# oMEGACat I: MUSE spectroscopy of 300,000 stars within the half-light radius
of $\omega$ Centauri

M. S. Nitschai Max Planck Institute for Astronomy, Königstuhl 17, D-69117
Heidelberg, Germany  N. Neumayer Max Planck Institute for Astronomy,
Königstuhl 17, D-69117 Heidelberg, Germany  C. Clontz Max Planck Institute for
Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany  Department of Physics
and Astronomy, University of Utah, Salt Lake City, UT 84112, USA  M. Häberle
Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany
A. C. Seth Department of Physics and Astronomy, University of Utah, Salt Lake
City, UT 84112, USA  T.-O. Husser Institut für Astrophysik und Geophysik,
Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen,
Germany  S. Kamann Astrophysics Research Institute, Liverpool John Moores
University, 146 Brownlow Hill, Liverpool L3 5RF, UK  M. Alfaro-Cuello Facultad
de Ingeniería y Arquitectura, Universidad Central de Chile, Av. Francisco de
Aguirre 0405, La Serena, Coquimbo, Chile  Space Telescope Science Institute,
3700 San Martin Drive, Baltimore, MD 21218, USA  N. Kacharov  Leibniz
Institute for Astrophysics, An der Sternwarte 16, 14482 Potsdam, Germany  A.
Bellini Space Telescope Science Institute, 3700 San Martin Drive, Baltimore,
MD 21218, USA  A. Dotter  Department of Physics and Astronomy, Dartmouth
College, Hanover, NH 03755 US  S. Dreizler Institut für Astrophysik und
Geophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077
Göttingen, Germany  A. Feldmeier-Krause Max Planck Institute for Astronomy,
Königstuhl 17, D-69117 Heidelberg, Germany  M. Latour Institut für Astrophysik
und Geophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1,
37077 Göttingen, Germany  M. Libralato AURA for the European Space Agency
(ESA), Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD
21218, USA  A. P. Milone Dipartimento di Fisica e Astronomia “Galileo
Galilei,” Univ. di Padova, Vicolo dell’Osservatorio 3, Padova, I-35122, Italy
R. Pechetti Astrophysics Research Institute, Liverpool John Moores University,
146 Brownlow Hill, Liverpool L3 5RF, UK  G. van de Ven Department of
Astrophysics, University of Vienna, Türkenschanzstrasse 17, 1180 Wien, Austria
K. Voggel Université de Strasbourg, CNRS, Observatoire astronomique de
Strasbourg, UMR 7550, F-67000 Strasbourg, France  Daniel R. Weisz Department
of Astronomy, University of California, Berkeley, Berkeley, CA, 94720, USA

(Received May 16, 2023; Revised August 11, 2023; Accepted August 28, 2023)

###### Abstract

Omega Centauri ($\omega$ Cen) is the most massive globular cluster of the
Milky Way and has been the focus of many studies that reveal the complexity of
its stellar populations and kinematics. However, most previous studies have
used photometric and spectroscopic datasets with limited spatial or magnitude
coverage, while we aim to investigate it having full spatial coverage out to
its half-light radius and stars ranging from the main sequence to the tip of
the red giant branch. This is the first paper in a new survey of $\omega$ Cen
that combines uniform imaging and spectroscopic data out to its half-light
radius to study its stellar populations, kinematics, and formation history. In
this paper, we present an unprecedented MUSE spectroscopic dataset combining
87 new MUSE pointings with previous observations collected from guaranteed
time observations. We extract spectra of more than 300,000 stars reaching more
than two magnitudes below the main sequence turn-off. We use these spectra to
derive metallicity and line-of-sight velocity measurements and determine
robust uncertainties on these quantities using repeat measurements. Applying
quality cuts we achieve signal-to-noise ratios of 16.47/73.51 and mean
metallicity errors of 0.174/0.031 dex for the main sequence stars
($18\text{\,}\mathrm{mag}$ $\rm<mag_{F625W}<$$22\text{\,}\mathrm{mag}$) and
red giant branch stars ($16\text{\,}\mathrm{mag}$ $<\rm
mag_{F625W}<$$10\text{\,}\mathrm{mag}$), respectively. We correct the
metallicities for atomic diffusion and identify foreground stars. This massive
spectroscopic dataset will enable future studies that will transform our
understanding of $\omega$ Cen, allowing us to investigate the stellar
populations, ages, and kinematics in great detail.

Galaxy nuclei(609) — Globular star clusters(656) — Star clusters(1567)

††journal: ApJ††facilities: VLT:Yepun (MUSE), HST (ACS)††software: PampelMuse
(Kamann et al., 2013), spexxy v5.2.21 https://github.com/thusser/spexxy,
Astropy v5.2.1 (Astropy Collaboration et al., 2013, 2018, 2022), clumpy
(Kimmig et al., 2015), Matplotlib v3.7.1 (Hunter, 2007)
https://doi.org/10.5281/zenodo.7697899, Pandas v1.5.3 (Wes McKinney, 2010;
pandas development team, 2020), Numpy v1.20.3 (Harris et al., 2020), SciPy
v.1.10.1 (Virtanen et al., 2020), MUSE pipeline v2.8.3 (Weilbacher et al.,
2016, 2020)

tablenum SIXtablenum

##  1 Introduction

Figure 1: Image of $\omega$ Cen. A three-color RGB image of $\omega$ Cen
created from MUSE WFM data using synthetic SDSS i, r, and g filters. The image
displays the coverage of all WFM data (both GTO and GO). The red cross
indicates the center of the cluster.

In recent years, we have been able to start decoding the formation history of
our Galaxy, thanks to large spectroscopic surveys, like the Gaia mission (Gaia
Collaboration et al., 2016), APOGEE (Allende Prieto et al., 2008; Majewski et
al., 2017), LAMOST/LEGUE (Deng et al., 2012) and GALAH (De Silva et al., 2015;
Buder et al., 2021). These surveys, combined with the framework established
through cosmological hydrodynamic simulations, have revealed the role that
mergers have played in the Milky Way’s formation history.

When less massive satellite galaxies merge with a larger host galaxy, several
things happen: The tidal effects of the host galaxy will cause the smaller
galaxy to disrupt and form stellar streams (Helmi & White, 2001; Mayer et al.,
2002). In addition, dynamical friction can cause the denser central regions of
the smaller galaxy to sink toward the center of the host galaxy before being
fully disrupted.

The Milky Way has had a quiet merger history, experiencing no recent major
mergers (Stewart et al., 2008). The last significant merger happened around 10
Gyr ago with the Gaia-Enceladus satellite (e.g. Haywood et al., 2018; Helmi et
al., 2018).

Most galaxies, including the Milky Way, contain a dense nuclear star cluster
(NSC) at their center (Neumayer et al., 2020), the densest stellar systems
known in the Universe. During a merger event, the NSC of the satellite galaxy
will survive without being disrupted, and live on in the halo of the host
galaxy (e.g., Pfeffer & Baumgardt, 2013).

