# Reliable stellar abundances of individual stars with the MUSE integral-field
spectrograph

Zixian Wang(王梓先),1,2 Michael R. Hayden,1,2 Sanjib Sharma,1,2 Maosheng
Xiang(向茂盛),4 Yuan-Sen Ting(丁源森),5,6,7,8,9 Joss Bland-Hawthorn,1,2,3 Boquan
Chen1,2
1Sydney Institute for Astronomy, School of Physics, A28, The University of
Sydney, NSW, 2006, Australia
2ARC Centre of Excellence for All Sky Astrophysics in Three Dimensions
(ASTRO-3D)
3Miller Professor, Miller Institute, UC Berkeley, Berkeley CA 94720
4Max-Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg,
Germany<EMAIL_ADDRESS>
5Research School of Computer Science, Australian National University, Acton
ACT 2601, Australia
6Research School of Astronomy and Astrophysics, Australian National
University, ACT 2611, Australia
7Institute for Advanced Study, Princeton, NJ 08540, USA
8Department of Astrophysical Sciences, Princeton University, Princeton, NJ
08544, USA
9Observatories of the Carnegie Institution of Washington, 813 Santa Barbara
Street, Pasadena, CA 91101, USA
E-mail: zwan0382<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present a novel approach to deriving stellar labels for stars observed in
MUSE fields making use of data-driven machine learning methods. Taking
advantage of the comparable spectral properties (resolution, wavelength
coverage) of the LAMOST and MUSE instruments, we adopt the Data-Driven Payne
(_DD-Payne_) model used on LAMOST observations and apply it to stars observed
in MUSE fields. Remarkably, in spite of instrumental differences, according to
the cross-validation of 27 LAMOST-MUSE common stars, we are able to determine
stellar labels with precision better than 75K in $T_{\mathrm{eff}}$, 0.15 dex
in $\log g$, and 0.1 dex in abundances of $[\mathrm{Fe/H}]$,
$[\mathrm{Mg/Fe}]$, $[\mathrm{Si/Fe}]$, $[\mathrm{Ti/Fe}]$, $[\mathrm{C/Fe}]$,
$[\mathrm{Ni/Fe}]$ and $[\mathrm{Cr/Fe}]$ for current MUSE observations over a
parameter range of $3800<T_{\mathrm{eff}}{}<7000$ K,
$-1.5<[\mathrm{Fe/H}]{}<0.5$ dex. To date, MUSE has been used to target 13,000
fields across the southern sky since it was first commissioned six years ago
and it is unique in its ability to study dense star fields such as globular
clusters or the Milky Way bulge. Our method will enable the automated
determination of stellar parameters for all stars in these fields.
Additionally, it opens the door for applications to data collected by other
spectrographs having resolution similar to LAMOST. With the upcoming BlueMUSE
and MAVIS, we will gain access to a whole new range of chemical abundances
with higher precision, especially critical s-process elements such as [Y/Fe]
and [Ba/Fe] that provide key age diagnostics for stellar targets.

###### keywords:

Galaxy: abundances - techniques: spectroscopic - Methods: neural network

††pubyear: 2021††pagerange: Reliable stellar abundances of individual stars
with the MUSE integral-field spectrograph–A

##  1 Introduction

The formation and evolution of the Milky Way is one of the outstanding
questions facing astrophysics today. The study of stars and stellar
populations is a pillar of Galactic Archaeology (Freeman & Bland-Hawthorn,
2002), as they contain the chemical imprint of the gas from which they formed
and serve as birth tags. This allows stars to be used as a fossil record to
unravel the history of the Milky Way. During the past decade, traditional
fiber-fed spectrographs employed by most large-scale spectroscopic surveys
like RAVE (Steinmetz et al., 2006), LAMOST (Deng et al., 2012; Zhao et al.,
2012), Gaia-ESO (Gilmore et al., 2012), GALAH (De Silva et al., 2015), and
APOGEE (Majewski et al., 2017) combined with astrometric and photometric
information from Gaia (Gaia Collaboration et al., 2018, 2021) provided
detailed chemodynamics for millions of stars from the solar neighborhood to
even several kilo-parsecs away (Bland-Hawthorn & Gerhard, 2016).

The large volume of spectroscopic observations is posing great challenges for
data analysis, particularly in deriving stellar labels (atmospheric parameters
and chemical abundances) precisely and efficiently from spectra. In the past
few years, with the use of radiation transfer codes (e.g. SME Valenti &
Piskunov 1996, Turbospectrum Alvarez & Plez 1998; Plez 2012, MOOG Sneden et
al. 2012), many model-driven (e.g. _The Payne_ Ting et al. 2019 and _StarNet_
Fabbro et al. 2018; Bialek et al. 2020) and data-driven methods (e.g. _The
Cannon_ Ness et al. 2015 and _Astro-NN_ Leung & Bovy 2019) and models in
between (e.g. _DD-Payne_ Xiang et al. 2019 and _Cycle-StarNet_ O’Briain et al.
2021) have been developed for this purpose. One benefit of the data-driven
approach is it can generate a model from a training set sample, rather than
traditional physics-based approaches using theoretical stellar atmospheres;
this is much easier to do and in general leads to more precise stellar
parameters as it can potentially make use of the full wavelength region of the
spectra.

However, one limitation of the data-driven methods is that some chemical
abundances could be determined by astrophysical correlations in the training
set, instead of physically motivated measurements from spectral features. This
has a non-negligible impact on the precision of some stellar labels,
especially those derived from low-resolution spectra, where many of the
absorption features are blended.

To overcome this issue, Ting et al. 2017; Ting et al. 2018 used the methods
outlined in _The Payne_ (Ting et al., 2019) to build a neural network to
determine stellar labels. They imported a new term in the loss function which
takes into account the similarity of gradient spectra from the data-driven
model and Kurucz model atmospheres (Kurucz, 1970, 1993, 2005), to regularize
the training process and force the model to measure labels from real
absorption features. They verified that more than 10 elements can be extracted
even from the low-resolution spectra as in LAMOST. Based on this approach
(Ting et al., 2017), Xiang et al. 2019 further developed the Data-Driven Payne
(hereafter _DD-Payne_) which used input training labels from the high-
resolution spectroscopic surveys APOGEE (Ting et al., 2019) and GALAH (Buder
et al., 2018) to determine stellar labels for LAMOST DR5 spectra. These
authors found that they could precisely estimate close to 20 stellar labels
for more than 6 million spectra. These studies highlight that if one has a
reliable training set then one can obtain precise elemental abundances even
from low-resolution spectra.

The methods outlined above demonstrate how one can measure stellar labels for
millions of spectra using machine learning approaches. However, all of the
surveys described previously are conducted using fiber-fed spectrographs,
which take spectra by plugging a series of optical fibers onto a plate based
on the positions of stars on the sky. Fibers are typically set to have a
minimum separation (e.g. $30^{\prime\prime}$ for GALAH;
$56-71.5^{\prime\prime}$ for APOGEE; $268.2^{\prime\prime}$ for LAMOST) during
each observation. And each fiber has a typical diameter of $2\sim
3^{\prime\prime}$. This means that these instruments can not observe dense
fields such as cores of globular clusters and the very dense regions of
Galactic bulge, where the separation of stars is less than $1^{\prime\prime}$.
However, stars in these fields also play an essential role in the Galactic
evolution, it is vital to obtain more complete spectroscopic observations in
these regions to unravel the history of the Milky Way.

The Multi-Unit Spectroscopic Explorer (MUSE) (Bacon et al., 2010) on the Very
Large Telescope is an integral field spectrograph, which is regularly used to
observe external galaxies and can be an ideal solution to deal with high
stellar density fields. With the advanced development of image slicer and
spectrometer, MUSE can perform both imaging and spectroscopy simultaneously.
The benefit is that each MUSE spectrum is obtained for a spatial pixel
($0.2^{\prime\prime}\times 0.2^{\prime\prime}$) on the sky rather than the
area of the fiber, so it is not restricted by the fiber size or collision
effects. The data format of MUSE is a 3-D data-cube, with 2D in spatial on the
sky and 1D in wavelength. Combining with the PSF-fitting spectral extraction
software PampelMUSE (Kamann et al., 2013), MUSE becomes the best instrument to
obtain spectra in fields with high stellar density.

There have been several studies on stars in globular clusters using spectra
from MUSE observations (Husser et al., 2016; Kamann et al., 2016). Near the
core of these clusters, more than 6000 spectra (e.g., 47 Tuc at a distance of
4 kpc analyzed by Kamann et al. 2016) can be extracted on average per MUSE
cube (in wide-field mode with a field of view of $1^{\prime}\times
1^{\prime}$). Currently, most studies focused exclusively on kinematics (e.g.
Kamann et al. 2016, 2018; Valenti et al. 2018). Some studies explored specific
spectral region or metallicity (e.g. Göttgens et al. 2019; Husser et al.
2020). However, these spectra contain a wealth of chemical information that
has not yet been fully explored. This is because currently there is no robust
and easy-to-use method to automatically derive chemical abundances for stars
in these fields.

The success of data-driven models in deriving about $20$ abundances from
LAMOST spectra highlights the potential of other low-resolution surveys, for
example MUSE, having wavelength coverage and resolution similar to LAMOST to
also derive abundances. Inspired by this, in this paper, we develop an
approach based on the _DD-Payne_ (Ting et al., 2017; Xiang et al., 2019), to
measure stellar labels from MUSE observations. Using this approach we derive
robust stellar labels, including effective temperature ($T_{\mathrm{eff}}$),
surface gravity ($\log g$), metallicity $[\mathrm{Fe/H}]$ and abundances of
four $\alpha$ elements, $[\mathrm{Mg/Fe}]$, $[\mathrm{Si/Fe}]$,
$[\mathrm{Ca/Fe}]$ and $[\mathrm{Ti/Fe}]$.

In Section 2, we introduce the data-sets used in our analysis and the spectral
extraction method used by us. In Section 3, we outline the procedures used to
measure stellar labels for MUSE spectra. We do two validation tests in Section
4. First, we verify the bias and dispersion of our approach by applying it to
common stars between LAMOST and MUSE. Second, for dense fields, we explore the
$[\mathrm{Fe/H}]$-$[\mathrm{Mg/Fe}]$ distribution of stars towards the bulge
region using MUSE observations and compare it with that obtained from the
high-resolution APOGEE survey. In Section 5, we explore and discuss the
dependence of label precision on magnitude and exposure time. In Section 6, we
discuss the exciting prospects of using MUSE to observe dense stellar fields
in the Milky Way and other galaxies. Finally, a summary of our results and
conclusions is presented in Section 7.

##  2 Data

###  2.1 MUSE

####  2.1.1 Overview

MUSE (the Multi-Unit Spectroscopic Explorer) (Bacon et al., 2010, 2014) is an
optical wide-field integral field spectrograph using the image slicing
technique mounted on the UT4 of the Very Large Telescope at the Paranal
Observatory in Chile. MUSE operates in two spatial modes, the wide-field mode
(WFM) and the narrow-field mode (NFM). The wide-field mode covers a FoV of
$1^{\prime}\times 1^{\prime}$ with $0.2^{\prime\prime}\times
0.2^{\prime\prime}$ spatial bins. The narrow-field mode covers a FoV of
$7.5^{\prime\prime}\times 7.5^{\prime\prime}$ with $0.025^{\prime\prime}\times
0.025^{\prime\prime}$ spatial bins. It operates in two wavelength modes, the
nominal mode covering 4800-9300 $\Angstrom$ and the extended mode covering
4650-9300 $\Angstrom$. It samples the wavelength in 1.25$\Angstrom$ bins at a
spectral resolution of R$\sim$3000\. To date, more than 13000 data-cubes have
been observed by MUSE and they are publicly available via the ESO Science
Portal Website111http://archive.eso.org/scienceportal/home. MUSE is typically
used to conduct studies on external galaxies but it has also been used to
study a wide variety of other things, e.g., exoplanets (Irwin et al., 2018;
Haffert et al., 2019), Galactic regions (Weilbacher et al., 2015; McLeod et
al., 2015) and resolved stellar populations of Globular clusters (Husser et
al., 2016; Kamann et al., 2018).

####  2.1.2 Reductions

The data format of MUSE observations follows the ESO science data product
standard for data-cubes. Each data-cube has three dimensions, two in spatial
and one in spectral. The data processing pipeline transforms the raw CCD-based
data into fully calibrated and corrected data-cubes, which can be directly
used for studies. The transformation processes include bias, dark and flat-
field reduction, wavelength and flux calibration, line spread function and
illumination correction, sky creation, and astrometrically correlation and
multiple exposures combination, which are discussed in detail in Weilbacher et
al. 2012, 2014, 2020. For this study, all the data-cubes we use are published
online and have been processed and calibrated using the MUSE Data Processing
Pipeline222https://www.eso.org/sci/software/pipelines/muse/.

