parameters and elemental abundances of $\sim$ 100,000 hot stars largely
expanding the temperature range. For cool stars, Li et al. (2021) derived the
atmospheric parameters of LAMOST M stars based on the methods SLAM (Zhang et
al., 2020a). Wang et al. (2020) and Guiglion et al. (2020) demonstrated that
data-driven methods are capable of estimating the stellar parameters and
chemical abundances of the medium-resolution spectra (R $\sim$ 7500) covering
a narrow band such as LAMOST DR7 and RAVE DR6. The data-driven methods learn
the gradient variation between the input fluxes of spectra and the output
stellar labels (or input stellar labels with output fluxes), but sometimes
they learn the correlation that is superficial to the data, not physical.
Besides, the extrapolation results beyond the range of training set parameters
are unreliable (Buder et al., 2021).

LAMOST-ii@ medium-resolution spectroscopic survey (LAMOST-ii@ MRS) is the
advanced project of the LAMOST-i@ low-resolution spectroscopic survey (Luo et
al., 2015). LAMOST MRS survey is expected to advance stellar physical science
research, such as detailed observations of various variable stars (Zong et
al., 2020; Wang et al., 2021), planet host stars (Chen et al., 2021a, b),
emission nebulae (Wu et al., 2021; Zhang et al., 2021; Ren et al., 2021), open
star clusters, young pre-main-sequence stars, etc (see Liu et al. (2020) for
more details). From the sixth Data Release, LAMOST began to release the
medium-resolution (R $\sim$ 7500) spectra by the LAMOST data-process pipeline,
two catalogs of the stellar parameters: one is by the LAMOST stellar
parameters pipeline (LASP; Luo et al., 2015); the other one containing
chemical abundances is by a parallel convolutional neural networks, SPCANet
(Wang et al., 2020). LASP derived the atmospheric parameters (Teff, log g,
[Fe/H]) based on spectral-fitting the interpolation of the empirical spectra
set–ELODIE v3.1 (Prugniel et al., 2007). While it is incapable of measuring
chemical abundances. Several non-physical truncations appear in the density
distribution of the LASP results (in the left-top panel of Fig.4) due to it
using four interpolators of templates in different temperature ranges. The
stellar parameters and chemical abundances by SPCANet (Wang et al., 2020) are
transferred from APOGEE-ASPCAP (García Pérez et al., 2016) catalog based on
the data-driven method. Independent and atmospheric model-based chemical
abundance measurements are essential for LAMOST MRS, not only for the
examination of the previous catalog but also to add physical support for each
element.

In this paper, we aim to analyze the medium-resolution spectra of LAMOST DR8
MRS by domain-adaptation fitting the MARCS atmospheric model theoretical
synthesis spectra. Five stellar parameters (Teff, log g, [Fe/H], $v_{mic}$ and
$v_{mac}$) and eleven chemical elements (C, Na, Mg, Si, Ca, Ti, Cr, Mn, Co, Ni
and Cu) of LAMOST MRS are firstly derived based on the atmospheric model by
cycle-starnet. The main structure of this paper is organized as follows.
Section.2 describes the observations of LAMOST DR8 MRS and the theoretical
spectra generated. Section.3 introduces the method used to match the observed
spectra and the synthetic model spectra. Section.4 shows the results of the
stellar parameters and chemical abundances of LAMOST DR8 MRS, also the
validation and analysis of the results are displayed. The final section is the
summary.

##  2 LAMOST-ii@ DR8 MRS

###  2.1 Observations and Data Reduction

The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) is a
4-meter reflecting Schmidt telescope located at the Xinglong Observatory
(40.4174∘ N, 117.5006∘ E) in Hebei, China. It has been operating normally for
10 years. The Medium-Resolution Spectroscopic survey has been carried out for
5 years so far, and its detection limit is G$\sim$17 mag. The light of sources
passes through 4000 fibers and is dispersed with a resolution of 7500 into two
separate bands (blue arm: 4950-5350 Å and red arm: 6300-6800 Å), and recorded
by 32 charge-coupled devices corresponding to 16 spectrographs. Each non-time-
domain spectrum is combined using multi-exposes (at least three exposures)
spectra for a star. The Tu-Ar arc lamp spectra exposed three times during one
observing night are used in the process of wavelength calibration of MRS
spectra. Unfortunately, no flux calibration process is done in MRS data
reduction, because there are not enough suitable flux standard stars for each
exposed plate (private communication with the LAMOST team).

Figure 1: LAMOST DR8 observations’ footprints. The low-resolution survey (LRS)
is shown in blue and the median-resolution survey (MRS) is in red. Figure 2:
Color-absolute magnitude diagram of the LAMOST DR8 MRS objects color-coded by
number density in log-scale. Here, the magnitude is calculated without
extinction correction. Figure 3: S/N density distributions of the LAMOST DR8
MRS blue (top panel) and red (bottom panel) arms as a function of the Gaia
photometric G magnitude are shown above. the errorbar in red represent S/N of
blue (top panel) and red arms (bottom panel) in different G mag bins, each of
which spans 0.5 magnitude.

LAMOST 8th data release (DR8) published 1,479,127 non-time-domain spectra and
4,559,091 time-domain spectra. The footprints of LAMOST DR8 observations (both
low-resolution and medium-resolution survey) and the color-absolute magnitude
(without extinction correction) diagram of the sources are shown in Fig. 1 and
Fig. 2, respectively. The distributions of the spectral signal-to-noise (S/N)
of LAMOST DR8 MRS blue and red arm spectra as a function of the $Gaia$
photometric $G$ magnitude employed from $Gaia$ DR3 are shown in Fig. 3. Ting
et al. (2017); Zhang et al. (2020b) used theoretical spectra to explore the
variation of star labels accuracy with S/N and found that the stellar labels
suffering large biases for the ”mock” medium-resolution (R=6000/7500) spectra
with S/N lower than 10. Most of the LAMOST MRS spectra with low data quality
as S/N lower than 10 are considered not suitable for deriving stellar
parameters or chemical abundances using spectral fitting methods. So, we
excluded these low-S/N ($\leq$ 10) spectra from our dataset. The radial
velocities of LAMOST MRS spectra are derived by cross-correlating with 2000
Kurucz model templates and calibrated by the RV standard stars, and the
precision of the MRS RVs reaches 1.36 $kms^{-}1$ with signal-to-noise (S/N)
higher than 10 (Wang et al., 2019). For this work, the relative radial
velocities among multiple exposure spectra of one observation were calculated
by self-correlation and corrected during the co-adding process. We separately
pseudo-continuum normalized the blue and red arms of LAMOST MRS spectra by
fitting a 5-order polynomial through multiple iterations and then Doppler-
shifted them to the rest-frame wavelength with their radial velocities
respectively. To get reliable stellar parameters, we need to recognize and
exclude the spectroscopic binary or multi-system spectra. Here, we eye-
recognized a sample of 500 spectra with obvious double or triple lines and a
sample of 1000 spectra of single stars to train a convolutional neural network
(CNN) model to classify the spectroscopic multi-system spectra. The CNN model
can identify target spectra with a test accuracy of 96%. The spectroscopic
binary spectra with double line features will be processed by a light curve-
based binary spectral model to measure their stellar parameters (Chen et al.
accepted).