NSCs in low-mass galaxies have very similar properties to massive globular
clusters (Georgiev & Böker, 2014; Neumayer et al., 2020), with half-light
radii of $1\text{\,}\mathrm{pc}10\text{\,}\mathrm{pc}$ and masses of
${10}^{6}\text{\,}\mathrm{M_{\odot}}{10}^{8}\text{\,}\mathrm{M_{\odot}}$.
Without their surrounding host galaxy, these stripped NSCs will look like
massive globular clusters. Hence, they will be able to hide amongst the
$\gtrsim$ 100 globular clusters in the galaxy. Recent semi-analytic models
predict 2–6 stripped nuclei in the halo of the Milky Way (Pfeffer et al.,
2014; Kruijssen et al., 2019). Because masses and star formation histories of
NSCs track the galaxies they live in (e.g. Kacharov et al., 2018; Sánchez-
Janssen et al., 2019; Fahrion et al., 2021), stripped nuclei can tell us about
the masses of their original hosts and the times of merging if we can identify
them.

An ongoing example of the galaxy merging process is the Sagittarius dwarf
spheroidal galaxy, whose stars are wrapped in a stream around the Milky Way,
created due to tidal stripping over the last several $\mathrm{Gyr}$ (Ibata et
al., 1997; Laporte et al., 2018). The nucleus of this galaxy was discovered to
be the globular cluster M54 long before the remainder of the galaxy was found.
Detailed studies of M54 have revealed that, unlike a typical globular cluster
(but typical of NSCs), it has stellar populations with a wide range of
metallicities and ages (e.g. Siegel et al., 2007; Alfaro-Cuello et al., 2019).

Figure 2: Image of $\omega$ Cen and footprint of the MUSE pointings. On the
left is a grayscale image created from the combined GO and GTO MUSE WFM data.
Overlaid blue colored squares indicate the GO AO pointings, red squares the
WFM GTO data, while the region without squares is where the non-AO GO WFM
pointings lie. On the right is the footprint of the individual pointings
showing the overlap of the data. At the center of the right-hand Figure, the
NFM data are within the yellow region at the center of the image, indicated
with a red cross.

$\omega$ Centauri ($\omega$ Cen, NGC 5139) is the brightest, most massive
globular cluster of the Milky Way ($\sim$
$3.55\text{\times}{10}^{6}\text{\,}\mathrm{M_{\odot}}\mathrm{,}$ Baumgardt &
Hilker, 2018), sitting at a distance of only $5.43\text{\,}\mathrm{kpc}$
(Baumgardt & Vasiliev, 2021). Due to the complexity of its stellar
populations, it has long been suspected to be the stripped former nucleus of a
galaxy that merged with the Milky Way a long time ago (e.g. Bekki & Freeman,
2003). Evidence for the multiple populations of stars in the cluster comes
from the multiple sequences in its color-magnitude diagram (CMD, e.g.
Anderson, 1997; Bedin et al., 2004; Bellini et al., 2010; Milone et al.,
2017), a large spread in metallicity (e.g. Freeman & Rodgers, 1975; Johnson &
Pilachowski, 2010), and possibly also in age (Hilker et al., 2004; Villanova
et al., 2014). How prolonged the star formation in $\omega$ Cen was is still
controversial, i.e., $4\text{\,}\mathrm{Gyr}5\text{\,}\mathrm{Gyr}$ Villanova
et al. (2007) vs. $1\text{\,}\mathrm{Gyr}2\text{\,}\mathrm{Gyr}$ Joo & Lee
(2013). Additional evidence for the stripping scenario comes from kinematic
information that finds the presence of a central stellar disk and a bias
toward tangential orbits in the outer parts (van de Ven et al., 2006).
$\omega$ Cen’s status as stripped nucleus has been further strengthened over
the last decade through its association with stellar streams and the Gaia-
Enceladus merger (e.g. Majewski et al., 2012; Ibata et al., 2019; Limberg et
al., 2022). $\omega$ Cen is, therefore, our closest NSC, closer than our own
Galactic center, and has much less extinction due to gas and dust. Due to its
proximity, it has a large angular size, making it easily observable. For these
reasons, $\omega$ Cen is the perfect laboratory for studying NSCs, stripped
nuclei and multiple populations. It can also inform us about the merger
history of our galaxy since it is likely that its progenitor was part of one
of the most massive early mergers of the Milky Way.

In order to study the cluster in detail and specifically the multiple
populations, spectroscopic data are important for metallicity and abundance
measurements. Due to the high crowding in the cluster many spectroscopic
surveys, like Gaia and APOGEE (Mészáros et al., 2021), are limited to a few
bright stars often only at the outskirts of dense clusters like $\omega$ Cen.
Other studies like Johnson & Pilachowski (2010); Johnson et al. (2020) have
spectroscopic data covering the central region but only for the brightest
stars. The largest spectroscopic survey for multiple Galactic globular
clusters, including $\omega$ Cen, has been presented in Kamann et al. (2018).
This survey is covering the very center of the cluster having thousands of
spectra from the main sequence (MS) up to the red giant branch (RGB). We aim
to further extend that sample out to the half-light radius.

The Multi-Unit Spectroscopic Explorer (MUSE) is the perfect instrument to
investigate individual stars in clusters as has been shown in other studies,
e.g. Husser et al. (2016); Kamann et al. (2018); Alfaro-Cuello et al. (2019,
2020); Kacharov et al. (2022). In this work, we present a large MUSE dataset,
covering $\omega$ Cen out to its half-light radius, and the spectroscopic
analysis of hundreds of thousands of individual stars, by far the largest
spectroscopic dataset ever assembled for $\omega$ Cen, or in any cluster. The
paper is divided into the following sections: In Section 2 we present the
observations and in Section 3 we describe the methods used to get the physical
parameters for our catalog. In addition, in Section 4 we explain the analysis
performed on that catalog to clean and test it. Further tests are also shown
in the Appendix. Finally, in Section 5 we summarize and give an outlook on
further works in progress using this catalog.

##  2 Data

###  2.1 Observations and Data Sets

The data presented in this paper were acquired with MUSE (Bacon et al., 2010,
2014), a second-generation Very Large Telescope (VLT) instrument located at
the UT4 at the Paranal Observatory in Chile. Two sets of data are combined in
this paper; the first are existing data, part of the MUSE guaranteed time
observations (hereafter “GTO data”), with program IDs: 094.D-0142, 095.D-0629,
096.D-0175, 097.D-0295, 098.D-0148, 099.D-0019, 0100.D-0161, 0101.D-0268,
0102.D-0270, 0103.D-0204, 0104.D-0257, 105.20CR, and 109.23DV. These GTO data
consist of 10 pointings with multi-epoch data that have been analyzed already
in several papers (Kamann et al., 2018; Husser et al., 2020; Latour et al.,
2021) as well as six central pointings using the MUSE narrow field adaptive
optics mode (NFM), presented in Pechetti et al. (2023). The second dataset is
from General Observer (GO) program 105.20CG.001 (PI: N. Neumayer); this
includes 87 new MUSE pointings taken between February 2021 and September 2022
– we refer to this dataset as the “GO data” and describe this dataset in more
detail below.