####  2.1.3 Stellar Spectral Extraction

To extract stellar spectra, we use the PampelMUSE package (Kamann et al.,
2013) which was specifically developed for 3D data-cubes in dense fields. It
assumes the data-cube to be a sum of many overlapping PSFs and sky background.
First, a single object is represented by a PSF function such as Moffat and
Gaussian, and assuming parameters in the PSF function change smoothly with
wavelengths. Next, the PSF photometry is employed to fit each star in each
wavelength layer and then all the layers are combined to generate a single
stellar spectrum. One great advantage of this method is that it can de-blend
the spectra of different stars. Therefore, MUSE observations combined with
PampelMUSE become an ideal way to study dense fields.

To get spectra in the field using PampelMUSE, a reference catalog with stellar
positions and magnitude is needed as input. Various reference catalogs can be
used, such as all-sky surveys (e.g. Gaia Gaia Collaboration et al. 2018, 2021,
Sky-Mapper Keller et al. 2007 or HST) or smaller surveys for specific
purposes. In this study, we mainly use LAMOST DR5 and VVV DR2 (Minniti et al.,
2017) as reference catalogs for the two validation test data, respectively.
Moreover, a transformation function of the filter band is needed when aligning
the MUSE data-cube slice with reference catalogs. Here we refer to the
transformation function from SVO Filter Profile
Service333https://svo.cab.inta-csic.es/main/index.php and use the Moffat
function as the PSF profile, which has better performance than the Gaussian
profile when fitting flux distribution of stars (see Figure 3 in Kamann et al.
2013).

After going through all processes in PampelMUSE, including source position
transformation, PSF fitting, sky background estimation and subtraction, and
unresolved star reduction, the output is a list of stellar spectra which are
identified as resolvable by the algorithm. A few additional cleaning steps
(removal of emission lines and non-stellar features) are performed on the
spectra and will be discussed in Section 4.2.1.

###  2.2 LAMOST

####  2.2.1 Overview

The LAMOST Galactic survey (Deng et al., 2012; Zhao et al., 2012; Liu et al.,
2013; Liu et al., 2015) is the first dedicated spectroscopic survey to obtain
spectra of millions of stars covering most of the sky. LAMOST DR5 has released
more than 8 million stellar spectra covering the optical wavelength regime
3700-9000 $\Angstrom$ with low-resolution R$\sim$1800\. For about 5 million
spectra, LAMOST DR5 also provides the basic stellar labels such as
$T_{\mathrm{eff}}$, $\log g$ and $[\mathrm{Fe/H}]$ which were derived with the
LAMOST stellar parameter pipeline (LASP; Wu et al. 2011; Luo et al. 2015).
There are also several value-added catalogs providing stellar labels with some
chemical abundances and extinction via different methods (e.g., Xiang et al.
2015; Li et al. 2016; Xiang et al. 2017). Despite LAMOST’s low spectral
resolution, Ting et al. 2017; Ting et al. 2018 has verified that $\geq$10
chemical abundances should be derivable with precision on the level of
$0.1\sim 0.2$ dex or better.

####  2.2.2 Data-Driven Payne

Given the success of machine learning and data-driven models in stellar
parameter determination, an effective way to estimate stellar labels from MUSE
spectra would be to develop a data-driven model for the MUSE spectra based on
stellar labels from other high-resolution spectroscopic surveys. Presently, we
do not have enough common stars (ideally $\sim 10^{4}$) covering a wide range
in the parameter space between MUSE and other surveys for a robust training
set. However, with LAMOST spectra having similar resolution and wavelength
range as MUSE (see Table 1), we can apply a model developed for LAMOST to MUSE
spectra. Ting et al. 2017; Xiang et al. 2019 (hereafter T17 & X19) had
developed a _DD-Payne_ model for LAMOST, which we discuss below. It was shown
to have good performance and hence we adopted it for our analysis.

_DD-Payne_ utilizes the neural network interpolator and the fitting technique
from _The Payne_ (Ting et al., 2019) combined with physical gradient spectra
from Kurucz spectral model (Kurucz, 1970, 1993, 2005) to regularize the
training process. This model can derive stellar labels of $T_{\mathrm{eff}}$,
$\log g$, micro-turbulence velocity ($V_{\rm mic}$) and 16 reliable chemical
abundances. Compared with other similar models (Ho et al. 2017; Wheeler et al.
2020), the biggest advantage of _DD-Payne_ is it can enforce these stellar
labels to be measured physically from the spectral features. For
$\rm{SNR}_{\rm{LAMOST}}^{\rm{g-band}}>50$ $\text{pix}^{-1}$, the typical
theoretical precision of the _DD-Payne_ abundances is $\sim$0.05 dex for Fe,
Mg, Ca, Ti, Cr and Ni, $\sim$0.1 dex for C, N, O, Na, Al, Si, Mn, and Co. This
study demonstrates that while obtaining reliable elemental abundances remains
challenging for low-resolution spectra, precise abundances are still derivable
for spectra with SNR$\sim$50 $\text{pix}^{-1}$.

Table 1: Comparison of MUSE and LAMOST survey. Survey | Wavelength range ($\Angstrom$) | Resolution
---|---|---
MUSE | 4750-9300 | R$\sim$3000
LAMOST | 3700-9000 | R$\sim$1800

###  2.3 Validation data and the motivations

We do two different validation tests. Since the model used by us is designed
for LAMOST spectra, the question is how precisely does it work when applied to
MUSE spectra? Therefore, for the first validation test, we run the model on
both the LAMOST spectra and the MUSE spectra of the same star and compare the
results. We cross-matched the LAMOST DR5 catalog from
X19444http://dr5.lamost.org/doc/vac with all the MUSE observations so far
published on the ESO website, and found 79 stars across 162 MUSE data-cubes.

Figure 1:  Distribution of 9 fields observed by MUSE (0101.B-0381(A), PI:
Zoccali) in the Galactic coordinate with the background taken by DSS2. The
nine square fields are marked in cyan and are divided into three areas. The
purple cross in the middle represents the Galactic center where $(l,b)=(0,0)$.
On the right-hand side are zoomed-in figures of these three areas guided by
yellow arrows. The white light picture of the MUSE data-cube is shown in each
square field.

The second validation is done by comparing the abundance distribution of stars
in the inner Galaxy (bulge region) with those obtained from the high-
resolution APOGEE survey. The Galactic bulge region has a very high stellar
density and its stars suffer from strong extinction. Hence, validation of
bulge stars is important to test the performance of our method in challenging
conditions. Therefore, for the second test, we selected 29 data-cubes
(0101.B-0381(A), PI: Zoccali) covering nine fields that are less than 3
degrees to the Galactic center. They are dense fields and provide a large
sample of stars for which to verify our spectroscopic abundances. Figure 1
shows the distribution of 9 fields in the Galactic coordinate with the
background taken by DSS2. The nine square fields are marked in cyan and are
divided into three areas. The purple cross in the middle represents the
Galactic center where $(l,b)=(0,0)$. On the right-hand side are zoom-in
figures of these three areas guided by yellow arrows. The white light picture
of the MUSE data-cube is shown in each square field. For each cube field,
there are three or four repetitive exposures. Galactic bulge fields present
some unique challenges and need some additional reprocessing, such as low SNR
wavelength cut-off, emission line masking, etc, which will be discussed in
detail in Section 4.2.1.

##  3 Methods

The feasibility of applying the _DD-Payne_ on MUSE observations is due to the
similar wavelength range and spectral resolution of the MUSE and LAMOST
spectrographs. The processes of deriving stellar labels from MUSE observations
include five steps:

  * •

Stellar spectra are extracted from MUSE data-cubes by running the automatic
spectra extraction algorithm PampelMUSE (Kamann et al., 2013) to obtain
spectra at R$\sim$3000\. This step was talked about in Section 2.1.3.

  * •

The R$\sim$3000 MUSE spectra are degraded by using the line spread function
(LSF) of these two instruments to R$\sim$1800.

  * •

The spectra are normalized by a pseudo-continuum derived in the same way as in
T17 & X19, to make it compatible with the LAMOST _DD-Payne_ model.

  * •

The degraded and normalized spectra are then fitted by three _DD-Payne_ models
of X19 to derive stellar labels.

  * •

For each label, the cross-correlation of gradient spectra between _DD-Payne_
and Kurucz spectral model (Kurucz, 1970, 1993, 2005) are calculated to check
if the label is estimated from real physical features rather than
astrophysical correlations.

  * •

All the stellar information is generated and combined to create an output
catalog.

The detailed process of each step and the calculating procedure is described
in the following sub-sections.

###  3.1 Degrading and normalizing the MUSE spectra

To make _DD-Payne_ executable on MUSE spectra, we need to make the MUSE
spectra as similar to LAMOST spectra in its wavelength grid and spectral
resolution as possible, which leads to the process of degrading and
interpolating MUSE spectra. This is the procedure that determines whether we
can derive precise stellar labels from MUSE spectra successfully.

To minimize the difference between LAMOST and MUSE, we employ the line spread
function (LSF) of both instruments from X19 and Bacon et al. 2017. The line
spread function is FWHM in each wavelength grid. The process of degrading is
performed by Gaussian kernel smoothing over the whole wavelength with
$\sigma\mathrm{(\lambda_{i})}$, which is calculated from the equation given by

$\sigma\mathrm{(\lambda_{i})}=\sqrt{\left(\frac{\mathrm{FWHM_{L}(\lambda_{i})}}{2.355}\right)^{2}-\left(\frac{\mathrm{FWHM_{M}(\lambda_{i})}}{2.355}\right)^{2}},$
(1)

where $\mathrm{FWHM_{L}(\lambda_{i})}$ and $\mathrm{FWHM_{M}(\lambda_{i})}$
are the LAMOST and MUSE line-spread function, respectively. After degrading,
the spectra will be normalized by a pseudo-continuum which is derived by
smoothing the spectra with a Gaussian kernel of 50$\Angstrom$ in width, which
is the same method employed by T17 & X19 for _DD-Payne_ training set spectra
normalization. This is also an important procedure to ensure the similarity
between these two sets of spectra.

Figure 2 shows the normalized spectra of one single star observed by both
LAMOST (in orange) and MUSE (in blue) and their residuals. The MUSE spectra
were degraded using the above method. The gray areas are the masked areas due
to telluric lines and other interference in the LAMOST wavelength grid, which
will not be processed by _DD-Payne_. This figure demonstrates that for the
same star, the difference between the LAMOST and the MUSE spectra is less than
0.03 even in regions with strong absorption lines. This is encouraging and is
essential for reliably estimating chemical abundances. For the LAMOST-MUSE
cross-validation data-cubes, the spectral SNR $\text{pix}^{-1}$ is in general
higher than 200, which is much more than the average SNR of spectra in LAMOST
($\sim$40). After degrading (binning), the SNR is expected to increase even
further.

###  3.2 Estimating stellar labels and errors

Figure 2:  Comparison of LAMOST spectra (in yellow) with MUSE spectra (in
blue) of the same star. The MUSE spectra have been degraded to the same
resolution. Then both spectra were normalized in the same way as X19 with a
pseudo-continuum derived by smoothing the spectra with a Gaussian kernel of
50$\Angstrom$ in width. Gray areas are the masked pixels (due to telluric
lines and other sources of interference) which will not be used when fitting
with _DD-Payne_. The bottom plot shows the residuals of these two spectra.
From the residuals, we can see that LAMOST spectra and MUSE spectra are
similar with residuals less than 0.03. The blue shaded area represents the
uncertainty of the residual, which is calculated using the flux error of the
LAMOST and MUSE spectra. The flux error of MUSE spectra is re-estimated by
multiplying $\sigma$ in the distribution of flux residuals of the fitting
divided by the flux error, see the right panel of Figure 3

.

Figure 3:  Comparison of MUSE spectra (in black) with model predicted spectra
(in red) from _DD-Payne-G_ on the same star as Figure 2. The left bottom plot
shows their residuals. The masked regions in grey in Figure 2 are not shown in
this plot. From the residuals we can see the difference between MUSE spectra
and predicted spectra is small, with the residuals less than 0.03 even in
absorption regions, demonstrating that _DD-Payne_ training models can fit the
MUSE spectra very well. The right panel shows the distribution of flux
residuals divided by the flux error. A Gaussian fit to the distribution yields
a standard deviation of 3.75, which demonstrates the underestimation of flux
error of MUSE spectra.