###  2.2 Stellar Parameters provided by LASP and SPCANet

LAMOST Stellar Pipeline (LASP; Luo et al., 2015) plays a continuous role in
deriving basic stellar parameters of LAMOST MRS spectra based on ULySS package
(Koleva et al., 2009), fitting with the empirical spectral templates–ELODIE v3
(Prugniel et al., 2007). Three basic stellar parameters of 51.32 % non-time-
domain and 11 % time-domain spectra were officially provided. Besides, a
catalog including 3 basic stellar parameters and 13 chemical abundances are
reported employing an updated version of neural networks SPCANet (Wang et al.,
2020) by transferring APOGEE DR16 ASPCAP (Jönsson et al., 2020) stellar
parameters and chemical abundances to LAMOST MRS spectra. Fig. 4 shows the
Kiel -diagram of LASP and SPCANet results of LAMOST DR8 MRS. It can be found
that significant differences exist in the Kiel-diagram by the two different
methods. Artificial structures appear in dwarfs at 7000 K, 4500 K, and 4000 K
and giants at 4000 K in LASP results due to fitting different kinds of
empirical interpolated spectra in different parameter spaces (Luo et al.,
2015). One-to-one comparisons of the stellar parameters also reflect that the
two methods show a dispersion of 196 K and 0.2 dex in the effective
temperature and surface gravity. The Teff by LASP is overestimated for hot
stars compared with SPCANet results. For [Fe/H], two kinds of results show
good agreement for most stars except part of stars with [Fe/H]SPCANET in
[-0.5, 0] dex having a slope greater than 1 component. It should be mentioned
that the results of the label-transfer method suffer from the selection effect
of the training labels from MRS-APOGEE common stars. And, the elemental
abundances predicted by SPCANet are only available for the stars with
effective temperatures between 4000 K and 5000 K, limited by the elements
availability of the training samples.

Figure 4: Density distributions in the Kiel-diagram of LAMOST MRS stellar
parameters by LASP(left-top) and SPCANet (Wang et al., 2020)(right-top).
Comparisons of three stellar parameters between the two methods are shown in
the bottom three panels and the red dotted lines indicate the one-to-one
lines.

##  3 Methods

In order to increase the physical interpretability and get rid of the
disadvantages of the data-driven approach, we use a stellar atmospheric model-
driven method to obtain the stellar parameters and chemical abundances of
LAMOST DR8 MRS. The forward modeling idea is used to obtain an atmospheric
model-based synthetic spectrum to model the observed spectrum, and further
realize the transferring of the stellar parameters and chemical abundances
from the synthetic model to observed spectra. However, due to the imperfection
of the existing stellar atmospheric model, the actual observed conditions
(such as skylight, anthropogenic light pollution), the instability of the
instrument effects, and the errors introduced by the data processing, a gap
exists between the synthetic spectra and the observed spectra (as Fig. 6 up-
left panel shows). Traditionally, the spectral pixels with large flux
differences between synthetic and observed spectra are masked and excluded to
optimize the fitting process, but it would be effective only for the stars
close to the standard stars which are used to evaluate the synthetic spectra.
O’Briain et al. (2021) proposed that the domain adaptation method can
automatically solve this problem based on deep-learning methods.

###  3.1 The theoretical synthetic spectra

Here, we generate the theoretical synthesis spectra of FGKM type stars (Teff:
3500-8000 K) as the theoretical part of the training data sets. We use 1D LTE
MARCS atmosphere models (Gustafsson et al., 2008) and the spectrum synthesis
code Turbo-Spectrum for radiative transfer (Plez, 2012) to calculate the
theoretical spectra. The solar chemical abundances of Grevesse et al. (2007)
are adopted here and the atomic and molecular line lists are from the latest
version of Gaia-ESO survey line lists (Heiter et al., 2015b, 2021). It is
worth mentioning that the line lists are state-of-art covering the visual
bands but it is not perfect for cool stars with temperatures below 4300 K
because of the incompleteness of molecular lines.

Unlike most of the official pipelines, we do not follow a fixed step to get
theoretical spectra on parameter grid points but randomly sample in a convex
hull of the MIST isochrones within an age range of 1-10 Gyr and a metal
abundance range of [-1.5, +0.5] dex, under the 17-dimensional stellar labels
(effective temperature Teff, surface gravity log g, metal abundance [Fe/H],
macroturbulence $v_{mac}$ and microturbulence $v_{mic}$ and 11 elements
[X/Fe]). The purpose of introducing isochrones here is to limit the range of
parameters for the generation of the theoretical spectra, which can cover most
of the parameters space of LAMOST MRS observations, but of course, individual
stars at particular evolutionary stages are lost. We generate 50,000 spectra
with stochastic combinations of stellar labels within the constraint ranges
above, which is a relatively time-consuming task. About 50,000 CPU hours are
spent using a 16-computer distributed cluster armed with a SPARK computing
system (Zaharia et al., 2016).

###  3.2 Reducing the Gap between LAMOST Observations and the theoretical
synthesis spectra

Whether a physical-driven method or a data-driven method, the essence is to
synthesize a spectrum model to fit the observation. The assumption is that the
spectra with the same morphology have the same stellar atmospheric parameters
and chemical abundances, which is the idea of forward modeling (a data model
or a physical model). When using spectral model-fitting technology to derive
stellar parameters, we need to ensure that both the observed spectra and the
model spectra follow the same distribution of the fluxes in the n-dim pixels
space. Recent studies (Bialek et al., 2020; O’Briain et al., 2021) have shown
that the distributions of the theoretical and the observed spectra do not
overlap in the high-dim fluxes space, so-called ”the gap”. The main reason is
that the theoretical model suffers the defects of the internal assumptions of
the physical model and the imperfect line lists, such as the determination of
oscillator strength $log~{}\textrm{gf}$, which can’t perfectly express the
spectral features the observed spectra contained. To deal with these
situations, most researchers adopt the approach by masking the ”bad” pixels of
which the difference between the observed and synthetic spectral fluxes suffer
large extent according to the standard stars (Ting et al., 2019). Bialek et
al. (2020) superimposed simulated Gaussian noise, rotational and radial
velocities, masking disturbed regions, and bad pixels to augment the
theoretical spectra to minimize the synthetic gap with the Gaia-ESO UVES
spectra, which would lead to the loss of much spectral information. However,
the cycle-starnet  (O’Briain et al., 2021, 2020) can handle a variety of
observed effects and noise patterns instead of masking spectral regions and
pixels.