MUSE is an integral-field spectrograph, based on image-slicing with 24
identical integral field units (IFUs). The field of view in the wide field
mode (WFM), which was used for the GO data, is
$59.9\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ $\times$
$60.0\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ for each pointing with a
spatial pixel scale of
$0.2\text{\,}\mathrm{\SIUnitSymbolArcsecond}\text{\,}{\mathrm{pix}}^{-1}$. The
instrument observes in the optical domain ($480\text{\,}\mathrm{nm}$\-
$930\text{\,}\mathrm{nm}$) with a resolving power increasing with wavelength
from 1770 to 3590 and a spectral sampling of
$0.125\text{\,}\mathrm{nm}\text{\,}{\mathrm{pix}}^{-1}$. For the GTO NFM data,
the field of view of each pointing is
$7.5\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ $\times$
$7.5\text{\,}\mathrm{\SIUnitSymbolArcsecond}$, they have a sampling of
$0.025\text{\,}\mathrm{\SIUnitSymbolArcsecond}\text{\,}{\mathrm{pix}}^{-1}$
and the resolving power is increasing with wavelength from 1740 to 3450. In
both the GO and GTO data, some central pointings are also taken using the VLT
Adaptive Optics Facility (AOF) (Arsenault et al., 2010; Ströbele et al.,
2012). In adaptive optics (AO) mode the NaD lines are blocked using a filter,
causing a gap in the spectra between $580\text{\,}\mathrm{nm}$ and
$597\text{\,}\mathrm{nm}$ (Weilbacher et al., 2016).

In the GO data, each field has three exposures with a rotation of
$90\text{\,}\mathrm{\SIUnitSymbolDegree}$ between them (no dithering), and the
exposure time was $200\text{\,}\mathrm{s}$. The observations were requested in
service mode at an airmass less than 1.4 and a seeing better than 0$\farcs$8\.
These conditions were almost always fulfilled, see Table 3 in the Appendix for
more details on the observing conditions. We note that one observing block (OB
1.3) was initially observed using AO with the wrong offset, causing a small
gap in our dataset. Therefore, it was repeated without AO in September 2022
once more, to fill in the gap.

We show the spatial coverage of our combined dataset in Fig. 1 and Fig. 2. The
combined dataset includes a total of 97 WFM pointings as well as six central
NFM pointings, providing complete coverage out to the half-light radius of
$\omega$ Cen (4.65’ or $7.04\text{\,}\mathrm{pc}$, Baumgardt & Hilker, 2018).

The reduction and analysis of the GTO data were already done, details on the
GTO WFM data are presented in Kamann et al. (2018), while the NFM data are
presented in Pechetti et al. (2023). For the GO data, we duplicated the GTO
WFM reduction procedure as closely as possible.

For the rest of the paper, most of the data reduction and analysis steps refer
to just the GO data, except where clearly specified to also include the GTO
data.

###  2.2 Data Reduction

We use the MUSE pipeline, version 2.8.3 (Weilbacher et al., 2016, 2020), to
reduce the GO data. This pipeline uses CPL (Streicher, 2016) and the EsoRex
(ESO CPL Development Team, 2015) packages and contains all necessary
procedures for the data reduction process, including bias subtraction, flat
fielding, illumination correction, and wavelength calibration. Further, the
pipeline flux calibrates the exposures using a standard star, corrects for the
barycentric motion of the Earth, and combines the three single exposures into
one for each field. We use the default settings for most parts of the
pipeline, except for sky subtraction, where we use a sky continuum file
containing zeroes as the model, so that only the emission lines are
subtracted, but not the sky continuum. Removing the sky continuum would also
remove starlight in a crowded region like ours since even the darkest spaxels
still contain starlight. This will leave sky continuum in our final data
cubes, but since we do a point spread function-based extraction (see Section
3.1) these emissions will not be in the spectra we extract but in the
background components determined during the extraction.

In addition, we are not doing any Raman correction since the field of view is
too crowded or the Telluric correction, since our spectral fitting routine can
remove them better. Hence, the Telluric lines are included in our spectral fit
and are removed then from the spectra, see Section 3.3.

The total MUSE data coverage is shown in Fig. 2, where the red squares
indicate where the WFM GTO pointings lie and the blue squares where the 12 new
WFM-AO pointings are, while all other pointings are WFM without AO, 75 in
total. The GTO NFM data are within the yellow region at the center of the
right panel of Fig. 2 (the small yellow square where the red cross lies). The
gaps in our GO pointings, visible in Fig. 3, in the center and upper part of
the image are filled in with the GTO pointings so that we have full coverage
of the cluster without gaps when combining the two datasets.

##  3 Analysis Methods

After the reduction of the MUSE mosaic, the next step is to get spectroscopic
information for individual stars. Therefore, we need to extract the spectra of
individual stars and measure physical parameters from these spectra.

###  3.1 Spectral Extraction

Figure 3: All extracted GO stars. The figure shows the positions of all
extracted GO stars using the Anderson & van der Marel (2010) photometric
catalog. The red cross indicates the center, while the holes at the top and at
the center are later filled with the GTO stars. Some edges are cut off because
the HST footprint does not perfectly cover the MUSE footprint. The overlap
regions are denser since more stars are observed due to the fact that there
are two or more exposures. The variation in the number of stars seen in
different fields is due to varying observing conditions that impact our
completeness.

To extract individual spectra for the stars in the MUSE fields we use
PampelMuse111https://PampelMuse.readthedocs.io/en/latest/about.html (Kamann et
al., 2013) and the Hubble Space Telescope (HST) catalog from Anderson & van
der Marel (2010). PampelMuse takes the photometry and position of the stars in
the HST catalog as a reference for the stars in the field of view of the MUSE
data. It fits the point spread function (PSF) as a function of wavelength.
Forced PSF photometry performed at each wavelength for all the stars in the
catalog allows PampelMuse to separate sources efficiently even in crowded
regions. The Anderson & van der Marel (2010) catalog includes F625W and F435W
magnitudes for $1.2\text{\times}{10}^{6}$ stars and covers a field of
$10\text{\,}\mathrm{\SIUnitSymbolArcminute}$ x
$10\text{\,}\mathrm{\SIUnitSymbolArcminute}$ with a pixel scale of
$50\text{\,}\mathrm{mas}\text{\,}{\mathrm{pix}}^{-1}$. We use a Moffat profile
(Moffat, 1969) for the PSF as defined in Section 4.2 of Kamann et al. (2013)
and allow it to vary its ellipticity, positional angle, $\beta$-parameter, and
full width at half maximum (FWHM), while the initial value for the FWHM is set
to be the mean value of the seeing at the time of the observation. The
extracted spectra also get a quality flag assigned from PampelMuse where 0 is
the best flag a spectrum can get. While there are 4 other criteria for the
flags there can also be a combination of them, 1: more than one source
contributing, 2: signal-to-noise ratio (SNR) $<$ 10, 4: the flux is negative,
and 8: the centroid of the source is outside the field of view of the data
cube).

We have performed an additional analysis on some OBs using a different
extraction setup and find that the final results for spectra with a SNR $>10$
do not change significantly, see Appendix B. In the next section, Section 3.2,
we show the completeness of this extraction for the GO dataset.

In total we extract with PampelMuse 355,682 stars from the GO MUSE dataset,
see Fig. 3, where we show their positions.

###  3.2 Completeness

Figure 4: GO Completeness plots. On the left is the overall GO completeness
(the combined completeness for all 87 GO pointings) for different SNR cuts,
from left to right the SNR is decreasing. The dashed line indicates 50 %
completeness and the dotted line is 18.86 mag in F625W. The right plot shows
for an SNR $>$ 10 the individual completeness for 3 pointings at different
radii from the center.

We investigate how complete our GO data are after the spectral extraction
compared to the HST catalog (Anderson & van der Marel, 2010).

For each MUSE pointing we mask the edges of the pointings by 5 arcsec, in
order to not get edge effects, and we divide our sample in 0.5-mag-wide bins
and define the completeness in each bin as the ratio between the number of
stars in the HST catalog and the number of stars for which we actually extract
a spectrum from the MUSE data. We computed the completeness excluding spectra
with an SNR lower than specific thresholds, i.e., 1, 5, 10, 15, 20, 25, and
30.