After degrading and normalizing the MUSE spectra to the LAMOST wavelength grid
and spectral resolution, the next step is to estimate the stellar labels using
the _DD-Payne_ models. There are three models (so-called _DD-Payne-G_ , _DD-
Payne-A_ and _DD-Payne-A-mp_ below) trained by X19 with different training
sets. The _DD-Payne-G_ model used spectra from LAMOST
($\rm{SNR}_{\rm{LAMOST}}^{\rm{g-band}}>50$ $\text{pix}^{-1}$ and
$\rm{SNR}_{\rm{LAMOST}}^{\rm{g-band}}>30$ $\text{pix}^{-1}$ for stars with
$[\mathrm{Fe/H}]{}<-0.6$) and stellar labels from GALAH DR2 (Buder et al.,
2018) while the _DD-Payne-A_ model adopted LAMOST spectra
($\rm{SNR}_{\rm{LAMOST}}^{\rm{g-band}}>50$ $\text{pix}^{-1}$) and stellar
labels from APOGEE-_Payne_ (Ting et al., 2019) for their respective cross-
matched common samples. The _DD-Payne-G_ derives stellar labels for
$T_{\mathrm{eff}}$, $\log g$, $[\mathrm{Fe/H}]$ and abundance ratios [X/Fe]
for 20 elements: Li, C, O, Na, Mg, Al, Si, Ca, Ti, V, Cr, Mn, Co, Ni, Cu, Zn,
Y, Ba, and Eu. _DD-Payne-A_ derive stellar labels of $T_{\mathrm{eff}}$, $\log
g$, micro-turbulence velocity ($V_{\mathrm{mic}}$), $[\mathrm{Fe/H}]$ and
abundance ratios for 15 elements: C, N, O, Na, Mg, Al, Si, Ca, Ti, Cr, Mn, Co,
Ni, Cu, and Ba. Since X19 described these models in great detail, we direct
the readers to this paper for more information about the selection criteria,
validation and comparisons of the performances of different models. However,
we plot the parameter ranges of these training sets in $T_{\mathrm{eff}}$,
$\log g$ and $[\mathrm{Fe/H}]$ in Figure 4 as square markers for later
comparison with the validation data in Section 4.1. In this work, we run all
these models to test their performances because behind the training sets are
GALAH and APOGEE spectra, which have different wavelength regions. The use of
all these models will build a complete set of elements and also test the non-
negligible systematics among the high-resolution surveys’ labels. In addition,
for some overlapped elements, we also compare their bias and dispersion, which
can provide a flexible choice of models for the users in the future. Based on
results from Figure 2 in X19, Li, Sc, V, Zn, Y, Eu were removed due to the
weak correlations of the gradients, and will not be considered in this study.

The process of applying the _DD-Payne_ to MUSE spectra is as follows: After
loading the _DD-Payne_ models, same as X19, several wavelength regions are
masked including areas with telluric bands, the very red wavelength region
($>8750\Angstrom$), and a region overlapped by the dichroic
$(5720-6060\Angstrom)$ where the LAMOST spectral performance is low (Xiang et
al., 2015). Each MUSE spectra is then fitted with both the _DD-Payne-G_ and
_DD-Payne-A_ model. Following the procedure outlined in X19, we also run an
additional model for stars being identified as metal-poor in _DD-Payne-A_
($[\mathrm{Fe/H}]{}<-0.6$) to improve the precision for metal-poor stars. This
_DD-Payne_ APOGEE metal-poor model (_DD-Payne-A-mp_) is trained by X19 based
on common metal-poor stars in APOGEE-_Payne_ and LAMOST DR5. For stars with
$[\mathrm{Fe/H}]{}<-1.0$ dex, only labels from _DD-Payne-A-mp_ model are
adopted. For stars with metallicity in $-1.0<[\mathrm{Fe/H}]{}<-0.6$ dex, we
take the weighted mean value of results from _DD-Payne-A_ and _DD-Payne-A-mp_
models, with weighting given below by Equation 2. For stars with
$[\mathrm{Fe/H}]{}>-0.6$ dex, we adopt the the _DD-Payne-A_ measurements.

$\begin{split}&\omega_{\rm MP}=([\mathrm{Fe/H}]_{\rm MR}+0.6)/(-0.4),\\\
&\omega_{\rm MR}=1-\omega_{\rm MP},\\\ &\text{[X/Fe]}=\omega_{\rm
MR}\times\text{[X/Fe]}_{\rm MR}+\omega_{\rm MP}\times\text{[X/Fe]}_{\rm
MP}.\end{split}$ (2)

Here MR is the label from _DD-Payne-A_ , and MP is the label from _DD-Payne-A-
mp_ , $\omega$ is the relative weight for each label [X/Fe]. In the following
sections, when we refer to the labels derived from _DD-Payne-A_ we mean this
combined set of results.

In addition, we determine the radial velocity and its error using the Doppler
equation at the same time during the fit, which is the same as _The Payne_
(Ting et al., 2019).

We also determine two values to represent the quality of fitting. One is the
reduced $\chi^{2}$, calculated given by

$\chi^{2}=\frac{1}{n}\sum_{i=1}^{n}\frac{\left(P_{i}-O_{i}\right)^{2}}{e_{i}^{2}},$
(3)

where $n$ is the number of wavelength pixels, $P_{i}$, $O_{i}$ and $e_{i}$ are
the best-fit spectra, observed spectra and the flux error in the $i$-th
wavelength pixel. The other is the Pearson correlation coefficient between the
pixel values of the observed and the best-fit _DD-Payne_ spectra.

Figure 3 illustrates the comparison of observed MUSE spectra (in black) with
the best fit by _DD-Payne_ (in red) for the same star as that in Figure 2. The
residual spectrum is shown in the bottom panel. The difference is less than
0.03 over most of the spectrum, including areas with strong absorption lines.
This demonstrates that _DD-Payne_ training models can reproduce the MUSE
spectra with high fidelity.

###  3.3 Assessing the precision of labels

Even though our best-fit model spectra are quite similar to observed MUSE
spectra, it is not guaranteed that all stellar labels from _DD-Payne_ are
estimated precisely. Many spectral features suffer from blending due to the
low spectral resolution. Since _DD-Payne_ is developed to avoid astrophysical
correlations, the imprecise stellar labels are due to weak or no absorption
features in the fitting wavelength window. When compared to LAMOST spectra,
MUSE loses information in the blue regions $3700-4750\Angstrom$, which
contains absorption features of many elements. Therefore, we cannot expect the
performance of _DD-Payne_ on the MUSE spectra to be as good as that on the
LAMOST spectra, even if MUSE spectra have higher SNR. To check the precision
of estimated stellar labels, we follow T17 & X19’s work, and for each stellar
label, we compare the gradient spectra of _DD-Payne_ with Kurucz spectral
model (Kurucz, 1970, 1993, 2005) and calculate their correlation coefficient.
If a label is physically measured from the spectral absorption features, the
gradient spectra predicted by _DD-Payne_ should be very similar to the Kurucz
spectral model, with a correlation coefficient close to 1. Otherwise, if a
weak or no absorption feature is identified for the label the correlation
coefficient will be very low. Due to the computational expense of calculating
the theoretical model, we use a template of Kurucz model gradient spectra from
X19 (see Table 1) which is calculated based on a list of reference stars
covering a wide range in the parameter space, from -2.5 to 0.5 dex in
$[\mathrm{Fe/H}]$ and 4000 to 7000 K in $T_{\mathrm{eff}}$. Therefore, for
each star, we compare the gradient spectra from _DD-Payne_ with one of the
template spectra having the closest parameter distance to the target star. The
parameter distance is defined by X19 as

$D=\sqrt{\left(\Delta T_{\mathrm{eff}}/100\mathrm{K}\right)^{2}+(\Delta\log
g/0.2)^{2}+(\Delta[\mathrm{Fe/H}]/0.1)^{2}}.$ (4)

Finally, the correlation coefficient of each label will be provided in the
final catalog as well as a flag based on the correlation values to represent
whether the label is precise or not. Here we assign the flag of 1 if the
correlation coefficient is larger than 0.5, otherwise, the flag is set to 0.
In this way, we will know which elements are determined precisely for each
star.

###  3.4 Building the catalog

Table 2: Descriptions of all the column names and information for the DD-Payne stellar label catalog. Column | Desceiption | Unit
---|---|---
stellar-id | Stellar ID of stars | String
ra | Right ascension from the input catalog (or RAJ2000) | deg
dec | Declination from the input catalog (or DEJ2000) | deg
snr-muse | Spectra signal-to-noise ratio calculated by median of all pixels | $\text{pix}^{-1}$
$T_{\mathrm{eff}}$ | Effective temperature | K
$T_{\mathrm{eff}}$-err | Uncertainty in $T_{\mathrm{eff}}$ | K
$T_{\mathrm{eff}}$-flag | Quality for the value based on the examination of the DD-Payne gradient spectra $\partial f_{\mathrm{\lambda}}/\partial T_{\mathrm{eff}}$ |
$T_{\mathrm{eff}}$-gradcorr | Correlation coefficients of $\partial f_{\mathrm{\lambda}}/\partial T_{\mathrm{eff}}$ between the DD–Payne and the Kurucz model |
$\log g$ | Surface gravity | in cgs
$\log g$-err | Uncertainty in $\log g$ | in cgs
$\log g$-flag | Quality for the value based on the examination of the DD-Payne gradient spectra $\partial f_{\mathrm{\lambda}}/\partial\mbox{$\log g$}$ |
$\log g$-gradcorr | Correlation coefficients of $\partial f_{\mathrm{\lambda}}/\partial\mbox{$\log g$}$ between the DD–Payne and the Kurucz model |
Vmic | Micro-turbulent velocity | km s-1
Vmic-err | Uncertainty of micro-turbulent velocity | km s-1
$V_{\mathrm{mic}}$-flag | Quality for the value based on the examination of the DD-Payne gradient spectra $\partial f_{\mathrm{\lambda}}/\partial V_{\mathrm{mic}}$ |
$V_{\mathrm{mic}}$-gradcorr | Correlation coefficients of $\partial f_{\mathrm{\lambda}}/\partial V_{\mathrm{mic}}$ between the DD–Payne and the Kurucz model |
$[\mathrm{Fe/H}]$ | Metallicity | $\,\mathrm{dex}$
$[\mathrm{Fe/H}]$-err | Uncertainty of metallicity | $\,\mathrm{dex}$
$[\mathrm{Fe/H}]$-flag | Quality for the value based on the examination of the DD-Payne gradient spectra $\partial f_{\mathrm{\lambda}}/\partial[\mathrm{Fe/H}]$ |
$[\mathrm{Fe/H}]$-gradcorr | Correlation coefficients of $\partial f_{\mathrm{\lambda}}/\partial[\mathrm{Fe/H}]$ between the DD–Payne and the Kurucz model |
$[\mathrm{X/Fe}]$ | Chemical abundance fraction to iron, sorted by Mg, Si, Ca, Ti | $\,\mathrm{dex}$
$[\mathrm{X/Fe}]$-err | Uncertainty of chemical abundance | $\,\mathrm{dex}$
$[\mathrm{X/Fe}]$-flag | Quality for the value based on the examination of the DD-Payne gradient spectra $\partial f_{\mathrm{\lambda}}/\partial\mathrm{[X/H]}$ |
$[\mathrm{X/Fe}]$-gradcorr | Correlation coefficients of $\partial f_{\mathrm{\lambda}}/\partial\mathrm{[X/H]}$ between the DD–Payne and the Kurucz model |
red-chi2 | Reduced $\chi^{2}$ of the spectral fit (hereafter $\chi^{2}$) |
corr-flux | Correlation coefficient of the muse and best-fitting model spectra |

After deriving two series of stellar labels for each star by applying _DD-
Payne-G_ and _DD-Payne-A_ models and assessing the precision of each label
value, we compile two catalogs. Table 2 presents a description of the columns
in the catalogs. Due to different science goals, wavelength coverage, and data
quality, the relative performances of the two models are different for
different stellar labels. Some elements are estimated better in one model as
compared to the other. In normal circumstances, the version of the label with
a larger gradient spectra correlation coefficient should be selected. In the
following Section 4.1, we discuss in detail the bias and precision of stellar
labels from these training models.

##  4 Results

In Section 3 we gave detailed steps for applying the _DD-Payne_ on MUSE
spectra, measuring their stellar labels and building the _DD-Payne-A_ and _DD-
Payne-G_ catalogs. To test whether our method can measure stellar labels from
MUSE observations with high precision, we now do two validations: First, we
compare the _DD-Payne_ -estimated stellar labels from common stars observed by
both MUSE and LAMOST; Second, we use our method to analyze the
$[\mathrm{Fe/H}]$ and $[\mathrm{Mg/Fe}]$ distributions of stars in the bulge
and compare our results with that of the previous high-resolution
spectroscopic studies. The motivation for each validation has been discussed
in detail in Section 2.3.

###  4.1 Validation 1: LAMOST-MUSE cross-validation samples

Figure 4:  Distributions of the _DD-Payne_ training set (Figure 5 in X19, in
square markers) and LAMOST-MUSE cross-validation samples (in star markers) in
the $T_{\mathrm{eff}}$-$\log g$ plane color-coded by $[\mathrm{Fe/H}]$. Left
panel: Distribution of the _DD-Payne-G_ training stars, the $T_{\mathrm{eff}}$
and $\log g$ are from a corrected version GALAH DR2 values (see Section 3 and
Appendix A of X19) The number of stars for each sample is noted in each
subplot. The LAMOST-MUSE cross-validation samples are selected following the
criteria of Section 4.1 and span reasonable parameter ranges than those from
_DD-Payne_ training sets. No stellar parameter is measured by extrapolation.