The unsupervised domain adaptation method cycle-starnet  (O’Briain et al.,
2021, 2020) has been shown to reduce the gap between the synthesis spectra and
observed spectra well. The main idea of this method is to map the synthesis
and observed spectra to a feature space through an auto-encoder and to
separate the shared and split features of the synthesis and the observed
spectra by using a Generative Adversarial Network (GAN; Cohen & Giryes, 2022).
Accordingly, the shared features represent the information shared by the
theoretical synthesis spectra with observed spectra; in theory, these should
represent the internal physical properties of the spectra. The split features
mainly express the unique information that the observed domain contains, which
could be the instrumental profiles (e.g., line spread function), errors due to
the data reduction (e.g., pseudo-continuum normalization), or variations that
are not found in the theoretical spectra (e.g. telluric lines from the Earth’s
atmosphere). Not only does Cycle-StarNet separate the shared and split
features in the spectra, but it also accomplishes the task of transferring
them to different domains through cross-combining features. For instance, we
can generate a theoretical synthesis spectrum with the observed pattern of a
given LAMOST MRS observed spectrum by combining the shared features of the
theoretical synthesis spectrum and the split features of the LAMOST MRS
spectrum, then generate the spectral fluxes by decoding the combined features.
Conversely, we can achieve the transfer to the theoretical domain by stripping
the split features from the observed spectra.

To achieve the purpose above, the cycle-starnet is designed with 3 main
components: an auto-encode network of the theoretical domain to map the
synthesis spectra to the feature space, an auto-encode network of the observed
domain to map the observed spectra to the feature space, and a generative
adversarial network to separate the share and split feature space by judging
the cycle- or transfer- generative spectrum. We modified the structure and
hyper-parameters (such as convolution kernel sizes, and the feature space
size) in the original version of cycle-starnet according to the bands and
resolution characteristics of LAMOST MRS, making it adaptable to domain-
transfer learning between LAMOST MRS observed and MARCS atmospheric model
synthetic spectra.

###  3.3 cycle-starnet training and test

To construct the training data set, we first build a theoretical spectrum
generative model (Ting et al., 2019) based on the theoretical synthesis
spectra, which can synthesize theoretical synthesis spectra with any
combination of stellar parameters within a certain range. Then we randomly
select 100,000 LAMOST MRS observed spectra and synthesize 100,000 theoretical
spectra. Each of the spectra sets is divided into three parts: 80,000 samples
for training, 10,000 for validation, and 10,000 for testing cycle-starnet. It
is worth mentioning that the number of theoretical spectra in the training
samples is the same as that of the observed ones, but they are not paired.

We trained cycle-starnet on 500,000 iterations to optimize the weight
parameters of its neuron nodes by minimizing the loss function (as shown in
Fig. 5). The loss function of cycle-starnet is weighted-composed of three
parts: transfer-loss, cycle-loss, and adversarial-loss. The transfer-loss
constrains the chi-square distance between the theoretical synthetic spectrum
and the ”synthetic” spectrum transferred by the observed spectrum, and the
chi-square distance between the observed spectrum and the ”observed” spectrum
transferred by the theoretical synthetic spectrum; the cycle-loss describes
the distances between the spectrum, both the theoretical and the observed, and
the spectrum after two times transfers back to their original domains; the
adversarial loss allows the spectra to achieve unsupervised domain transfer in
different domains. About 10 hours was cost to train the model each time using
an NVIDIA Tesla v100 GPU.

Figure 5: Training losses of the cycle-starnet as a function of epochs. The
loss function of cycle-starnet consist of three parts: transfer-loss
($X_{synth->obs}$, $X_{obs->synth}$), cycle-loss ($X_{synth->synth}$,
$X_{obs->obs}$, $X_{synth->obs->synth}$, $X_{obs->synth->obs}$) and
adversarial-loss($C_{synth}(X_{real})$, $C_{synth}(X_{fake})$,
$C_{obs}(X_{real})$, $X_{obs}(X_{fake})$).

We used 10000 LAMOST MRS spectra and 10000 theoretical synthetic spectra to
test the model. A method, t-distributed stochastic neighbor embedding (t-SNE),
is employed to examine the distributions of the spectral sets before and after
domain transfer, also their features in hidden space (shown in Fig.6). T-SNE
is a statistical method for visualizing high-dimensional data by a non-linear
reduction in a low-dimensional space of two or three dimensions.
4000-dimensional flux spectra can be modeled as two-dimensional points in the
way that similar spectra are modeled by nearby points and dissimilar objects
are modeled by distant points with high probability.

The T-SNE test results show that there is a clear gap between the LAMOST and
synthetic spectra, which is why it is inappropriate to match them directly.
The spectra transferred by the cycle-starnet model make their distributions in
the same domain overlap together, and the shared features of the theoretical
and observed spectra in the hidden space follow the same distribution, which
indicates that the extracted features of the theoretical and observed spectra
during the transfer process are physical-based, not data-based. The cycle-
starnet successfully morphs the synthetic domain to the observed domain, and
effectively reduces the fitting residuals, especially for the cool stars.

Figure 6: T-SNE test pairs of two of 10,000 synthetic spectra $X\\_{synth}$,
10,000 LAMOST MRS observed spectra $X\\_{obs}$, 10,000 $X\\_{synth\\_obs}$
spectra, 10,000 $X_{obs\\_synth}$ in the observed domain (bottom-right panel),
synthetic domain (bottom-left panel) and their shared feature (top-right
panel) mapped into two-dim space by cycle-starnet.

###  3.4 Domain-transfer Spectral Fitting

After finishing the model training, we can search the best-fit synthetic
spectrum for a given observed spectrum either in the synthetic domain (SD) or
the observed domain (OD). The chi-square distance between the original
spectrum and the domain-transferred spectrum is minimized (according to
equations 10 and 11 of the paper O’Briain et al. (2021)) and the corresponding
stellar labels are obtained for the observed spectrum. For LAMOST DR8 MRS
spectra, we process the domain-transfer fitting in both the synthetic and
observed domain by searching the best-fit stellar labels based on the L-BFGS
algorithm which is an iterative method to solve unconstrained nonlinear
optimization problems. The minimized fitting distance in the synthetic domain
is obviously smaller than the one in the observed domain because transferring
the observed spectrum to the theoretical domain is a process of de-noising
while transferring the theoretical spectrum to the observed domain is the
opposite. The whole process is accomplished under the GPU framework and costs
about one week.

###  3.5 Constrain of the surface gravity with the photometric and astrometric
data

The region of LAMOST MRS spectra is not very sensitive to surface gravity
(Zhang et al., 2020b; Wang et al., 2020). So it is difficult to obtain
accurate log g only using spectral information. Fortunately, the Gaia EDR3
provides us with accurate parallaxes for most of LAMOST MRS stars. Combined
with relatively complete photometric data, the surface gravity of LAMOST
objects can be further constrained as follows.