We show the overall completeness curves as a function of magnitude for
different SNR cuts in the left panel of Fig. 4. The completeness is almost 100
% for the brightest stars and falls off towards fainter stars. The left panel
shows that the overall completeness is above 50 % for stars brighter than
$\sim$18.86 mag (F625W Filter) for an SNR threshold of 10, while for higher
SNR this is shifted to lower magnitudes. The right panel shows that in the
central regions, the completeness is lower for the fainter stars due to
crowding.

Figure 5: CMD of GO stars. CMD of the stars in the GO dataset. The black dots
show the stars with fixed log(g) in our spexxy fit while the orange points
have free log(g) and the purple are the HB stars which are disregarded in the
current analysis. The yellow points indicate the position of the isochrone
used to infer the log(g).  Figure 6: Example spectra. (a)-(d); Spectra of
stars at different stages of evolution plotted in black, with best-fitting
spexxy models in red. The light red shaded areas are the excluded/masked
regions during the fit; note that the RGB star (d) is observed with AO and the
NaD line is blocked. The bottom panels show the data-model residuals in blue.
We note that the deep broad absorption features at 6800 and 7600 Å are
telluric features that are fit by spexxy along with the stellar properties.
The best-fitting parameters for SNR, [M/H], $\rm v_{los},T_{eff}$ and the
log(g) value are given on top of each spectrum.

###  3.3 Spectral fitting

After extracting the spectra, we use
spexxy222https://github.com/thusser/spexxy version 2.5 to measure the physical
parameters of the stars. The observed spectra are compared to synthetic
spectra from the Phoenix library (Husser et al., 2013) to derive each star’s
effective temperature $\rm T_{eff}$, and metallicity [M/H] using a $\chi^{2}$
minimization. The range of the spectral parameters are: $-4$ dex$\leq[M/H]\leq
1$ dex, $2300\text{\,}\mathrm{K}$$\leq T\leq$ $15\,000\text{\,}\mathrm{K}$ and
$0\leq log(g)\leq 6$. We also include a spexxy fit to the telluric absorption
lines (which were not corrected previously, see Section 2.2) for $\rm H_{2}O$
and $\rm O_{2}$. We use all spectra we could extract in this analysis part
regardless of their quality at this point.

The initial values for log(g) and $\rm T_{eff}$ were determined as outlined in
Husser et al. (2016); Kamann et al. (2018). In summary, the photometry from
Anderson & van der Marel (2010) was fitted with an isochrone from the PARSEC
database (Marigo et al., 2017) and each observed star was assigned the stellar
parameter from the nearest isochrone point, in the magnitude-color plane. For
that, a two dimensional polynomial is fitted to the temperature and log(g)
from the isochrone as a function of color and magnitude. This isochrone has an
age of $13.7\text{\,}\mathrm{Gyr}$, a metallicity of -0.94 dex, extinction
($A_{\rm v}$) of 0.23 mag, a distance of $5320\text{\,}\mathrm{pc}$, and is
shown as yellow dots in Fig. 5. Since it is known that $\omega$ Cen has
multiple populations, one isochrone is not ideal to describe all populations
but here we only want to get initial values and a reliable log(g) for our
spectral fit. A detailed population analysis will follow in upcoming work. The
same is true for binary stars or multiple stellar systems, which are also
offset in the color-magnitude diagram (CMD). However, the binary fraction of
$\omega$ Cen is small, less than 5 % (Elson et al., 1995; Mayor et al., 1996)
and in recent work even lower at $2.70\%\pm 0.08\%$ (Bellini et al., 2017b)
and because of multiple populations, the binary sequence is also intertwined
with the main sequence track. Since log(g) does not strongly affect the [M/H]
determination (Husser et al., 2016; Kamann et al., 2016, see also Section C.1)
and we only require reliable log(g) parameters, one isochrone is sufficient
even if the cluster is much more complex. We show the CMD in Fig. 5. During
the fit with spexxy, log(g) is fixed to the value provided by the isochrone
ranging from 0 to 6, the $\alpha$-enhancement is kept constant at
[$\alpha$/Fe]=0.3 dex (similar to Latour et al., 2021), while $\rm T_{eff}$
and [M/H] are determined. spexxy also measures the line-of-sight (LOS)
velocity, $\rm v_{los}$, for the observed spectra. For that, we need initial
values, which we get from a first cross-correlation with templates before
starting the run with spexxy. If the result of the cross-correlation is not
good enough, and we obtain $r_{cc}\leq 4$ from the r-statistics (Tonry &
Davis, 1979), we set the initial value to
$234\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$, which is the mean LOS
velocity of the whole cluster (Baumgardt et al., 2019).

For the spectral fit, we use the whole wavelength range of the MUSE spectra,
excluding only the NaD line or AO region ($578\text{\,}\mathrm{nm}$ $-$
$599\text{\,}\mathrm{nm}$) and any other bad pixels identified. Four example
spectra are shown in Fig. 6 together with their best-fitting template spectrum
in red. The light red shaded areas are the masked regions excluded from the
fit. In addition, the SNR is also determined by spexxy from the fit residuals
providing a good indicator of the quality of the data.

In summary, with spexxy we derive values for [M/H], $\rm v_{los}$, $\rm
T_{eff}$, SNR, telluric parameters and their statistical errors. However, the
results for stars lying further away from the isochrone (e.g. blue stragglers
sequence (BSS) or asymptotic giant branch stars (AGB)) that is used to provide
the log(g) values have to be considered biased. Hence, for stars not lying on
the main isochrone, i.e. stars indicated with orange dots in Fig. 5, we rerun
spexxy allowing the log(g) parameter to vary freely during the fit. These
stars are either not following the main CMD track (this might be nonmember
stars or have unreliable photometry measurements from HST) or belong to the
BSS or AGB. For stars that could be BSS/AGB or be part of the main CMD track,
we keep both sets of values with free and fixed log(g). These are the orange
dots that lie on top of black dots in Fig. 5. This increases the number to
356,065 measurements due to the duplicates added from the overlap regions.

For the further analysis, we do not include the horizontal branch (HB) stars,
indicated as purple dots in Fig. 5. Stars hotter than $\sim$11,000 K have
chemically peculiar atmospheres due to diffusion and require dedicated model
atmospheres for proper analysis (see Latour et al., 2023). The analysis of the
HB stars included in our GO data will be presented elsewhere.

##  4 Analysis

In Section 3 we explained how we get a spectroscopic catalog from our MUSE
data. This catalog needs to be further analyzed to remove contamination from
foreground/background stars and to obtain robust measurements. Our overall
goal is to keep as many stars as possible in the catalog and provide all
parameters needed to perform the relevant quality cuts depending on the
science case.

For our final catalog, we combine both the GO and GTO datasets. The GTO
catalog contains 795,944 measurements belonging to 75,416 unique stars (see
Section 4.3). As described in the previous section, the GO analysis followed
that of the GTO data with three main differences: (1) the GTO data have
multiple epochs of observations as opposed to a single epoch for the GO data,
(2) the GTO use two HST catalogs for source positions, the catalog created by
Anderson et al. (2008) for the ACS survey of Galactic GCs (Sarajedini et al.,
2007) and the Anderson & van der Marel (2010) catalog, and (3) during spexxy
fits the log(g) for the BSS in the GTO data set was kept fixed to 4.2 dex,
while we fit for log(g) for these stars.