We follow the steps described in Section 3 and derive stellar labels of common
stars in LAMOST and MUSE using both _DD-Payne-G_ and _DD-Payne-A_ models. To
ensure the precision of labels, we use the selection criteria given by

$\left\\{\begin{array}[]{l}$$\mathrm{SNR_{\mathrm{LAMOST}}}$${}>35\text{pix}^{-1}(\sim\rm{SNR}_{\rm{LAMOST}}^{\rm{g-band}}>23\text{pix}^{-1})\\\
$$\mathrm{SNR_{\mathrm{MUSE}}}$${}>80\text{pix}^{-1}\\\ \end{array}\right.$
(5)

Here $\mathrm{SNR_{\mathrm{LAMOST}}}$ and $\mathrm{SNR_{\mathrm{MUSE}}}$ is
the median signal-to-noise ratio of the LAMOST and MUSE spectra, respectively.
We made a cut-off of $\mathrm{SNR_{\mathrm{LAMOST}}}$ to ensure the correction
of stellar parameters measured from LAMOST spectra, this threshold is looser
than the criteria of _DD-Payne_ training set
($\rm{SNR}_{\rm{LAMOST}}^{\rm{g-band}}>30$ $\text{pix}^{-1}$) to keep more
common stars. The threshold of $\mathrm{SNR_{\mathrm{MUSE}}}$ cut-off is more
strict than that of $\mathrm{SNR_{\mathrm{LAMOST}}}$ because the SNR of MUSE
spectra is somehow overestimated after data reduction pipeline, which is
confirmed by looking at the spectra of the two validation data and the
distribution of flux residuals of the fitting divided by the flux error (the
right panel of Figure 3). Nevertheless, most MUSE spectra have SNR
$\text{pix}^{-1}$ greater than 200. This is because these observations
typically have long exposure time, as they were targeting external galaxies
which are much fainter than the stars we are interested in. Finally, we end up
with 27 common stars in _DD-Payne-G_ and _DD-Payne-A_ results, during which
the $\chi^{2}$ is mostly concentrated in 4$\sim$25, meaning the
$\mathrm{SNR_{\mathrm{MUSE}}}$ is overestimated by a factor of 2$\sim$5\. Star
markers/diamonds in Figure 4 represent this cross-validation sample. These
stars span a reasonable range of $T_{\mathrm{eff}}$, $\log g$ and
$[\mathrm{Fe/H}]$ than those from _DD-Payne_ training sets. One star is
measured by extrapolation, which will be discussed in Section 4.1.1.

####  4.1.1 Bias and precision check for main labels

Figure 5:  Differences of stellar labels derived from MUSE spectra with those
from LAMOST spectra using _DD-Payne-G_ (left column) and _DD-Payne-A_ (right
column) models as a function of $[\mathrm{Fe/H}]$from MUSE spectra,
respectively. All the stars in these plots have LAMOST spectra with SNR higher
than 35 $\text{pix}^{-1}$. The median and dispersion of all points are marked
in the upper left corner of each panel, the dispersion is calculated as half
of the difference between 15.87 and 84.13 percentile values.

In this section, we focus on $T_{\mathrm{eff}}$, $\log g$ and several chemical
abundances which we reported with confidence in the abstract. Figure 5 shows
the differences of _DD-Payne_ -estimated stellar labels from MUSE and LAMOST
spectra, as a function of $[\mathrm{Fe/H}]$. The median and dispersion of all
points are marked in the upper left corner of each panel, where the dispersion
is calculated as half of the difference between 15.87 and 84.13 percentile
values. The median and dispersion are indicative of the bias $\mu$ and
precision $\sigma$ of our label estimates, respectively. The left and right
panels show results for the _DD-Payne-G_ and _DD-Payne-A_ models,
respectively. This figure demonstrates that the dispersion of
$\Delta$$T_{\mathrm{eff}}$ is about 75K, $\Delta$$\log g$ is around 0.15 dex
for both the _DD-Payne-G_ and _DD-Payne-A_. As for chemical abundances, the
dispersion is less than 0.1 dex in general and we consider this to be precise,
as this is roughly the uncertainty in the LAMOST labels themselves. Therefore,
most of the stellar labels from MUSE spectra and LAMOST spectra are in good
agreement in Figure 5. Even though the dispersion of some elements (e.g.
$[\mathrm{Si/Fe}]$ from _DD-Payne-G_ and $[\mathrm{Cr/Fe}]$ from _DD-Payne-A_)
is slightly higher, it is still close to 0.1 dex. The $\alpha$-elements listed
in this figure are some of the most useful ones as they can be used to
constrain intrinsic stellar properties such as evolutionary stage, distance,
birth radius, extinction, and even age (Ness et al., 2019; Hayden et al.,
2020; Sharma et al., 2022). Therefore, this agreement shows the usefulness of
_DD-Payne_ based estimates from MUSE observations for Galactic studies. The
bias in this figure reflects the differences between LAMOST and MUSE
instruments and the different performances when losing wavelength in
$3700-4750\Angstrom$. However, it can be seen that all of them are smaller
than the dispersion. Therefore, in this work we do not perform the bias
correction on any label. Whether to do it will be re-investigated when we have
a larger sample.

In addition, by comparing the dispersion of the same elements under different
model estimates, we also found that except $[\mathrm{Fe/H}]$,
$[\mathrm{Ti/Fe}]$ and $[\mathrm{Cr/Fe}]$, all the labels calculated using the
_DD-Payne-A_ model have lower dispersion than that from the _DD-Payne-G_
model. The dispersion of $[\mathrm{Mg/Fe}]$ from the _DD-Payne-A_ model is
even less than 0.05 dex. Since we derived labels from the same spectra, the
reason must be the relative performance of the different models. Additionally,
when comparing the derived gradient spectra with Kurucz spectral model for
these labels, _DD-Payne-G_ with lower correlation coefficients, which
indicates _DD-Payne-A_ model has better performance. This is because the
training set of _DD-Payne-A_ is larger than that of _DD-Payne-G_ , so the
measured stellar labels will be more precise.

There is one star in the panel of _DD-Payne-A_ measured by extrapolation since
the $[\mathrm{Fe/H}]$ is less than -1.5 dex, which is shown in the right panel
of Figure 4 as a "diamond". By looking at the parameter differences in each
panel, we can see from Figure 5 that $T_{\mathrm{eff}}$, $\log g$,
$[\mathrm{Fe/H}]$, $[\mathrm{Mg/Fe}]$ and $[\mathrm{Si/Fe}]$ measured from
MUSE spectra of this star have good agreements with those measured from LAMOST
spectra. But for the other parameters, the differences are larger. Note that
the LAMOST spectra of this star was also measured by extrapolation, whether
this indicates anything about extrapolation will be investigated when we have
more stars.

####  4.1.2 Bias and precision check for all labels

Figure 6:  The bias (top panel) and precision (bottom panel) of all stellar
labels derived from _DD-Payne-G_ model, respectively. The bias and precision
are calculated in the same way as Figure 5 by taking the median and half the
difference between 15.87 and 84.13 percentile values. We list all measured
labels and arrange them from small to large according to the precision of the
elements. We also plotted results in the Bulge case which loses pixels between
$(4750-5991\Angstrom)$. From these two plots, for the _DD-Payne-G_ model, Fe,
Mg, Ni, Si are precisely estimated with $\sigma$ close to or better than 0.1
dex when fitting MUSE spectra between both $(4750-8750\Angstrom)$ and
$(5991-8750\Angstrom)$. As for bias, most of the elements are within 0.1 dex
except Co, Mn, Na, and Al.  Figure 7:  The same plot as Figure 6 but now using
_DD-Payne-A_ model. From these two plots, for _DD-Payne-A_ model, Fe, C, Si,
Mg, Ni, and Ca are well estimated with $\sigma$ less than 0.1 dex when fitting
MUSE spectra between both $(4750-8750\Angstrom)$ and $(5991-8750\Angstrom)$.
Besides, MUSE $(5991-8750\Angstrom)$ shows a larger bias and dispersion. As
for bias, most of the elements are within 0.1 dex except Mn, O, N, and Cu.
Comparing with results from _DD-Payne-G_ model, for the same element, _DD-
Payne-A_ model has better precision.

Other than the parameters discussed in the previous section, we also estimated
abundances for additional elements, with 23 stellar labels for _DD-Payne-G_
and 16 labels for _DD-Payne-A_. However, the dispersion for many of the
abundances is not shown as they are much larger than those analyzed in Figure
5. This is because, unlike LAMOST, MUSE does not have any pixels in the
wavelength range $3700-4750\Angstrom$, which contains a large number of
absorption features. In this section, we will further discuss the precision of
these labels and compare them with the results of cross-validation samples
between LAMOST and GALAH or APOGEE.

We perform the same analysis in Figure 5, and derive bias ($\mu$) and the
dispersion ($\sigma$) for all labels in Figure 6 and Figure 7. In each plot
stellar labels from MUSE are determined in two regions:
$\lambda=(4750-8750\Angstrom)$ (in blue) and $\lambda=(5991-8750\Angstrom)$
(in yellow), corresponding to normal spectra and spectra in high extinction
fields such as the Galactic bulge. We also over-plot the dispersion of label
differences between those from LAMOST spectra and GALAH DR2 (Buder et al.,
2018) or APOGEE-_Payne_ (Ting et al., 2019) in red.

For the LAMOST-MUSE cross-validation sample (the blue line), elements such as
Na, Al, O, and Ba in _DD-Payne-G_ model and Mn, Al, O, N, and Cu in _DD-Payne-
A_ have high median and dispersion (larger than 0.1 dex). This can be due to
two reasons. We find that the bias and dispersion of Na, Al, O, and Ba in
cross-validation samples are also high. For these elements, the high
dispersion is the inheritance from the _DD-Payne_ models. However, for Mn and
N, the high dispersion is due to the loss of the blue wavelength region
($3700-4750\Angstrom$) from the MUSE spectra compared to the larger wavelength
region covered by LAMOST. This can be seen in Figure 7, where $\mu$ and
$\sigma$ show a large discrepancy between the LAMOST-GALAH/APOGEE cross-
validation estimates and the LAMOST-MUSE cross-validation estimates. This is
further confirmed by the gradient spectra of these two elements (See Figure 22
in X19), where the dominant absorption features of Mn and N are in
$3700-4750\Angstrom$, which the MUSE spectra are lacking.

In general, for most of the labels in these two figures, the dispersion of the
cross-validation estimates and MUSE estimates are in agreement. Therefore, it
can be verified that the models designed for LAMOST spectra can be applied to
MUSE spectra, and measure some of labels ($T_{\mathrm{eff}}$, $\log g$,
$[\mathrm{Fe/H}]$, [Ni/Fe], [Cr/Fe], [C/Fe] and $\alpha$ abundances) with
similar precision. It is worth noting that there are several elements in these
figures in which MUSE has higher precision than the LAMOST cross-validations,
for example, Fe, Cr, Mg in _DD-Payne-G_ and Mg in _DD-Payne-A_ , this is due
to the small number of stars in the common sample of LAMOST and MUSE.

For the LAMOST-MUSE cross-validation estimates in the wavelength region of
$\lambda=(5991-8750\Angstrom)$ (the yellow line). Both bias and dispersion are
larger than when it is fitted in $4750-8750\Angstrom$ (the blue line). This is
because more absorption features in the region of $4750-5991\Angstrom$ are
lost. Nevertheless, some elements such as $[\mathrm{Fe/H}]$,
$[\mathrm{Mg/Fe}]$, $[\mathrm{Si/Fe}]$ in _DD-Payne-G_ and $[\mathrm{Fe/H}]$,
$[\mathrm{Mg/Fe}]$, $[\mathrm{Ca/Fe}]$, $[\mathrm{C/Fe}]$, $[\mathrm{Ni/Fe}]$,
$[\mathrm{Si/Fe}]$ in _DD-Payne-A_ still have dispersion lower than 0.1 dex.
This indicates that after further losing pixels in the wavelength range of
$4750-5991\Angstrom$ due to high extinction from the bulge, we still can
recover some stellar labels for these fields.

####  4.1.3 Theoretical precision prediction

Figure 8:  Estimation of the theoretical precision for a typical solar-
metallicity K-Giant with a g-band SNR of 50 $\text{pix}^{-1}$ in three
different scenarios. The LAMOST spectra cover the wavelength range between
$3700-8750\Angstrom$. Both MUSE $(4750-8750\Angstrom)$ and MUSE
$(5991-8750\Angstrom)$ have the same resolution as LAMOST. The theoretical
precision is predicted by using the _Chem-I-Calc_ method which is an efficient
method for computing the expected precision of stellar labels determined via
full spectral fitting (Sandford et al., 2020). When losing wavelength pixels
in wavelength $3700-4750\Angstrom$ (LAMOST versus MUSE $(4750-8750\Angstrom)$,
the precision of all the labels is getting slightly worse by an average factor
of 1.17, but there is no label having a large change. When further losing
wavelength pixels in the range of $4750-5991\Angstrom$ (i.e., for MUSE cubes
in high extinction fields), the precision of all the labels is worse by an
average factor of 2.16. However, there are some labels such as Cr, N, Na, and
C which have much larger shifts towards larger uncertainties by a factor of
2.66, 4.30, 4.02, 3.53, respectively due to the loss in wavelength coverage.