In this work, we employee the Gaia distances (Bailer-Jones et al., 2021) and
Ks magnitudes of 2MASS survey (Skrutskie et al., 2006). The Milky Way 3D dust
map (Green et al., 2019) is used to correct the extinction for the apparent
magnitude. After deriving the absolute magnitude of Ks ($M_{Ks}$) by

$M_{Ks}=K_{s}-5*log(\frac{Distance}{10})-A(K_{s}),$

we calculate the bolometric luminosity of a star by

$log(\frac{L_{\textrm{bol}}}{L_{\textrm{bol},\odot}})=-0.4*(M_{Ks}+BC_{Ks}-M_{bol,\odot}),$

where, $BC_{Ks}$ is the bolometric correction based on Choi et al. (2016),
$M_{bol,\odot}$ is the bolometric absolute magnitude of Sun (we set as
4.7554). Then, the surface gravity can be literally calculated as GALAH DR3
(Buder et al., 2021) by

$log~{}g=log~{}g_{\odot}+log(\frac{M}{M_{\odot}})+4*log(\frac{\textit{T}_{\textrm{eff}}}{\textit{T}_{\textrm{eff},\odot}})-log(\frac{L_{\textrm{bol}}}{L_{\textrm{bol},\odot}}),$

where $M$ is the mass of star, $M_{\odot}$ is the mass of Sun,
$\it{T}_{\textrm{eff}}$ is derived from LAMOST MRS spectrum,
$\textit{T}_{\textrm{eff},\odot}$ is 5777 K, $log~{}g_{\odot}$ is 4.44 dex.
Here, the stellar mass $M$ is the only unknown quantity, we estimate the
stellar mass by interpolating MIST isochrones as given: spectra-derived Teff,
log g, [Fe/H], and distance from Bailer-Jones et al. (2021). Then we can
further calculate the new log g by the above 3 equations, and then update the
stellar mass by interpolating isochrones with the updated log g, iterate the
steps above until the stellar mass converges, and finally get the star mass
$M$.

##  4 Results

Figure 7: Distribution of LAMOST DR8 MRS stellar parameters (Flagquality=0) by
cycle-starnet in Kiel diagram color-coded by [Fe/H] (left panel) and number
density (right panel). The MIST isochrones are superimposed on the left
diagram. The dashed and solid lines represent ages of 1.5 Gyr and 8 Gyr,
respectively. For each age, the color red, yellow, light blue, and blue
represent [Fe/H] of -1.0 dex, -0.5 dex, 0, and +0.5 dex, respectively. Figure
8: Distribution of elemental abundances [X/Fe] estimated by cycle-starnet,
plotting as a function of [Fe/H] for LAMOST DR8 MRS, color-coded by number
density in log-scale.

We derived 5 atmospheric parameters (Teff, log g, $[Fe/H]$, $v_{mac}$,
$v_{mic}$) and 11 chemical abundances of 1.38 million LAMOST DR8 MRS spectra
with S/N $\geq$ 10\. For 64.37% of the spectra, their surface gravities are
revised based on the photometric and astrometric information. The distribution
of the Kiel-diagram color-coded by the metallicity [Fe/H] and number density
is shown in Fig. 7. Our results show good agreement with the MIST isochrones,
and the main sequence and red clumps are evident. The temperature range of our
results is from 3230 K to 8000 K. For stars with temperatures higher than 7500
K and lower than 3600 K, the stellar parameters become less reliable because
of large inconsistency between the observed spectrum and the theoretical
synthetic spectrum in this parameter space, which is reflected by the fitting
$\chi^{2}$ value exceeds 2.5 and the large fitting error ($<$ 0.1) of log g.
Because these stars with few spectral features may be reconsidered as metal-
poor stars by the code. It should be cautious when using the results of these
stars hotter higher than 7500 K.

We derive 11 elemental abundances, including C, Na, 3 alpha elements (Mg, Si,
Ca), and 6 iron-peak elements (Ti, Cr, Mn, Co, Ni, Cu). Although in the
synthesis process of the theoretical spectra we introduced carbon, nitrogen,
and oxygen elements, limited by the resolving power of 7500 and the narrow
band region of LAMOST MRS spectra, it is challenging to obtain accurate
abundances of these three elements, particularly nitrogen and oxygen. We only
keep carbon in the final catalog by constraining its fitting ${\chi}^{2}$ in a
small range (${\chi}^{2}\leq 1.5$). The chemical abundances [X/Fe] as
functions of [Fe/H] are shown in Fig. 8, where [$\alpha$/M] is the mean of
alpha elements. Through the [$\alpha$/M] abundance distribution, we can see
that the structures of the chemical thin disk, thick disk, and halo stars are
revealed and the abundances seem to be underestimated for thick disk and halo
stars. For iron-peak elements, most of them show similar distributions to
previous studies, except that manganese has a larger slope and cobalt has a
larger dispersion, compared to these studies based on different techniques and
particularly spectra that are of much higher quality (Romano et al., 2010;
Battistini & Bensby, 2015; Ernandes et al., 2018). Non-LTE correction for Mn
is necessary (Bergemann & Gehren, 2008), while the theoretical model we used
is the 1D LTE model.

###  4.1 Accuracy Analysis

Accuracy refers to the degree of closeness of the measurements to the ”true”
values of the quantity being measured. The $Gaia$ benchmark stars (Jofré et
al., 2014; Blanco-Cuaresma et al., 2014b; Heiter et al., 2015a; Jofré et al.,
2015; Hawkins et al., 2016) can be used as anchor points for the ”true”
values, which show good consistency. Regrettably, the LAMOST MRS observations
were unable to include Gaia benchmark stars due to their brightness
limitations, and some of these stars are located in the southern sky, beyond
LAMOST’s observable regions. The PASTEL catalog (Soubiran et al., 2010, 2016)
is a common option, which is a comprehensive and regularly updated database of
stellar parameters, such as effective temperature, surface gravity, and
metallicity. These stellar properties are compiled from a wide variety of
sources, including published literature and other catalogs. We employ the
PASTEL catalog to evaluate the accuracy of our stellar parameters in the
following sub-section.4.1.1. Besides, the asteroseismic sample is one of the
best choices to evaluate the accuracy of log g, here we also choose the Kepler
DR25 golden sample (Mathur et al., 2017) and APOKASC catalog (Pinsonneault et
al., 2014, 2018) to analysis our log g in sub-section.4.1.2. In sub-
section.4.1.3, comparison with sources observed by other surveys, covering
different bands with medium/high resolving power, can also reflect the
accuracy among them.

####  4.1.1 Accuracy evaluated by PASTEL catalog

We cross-match our results with the PASTEL catalog (Soubiran et al., 2010,
2016) getting 934 common stars. We excluded 82 suspect binary or multi-system
objects by checking whether two or more sources appear in 5 arcsec view of
their Pan-Starrs or 2MASS photometric images. After subtracting the null
values of the parameters in the PASTEL catalog, the remaining available sample
is 670, 244, 502 for Teff, log g and [Fe/H], respectively. We used the
standard deviation of the weighted bias to measure the accuracy of the Teff,
calculated as follows:

$\displaystyle\sigma_{X,i}=\sqrt{(\sigma_{X_{i,LA}})^{2}+(\sigma_{X_{i,PA}})^{2}},$
$\displaystyle w_{X,i}=\frac{1}{\sigma_{X,i}},$
$\displaystyle\mu_{X,weighted}=\sum_{i}\frac{(X_{i,LA}-X_{i,PA})*w_{X,i}}{\sum
w_{X,i}},$ $\displaystyle
S_{X,weighted}=\sqrt{\frac{1}{N}\sum_{i}(X_{i,LA}-X_{i,PA}-\mu_{X,weighted})^{2}},$

where $X$ represent one of Teff, log g, [Fe/H], $\sigma_{X_{i,LA}}$ is error
of LAMOST, $\sigma_{X_{i,PA}}$ is error of PASTEL, $w_{X,i}$ is the weight of
star i, $\mu_{X,weighted}$ is weighted bias of stellar parameters and
$S_{X,weighted}$ is the standard deviation of the weighted bias.