###  4.1 Reliability parameter

To have one overall parameter evaluating the quality of the derived LOS
velocities, we calculate a reliability parameter $R$, as explained in Sect.
3.2 of Giesers et al. (2019):

$\displaystyle
R=(2R_{SNR}+10R_{cc}+R_{\epsilon_{vcc}}+3R_{v}+2R_{\epsilon_{v}}$
$\displaystyle+5R_{v=vcc})/23.$ (1)

The different components can be either false (0) or true (1), allowing the
range of $R$ to be from 0 to 1 with higher values being more reliable than
lower ones. The first component, $R_{SNR}$, is a SNR cut, while the other
parameters are different checks of the credibility of the LOS velocity
calculations. In detail, they check the quality of the cross-correlation
($R_{cc}$), if the cross-correlation and the full-spectrum fit uncertainty are
plausible ($R_{\epsilon_{vcc}}$ & $R_{\epsilon_{v}}$), if the full-spectrum
fit velocity is agreeing with the expected cluster or foreground velocity and
with the cross-correlation ($R_{v}$ & $R_{v=vcc}$).

First, we consider a minimum SNR of 5 to be reliable:

$R_{\mathrm{SNR}}=\mathrm{SNR}\geq 5.$ (2)

That is however not our suggested SNR cut for the whole catalog, which should
be higher (Section 4.7), but only for the velocity calculation which does not
need that high SNR. In addition, we use the FWHM result from our cross-
correlation and the r-statistics (Tonry & Davis, 1979) to check the quality of
the cross-correlation which gave the initial LOS velocities for the fit with
spexxy:

$R_{cc}=r_{cc}\geq 4~{}\&~{}FWHM>10\AA.$ (3)

Further, a plausible velocity uncertainty of
$0.1\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ for the velocity from
spexxy and from the cross correlation is required:

$\displaystyle
R_{\epsilon_{v}}=\epsilon_{v}>$0.1\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$
(4) $\displaystyle
R_{\epsilon_{vcc}}=\epsilon_{vcc}>$0.1\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$.$
(5)

Additionally, the velocity output from spexxy should be plausible. This means
that it should match the velocity of either the cluster or the Galactic field
stars. Hence, the values are checked to be within 3$\sigma$ of the cluster
velocity and the cluster dispersion, $v_{cl}$ = (232.7
$\pm$0.2)$\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ and $\sigma_{cl}$ =
$17.6\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ (Baumgardt & Hilker,
2018), or that they agree with the foreground stars. For the cluster
membership, we calculate:

$R_{v_{1}}=\frac{|v-v_{cl}|}{\sqrt{\epsilon_{v}^{2}+(\sigma_{cl}+\epsilon_{v_{cl}})^{2}+a^{2}}}\leq
3.$ (6)

With $a$ being $30\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ which is
added to the broadening in order to account for the orbital motions of binary
stars, as their measured velocities would not necessarily be covered by the
cluster distribution. For the foreground stars:

$R_{v_{2}}=\frac{|v-0km~{}s^{-1}|}{\sqrt{\epsilon_{v}^{2}+(50km~{}s^{-1})^{2}}}\leq
3,$ (7)

with $50\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ being the estimate for
the foreground stars from the Besançon model (Robin et al., 2003) used in
Section 4.4. The total $R_{v}$ is true if at least one of the $R_{v_{1,2}}$ is
true. Similarly, a maximum 3$\sigma$ difference is allowed between the cross-
correlation results and the final spexxy results, while allowing a maximal
velocity error of $40\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ for the
cross-correlation:

$R_{v=vcc}=\frac{|v-v_{cc}|}{\sqrt{\epsilon_{v}^{2}+\epsilon_{cc}^{2}}}\leq
3.$ (8)

We include the total $R$ parameter for all stars in the catalog.

###  4.2 Error Analysis

$1$ dataset a b Maximum scaling Minimum scaling Maximum Minimal Parameter
Model/Data Model/Data fractional residual fractional residual GO [M/H] 0.887
0.007 1.644/1.938 1.401/1.200 0.179 0.226 GO $\rm v_{los}$ -0.143 0.062
2.819/2.943 1.229/1.351 0.243 0.186 GO $\rm T_{eff}$ 1.791 -0.003 1.639/1.701
1.292/1.213 0.279 0.169 GTO [M/H] 0.866 -0.002 1.359/1.402 1.293/1.246 0.071
0.051 GTO $\rm v_{los}$ -0.137 0.009 1.354/1.346 0.979/0.982 0.022 0.021 GTO
$\rm T_{eff}$ 1.463 -0.014 1.521/1.596 0.976/1.137 0.209 0.125

Table 2: Error Analysis

Note. — Column 1: The dataset and parameter used for the error analysis;
column 2, and column 3, are the best fitting parameters for the first order
polynomial, g(x) = a + b$\cdot$ x, where x the SNR and y the
$\sigma^{2}(\Delta y$). Columns 4 and 5 are the maximum/minimum scaling we get
from our best fit and what the actual data have; columns 6 and 7 are the
Maximum and Minimum fractional residuals, which are always under 30 %.

Figure 7: Error analysis CDF. The cumulative distribution of the $\Delta[M/H]$
in black for SNR $>10$ for the GO data and in red the distribution if it was a
normal distribution. The dashed black line is the distribution after the error
correction.

Figure 8: Error analysis correction. Top panels: The x-axis is the SNR and the
y-axis is the $\sigma^{2}$ of the $\Delta[M/H]$ for the GO data on the left
and the GTO data on the right. The red line is the best-fitting first-order
polynomial, the black dots are our data values, and the light red shaded area
is the region below an SNR of 10, which we exclude from the analysis. Bottom
panels: The x-axis is the SNR and the maximum percentage of counts one star
has in each bin. The red dashed line shows the maximum number of measurements
each star can have, which is clearly always below 10 % of the total number of
measurements in each bin, making sure the statistics in each bin are not the
result of only one star.

To get a better understanding and estimate of the errors on our fitted
parameters, we use stars with multiple observations (see Section 4.3),
allowing us to compare the different results we get for the same star, similar
to Husser et al. (2016); Kamann et al. (2018). From that, we can compare the
statistical uncertainty we get from the spectral fitting routine with the
scatter from the repeat measurements. This allows us to estimate how accurate
the errors from the spectral fitting routine are, and any scaling factor
needed to correct them. We do this analysis for our main results from spexxy:
the metallicity, line-of-sight velocity, and effective temperature, using only
the individual measurements used to compute the mean parameters, as described
in the following section (Section 4.3), for the error analysis.

We calculate:

$\Delta y=\frac{y_{i}-y_{j}}{\sqrt{\epsilon_{i}^{2}+\epsilon_{j}^{2}}},i\neq
j$ (9)

where $y_{i},y_{j}$ are the different results we get from spexxy (where $y$ =
[M/H], $\rm v_{los}$ or $\rm T_{eff}$) for the same star in two different
observations, and $\epsilon_{i},\epsilon_{j}$ are their spexxy errors. Some
stars are in more than two observations (maximum in 4 for the GO data, 66 for
the GTO data) so we calculate $\Delta y$ for each combination of different
results, giving us 24,216 values for the GO dataset and 2,016,633 for the GTO.