In Section 4.1.1 and Section 4.1.2 we discussed the bias and precision of
stellar labels from MUSE spectra in comparison with results from LAMOST
spectra and discussed the influence of losing wavelength pixels in
$3700-4750\Angstrom$ and $4750-5991\Angstrom$. The theoretical precision,
which is the standard deviation of each label X (written as
$\mathrm{X_{-}err}$ in Table 2) as a by-product of _DD-Payne_ , will also be
affected by the changes in wavelength coverage. Since we don’t have enough
LAMOST and MUSE common stars with a given SNR, we use the method _Chem-I-Calc_
(Sandford et al., 2020) to forecast the theoretical precision, which uses _ab
initio_ spectral model and the Cramér-Rao Lower Bound (CRLB) to quantify the
chemical information content of stellar spectra in terms of theoretical
precision. Figure 8 shows the predicted theoretical precision of stellar
labels for a typical solar-metallicity K-Giant with a g-band SNR of 50
$\text{pix}^{-1}$ in three different scenarios. By comparing these scenarios,
we find that when losing wavelength range in $3700-4750\Angstrom$ (cyan versus
blue), the theoretical precision of all the labels is getting slightly worse
by an average factor of 1.17, but there is no label having a large change.
When further losing wavelength pixels in wavelength $4750-5991\Angstrom$ (blue
versus pink), the precision of all the labels is getting worse by an average
factor of 2.16. However, there are some labels such as Cr, N, Na, and C which
have a much greater theoretical precision change with a factor of 2.66, 4.30,
4.02, 3.53, respectively, as we lose critical absorption lines in a more
restricted wavelength range. This is shown in the gradient spectra of these
labels from Figure 22 of X19, where they show that there are no significant
features for these abundances in the remaining wavelength range. Fortunately,
precision of labels like $T_{\mathrm{eff}}$, $\log g$, $[\mathrm{Fe/H}]$, and
some $\alpha$ elements are not significantly affected.

###  4.2 Validation 2: observations towards the Galactic bulge

From the above sections we have shown that we can derive stellar labels
precisely for individual stars in MUSE observations via the utilization of the
_DD-Payne_. Here we want to demonstrate that our method is also useful to
determine stellar labels for stars in dense fields. The Milky Way bulge is one
of the densest regions of the Galaxy. In the past decades, there have been
many fiber-fed spectroscopic surveys focusing on the bulge to study its
chemical distribution such as Gaia-ESO (Gilmore et al., 2012), ARGOS (Ness et
al., 2013), and GIBS survey (Pasquini et al., 2002), which have revealed
multiple stellar components with different mean metallicity. A highlight of
this study is from Rojas-Arriagada et al. 2019 who revealed the bimodality in
$[\mathrm{Mg/Fe}]$-$[\mathrm{Fe/H}]$ distribution using the bulge stars from
APOGEE DR14 (Abolfathi et al., 2018). In terms of the integral-field
spectroscopic survey, Valenti et al. 2018 observed four fields with MUSE
towards the inner bulge and measure radial velocity based on the CaT region of
spectra and reached $\sigma V_{\mathrm{gc}}\sim$ 140 km s-1. They also found
that the velocity dispersion peak is symmetric with respect to the distance
$z$ from the Galactic plane. To summarize previous bulge studies, chemical
element distributions have been studied based on high-resolution fiber-fed
spectroscopic surveys, and kinematics has been studied using IFS data. Since
our method can precisely determine stellar labels from MUSE spectra, this
should enable us to study the chemodynamics of the Milky Way bulge using IFS
data.

####  4.2.1 Data refinement

Figure 9:  The detailed process of spectral processing of one bulge star in
the MUSE data-cube. (a) Original MUSE spectra after degrading which
demonstrates the high extinction in the Galactic center causing almost no flux
in short wavelength. (b) Spectra after normalization, which shows the
extremely high extinction makes the short-wavelength spectra between
$(4750-5991\Angstrom)$ impossible to fit. (c) The predicted spectra and
original MUSE spectra of this star. (d) The residuals of predicted spectra and
the original MUSE spectra.  Figure 10:  H-R diagrams of stars with good
fitting to the model defined by Equation 6. The left-hand side panel is color-
coded with $R_{\mathrm{gc}}$ (distance to the Galactic center) in cylindrical
Galactocentric coordinates, where distance from the Sun to the Galactic Center
is adopted as $R_{\odot}$$=8.2$ kpc, $z_{\odot}=25$ pc (Bland-Hawthorn &
Gerhard, 2016). The right-hand side panel is color-coded with extinction
$A_{V}$. Both $R_{\mathrm{gc}}$ and $A_{V}$ are predicted by BSTEP (Sharma et
al., 2018) taking parameters of $T_{\mathrm{eff}}$, $\log g$,
$[\mathrm{Fe/H}]$, $[\mathrm{Mg/Fe}]$ from DD-Payne and $m_{J}$, $m_{Ks}$,
$m_{H}$ magnitude from VVV DR2.

The bulge data processing begins with the steps outlined in Section 3. The
spectra are extracted from the 29 bulge data-cubes using PampelMUSE with VVV
DR2 (Minniti et al., 2017) as the input photometry catalog. Next, the spectra
are degraded to LAMOST spectral resolution of R$\sim$1800\. Figure 9 shows the
degraded spectra, both raw and normalized, of one bulge star
(VVV-J175141.74-282207.85) extracted from the data-cube.

The bulge stars pose several challenges for data reduction. They have large
heliocentric distances, which means they are typically faint and have low SNR.
These stars also typically lie along lines of sight with high extinction,
making SNR quite low in the shorter wavelength regions. Finally, subtracting
the night sky emission lines from faint stellar spectra is challenging. This
highlights the challenges associated with reducing the spectra in the bulge
region and reinforces the need to adopt additional data refinement procedures.

To remove emission lines, we attempted to apply the Zurich Atmosphere Purge
(ZAP) (Soto et al., 2016), which is an approach based on principal component
analysis (PCA) to reduce emission lines for faint spectra in data-cubes.
However, using ZAP has some undesirable side effects. By adjusting some
tunable parameters in ZAP, we can increase the efficiency of subtracting the
emission lines, but then ZAP has a significant impact on the absorption lines
which are desirable for estimating chemical abundances. Strangely, the spectra
of bright stars were also found to become noisy. In the end, we find the most
effective way to deal with emissions is to replace emission pixels with the
average value of adjacent non-emission pixels In this way, we can retain more
pixels in the spectra.

In addition, due to extinction in the bulge, the flux and hence the SNR in
short-wavelength ranges is not enough to extract useful information (See panel
(a) and (b) in Figure 9). The NaD doublet line $(5803-5966\Angstrom)$ is also
masked in data-cubes that are observed using the adaptive optics module.
Therefore, we decided to discard information for wavelengths less than
$5991\Angstrom$. We also mask the following telluric bands;
$6270-6305\Angstrom$, $6850-6966\Angstrom$, $7160-7320\Angstrom$,
$7585-7715\Angstrom$, $8130-8310\Angstrom$. The widths of the telluric bands
are narrower than those used by X19, this was done to increase the number of
useful wavelength pixels. This range was determined after many tests to ensure
that the unmasked pixels provide useful information about the chemical
elements. Figure 6 and Figure 7 can indicate that when losing pixels in
$4750-5991\Angstrom$, the dispersion of some elements is still below 0.1 dex.
In panel (c) of Figure 9 shows the best-fit model spectra in red, alongside
the original spectra in black. It is clear from the comparison between LAMOST
and MUSE samples presented in Figure 3, that the spectra of bulge stars have
more noise, due to a combination of these stars having higher extinction and
lower average SNR. In addition, the distribution of residuals between the
observed and the best-fit model spectra for a bulge star (Figure 9 panel (d))
is larger than that for the star in Figure 3, which shows the difficulty of
fitting spectra in the bulge fields.

After these refinement and masking steps, stellar labels are derived from two
_DD-Payne_ models. We adopt the labels from the _DD-Payne-A_ model and elect
not to use the _DD-Payne-G_ model to compare directly with high-resolution
APOGEE data which has ample stars in the bulge. Given the loss of precision
due to the omission of the blue wavelength region, we only adopt the
$[\mathrm{Mg/Fe}]$ when studying $\alpha$ abundances for the bulge fields.

Our final MUSE bulge catalog is comprised of 8720 individual spectra
containing 2721 unique stars, with the following columns $T_{\mathrm{eff}}$,
$\log g$, $[\mathrm{Fe/H}]$ and $[\mathrm{Mg/Fe}]$. On average, from each cube
about 300 spectra were extracted and 40% of them have
$\mathrm{SNR_{\mathrm{MUSE}}}$${}>80$ $\text{pix}^{-1}$. Compared with typical
MUSE wavelength coverage, the bulge spectra lose the bluer regions of the
spectrum, between $4750-5991\Angstrom$, so we adopt more strict selection
criteria compared to our LAMOST verification sample with

$\left\\{\begin{array}[]{l}$$\mathrm{SNR_{\mathrm{MUSE}}}$${}>80\text{pix}^{-1}\\\
\rm{corr_{-}flux}>0.85\\\ \end{array}\right.$ (6)

Here the SNRMUSE is the SNR $\text{pix}^{-1}$ in wavelength higher than
$5991\Angstrom$. Since there are multiple spectra for each star, we selected
the observation having the highest corr-flux between the MUSE and model-
predicted spectra, to represent the most physical fitting.

Figure 11:  Top: Spatial distribution in cylindrical Galactocentric
coordinates ($R_{\mathrm{gc}}$,z) of stars observed in three nine bulge
fields. The distance to the Galactic center is adopted as $R_{\odot}$$=8.2$
kpc, $z_{\odot}=25$ pc, same as Figure 10. The red dots are stars with
$R_{\mathrm{gc}}$$<3.5$kpc. Middle: Extinction-$R_{\mathrm{gc}}$ distribution
of all-stars with good fitting to the model defined by Equation 6 in dots
color-coded by absolute J mag. The red curve shows the median value of each
distance bin and the blue fill shows the standard deviation of each bin.
Bottom: Extinction $A_{V}$ as a function of Galactocentric radius $R$ for
various lines of sight from the Sun. The extinction is based on an analytical
model from Sharma et al. 2011 consisting of an exponential disc with warp and
flare; scale length $R_{\rm d}=4.2$ kpc and scale height $0.88$ kpc. From
lines towards the center, we could see that with the larger line of sight
latitude, the extinction will become a constant more quickly, which is in
agreement with the left bottom plot.

####  4.2.2 Distance estimation and its relationship with extinction

To discriminate bulge stars from other foreground stars, we make use of
stellar distance. The distance was estimated by BSTEP (Bayesian stellar labels
estimator) (Sharma et al., 2018), a Bayesian scheme that is used for
predicting stellar ages, distances, and extinction from a set of observables
given by

$\mathbf{y}=\left(l,b,m_{J},m_{Ks},T_{\mathrm{eff}},\log
g,[\mathrm{Fe/H}]_{\rm eff}\right),$ (7)

Briefly speaking, for each star, if we know its position, $T_{\mathrm{eff}}$,
$\log g$, $[\mathrm{Fe/H}]$ and magnitude, its intrinsic parameters such as
distance, age, and extinction can be derived by making use of isochrones
(Sharma, 2017). The isochrones employed in this study are from Bressan et al.
2012. For our catalog, parameters of $T_{\mathrm{eff}}$, $\log g$,
$[\mathrm{Fe/H}]$ are determined by _DD-Payne_. As for $m_{J}$, $m_{Ks}$, they
are derived from VVV DR2 catalog.

Figure 10 shows the H-R diagram of stars with model spectra with good fitting
to the model defined by Equation 6 and color-coded by Galactocentric
cylindrical radial distance $R_{\mathrm{gc}}$ and extinction $A_{V}$. We
identify bulge stars with $R_{\mathrm{gc}}$$<3.5$kpc. The left panel shows
that bulge stars are predominantly giants. The right panel shows that bulge
stars have extinction $A_{V}$ in the range 4-6 mag. Note, there is a selection
bias in the sense that low extinction stars are more likely to be detected. In
fact, extinction towards the Galactic center can be as high as $A_{V}=50$ mag
(Nataf et al., 2016).

In Figure 11 we explore the extinction in more detail. The top panel shows the
$(R_{\mathrm{gc}},z)$ distribution of stars in nine MUSE cubes. The line of
sight of three fields can be seen. Stars with distances beyond the Galactic
center have low temperature ($T_{\mathrm{eff}}{}<4300$ K) and surface gravity
($\mbox{$\log g$}{}<1$), which fall outside of the label ranges for which we
can reliably determine $\alpha$ abundances, so these stars were removed. The
middle panel of Figure 11 shows a scatter plot of extinction and
$R_{\mathrm{gc}}$ color-coded by absolute magnitude in $J$ band. The median
value of extinction is shown by the red line, along with 25 and 75 percentile
dispersion as a shaded blue region. This figure demonstrates that MUSE can
successfully extract bulge giant stars with extinction up to $A_{V}=6$ mag. To
understand the trend of extinction with $R_{\mathrm{gc}}$, in the bottom panel
of Figure 11 we show extinction $A_{V}$ as a function of Galactocentric radius
$R_{\mathrm{gc}}$ for various lines of sight from the Sun as predicted by a
theoretical model in Galaxia (Sharma et al., 2011) consisting of an
exponential disc with warp and flare; scale length $R_{\rm d}=4.2$ kpc and
scale height $0.88$ kpc. It can be seen that if the latitude $|b|$ is greater
than 5 degrees, the extinction first increases as we go towards smaller $R$,
but then flattens and reaches a plateau at distances 1-2 kpc away from the
sun. A similar trend is seen in the observed data in the middle panel. This
flattening is due to the finite height of the dusty disc responsible for the
extinction. For a given line of sight as long as we are in the dusty disc, the
extinction increases with distance, but once we are out of the dusty disc
there is no further increase in extinction. The model qualitatively explains
the trend seen in the observed data, but there are differences. The extinction
for $b=5$ degrees is not high enough compared to our observations. For lower
$|b|$ extinction can be high but the rise with distance is much slower. These
differences suggest that the scale height of the disc in the model is too
high.