Fig.9 shows the biases with standard deviations of the differences between our
results and the PASTEL catalog. It can be found that our Teff exists a bias of
-39 $\pm$ 150 K to PASTEL’s measurements, 0.07 $\pm$ 0.17 dex for log g, and
-0.08 $\pm$ 0.15 dex for [Fe/H]. For log g, we used other reference samples to
evaluate, although its accuracy relative to PASTEL is shown in the figure.
Here, we could only perform a statistical analysis of the accuracy of the
overall sample rather than the accuracy of each parameter at different S/N
levels, limited by the number of common stars we have.

Figure 9: Comparisons (top panels) and residuals (bottom panels) of three
stellar parameters (Teff in the left, log g in the middle, and [Fe/H] in the
right) between LAMOST MRS by Cycle-StarNet and PASTEL catalog. Biases and the
corresponding scatters of three are error-weighted and calculated.

####  4.1.2 Accuracy evaluated by the asteroseismic sample

We employ two asteroseismic samples: one is Kepler DR25 (Mathur et al., 2017;
Huber et al., 2014) in which the properties of golden samples contain log g
are measured by asteroseismology; another one is APOKASC catalog (Pinsonneault
et al., 2014, 2018) which report stellar parameters of 6676 evolved stars
joint with APOGEE spectroscopic and Kepler asteroseismic data based on
independent techniques. By cross-matching our sample with these two datasets,
we get 8034 and 4493 common samples respectively. After comparing our results
with the asteroseismic log g samples, we calculate the standard deviation of
the weighted bias as accuracy, shown in Fig. 10. The bias between Kepler
golden sample log g and ours is 0.04 dex with 84% quantile of 0.11 dex and 16%
quantile of -0.11 dex. And for comparison with the APOKASC sample, we get
nearly the same accuracy as the Kepler golden sample. We take 0.11 dex as the
accuracy of our log g. The proportion of giants (93%: log g $\leq 3.8$) in the
MRS-Kepler golden sample is much larger than that of dwarfs (7%: log g $\geq
3.8$), so the accuracy here is more likely to reflect the properties of the
giants, which also directly shown in the comparison of LAMOST MRS-APOKASC
common samples.

Figure 10: Residuals density distribution of log g between LAMOST MRS by
Cycle-StarNet and Kepler DR25 asteroseismic catalog in the top panel. The
bottom panel show that of LAMOST MRS and APOKASC catalog for their common
stars. In each panel, the value of the horizontal lines is 0. Bias is given as
the median of the residuals combined with the 84% quantile and 16% quantile.

####  4.1.3 Accuracy evaluated by other surveys

The development of large-scale spectroscopic surveys has provided us with many
homogeneous spectral data sets. Their respective scientific goals determine
their observed bands, resolving powers, and observation selection. These
respective spectroscopic surveys inevitably adopt different spectral analysis
methods to obtain the stellar atmospheric parameters and chemical compositions
as they can. Here we employ data sets from three spectroscopic surveys (APOGEE
DR16, GALAH DR3, RAVE DR6) to analyze the accuracy of LAMOST MRS stellar
labels results.

Figure 11: Density distribution in Kiel-diagram of LAMOST DR8 MRS by cycle-
starnet, APOGEE (ASPCAP) DR16, GALAH DR3, and RAVE DR6. The color indicate
number densities of spectra in log-scale. Figure 12: Comparison of three
stellar basic parameters between LAMOST DR8 MRS (cycle-starnet) and APOGEE
(ASPCAP) DR16 (top panel), GALAH DR3 (middle panel), and RAVE DR6 (bottom)
survey datasets color-coded by the number density. From left to right, the
panels are for Teff, log g, [Fe/H] respectively. The numbers of the samples,
medians and scatters of the differences of each stellar parameter are marked
in each panel. And the residuals vary with each stellar parameter are shown
below. The dashed lines are the reference lines.

  1. 1.

APOGEE DR16 (Ahumada et al., 2020) published 473,307 median-high resolution (R
$\sim$ 22,500) near-infrared spectra of 437,445 stars observed by APOGEE-north
and APOGEE-south survey. Their stellar parameters and elemental abundances are
derived by fitting the new version of MARCS templates (Jönsson et al., 2020)
and are calibrated based on photometry, astroseismology, and clusters. We
cross-match our results with APOGEE DR16 and get a dataset of 11,842 LAMOST
MRS spectra with APOGEE stellar labels with STARFLAG=0, ASPCAPFLAG=0, and
PARAMFLAG=0 from the ASPCAP catalog, and Flag_Teff=0, Flag_logg=0, and
Flag_[Fe/H]=0 from LAMOST DR8 MRS cycle-starnet catalog.

  2. 2.

GALAH DR3 (Buder et al., 2021) has published 768423 high resolution (R $\sim$
28,000) optical spectra of 342,682 stars with stellar parameters (Teff, log g,
[Fe/H], $v_{mic}$, $v_{broad}$, $v_{rad}$) estimated by the model-driven
Spectroscopy Made Easy (SME) and 1D MARCS model atmosphere. Also, astrometry
from Gaia DR2 and photometry from 2MASS are employed to break the
spectroscopic degeneracies and 30 different elements measured based on
LTE/non-LTE computations. We cross-match our results with GALAH DR3 and get
21,015 LAMOST-ii@ MRS spectra with corresponding stellar parameters after
setting quality flags in both GALAH DR3 and LAMOST DR8 MRS cycle-starnet
catalog.

  3. 3.

RAVE DR6 (Steinmetz et al., 2020a, b) published 518,378 median-resolution (R
$\sim$ 7500) spectra of 451,783 stars with two versions of stellar parameters
derived by pipelines: MADERA (MAtisse and DEgas used in RAVE) and BDASP
(Bayesian Distances Ages and Stellar Parameters). An asteroseismic-based
calibration of stellar atmospheric parameters is used for giants. The
abundance of the elements Fe, Al, and Ni, and an overall [$\alpha$/M] ratio
are determined with the pipeline GAUGUIN. We cross-match our results with RAVE
DR6 and get a set of 833 LAMOST-ii@ MRS spectra with corresponding RAVE DR6
stellar parameters after restricting the quality with the flags in RAVE DR6
and LAMOST DR8 MRS Cycle catalog. Here, we choose the latter version of the
parameters for comparative analysis and do not use RAVE’s chemical element
abundance for analysis.

The number density distributions of four surveys’ datasets in the Kiel-diagram
are shown in Fig.11. For dwarfs, LAMOST MRS shows the same trend as GALAH and
RAVE whose parameters are derived using Gaia parallax and photometric
information, while APOGEE’s dwarfs are different for that ASPCAP uses one
asteroseismic calibration relation for warmer dwarfs and another approximate
calibration based on isochrones for cooler dwarfs (Jönsson et al., 2020). For
giant branches and red clumps (RC), four surveys show similar distributions.