Afterwards, we bin all $\Delta y$ values in SNR bins depending on the mean SNR
of the two measurements, $SN_{i}$ and $SN_{j}$. We defined the SNR bins so
that for the GO and GTO data, the statistics of no SNR bin can be dominated by
just one star with multiple measurements if placed in the same bin. In the
bottom panel of Fig. 8 we show the maximum percentage of counts (f =
max[counts one star]/total number counts, per bin) one star has in each bin,
whereas for the GO data it is always below 5 % and for the GTO below 10 %. The
distributions of $\Delta y$ in each of the SNR bins, if the spexxy errors are
accurately estimated, should be a Gaussian with $\sigma=1$ and the mean at 0.

In Fig. 7 we show an example of the cumulative distribution for the
metallicity errors before any correction (black solid line) in comparison to a
normal distribution (red line). We find that, as in this example for SNR $>$
10, the spexxy errors typically are underestimated relative to the repeat
measurements, which are a better estimate of the true errors. We, therefore,
multiply the spexxy errors by a scaling factor, $\rm\sqrt{1+g(SNR)}$, to get
more accurate errors for each star. After applying the scaling of the errors
(see next paragraph), the cumulative distribution of the repeat measurement
$\Delta$[M/H] (black dashed line) follows the normal distribution.

If we plot the variance $\sigma^{2}$ ($\sigma$ calculated as half of the
difference between the 15.86 percentile and 84.14 percentile) of this
distribution as a function of SNR, we can see that $\sigma^{2}$ is higher than
1 towards larger SNR, see Fig. 8. We can describe this trend using a simple
function, y = 1 + g(x), with g(x) being a linear function, in order to get an
estimate of the error correction needed as a function of SNR. We exclude the
SNR bins below 10 for the fitting of the line. In Table 2 we list the best
fitting parameters for the scaling relation and the values for the maximum and
minimum scaling for SNR $>$ 10\. To quantify how accurately the linear
function captures the repeat measurement data, we also include the
maximum/minimum fractional residual to this fit (i.e. the fractional error on
the point that lies farthest from the line in Fig. 8).

The derived scaling functions are then applied to all data according to their
SNR. The mean scaled errors for 40 $<$ SNR $<$60 are $\epsilon_{v_{los}}$ =
$3.11\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$, $\epsilon_{T_{eff}}$ =
$36\text{\,}\mathrm{K}$ and $\epsilon_{M/H}$ = 0.057 dex. These new, scaled
errors are more accurate estimates of the true errors and hence we will always
use them in the following analysis.

###  4.3 Combining multiple measurements

The next step is to combine measurements for each observed star. Due to the
multiple epochs of observations in the GTO data, each star has been observed
multiple times, and the spectra were analyzed independently, such that the
795,944 measurements belong to 75,416 unique stars. For the GO data, only
stars in the overlap regions of the different pointings (green and yellow
regions in Fig. 2) have been observed more than once, with 303,822 unique
stars out of the 356,065 measurements. In addition, there are also overlapping
regions in the GTO and GO data where stars are in both datasets.

To combine multiple measurements of stars, we do a mean calculation for both
datasets together after scaling the errors. First, we require the measurements
to have a successful spexxy fit, meaning a fit to the templates could be
performed without problems and the final parameters are not close to their
limits set for the fit. These cuts leave us with 744,344 GTO measurements and
335,834 GO measurements.

For stars with multiple measurements, we then calculate the mean values using
a subset of measurements selected in a procedure based on their reliability
value (Section 4.1), magnitude accuracy from the spectral extraction, the
distance to the edge of the detector, and an SNR cut. We use a threshold
reliability value of 0.5, and magnitude accuracy (the relative accuracy of the
magnitude from the extracted spectrum vs. the HST catalog) $<$0.6. We continue
with measurements that meet these thresholds, or if there are none for a
single star, we keep all measurements for the next steps in the combination.

Next, to use comparable measurements in the mean calculation, we first find
the highest SNR spectrum and check if it is at least $5\text{\,}\mathrm{pix}$
(1″) away from the edge of the pointing. If it is, we consider it the best
measurement for the given star. If it is not, we check the second-highest SNR
spectrum and set that as the best measurement or, if it is also too close to
the edge, we return to the highest SNR spectrum as the best measurement.
Having found the best measurement, we require all remaining measurements to
have at least half the SNR of the best measurement or in general higher than
20, at least as good of an extraction quality flag as the best, and if the
best measurement was more than $5\text{\,}\mathrm{pix}$ away from the edge,
the other measurements have to be, too. The measurements that pass these tests
are in general comparable to the best measurement and are used to calculate
the mean measurements for a given star. If there is only one measurement, then
that is used as a single entry for that star.

For the mean calculation of [M/H], $\rm v_{los}$ and $\rm T_{eff}$ we
calculate the inverse-variance weighted mean, using the scaled errors (see
Section 4.2):

$\displaystyle\hat{y}=\frac{\Sigma_{i}y_{i}/\epsilon_{si}^{2}}{\Sigma_{i}1/\epsilon_{si}^{2}}$
(10)
$\displaystyle\epsilon_{s\hat{y}}=\sqrt{\frac{1}{\Sigma_{i}1/\epsilon_{si}^{2}}}.$
(11)

$\epsilon_{s\hat{y}}$ is the error to the inverse-variance weighted mean,
similarly we calculate the combined not scaled spexxy errors. The scaling
factor and SNR are normal unweighted mean values, while for the quality
parameters: distance to the edge, magnitude accuracy, extraction quality flag,
and reliability parameter, we keep the minimum value (maximum for the
extraction quality flag) included in the combined value. For the log(g)
parameter we give the unweighted mean value, indicating if it was kept fixed
or free during the fit, if we used both free/fixed we give both means.

This leaves us with a combined catalog of 342,796 unique individual stars with
physical parameters. We describe recommended quality cuts for using this
catalog further in Section 4.7. We match this catalog with the HST catalog by
Anderson & van der Marel (2010), but note that 1,432 stars in the GTO data
which were extracted using the Anderson et al. (2008) catalog could not be
matched; these stars are included in the catalog without Anderson & van der
Marel (2010) magnitudes.

###  4.4 Membership

Figure 9: Membership probabilities using radius and velocity for a SNR$>$10.
The stars’ radial distances to the cluster center in arcminutes are plotted
against their line-of-sight velocities. The points are color-coded according
to their membership probability, yellow being 1.  Figure 10: Atomic diffusion
correction. Top left: CMD of all stars with HST photometry colored by their
metallicity. Top right: A grid of the median metallicity correction when
considering isochrones that model atomic diffusion. Bottom: CMD of all stars
from the top left panel, now with the relevant atomic diffusion correction
applied. Stars with $\rm SNR<10$ and less reliable photometry are plotted with
transparency in each panel.

To decide which stars likely belong to $\omega$ Cen, we assign the stars a
membership probability $P_{M}$ that we can use to exclude foreground or
background stars belonging to the Milky Way. We determine this probability
using the python package clumpy333https://github.com/bkimmig/clumpy (Kimmig et
al., 2015) which is based upon Walker et al. (2009). This code can use either
radius and velocity only for the estimate or can include another parameter,
like the metallicity, to get the membership probability. As a foreground
velocity distribution, we use the Besançon model (Robin et al.,
2003)444https://model.obs-besancon.fr/ws/ with 1 degree on each side centered
on $\omega$ Cen and the model maximum absolute velocities are reaching up to
$500\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$.