####  4.2.3 $[\mathrm{Mg/Fe}]$-$[\mathrm{Fe/H}]$ distribution in the Galactic
bulge

Figure 12:  Distribution of stars satisfying $|z|<0.5$ kpc in the
($[\mathrm{Mg/Fe}]$-$[\mathrm{Fe/H}]$) plane as a function of
$R_{\mathrm{gc}}$, with $R_{\mathrm{gc}}$ increasing from left to right. Top:
The $[\mathrm{Mg/Fe}]$-$[\mathrm{Fe/H}]$ distribution of stars in APOGEE-
_Payne_ (Ting et al., 2019). Bottom: The same distribution of stars in MUSE
data-cubes towards the Galactic bulge with abundances measured by _DD-Payne-A_
model (hereafter MUSE-_DD-Payne-A_). The labels are calibrated by adding an
offset for $[\mathrm{Mg/Fe}]$, which is due the
$[\mathrm{Mg/Fe}]$-$T_{\mathrm{eff}}$ trend inherited from APOGEE-_Payne_ (see
details in Appendix A), respectively. In each panel, the black dots mark stars
in this location and the distribution is smoothed by a Gaussian kernel
function and then used to plot the color maps. For each $R_{\mathrm{gc}}$ bin,
the APOGEE-_Payne_ and MUSE-_DD-Payne-A_ distributions are in agreement with
the densest peak at the same location. This validates the precision of the
MUSE results in dense regions.

We next analyze the abundance distribution of stars towards the bulge. We make
some additional quality selections to guarantee all the stars have precisely
estimated parameters:

$\left\\{\begin{array}[]{l}[\mathrm{Fe/H}]>-1.5\mathrm{dex}\\\
T_{\mathrm{eff}}>4300\mathrm{K}\\\
\mathrm{[\mathrm{Mg/Fe}]{}_{-}gradcorr}>0.65\\\ \chi^{2}<20\\\
\end{array}\right.$ (8)

Here stars with $[\mathrm{Fe/H}]$$<-1.5$ dex and $T_{\mathrm{eff}}$$<4300$K
are removed as it has been demonstrated in X19 that $[\mathrm{Mg/Fe}]$ for
these giants are erroneous with low gradient spectra correlation coefficients
(see their Figure 2). Moreover, we apply a cut in the $\chi^{2}<20$ to remove
stars with poor fittings from _DD-Payne_ according to the $\chi^{2}$
distribution of the LAMOST-MUSE cross-validation sample. The removed stars are
primarily giants with low $T_{\mathrm{eff}}$ ($<4300$ K) and $\log g$ ($<1.5$
dex), which shows low correlation in gradient spectra of _DD-Payne_ (see
Figure 2 of X19). We also limit our analysis to stars with correlation
coefficient gradient spectra for $[\mathrm{Mg/Fe}]$ to larger than 0.65. After
applying all the selection criteria, we end up with 75 stars physically
located in the Galactic bulge.

Panel (a) and (d) of Figure 12 show the $[\mathrm{Mg/Fe}]$-$[\mathrm{Fe/H}]$
distribution of stars in MUSE data-cubes towards the Galactic bulge with
values measured by _DD-Payne-A_ model (hereafter MUSE-_DD-Payne-A_) with
comparison of the same plot using stars from APOGEE-_Payne_ (Ting et al.,
2019). We use the Gaussian kernel estimation and plot the density color map.
The selection criteria of APOGEE stars is the same as that in Rojas-Arriagada
et al. 2019 and the distances were estimated by Santiago et al. 2016.
$[\mathrm{Mg/Fe}]$ in MUSE-_DD-Payne-A_ are calibrated by adding an offset.
This is because there is a non-negligible
$[\mathrm{Mg/Fe}]$-$T_{\mathrm{eff}}$ trend in _DD-Payne-A_ model, which is
inherited from the APOGEE-_Payne_ values in the training set (See Figure 14 in
X19). The average temperature differences between stars in APOGEE-_Payne_ and
MUSE-_DD-Payne-A_ in the bulge will lead to roughly 0.08 dex deviation in
$[\mathrm{Mg/Fe}]$. So we calibrate this deviation here. This trend is beyond
the scope of this study, and more details will be discussed in the Appendix A.
In Figure 12, both panel (a) and (d) demonstrate two sequences of stars in the
bulge: Metal-poor/$\alpha$-rich sequence with center in ($[\mathrm{Mg/Fe}]$,
$[\mathrm{Fe/H}]$) space at $(0.36,-0.43)$ and metal-rich/$\alpha$-poor
sequence at $(0.19,0.18)$. These two centers are in agreement in MUSE-_DD-
Payne-A_ and APOGEE-_Payne_ samples. In addition, the two sequences merge at
$[\mathrm{Fe/H}]$$\sim-0.07$ dex in both panels. All these agreements reassure
and validate the precision of the MUSE results, and the ability of _DD-Payne_
to measure stellar labels in dense fields.

However, The two plots also show differences. The $\alpha$-rich stars in the
MUSE-_DD-Payne-A_ are less dense than those in APOGEE-_Payne_ and the
distribution is also broader. Therefore, the small sample size of MUSE is
certainly a limiting factor in comparing the two panels. Another important
factor that is different in the two panels is the distribution of stars in the
$(R_{\mathrm{gc}},z)$ plane (See the top panel of Figure 11), neither is the
apparent magnitude selection. MUSE data is restricted to 3 lines of sight,
which are all close to the plane.

####  4.2.4 $[\mathrm{Mg/Fe}]$-$[\mathrm{Fe/H}]$ distribution of other regions

In the top panel of Figure 11, we can see that in addition to the bulge stars,
there are many foreground stars observed in these nine fields. We can also
study the $[\mathrm{Mg/Fe}]$-$[\mathrm{Fe/H}]$ distribution of these stars and
compare them with distributions in APOGEE-_Payne_. Here, we select the stars
with $R_{\mathrm{gc}}$ between $3\sim 5$ and $5\sim 7$ kpc, and plot the
$[\mathrm{Mg/Fe}]$-$[\mathrm{Fe/H}]$ distributions in the panel (b), (e), (c),
(f) of Figure 12, respectively. This is similar to Hayden et al. 2015; Sharma
et al. 2021, which used stars in APOGEE DR12 and plotted
$[\mathrm{\alpha/Fe}]$-$[\mathrm{Fe/H}]$ distributions in different Galactic
locations. Here the $[\mathrm{Fe/H}]$ and $[\mathrm{Mg/Fe}]$ values in MUSE-
_DD-Payne-A_ are calibrated for the same reason as before. In this figure, for
the same $R_{\mathrm{gc}}$, the distributions of stars in MUSE-_DD-Payne-A_
and APOGEE-_Payne_ samples are in good agreement, with the centers at the same
($[\mathrm{Mg/Fe}]$, $[\mathrm{Fe/H}]$) locations. All the panels are
dominated by low-$\alpha$ stars, and the overall trends are consistent.
Despite the small number of MUSE stars (52 in panel (e) and 103 in panel (f)),
the good agreement with APOGEE-_Payne_ is once again reassuring and validating
the precision of the MUSE results.

##  5 Estimating exposure times to achieve a given uncertainty

The uncertainty $\sigma_{\rm X}$ of a stellar label $X$ derived with MUSE
using the _DD-Payne_ depends on the signal to noise ratio (SNR hereafter) of
the spectra, which in turn depends on the exposure time $T_{\rm exp}$ and the
magnitude of a star. The brighter the star and longer exposure time, the
higher the SNR and thus the more precise the stellar labels will be.
Therefore, when doing a survey or planning future observations, one should
ensure that the exposure time is long enough to reach the expected
uncertainty. In the next sections, we provide formulas to estimate the
$\sigma_{\rm X}$ as a function of $V$ band magnitude and exposure time, to
provide a reference for future MUSE observations. To do this, we first
estimate the $\sigma_{\rm X}$ as a function of SNR. Next, we estimate the SNR
as a function of magnitude $V$ and $T_{\rm exp}$.

###  5.1 Uncertainty of stellar labels as a function of SNR

Figure 13:  Prediction of precision of stellar labels as a function of SNR. It is derived by estimating the theoretical precision using _Chem-I-Calc_ from typical K-giant spectra from MUSE Exposure Time Calculator in different SNRs. Then a factor is applied to transfer the theoretical precision to real precision for each label which is calculated by Equation 10. Table 3: Parameters for the equation 11 of uncertainty as a function of SNR. stellar label | $A_{X}$ | $B_{X}$ | stellar label | $A_{X}$ | $B_{X}$
---|---|---|---|---|---
$T_{\mathrm{eff}}$ | -0.9875 | 1.652 | $[\mathrm{Ca/Fe}]$ | -0.9834 | 0.868
$\log g$ | -0.9922 | 1.052 | $[\mathrm{Ti/Fe}]$ | -0.991 | 0.856
$[\mathrm{Fe/H}]$ | -0.9746 | 0.5823 | $[\mathrm{C/Fe}]$ | -0.9891 | 0.5737
$[\mathrm{Mg/Fe}]$ | -0.9862 | 0.4486 | $[\mathrm{Ni/Fe}]$ | -0.9925 | 0.8681
$[\mathrm{Si/Fe}]$ | -0.9886 | 0.7546 | $[\mathrm{Cr/Fe}]$ | -0.9835 | 0.7855

Figure 13 shows the uncertainty $\sigma_{X}$ of a stellar label $X$ as a
function of SNR. We firstly derive theoretical uncertainty $\sigma_{X,{\rm
Theoretical}}$ using _Chem-I-Calc_ (Sandford et al., 2020) from a typical
K-giant spectra. SNR is estimated from MUSE Exposure Time
Calculator555https://www.eso.org/observing/etc/bin/gen/form?INS.NAME=MUSE+INS.MODE=swspectr.
The air-mass and seeing are set as 1.5 and $0.8^{\prime\prime}$. Then
$\sigma_{X}$ is calculated by

$\sigma_{X}=\sigma_{X,{\rm Theoretical}}({\rm SNR})f_{X,{\rm corr}},$ (9)

where $f_{X,\rm corr}$ is the scale factor applied to transform the
theoretical uncertainty to the observed uncertainty for each label $X$. The
factor is calculated from MUSE repeat observations by computing the dispersion
of pairwise differences as follows.

$f_{X,\rm corr}=\text{std-dev}\left(\frac{X_{m}-X_{n}}{\sigma^{2}_{X,{\rm
Theoretical},m}+\sigma^{2}_{X,{\rm Theoretical},n}}\right),$ (10)

where $m$ and $n$ represent the repeated observations of a star.
$\sigma_{X,{\rm Theoretical}}$ is the theoretical uncertainty of a spectra as
given by _Chem-I-Calc_. Comparing with the error from _DD-Payne_ , _Chem-I-
Calc_ estimates are normally 1.5 times smaller (see Fig. 21 in Sandford et al.
2020), so we multiply this factor. Then $\sigma_{X,{\rm Theoretical}}$
mentioned in this section means the theoretical uncertainty of multiplying
1.5. Figure 13 indicates that the uncertainty will decrease as the SNR
increases. Generally, $[\mathrm{Mg/Fe}]$ has the lowest uncertainty with
$\sigma_{[\mathrm{Fe/H}]}<0.1$ dex for SNR higher than 29.44
$\text{pix}^{-1}$. As for other elements, to make the uncertainty less than
0.1 dex, the SNR needs to be higher than $\sim$39.00, 42.02, 59.54, 79.35,
74.62, 76.24, 65.39 $\text{pix}^{-1}$ for $[\mathrm{C/Fe}]$,
$[\mathrm{Fe/H}]$, $[\mathrm{Si/Fe}]$, $[\mathrm{Ca/Fe}]$, $[\mathrm{Ti/Fe}]$,
$[\mathrm{Ni/Fe}]$ and $[\mathrm{Cr/Fe}]$, respectively. To facilitate the
calculation of the SNR required to achieve a given uncertainty, we provide
analytical fits to the uncertainty curves shown in Figure 13. The curves are
fitted with the functional form of

$\log\sigma_{X}=A_{X}\log({\rm SNR})+B_{X},$ (11)

The coefficients $A_{X}$ and $B_{X}$ for each label are listed in Table 3.