The comparison of three stellar basic parameters between LAMOST MRS and the
other three survey datasets is shown in Fig. 12. In terms of effective
temperature comparison, our results are most consistent with those of APOGEE,
followed by GALAH, and finally RAVE. The scatters of the differences are
contributed by both the error of LAMOST MRS and the comparison data sets. For
log g, the differences between LAMOST MRS gravity and GALAH, RAVE have small
and similar dispersion ($\sim$ 0.1 dex), and the difference with APOGEE is
larger, mainly because the former three all adopt the calibrations based on
Gaia’s parallax. The differences in metallicity between LAMOST MRS and APOGEE,
GALAH are at the same levels, less than RAVE, which shows the advantage of
high-resolution spectroscopy for calculating metal abundances.

Figure 13: Residuals density of elemental abundances between LAMOST DR8 MRS by
cycle-starnet and APOGEE DR16 ASPCAP in left panels and GALAH DR3 in right
panels. The distribution of the residuals is displayed beside. Biases and
scatters of each element are marked in the text. The dashed line is the value
of zero in each panel.

Fig.13 shows the differences of 11 elements between LAMOST MRS and APOGEE
DR16, GALAH DR3 very with [X/Fe]. Overall, the agreements with APOGEE DR16
seem better than GALAH DR3. The differences of $\alpha$ elements show less
than those of [C/Fe], [Na/Fe], [Cr/Fe], [Co/Fe], and [Cu/Fe] which suffer
large scatter and negative correlation trends with the elemental abundances.
Because the blue bands of LAMOST MRS spectra are mainly dominated by Mg-ii@
triplet and the red bands cover most Si lines. For the iron-peak element poor
stars, most weak spectral characteristics in MRS spectra suffering median
resolving power and low S/N make the measurements overestimated.

###  4.2 Precision Analysis

Precision refers to the degree of reproducibility of the measurement results.
Among the sub-projects carried out by LAMOST MRS, the time-domain survey
project is one of the very distinctive projects, many sources of which are
repeatedly observed under different observed conditions. This provides a good
opportunity for us to evaluate the precision of our results. Besides, the
molecular cloud origin of the cluster led to the homogeneous chemical
abundance pattern (De Silva et al., 2006; Carrera & Pancino, 2011; Bovy,
2016), which provides us a strategy to evaluate the precision of our
metallicity and elemental abundances. Here, we analyzed repeated observations
under different observing conditions in sub-section.4.2.1 and studied
elemental abundances in star clusters in sub-section.4.2.2 to assess the
precision of our measurements.

Figure 14: Repeated errors of LAMOST MRS stellar parameters and chemical
abundances derived by cycle-starnet, plotted as a function of S/N. The
1-$\sigma$ values of the errors in each S/N bin are represented by black dots,
and the fitting relationship is shown by a red curve with corresponding
expression text in the upper right corner of each panel. In the top panel, we
show the number of spectra in each S/N bin in light blue hist bars. Except for
the [C/Fe], the number (ratio) of spectra in each S/N bin for other elements
is basically the same as that shown in the top panel.

####  4.2.1 Precision assessed by repeated observations

We calculated the standard deviation of the repeated observation properties as
precisions of stellar parameters and chemical element abundances based on
LAMOST MRS sources repeat observed more than 6 times. Fig14 shows the trend of
precision as a function of S/N and the number of spectra used in each S/N bin.
It can be seen that the precision of the stellar labels decreases with the
increase of the S/N, and tends to be stable after S/N higher than 100. For
effective temperature, surface gravity, and metallicity, their precision is 76
K, 0.014 dex, and 0.096 dex at the S/N level of 10. When the S/N is increased
to 100, the precision level converges at 22 K, 0.006 dex, and 0.043 dex. For
the elemental abundances C, Na, Mg, Si, Ca, Ti, Cr, Mn, Co, Ni, and Cu their
level of precision is 0.05 dex at S/N of 10 and eventually converges at 0.01
dex at S/N of 100. We fit the precision of each stellar parameter by an
exponential relation:

$Err_{\textrm{repeat,x}}=a*e^{-b*S/N}+c,$

where $Err_{\textrm{repeat,x}}$ represents the precision of the stellar label
$x$, the $S/N$ represents the signal-to-noise of the observation, and $a,b,c$
are the fitting coefficients (the values are in the Fig14).

For each observation, the error of the stellar label consists of two parts:
one is the precision predicted by the relation of repeat observations with
S/N; the other one is the fitting error contributed by the spectral fitting
process. The final errors of the stellar parameters and chemical abundances
are calculated following the equation:

$Err_{\textrm{final,x}}=\sqrt{Err_{\textrm{repeat,x}}^{2}+Err_{\textrm{fit,x}}^{2}},$

where $Err_{\textrm{final,x}}$ represents the final error of the stellar label
$x$, $Err_{\textrm{repeat,x}}$ represents the repeated error and
$Err_{\textrm{fit,x}}$ represents the fitting error.

####  4.2.2 Precision validated by open clusters

Figure 15: Distribution of cycle-starnet estimates of nine open clusters in
the Kiel-diagram, color-coded by their metallicities. The MIST isochrones are
drawn based on the cluster’s ages and metallicities provided by Bossini et al.
(2019); Monteiro et al. (2020); Dias et al. (2021) except Stock 2. Figure 16:
Metallicities derived by cycle-starnet from LAMOST DR8 MRS spectra of 9 open
clusters, shown as a function of their effective temperatures. If reported in
the OCCAM survey catalog (Donor et al., 2020), the ranges of the clusters’
metallicities are shown as red shadows, otherwise, blue shadows show the
[Fe/H] ranges from the open clusters catalog (Bossini et al., 2019; Monteiro
et al., 2020; Dias et al., 2021). The means and dispersions are marked using
the corresponding colors. The grey ones represent values calculated by LAMOST
MRS samples in each panel. Figure 17: Residuals between LAMOST MRS elemental
abundances with respect to the reference values of the member stars of 9
clusters (ASCC 16, ASCC 19, ASCC 21, Melotte 20, Melotte 22, NGC 2632, NGC
2682, NGC 6811 and NGC 752), shown as a function of spectral S/N. The blue
horizontal lines is the value of 0 in each panel. The error-bar of mean bias
in S/N bins ([10, 50], [50, 100], [100, 150], [150, 200], [200, )) is shown in
red. 1-$\sigma$ of the residuals represent its precision for each element in
the legend. Figure 18: Same as Fig. 13 but for the elements by cycle-starnet
(this work) and SPCANet (Wang et al., 2020) as a function of elements [X/Fe].
The residual is represent SPECNet - cycle-starnet (this work).