The package uses an iterative maximization technique to get the probability
and the systemic velocity and dispersion. Three separate memberships are going
into the total membership probability including information about radius,
velocity, and the foreground model: i) the probability of being a member which
assumes that the stars follow a Gaussian velocity distribution centered on the
mean velocity of the cluster, ii) the non-membership probability including the
Besançon model information assuming a velocity dispersion of
$20\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$, and iii) the probability
depending on the radius assuming a radial decrease in membership. After every
iteration, the mean velocity, velocity dispersion, and probability are updated
until they converge. We perform 50 iterations and the initial values are 0.5
for the probabilities and $4\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$
for the central dispersion of the cluster.

The membership output for SNR $>$ 10 is shown in Fig. 9 when using only
velocity and radius from the center ($\mathrm{R}A_{c}$ = 13:26:47.24 and
$\mathrm{D}ec_{c}$ =-47:28:46.45, Anderson & van der Marel, 2010) as input. We
clearly can see the separation between the foreground stars and the members
(over 95 % probability) in the velocity radius plane, with 98.8% (338,531
stars) of stars being members and only 1.2% (4,266 stars) not. We choose to
use the membership that does not include metallicity information for the
following analysis since the [M/H] distribution of the cluster is too broad
and hence not that easily distinguishable from the foreground. We note that
117 stars have no membership probability since their velocity exceeds the
$500\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ from the foreground model,
however, these stars have low SNR ($\leq 5$).

###  4.5 Atomic Diffusion Correction

In the left panel of Fig. 10 we show the CMD of our full MUSE catalog with
each point colored by its metallicity [M/H]. The stars near the main sequence
turn-off (MSTO) seem to be more metal-poor than stars falling directly above
and below this region. A similar offset in metallicity was seen by Husser et
al. (2016) in NGC 6397, who find a $\sim$0.3 dex variation in the mean
metallicity along the MS, with the lowest metallicity at the turn-off. Other
analyses have also found a decrease in the observed metallicity (up to 0.25
dex, King et al., 1998) (in M92/NGC 6341) compared to stars of the same
population along the MS and subgiant branch (SGB).

This shift can be explained by several internal transport processes including
atomic diffusion (gravitational settling of heavier elements), thermal
diffusion, radiative acceleration, and turbulent mixing (VandenBerg et al.,
2002). For stars evolving through the MSTO, heavier elements begin to sink
below the outer layers of the star causing them to be undetectable via
spectroscopy. The consequence is that the observed metallicity of these stars
is lower than the abundance they were originally born with. Once a star enters
the SGB, convection in the outer layers begins and heavier elements are then
dredged up to the surface where they are once again observable. Therefore,
these stars no longer exhibit the offset in metallicity attributed to atomic
diffusion. It is also noted in Korn et al. (2007) and Nordlander et al. (2012)
that this phenomenon has a larger effect on extremely metal-poor stars, which
is where we also see the greatest offset. We note that hereafter we refer to
our correction for these effects as an ”atomic diffusion correction.”

Figure 11: [M/H] of RGB vs. MSTO post AD correction. The figure shows how the
atomic diffusion correction causes the [M/H] distribution to be more
consistent between the MSTO and the RGB (when considering both to have MSTO-
like errors).

To correct for this effect on our metallicity measurements, we use MIST
isochrones (Dotter, 2016; Choi et al., 2016), which take into account atomic
diffusion. We use the distance modulus for the isochrones and apply extinction
and reddening corrections to our photometry. Specifically, we assume $\rm
A_{v}$ = 0.372 mag (Harris, 1996; Bellini et al., 2017a) and use the values
for $\rm A_{\lambda}/A_{V}$ of 1.34148 and 0.85528 for F435W and F625W
respectively 555Obtained from http://stev.oapd.inaf.it/cgi-bin/cmd, Girardi et
al. (2008)., giving us $\rm A_{\lambda,435}=0.499$ mag and $\rm
A_{\lambda,625}=0.318$ mag. We then subtract $\rm A_{\lambda}$ from the
relevant magnitudes to obtain our corrected photometry.

We use a series of isochrones with $\rm Age=10\ Gyr$ and
$\rm-4.0<\langle[Fe/H]\rangle<0.5$. We increase the CMD coverage of the MIST
isochrones (which are available in steps of 0.5 to 0.25 dex in metallicity) by
interpolating between equivalent evolutionary points to generate isochrones
between the given models. We then iterate this process until we obtain good
coverage across the CMD and a metallicity precision of 0.03 to 0.06 dex. For
each interpolated isochrone, we calculate the difference between its overall
metallicity and the surface metallicity at each point along it. We grid these
differences in the CMD using color bins of 0.05 mags and F625W bins of 0.12
mags, finding the median correction in each bin. To derive the atomic
diffusion (AD) correction for individual stars, we interpolate within this 2D
grid of corrections. The bottom panel of Fig. 10 shows that these corrections
shift the metallicities the most in the MSTO region, while the right panel
shows that applying the AD correction narrows the spread in mono-metallic
tracks along the full CMD. We also plot the [M/H] distribution of the RGB
stars vs. the MSTO (see Fig. 11). To aid more direct comparison, we also plot
the [M/H] of the RGB with ”MSTO-like” errors (meaning for each RGB star we
randomly sample a MSTO star error then resample the given RGB metallicity from
a Gaussian with a sigma equivalent to the new error. Because RGB metallicities
are more well-measured, this demonstrates the overall spread in RGB
metallicities if they had the same uncertainties as fainter MSTO stars).
Before the correction, it is clear that the MSTO stars are shifted to lower
metallicities by $\sim 0.2$ dex while after the correction the distributions
are significantly more consistent, as expected.

Using atomic diffusion corrected metallicities allows us to group stars across
the CMD by their birth metallicity, not their observed atmospheric
metallicity. This enables us to more accurately group stars with similar
abundances and better understand the processes that enrich each population. We
include both the raw and atomic diffusion corrected values for the
metallicities in our catalog and we use the corrected values in all analyses
forthcoming.

###  4.6 Perspective rotation

Figure 12: Perspective rotation. The figure shows the position of the data
color coded with the perspective rotation value for each star. The red cross
is indicating the center and the velocity values increase from the bottom left
to the top right corner of the plot.

$\omega$ Cen takes up a large angle on the plane of the sky. Therefore, there
is a non-negligible apparent rotation caused by the different projection of
the space motion at different positions on the sky. This is known as
perspective rotation (van de Ven et al., 2006). To correct for it we need to
subtract from the line-of-sight velocity the perspective rotation term:

$\displaystyle v_{pr}[\mathrm{km~{}s^{-1}}]=1.3790\cdot 10^{-3}\cdot D\cdot$
$\displaystyle\left(-\Delta RA\cdot cos(Dec)\cdot\mu_{RA}^{sys}+\Delta
Dec\cdot\mu_{Dec}^{sys}\right)$ (12)

with the distance to the center $\Delta RA$, $\Delta Dec$ in units of arcmin,
distance to the cluster D = (5.43 $\pm$ 0.05) kpc (Baumgardt & Vasiliev,
2021), proper motion in RA $\mu_{RA}^{sys}=(3.25\pm 0.022)$ mas
$\mathrm{yr^{-1}}$ and proper motion in Dec $\mu_{Dec}^{sys}=(-6.746\pm
0.022)$ mas $\mathrm{yr^{-1}}$ from Vasiliev & Baumgardt (2021).