###  5.2 SNR as a function of magnitude and exposure time

Figure 14:  SNR of MUSE spectra at $R\sim 3000$ as a function of $V$ magnitude
(purple line) for an exposure time of one hour. Each colored line represents
the threshold where the uncertainty of a label reaches 0.1 dex (or 10 K),
which is derived using equation 11. All chemical abundances can be derived
with uncertainty less than 0.1 dex till $V=18.5$ mag, for $[\mathrm{Mg/Fe}]$,
$[\mathrm{C/Fe}]$ and $[\mathrm{Fe/H}]$ even till $V=19.7$ mag.

Using equation 11, with the known SNR we can obtain the uncertainty of stellar
labels from its spectra. We know SNR depends on magnitude $V$, exposure time
$T_{\exp}$, and air-mass. Therefore, when making science goals, what we care
about is how long the exposure time is needed to achieve the required label
uncertainty for stars with different magnitudes. Here we provide an analytical
function to calculate SNR with given $V$ magnitude and exposure time
$T_{\exp}$ as

${\rm SNR}={\rm SNR}_{\rm 1hr}(V)\sqrt{\left(T_{\exp}/3600\mathrm{s}\right)}.$
(12)

Here ${\rm SNR}_{\rm 1hr}(V)$ is the SNR estimated from the K-giant spectra by
the MUSE Exposure Time Calculator for an exposure of one hour. The analytical
function is given by

${\rm SNR}_{\rm 1hr}(V)=\frac{462.34\times
10^{0.4(14.83-V)}}{\sqrt{0.00223+10^{0.4(14.83-V)}}},$ (13)

This idea is taken from Sharma et al. 2018. For the above equations, we set
the air-mass as 1.5 and seeing as $0.8^{\prime\prime}$. Therefore, by
combining equations 11-13, with a given magnitude $V$ and exposure time
$T_{\exp}$, one can predict the uncertainty of each label.

Figure 14 provides the SNR as a function of $V$ magnitude for an one-hour
exposure (purple line). We also plot the threshold of maximum magnitude for
each label where the uncertainty reaches 0.1 dex or 10K, which are derived by
Figure 13. As we can see, all chemical abundances can be derived with
uncertainty less than 0.1 dex till $V=18.5$ mag, for $[\mathrm{Mg/Fe}]$,
$[\mathrm{C/Fe}]$ and $[\mathrm{Fe/H}]$ even till $V=19.7$ mag. This figure
combining with equations 11-13 can be used as a guide for future research,
providing an indication of the exposure time for different magnitude stars to
achieve the expected uncertainty.

##  6 Discussions

###  6.1 Performance of MUSE stellar label extraction under different
scenarios

Ideally, the methods outlined in this paper to determine stellar labels would
be applicable to all stars in MUSE data-cubes. However, the label ranges of
the _DD-Payne_ training set do not cover the space for all potential
observations: for stars outside of this parameter space, for example having
very low metallicity $([\mathrm{Fe/H}]<-1.5)$ or very high effective
temperatures $(T_{\mathrm{eff}}>7000K)$, labels are determined through
extrapolation of the model. Despite this, some studies have shown _DD-Payne_
can do some moderate extrapolation in the linear region of the gradient
spectra varying with labels. This is because _DD-Payne_ imposes the gradient
spectra to be similar to that of the Kurucz models (Kurucz, 1970, 1993, 2005),
which is an advantage of such a hybrid method compared to pure data-driven
models. For example, the LAMOST $[\mathrm{Fe/H}]$ estimates can be robust down
to $-2.5$ dex (see Fig. 10 of Conroy et al. 2019); _DD-Payne_ can also
generate reasonable [Ba/Fe] stars with $1<{\rm[Ba/Fe]}<3$ dex and
$T_{\mathrm{eff}}{}>7000$K (Xiang et al., 2020).

Typically in MUSE data, stellar spectra come from the following types of
fields: random individual stars near a galaxy, high extinction fields, and
globular clusters. In each of these scenarios the performance of the
spectroscopic analysis is different and some of them pose unique challenges
for analysis.

For individual stars near a galaxy, they typically have high SNR, as
observations in galaxy fields generally have long exposure times. Therefore,
as long as the PSF does not overlap with the nearby galaxy, it is relatively
simple to extract and estimate the stellar labels. All of the common stars
between MUSE and LAMOST belong to this case; one typical spectrum is shown in
Figure 3. For these stars, stellar labels will have high precision due to
their high SNR, as well as the fact that most of them belong to the nearby
disk, which are stellar populations that are well covered by the _DD-Payne_
training sets.

For stars in high extinction fields, such as the bulge, the spectra are
restricted to a narrower range in wavelength and the SNR of the extracted
spectra is in general low (due to a combination of large distance and dust).
For low SNR, in addition to SNR directly affecting precision, the emission
lines are comparatively stronger and more difficult to remove. The above-
listed factors lead to lower precision in stellar labels. Hence, in high
extinction regions, one can only study giants which are intrinsically bright.
Therefore, we can only get reliable label estimates for stars with relatively
low extinction ($A_{V}<6$ mag) along the bulge lines of sight, which was shown
in the middle plot of Figure 11. As for stars of $A_{V}>6$ mag in the Galactic
center, the dust will make the giants difficult to observe with typical MUSE
exposure times.

For globular clusters, which have high stellar density, our work will be of
particular importance. It will provide an automated way to determine high
precision stellar labels for these dense fields down to the center of the
cluster; previous studies using fiber-fed spectrographs were often limited to
the outskirts of these objects. Additionally, it is possible to increase the
precision of stellar parameters and several abundance estimations by making
use of full wavelength fitting, which has not been done so far. Previously,
the MUSE GC survey (Husser et al., 2016; Kamann et al., 2016) observed 26
globular star clusters, with most of these studies focusing on specific
features of spectra or just metallicity, e.g. emission-line studies (Göttgens
et al., 2019), the dynamics using CaT absorption lines (Kamann et al., 2018),
the relative abundance variations using the equivalent widths (Latour et al.,
2019), metallicity distributions (Husser et al., 2020; Latour et al., 2021).
Our method has the potential to enable more chemical abundances measured
automatically by the full-wavelength fitting frameworks, rather than applying
any spectral library to execute the fittings. Even though globular clusters
typically have $[\mathrm{Fe/H}]{}<-1.0$ dex, some of them are still in the
parameter range of _DD-Payne_ , and the moderate linear extrapolation ability
of _DD-Payne_ still enables this method to measure robust stellar labels. We
will perform the test of it in the future work.

###  6.2 Computational challenges in spectral extraction

In this work, the spectral extraction processes are executed using PampelMUSE
(Kamann et al., 2013). The typical time spent on extracting spectra from each
data-cube with a 24-core CPU and 32GB RAM is $\sim 30$ minutes and it is
independent of the number of stars in the field. Therefore, for the
verification data analyzed in this paper (the cross-match of LAMOST and MUSE),
we spent more time on spectral extraction for these cubes compared to the
data-cubes in the bulge, even though there were two orders of magnitude more
spectra extracted from the bulge fields. Hence, to perform a survey of all
individual stars in publicly available MUSE data-cubes, the most time-
consuming step will be the extraction of spectra.

For individual stars in sparse fields or more limited studies focused purely
on kinematics in dense fields, it is also possible to use other stellar
extraction strategies such as aperture photometry in IRAF for each layer
subtracted by the sky estimated locally (e.g. Valenti et al. 2018). This
approach has the advantage of retaining as many stars as possible and has a
more accurate estimate of the sky background, which will lead to reduced
artifacts in the final spectra (Valenti et al., 2018). For regions with modest
crowding (i.e., $<200$ stars per field), aperture photometry and PSF-fitting
could yield similar results. However, PSF-fitting is still necessary when
dealing with more crowded fields ($>200$ stars per field) as there will be
significant blending for stars in these dense regions. Kamann et al. 2013
tested the performance of PampelMUSE PSF-fitting using a simulated MUSE data-
cube towards the center of a globular cluster 47 Tuc. Under the average seeing
of 0.8 arcsec, $\sim$5000 useful spectra could be extracted. In good
conditions, this value can be 3 or 4 times larger. With severe crowding,
aperture photometry will suffer from significant blending between stellar
spectra. Therefore, for globular clusters, we still recommend PampelMUSE.

###  6.3 Future research

There are several aspects in the data pipeline that can be improved in the
future. In the methods outlined in this paper, stellar labels are estimated
from the _DD-Payne_ , which depends sensitively on the precision of labels in
GALAH DR2 (Buder et al., 2018) and APOGEE-_Payne_ (Ting et al., 2019). Given
that improved versions of both these catalogs are now available, GALAH DR3
(Buder et al., 2021) and APOGEE DR16 (Ahumada et al., 2020), one needs to
update the _DD-Payne_ models. In addition, we can train a new _DD-Payne_ model
if a sufficient number of common stars in MUSE and other high-resolution
spectroscopic surveys for a training set is available. The advantage is that
there will be no need to degrade the MUSE spectra to a lower resolution, which
will help extraction of blended features. In addition, some absorption lines
such as [Na/Fe] and [O/Fe] are masked in the LAMOST spectra due to dichroic
issues in the wavelength range $(5803-5966\Angstrom)$. This range can now be
used when working in MUSE non-AO mode. It will enable to estimate precise
sodium and oxygen abundances, which is essential in identifying different
stellar populations in globular clusters (Bastian & Lardo, 2018). The primary
difficulty for retraining is having a training set that is both large and
covers a wide range of parameter space.

In the future, the method outlined here can be utilized for many purposes. A
survey can be executed based on stars from publicly available MUSE data-cubes
using Gaia eDR3 (Gaia Collaboration et al., 2021) and SkyMapper (Keller et
al., 2007) as photometric input catalogs. Our method can be applied to
estimate their stellar labels and compile a catalog that will be useful for
Galactic archaeology studies. For the Galactic bulge, our method has the
opportunity to study the chemistry and dynamics of the Galactic center in
greater detail. However, more observational data is needed, such as fields in
Baade’s window, which are less affected by the dust. In addition, this method
can be applied to globular clusters observed by Husser et al. 2016; Kamann et
al. 2016 to study their chemistry, and identify multiple stellar populations
if any, and their connection to kinematics. Moreover, the interest in using
MUSE for spectroscopy of resolved stellar populations has been growing quite
strongly, even beyond the limits of the Galaxy (e.g. Roth et al. 2019), our
method can also provide parameter estimations for these targets.

With the launch of the BlueMUSE project (Richard et al., 2019), we will obtain
spectra in the wavelength range between $3500-5800\Angstrom$, which is also
covered by LAMOST. As mentioned previously, the loss of the blue portion of
the spectrum in MUSE is the primary reason why we are not able to estimate as
many precise chemical elements as those determined from LAMOST spectra.
BlueMUSE will provide the opportunity to measure these abundances with higher
precision, and for more elements that are currently not available; critically
the s-process elements such as [Y/Fe] and [Ba/Fe] which provide key age
diagnostics for stellar targets (Hayden et al., 2020). The blue portion will
also bring strong absorption features for determining precise abundances of
Na, C, N, and O, which are essential for identifying multiple populations in
globular clusters. In addition, MAVIS (McDermid et al., 2020), which is the
new IFS instrument being built for ESO’s VLT AOF (Adaptive Optics Facility,
UT4 Yepun) also covers a wavelength range $3700-10000\Angstrom$ similar to
BlueMUSE and MUSE. With the lower spatial sampling of
$0.02^{\prime\prime}-0.05^{\prime\prime}$, we have the opportunity to study
the core of globular clusters with more stars providing an insight into its
chemistry and dynamics. Because of the similar wavelength coverage of _DD-
Payne_ and these instruments, our method can be directly applied to them.

Finally, based on the fact that the study of resolved stellar populations
represents one of the major science cases for the European Extremely Large
Telescope (ELT) (Gilmozzi & Spyromilio, 2007; Hook, 2009), it is reassuring
that our method is paving the way for future studies in multi-dimensional
chemical space. For the Galactic bulge, ELT will allow us to measure chemical
abundances all the way down to the main sequence turn-off stars (Minniti &
Zoccali, 2007). For these targets, we can use BSTEP (Sharma et al., 2018) to
map the age distribution and reveal the detailed formation and evolution
history of the innermost bulge, the peanut bar, and the long bar.

For Local Group galaxies, the ELT can also derive more stellar spectra of
bright main-sequence (potentially even turn-off) stars and giants with
necessary SNR than VLT (e.g. McLeod et al. 2019; Carini et al. 2020); this
includes the SMC and LMC, as well as more distant galaxies such as Andromeda
and M33, extending Galactic Archaeology beyond the Milky Way to the Local
Group. With the unprecedented detection sensitivity of ELT, our method can
provide a way for future stellar label estimation and science goals for the
ELT-related IFS instruments, to measure stellar labels of stars beyond the
Local Group (Wyse & Gilmore, 2005; Evans, 2008; Greggio et al., 2012).

##  7 Summary

In this study, we applied _DD-Payne_ (Xiang et al., 2019), which was developed
for LAMOST spectra, on MUSE data-cubes and estimated $T_{\mathrm{eff}}$, $\log
g$, $[\mathrm{Fe/H}]$ and chemical abundances of Mg, Si, Ti, Ca for individual
stars in MUSE data-cubes.