Cantat-Gaudin et al. (2018) made use of Gaia DR2 astrometry and photometry
information and obtained a catalog of the members and properties for 1229
clusters based on an unsupervised membership assignment algorithm. Cantat-
Gaudin & Anders (2020) expanded the number of the clusters to 1481. Bossini et
al. (2019) derived parameters (age, distance modulus, and extinction) for 269
open clusters by applying a Bayesian tool to fit stellar isochrones to Gaia
DR2 photometric data of the members. Monteiro et al. (2020); Dias et al.
(2021) presented a homogeneous catalog of fundamental parameters of 1743 open
clusters in the Milky Way based on Gaia DR2 data. Cross-matching with the
catalog of these open cluster members by a radius of 3 arcsecs, we obtain a
raw sample of 3229 stars. To improve the reliability, we applied two
conditions to the sample:
$4000K<\textit{T}_{\textrm{eff}}<7500~{}K~{}\textrm{and}~{}\textrm{Prob}_{\textrm{member}}>0.75$
(the open clusters members catalog (Cantat-Gaudin & Anders, 2020) provides a
value for each star representing its probability belonging to the identified
cluster). 891 objects are left with available stellar parameters after
removing the eye-checked optical binaries based on their photometric images
(same process as above in the last subsection). For each individual star with
multiple observations, we retained the one with the highest
$\textrm{S/N}_{\textrm{blue}}$ value and removed the rest repeated
observations. 9 clusters with more than 30 members with available measurements
of LAMOST MRS are finally selected, including Melotte 20, Melotte 22, NGC
1039, NGC 2168, NGC 2281, NGC 2682, NGC 752, Stock 2, and Trumpler 2. Totally,
we got 687 samples of open cluster member stars used to derive the precision
of the metallicity.

The effective temperatures and gravities derived by the LAMOST MRS spectra for
the clusters’ members are shown in Fig.15, in which the ages and metallicities
of MIST isochrones are employed from Bossini et al. (2019); Monteiro et al.
(2020); Dias et al. (2021). Our results (Teff, log g, and [Fe/H]) fit the
isochrones with the properties of the literature well except for individual
stars, which can roughly indicate that most of the samples we selected are
members of the target clusters. Their [Fe/H] as a function of Teff are shown
in Fig.16. For Melotte 20, Metlotte 22, NGC 2682, and NGC 752, we adopted the
metallicities and dispersions by OCCAM survey (Donor et al., 2020), and for
the rest five clusters, the values and dispersions of [Fe/H] are provided in
the literatures (Bossini et al., 2019; Monteiro et al., 2020; Dias et al.,
2021) as references. We also calculated the mean metallicity and dispersion of
each cluster based on our results of the member stars. The dispersions are
found to be consistent with the measurements provided by the OCCAM survey
(Donor et al., 2020) and the literature, although biases exist for the zero
points to some clusters, especially for the Trumpler 2 suffering 0.23 dex
bias. For most clusters, their [Fe/H] dispersions are below 0.1 dex.

For each chemical abundance, we used the cluster member stars with LAMOST
elements comparing with the reference values of the clusters by OCCAM survey
(Donor et al., 2020), and took the standard deviations of the weighted biases
(calculation process same as the accuracy of stellar parameters above) as the
precision.

The OCCAM survey (Donor et al., 2020; Myers et al., 2022), based on the data
collected by APOGEE, specifically focuses on analyzing the ages, distances,
reddening, and chemical abundances of stars in open clusters to gain insights
into the formation and evolution of the Milky Way and its stellar populations.
The OCCAM DR17 catalog contains 153 clusters properties based on 26,699 APOGEE
observations. We got 3720 LAMOST MRS spectra (S/N $\geq$ 10) of 52 clusters
from which we selected 9 open clusters (ASCC 16, ASCC 19, ASCC 21, Melotte 20,
Melotte 22, NGC 2632, NGC 2682, NGC 6811 and NGC 752) by filtering the number
of the cluster members observed by LAMOST larger than 50.

The residuals between LAMOST MRS elemental abundances with respect to the
reference values of the members of 9 open clusters are displayed in Fig.17. It
should be noted that the OCCAM DR17 catalog does not provide copper abundance
information, so no copper precision can be provided here. Although plotted
error bars of the residuals in S/N bins in the figure, we did not provide the
precision by clusters at each S/N level because the number of samples averaged
in each S/N bin is insufficient to provide statistically significant values.
Additionally, the precision does not vary significantly as the S/N changes.
Finally, we got the overall precision is 0.05 dex, 0.17 dex, 0.10 dex, 0.06
dex, 0.07 dex, 0.08 dex, 0.08 dex, 0.14 dex, 0.13 dex, and 0.04 dex of
elements (C, Na, Mg, Si, Ca, Ti, Cr, Mn, Co and Ni). The results of LAMOST MRS
show different homogeneity within acceptable dispersion for different
clusters, a large zero-point shift of C, and a large scatter for Na. The
homogeneity illustrates LAMOST MRS data can contribute to the study of
elements in star clusters. We displayed the elemental abundances of several
clusters calculated using LAMOST MRS observations in the APPENDIX.

###  4.3 The Contents of the LAMOST-ii@ MRS Value-added Catalogue

This work provides a catalog of stellar parameters and chemical elements (C,
Na, Mg, Si, Ca, Ti, Cr, Mn, Co, Ni, and Cu) of 1.38 million LAMOST-ii@ MRS
spectra. Although not the first publication of chemical abundances for LAMOST
MRS, it is the first one based on the ab initio atmospheric model and the
first application of Cycle-StarNet to more than 1 million real data sets. The
method incorporates the physical model and data-driven approaches to improve
the shortcomings of the low signal-to-noise ratio of observed spectra and
imperfections of theoretical synthetic spectra in the fitting process. The
catalog is available online and contains information: the identifier for the
corresponding star (starid), LAMOST spectrum identifier ($\rm{medid}$), Gaia
identifier for 69 percent of spectra ($Gaia\\_source\\_id$), coordinate
information (right ascension (RA), declination (Dec)), signal-to-noise of the
spectra (S/N of blue and red arm), effective temperature (Teff), surface
gravity (log g), metallicity [Fe/H], macroturbulence, microturbulence,
elemental abundance ([X/Fe]), their errors and quality flags, and the total
quality flag reported. A description of columns of the catalog is shown in Tab
1 and the full catalog can be accessed online at http://paperdata.china-
vo.org/LAMOST/LAMOST_DR8_MRS_CSN_parameters_abundances.csv.