By comparing our MUSE results with that of LAMOST using common stars, we show
that despite instrumental differences, it is possible to extract precise
stellar parameters and abundances with typical dispersion of
$T_{\mathrm{eff}}$, $\log g$ and other chemical abundances less than 75K and
0.15 dex and 0.1 dex, respectively.

In dense fields, which is the unique advantage of the MUSE instrument, we
selected 29 data-cubes towards the Galactic center. Based on previous studies
(Rojas-Arriagada et al., 2019; Hayden et al., 2015; Sharma et al., 2021), by
comparing the $[\mathrm{Fe/H}]$-$[\mathrm{Mg/Fe}]$ distribution estimated by
our method in the bulge and inner disk region with stars from APOGEE-_Payne_ ,
we found excellent agreements in two sequences with similar center values and
overall trends. This indicates the ability of our method to measure chemical
abundances in regions with high stellar density and extinction. In addition,
we also studies the extinction as a function of $R_{\mathrm{gc}}$ in the
direction of the Galactic center and compared these results with the
prediction from Galaxia (Sharma et al., 2011). We found there is a qualitative
agreement with the overall trends, but the scale height of the dust predicted
by Galaxia is higher than observations.

In addition, we provided analytical formulas to predict the precision of each
label as a function of $V$ magnitude and exposure time. This can be used for
observational proposal designing before a survey to achieve the expected label
uncertainty.

In the future, this method can be applied to do a survey for all individual
stars in public MUSE cubes and estimate their stellar labels. The result can
be a supplementary catalog for all-sky spectroscopic surveys. For the Galactic
bulge, more observations are needed to expand the sample size. By combining
the chemical and kinematic information, there is a great opportunity to study
the evolution and assembly history of the Galactic center. This method can
also be applied to MUSE observations on globular clusters, to study the
connection between kinematics and multiple populations.

This is the first time to measure stellar labels using full wavelength fitting
in dense fields observed by the MUSE instrument. We demonstrate that despite
PSF/LSF being different, it is possible to apply a model trained on spectra
from one instrument to another. Given a large number of spectrographs having
wavelength similar to LAMOST, our results suggest that one can easily do
detailed spectroscopic analysis with them. In the future, this method can be
used directly for BlueMUSE (Richard et al., 2019) and MAVIS (McDermid et al.,
2020). It will also help with the label measurement development for IFS
instruments on ELT (Gilmozzi & Spyromilio, 2007), to study Galactic
archaeology from the Milky Way to somewhere more than 10 Mpc away.

## Acknowledgements

We thank Xu Zhang, David M. Nataf, Thorsten Tepper Garcia, Sven Buder, and
Jesse Van de Sande for their very useful comments.

This research has made use of the services of the ESO Science Archive
Facility. The results are based on public data released from the MUSE
commissioning observations at the VLT Yepun (UT4) telescope. This work has
also made use of the data from LAMOST. 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 was also based on data products from VVV Survey
observations made with the VISTA telescope at the ESO Paranal Observatory
under programme ID 179.B-2002.

This research has made use of the VizieR catalogue access tool, CDS,
Strasbourg, France (DOI: 10.26093/cds/vizier). The original description of the
VizieR service was published in Bonnarel et al. 2000;
Astropy666http://www.astropy.org, a community-developed core Python package
for Astronomy (Astropy Collaboration et al., 2013, 2018), numpy (Harris et
al., 2020), scipy (Virtanen et al., 2020), matplotlib (Hunter, 2007), ZAP
(Soto et al., 2016), PampelMUSE (Kamann et al., 2013), DD-Payne (Xiang et al.,
2019) and MPDAF (Piqueras et al., 2017).

We acknowledge the University of Sydney HPC service at The University of
Sydney for providing HPC resources that have contributed to the research
results reported in this paper.

ZW is supported by the China Scholarship Council and Australian Research
Council Centre of Excellence for All Sky Astrophysics in Three Dimensions
(ASTRO-3D) through project number CE170100013. YST is grateful to be supported
by the NASA Hubble Fellowship grant HST-HF2-51425.001 awarded by the Space
Telescope Science Institute. YST acknowledges financial support from the
Australian Research Council through DECRA Fellowship DE220101520.

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

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##  Appendix A The [Mg/Fe]-Temperature trend in the model

Figure 15:  Stellar $[\mathrm{Mg/Fe}]$ as a function of $T_{\mathrm{eff}}$ for
stars in different metallicity bins. The top row shows the results from
APOGEE-_Payne_ (Ting et al., 2019), the the bottom row the LAMOST-_DD-Payne-A_
results (X19). The dots and filled ranges illustrate the median values and
standard deviations at different $T_{\mathrm{eff}}$ bins. Both of the results
demonstrate that there is a $T_{\mathrm{eff}}$-$[\mathrm{Mg/Fe}]$ trend in all
the metallicity bins. The slopes of these trends are illustrated in Table 4.
In addition, the trends in APOGEE-_Payne_ and LAMOST-_DD-Payne-A_ are
consistent because _DD-Payne-A_ is trained from labels in APOGEE-_Payne_ and
inherited its features.  Figure 16:  Stellar $[\mathrm{Mg/Fe}]$ as a function
of $T_{\mathrm{eff}}$ for stars in seven open clusters (the name and stellar
number are marked in each panel). The stars are from LAMOST DR5 and selected
by the criteria in Zhong et al. 2020. Their $[\mathrm{Mg/Fe}]$ and
$T_{\mathrm{eff}}$ are then measured by the _DD-Payne_ models. The results
measured by _DD-Payne-A_ show clear $[\mathrm{Mg/Fe}]$-$T_{\mathrm{eff}}$
trends with larger slopes than _DD-Payne-G_. Since the metallicity and
abundances of stars in open clusters are homogeneous, which means no galactic
evolution or selection function applied, the trends illustrated here are
caused by labels in APOGEE-_Payne_.  Figure 17:  $T_{\mathrm{eff}}$ density
histograms of stars in Figure 12 as a function of $R_{\mathrm{gc}}$. Results
from APOGEE-_Payne_ (Ting et al., 2019) are illustrated in black, and the red
shows the MUSE-_DD-Payne-A_ results. The medians ($\mu$) are marked on each
panel. This figure shows the difference of $T_{\mathrm{eff}}$ in the APOGEE-
_Payne_ and MUSE-_DD-Payne-A_ samples, which can lead to a shift in
$[\mathrm{Mg/Fe}]$.

The $[\mathrm{Mg/Fe}]$-$T_{\mathrm{eff}}$ trends was found in the _DD-Payne_
model in X19 (see Figure 14), where for dwarfs with
$-0.2<[\mathrm{Fe/H}]<0.2$, $[\mathrm{Mg/Fe}]$ measured by _DD-Payne-A_
decreases with $T_{\mathrm{eff}}$. In addition to $[\mathrm{Mg/Fe}]$, some
other abundances also show similar non-negligible trends. X19 verified that
these trends are inherited from the APOGEE-_Payne_ values in the training set.
Since no abundance calibration was applied to APOGEE-_Payne_ values (Ting et
al., 2019), the $[\mathrm{Mg/Fe}]$-$T_{\mathrm{eff}}$ trend should come from
the neural network model _The Payne_ , i.e., stellar astrophysics.

To investigate this trend, we take APOGEE-_Payne_ (Ting et al., 2019) and
LAMOST-_DD-Payne-A_ (X19) catalogs, separate stars into giants and dwarfs and
divide them into different $[\mathrm{Fe/H}]$ bins, then plot the
$[\mathrm{Mg/Fe}]$-$T_{\mathrm{eff}}$ distributions in Figure 15. Selection
criteria are applied to these two samples to discard stars with bad fittings:
For APOGEE-_Payne_ , excluding stars with any of the flags: "quality"$=$"bad"
and $\chi^{2}>20$; For LAMOST-_DD-Payne-A_ , excluding stars with any of the
flags: $\rm SNR_{g}<30$, $\chi^{2}>20$, "qflag-chi2"$=$"bad" and "flag-
singlestar"$=$"no". The dots and filled ranges illustrate the median values
and the standard deviations at different $T_{\mathrm{eff}}$ bins. In this
Figure, both the giants and dwarfs demonstrate that there is a clear
$T_{\mathrm{eff}}$-$[\mathrm{Mg/Fe}]$ trend in all the metallicity bins. The
slopes of these trends (illustrated in Table 4) in the two catalogs are
similar as well.

Another reason leading to this trend is the Galactic evolution and selection
functions, i.e., stars with higher $T_{\mathrm{eff}}$ tend to be younger, and
therefore have lower $[\mathrm{Mg/Fe}]$ than stars with lower
$T_{\mathrm{eff}}$. Even though the metallicity bins in Figure 15 are chosen
to be small, it is not sufficient to conclude the
$[\mathrm{Mg/Fe}]$-$T_{\mathrm{eff}}$ trend is all caused by the model. To
explore the proportion of this trend due to the model, we select seven open
clusters from LAMOST DR5 and plot $[\mathrm{Mg/Fe}]$ as a function of
$T_{\mathrm{eff}}$ in Figure 16, where the name and star number are marked in
each panel. The stars in the open clusters are selected by the criteria in
Zhong et al. 2020. Their $[\mathrm{Mg/Fe}]$ and $T_{\mathrm{eff}}$ are then
measured by the _DD-Payne_ models. In all the panels, results from _DD-Payne-
A_ show clear $[\mathrm{Mg/Fe}]$-$T_{\mathrm{eff}}$ trends with larger slopes
than those from _DD-Payne-G_ , which is $-0.082$ dex/1000K on average. Since
open clusters are found to be chemical homogeneous (Bovy, 2016; Ness et al.,
2018), which means no galactic evolution or selection function is applied, the
trend illustrated here is verified to be caused by the model. Combining with
the slopes in Figure 15, for stars with $[\mathrm{Fe/H}]{}\sim 0$, which is
the approximate $[\mathrm{Fe/H}]$ for these open clusters, the average slope
is $-0.124$ dex/1000K. Therefore, the contribution of this trend is comparable
but higher from the model (stellar astrophysics).

In APOGEE-_Payne_ (Ting et al., 2019), the authors chose to not calibrate the
abundance trend because at the $T_{\mathrm{eff}}$ of APOGEE range
(4000K-5000K), it was shown that an ab-initio fitting of the spectra will not
incur much [Mg/H]-$T_{\mathrm{eff}}$ trend (see their Figure 15). However, we
found that even with the ab-initio fitting, for stars with a wider
$T_{\mathrm{eff}}$ range, in the $[\mathrm{Mg/Fe}]$ scale, the values in
APOGEE-_Payne_ do have a non-negligible trend, which is similar to the APOGEE
pipeline ASPCAP (Holtzman et al., 2015) and requires calibration.

Therefore, when plotting the $[\mathrm{Mg/Fe}]$-$[\mathrm{Fe/H}]$
distributions, additional calibration should be added to eliminate this
impact. In Figure 17, we plot the $T_{\mathrm{eff}}$ density histograms of
stars in Figure 12 in different $R_{\mathrm{gc}}$ regions. Results from
APOGEE-_Payne_ are illustrated in black, and the red shows the MUSE-_DD-Payne-
A_ results. The medians ($\mu$) are marked on each panel. This figure
illustrates the difference of $T_{\mathrm{eff}}$ in the APOGEE-_Payne_ and
MUSE-_DD-Payne-A_ samples. Stars with $5<R_{\rm gc}<7$ kpc in MUSE-_DD-Payne-
A_ are mostly dwarfs, and the other samples are mostly giants. Referring to
Figure 15, we can roughly estimate that for stars in the bulge, $3<R_{\rm
gc}<5$ and $5<R_{\rm gc}<7$ kpc, the deviations of $[\mathrm{Mg/Fe}]$ between
two samples are $\sim 0.08,0.06$ and $0.08$ dex, respectively. These are the
values added to $[\mathrm{Mg/Fe}]$ in Figure 12 for calibrating.

Table 4: Slope for the $[\mathrm{Mg/Fe}]$-$T_{\mathrm{eff}}$ trend (dex/1000K) in different metallicity bins for stars in APOGEE-_Payne_ and LAMOST-_DD-Payne-A_. $[\mathrm{Fe/H}]$ bins | APOGEE-_Payne_ | LAMOST-_DD-Payne-A_
---|---|---
giants | dwarfs | giants | dwarfs
$(-0.8,-0.6)$ | -0.025 | -0.117 | -0.044 | -0.141
$(-0.6,-0.4)$ | -0.086 | -0.105 | -0.092 | -0.132
$(-0.4,-0.2)$ | -0.125 | -0.080 | -0.111 | -0.098
$(-0.2,0.0)$ | -0.128 | -0.071 | -0.142 | -0.093
$(0.0,0.2)$ | -0.118 | -0.064 | -0.162 | -0.104
$(0.2,0.4)$ | -0.131 | -0.078 | -0.186 | -0.132
$(0.4,0.6)$ | -0.165 | -0.130 | -0.212 | -0.154