Table 1: Description of the columns of LAMOST DR8 MRS stellar parameters and chemical abundances catalog. Col. | Name | Description
---|---|---
1 | $\rm{starid}$ | ID for corresponding star based on the R.A. and decl., with the form of “LAMOST Jddmmss ddmmss”
2 | $\rm{medid}$ | LAMOST spectral ID, inform of Date-PlateID-SpectrographID-FiberID-MJM-PiplineVersion
3 | Gaia$\\_{\textrm{source}\\_\textrm{id}}$ | Gaia source id by cross-matching Gaia DR2
4 | RA | Right ascension of J2000 (∘)
5 | Dec | Declination of J2000 (∘)
6 | $\textrm{S/N}\\_\textrm{blue}$ | Signal-to-noise of the blue arm
7 | $\textrm{S/N}\\_\textrm{red}$ | Signal-to-noise of the red arm
8 | $\textit{T}_{\textrm{eff}}$ | Effective temperature (K)
9 | log g | Surface gravity (dex)
10 | [Fe/H] | Metallicity with respect to hydrogen (dex)
11 | $v_{mac}$ | Macroturbulence (km/s)
12 | $v_{mic}$ | Microturbulence (km/s)
13-23 | [X/Fe] | elemental abundance with respect to iron (dex)
24 | Err$\\_\textit{T}_{\textrm{eff}}$ | Error of the $\textit{T}_{\textrm{eff}}$ (K)
25 | Err_logg | Error of the log g (dex)
26 | Err_[Fe/H] | Error of the metallicity (dex)
27 | Err_vmac | Error of the macroturbulence (km/s)
28 | Err_vmic | Error of the microturbulence (km/s)
29-39 | Err_[X/Fe] | Error of the elemental abundance with respect to iron (dex)
40 | Flag$\\_\textit{T}_{\textrm{eff}}$ | Quality flag of the $\textit{T}_{\textrm{eff}}$: 0 for good, while 1 for bad
41 | Flag_logg | Quality flag of the log g: 0 for good, while 1 for bad
42 | Flag_[Fe/H] | Quality flag of the metallicity: 0 for good, while 1 for bad
43 | Flag_vmac | Quality flag of the macroturbulence: 0 for good, while 1 for bad
44 | Flag_vmic | Quality flag of the microturbulence: 0 for good, while 1 for bad
45-55 | Flag_[X/Fe] | Quality flag of the elemental abundance with respect to iron: 0 for good, and 1 for bad
56 | Flag_Quality | Quality flag of the results: 0 for good, 1 for bad spectra, 2 for large fitting k-square value ($\leq$ 1.5),
|  | 3 for without log g calibrated, and 4 for suspected binary or multi-system.

Besides, a comparison of eight elements (C, Mg, Si, Ca, Ti, Cr, Ni, and Cu in
common) with the updated version of the data-driven catalog provided by Wang
et al. (2020) are displayed in Fig. 18. For most stars, the residuals of the
elements (Mg, Si, Ti, Cr, Ni) obtained by two methods are around 0 with
dispersion less than 0.06 dex, while the residuals of C and Ca have different
slopes of trends. For [Cu/Fe], a bias of -0.08 dex exists with a slope when
[Cu/Fe] is higher than 0.2 dex, which also appears in comparison with APOGEE.

##  5 Summary

The traditional measurement of chemical abundances is mainly for high-
resolution spectroscopy. For individual elements, selecting the spectral lines
of the special window to fit the theoretical model or calculating the
equivalent width (EW) of the characteristic lines to derive the element
abundances. It often requires relatively clean absorption line features, which
further require a high resolving power and a high signal-to-noise ratio of a
spectrum. For medium-resolution spectra, the characteristic lines of
individual elements always suffer contamination and blend. The full spectrum
fitting provides the possibility to extract chemical information from the
medium-/low-resolution spectra, although the precision may not be so high and
the accuracy needs to be further calibrated by benchmark stars or clusters.

We derived the fundamental stellar parameters (Teff, log g, [Fe/H], $v_{mic}$
and $v_{mac}$) and 11 chemical abundances ([C/Fe], [Na/Fe], [Mg/Fe], [Si/Fe],
[Ca/Fe], [Ti/Fe], [Cr/Fe], [Mn/Fe], [Co/Fe], [Ni/Fe], and [Cu/Fe]) for 1.38
millions FGKM-type stars of the Medium-Resolution Spectroscopic Survey (MRS)
from LAMOST-ii@ DR8 by fitting MARCS theoretical synthetic spectra. We use a
domain adaptation method to reduce the gap between the observed and synthetic
spectra and realize the measurement of 5 stellar parameters and 11 abundances
simultaneously. The surface gravities of the stars are calibrated after the
bolometric luminosities are estimated based on the 2MASS photometric data and
Gaia parallaxes.

The accuracy of the stellar labels is evaluated by the PASTEL catalog,
asteroseismic log g dataset, and three other spectroscopic surveys (APOGEE
DR16, GALAH DR3, and RAVE DR6). The accuracy can reach 150 K to the PASTEL
catalog for Teff, 0.11 dex to the asteroseismic samples for log g, and 0.15
dex to the PASTEL catalog for [Fe/H]. Our results show consistency to APOGEE,
GALAH, and RAVE with minor biases and different degrees of scatters.

The precision is assessed using repeated observations and validated by open
cluster members. For Teff, log g and [Fe/H], their precision can achieve 76 K,
0.014 dex, and 0.096 dex at the S/N level of 10. When the S/N is increased to
100, the precision level converges at 22 K, 0.006 dex, and 0.043 dex. For the
elemental abundances C, Na, Mg, Si, Ca, Ti, Cr, Mn, Co, Ni, and Cu their
precision is 0.06-0.2 dex at S/N of 10 and eventually converges at 0.01 dex at
S/N of 100. The precision of LAMOST MRS open cluster members are show scatters
of about 0.04-0.10 dex for elements except for Na, Mn, and Co.

A full catalog is provided online at http://paperdata.china-
vo.org/LAMOST/LAMOST_DR8_MRS_CSN_parameters_abundances.csv. In the future, the
age information of LAMOST MRS stars can be derived based on these stellar
atmospheric parameters. Combined with kinematic parameters, we will analyze
the chemical kinematic evolution of the Milky Way in the next work.

We thank the cluster catalog supplied by Dr. W. S. Dias and advices from Dr.
Sven Buder, Dr. Chao Liu, and Dr. Xiao-Ting Fu. This work was funded by the
National Natural Science Foundation of China (Grant No.12103068, 11390371,
11703053, 11973060, 12090044), the National Key R&D Program of China (Grant
No.2019YFA0405102), the Cultivation Project for LAMOST Scientific Payoff and
Research Achievement of CAMS-CAS and the Science Research Grants from the
China Manned Space Project with NO.CMS-CSST-2021-B05. Y.S.T. acknowledges
financial support from the Australian Research Council through DECRA
Fellowship DE220101520. Guoshoujing Telescope (the Large Sky Area Multi-Object
Fiber Spectroscopic Telescope LAMOST) is a National Major Scientific Project
built by the Chinese Academy of Sciences. Funding for the project has been
provided by the National Development and Reform Commission. LAMOST is operated
and managed by the National Astronomical Observatories, Chinese Academy of
Sciences.

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Figure 19: The elemental abundances by cycle-starnetdisplayed by grey points
with errors as a function of Teff of the clusters (Melotte 20, Melotte 22, NGC
2682, NGC 752, NGC 1039, NGC 2168, NGC 2281 and Stock 2), of which has
reference abundances range from the OCCAM DR17 catalog shown in red shadow.

Stellar clusters provide an excellent means to evaluate the precision of
chemical abundance measurements. We utilized nine stellar clusters to evaluate
the precision of chemical abundance measurements in LAMOST MRS spectra (in
Figure. 19). These clusters serve as ideal samples for assessment, as their
member stars share similar ages, compositions, and distances. By comparing the
variations in chemical abundances among stars within these clusters to the
measurement uncertainties, we can gain insights into the precision and
reliability of LAMOST MRS measurements.