The resulting velocity calculated with Section 4.6 is shown in Fig. 12, and
the maximum value for the perspective rotation in our dataset is
$0.35\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$.

###  4.7 Catalog

Figure 13: SNR in the catalog. The CMD of the stars in the catalog color coded
with their SNR as calculated from spexxy.

Figure 14: Comparison to literature values. On the left is the [Fe/H]
distribution for the Johnson & Pilachowski (2010); Johnson et al. (2020), the
black solid line, and from the MUSE results, the black dashed line, for all
the matched stars in both catalogs. In red is the [M/H] distribution for the
matched stars of the Mészáros et al. (2021) data, solid line, and the MUSE
data. On the right, we plot the literature values against the difference
between the two [Fe/H] or [M/H] values. The black dashed line indicates where
both values agree.

Having performed all the data reduction, stellar spectra extraction, and
analysis steps described in Section 2, 3 and 4, we have a final spectroscopic
catalog with 342,797 stars (GTO: 58,143, GO: 272,633 and combined GO/GTO:
12,021). All the parameters given in this catalog are described in Appendix E
and the SNR of the stars in the CMD is shown in Fig. 13. The catalog will be
published together with this paper in a machine-readable format.

Since 1,432 GTO stars are not in the Anderson & van der Marel (2010) catalog,
they do not have magnitudes in the F625W and F435W filters, and therefore no
atomic diffusion correction (ADC) could be performed. We will update the ADC
for these stars in a subsequent paper using a new HST catalog (Häberle et al.
in prep) that includes new data acquired under the program GO-16777 (PI: A.
Seth).

Our catalog has no quality cuts, as each science case can decide the best cuts
for its own purpose. However, the quality cuts we suggest are as follows:

  * •

Membership probability: $P_{M}>$ 95 per cent

  * •

Magnitude accuracy during extraction with PampelMuse $\geq 0.6$

  * •

Reliability: $R\geq 0.5$

  * •

Distance to MUSE IFU edge: $\geq$ 5 pixel (1″)

  * •

Signal-to-Noise ratio: SNR $>10$ (see Appendix B and Appendix D).

The above cuts yield 156,871 stars and of these, only 143 GTO stars lack
photometry in the Anderson & van der Marel (2010) catalog. These 156,871 stars
have a mean metallicity error of 0.15 dex, a median $\rm v_{los}$ error of
$6.26\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ and a median $\rm
T_{eff}$ error of $102\text{\,}\mathrm{K}$. In more detail, the mean
metallicity error for MS stars ($18\text{\,}\mathrm{mag}$
$\rm<mag_{F625W}<$$22\text{\,}\mathrm{mag}$) is 0.174 dex and for RGB stars
($16\text{\,}\mathrm{mag}$ $<\rm mag_{F625W}<$$10\text{\,}\mathrm{mag}$) 0.031
dex. We decided on these cuts in order to have reliable results but still keep
as many stars as possible, stricter cuts will give smaller uncertainties. The
SNR cut of 10 is consistent with all our tests in Appendix B, Appendix C and
Appendix D, which show that below that value biases because of different
assumptions and setups can play a role. The distance to the edge is chosen to
verify that the stars are not outside or exactly at the edge of the IFU where
only part of the starlight can be extracted. The other parameters are
reasonable cuts for the extraction accuracy, reliability, and membership, but
stricter cuts can be applied for higher precision.

Additionally, the median systemic LOS velocity, corrected for the perspective
rotation and sign the above quality cuts, is $\rm v_{los}=(232.99\pm
0.06)~{}km~{}s^{-1}$ with the error found using bootstrapping and even without
the reliability quality cut the result does not change. This value is close to
previous values, e.g. $\rm(232.7\pm 0.2)~{}km~{}s^{-1}$ Baumgardt & Hilker
(2018) using ESO/VLT, Keck spectra, and literature values, being just slightly
out of the 1$\sigma$ range, while $\rm(234.28\pm 0.24)~{}km~{}s^{-1}$
Baumgardt et al. (2019) where they used Gaia DR2 data, which due to crowding
do not have many stars in the central region where we observe, being outside
of the 3$\sigma$ range due to the small errors.

One should note that these are quality cuts based on our spectroscopic
analysis, while the photometry and astrometry are added from the HST catalogs
(Sarajedini et al., 2007; Anderson & van der Marel, 2010). We are preparing a
new astrometric and photometric catalog (Häberle et al. in prep) that will
provide updated values for the magnitudes and positions.

###  4.8 Literature Comparison

In this subsection, we present a first comparison of our findings with
previous works. For the comparison, we use other previous studies that use
spectroscopic data and not just photometry.

To compare our [M/H] values from spexxy (without AD correction) to literature
values for [Fe/H] from RGB stars (e.g.: Johnson & Pilachowski, 2010; Johnson
et al., 2020) we need to transform [M/H] to [Fe/H] values. We use the
following formula (Salaris et al., 1993):

$[Fe/H]=[M/H]-\log(0.638\cdot 10^{[\alpha/Fe]}+0.362)$ (13)

with $[\alpha/Fe]$ set to 0.3 in spexxy. This transformation accounts for the
contribution of the assumed $\alpha$ enhancement to our assumed [M/H] values,
while the literature values derive separate abundances for several $\alpha$
elements (Johnson & Pilachowski, 2010).

We match the Johnson & Pilachowski (2010); Johnson et al. (2020) catalogs to
ours using only the brightest stars (F625W $<$ 14 mag) by finding the closest
star that is no more than $1\text{\,}\arcsec$ away, in order to find real
matches but not have too strict criteria and eliminate matches due to slight
offsets in the coordinates. The [Fe/H] of the 524 matched stars are shown in
Fig. 14. The measurements are strongly correlated with a mean offset between
them of 0.03 dex and a scatter of 0.17 dex, with the literature values being
slightly more metal-rich but still close to zero showing no strong systematic
offset and the scatter representing the statistical discrepancy. We note that
our matching criteria and differences in astrometry could result in some
mismatched stars. Unfortunately, this cannot easily be improved using
photometry, as there are no common filters between the catalogs. In addition,
we do not find as low metallicity stars as in Johnson et al. (2020), which
seem to have the biggest deviation from our data.

Further, we also match our [M/H] values to the metallicity from Mészáros et
al. (2021) where they used APOGEE measurements. Since, most of the
spectroscopic surveys, like Gaia and APOGEE, have problems with crowding in
the central cluster region where we observe, there is almost no overlap.
However, we could match 74 stars, and the results are also shown in Fig. 14.
The measurements have a mean offset between them of 0.06 dex and a scatter of
0.28 dex.

##  5 Conclusion

In this work, we present an extensive catalog of stars obtained with 87 new
MUSE pointings plus the already existing 10 WFM and 6 NFM GTO pointings for
$\omega$ Cen, covering out to the half-light radius.

We describe the data and the analysis steps used to create the final catalog
of stars. First, we reduce the data and extract individual spectra of stars
using PampelMuse (Kamann et al., 2013). Afterwards, we use the spectral
fitting routine spexxy to measure the LOS velocities, effective temperatures,
and metallicities of these stars. We perform multiple tests including
exploiting a large number of repeated measurements to verify our results. We
provide several parameters to quantify the reliability of the results and also
include several necessary corrections to our measurements. We end up with
342,797 stars after all of our analysis steps without any quality cuts.
However, for most use cases we suggest several quality cuts: SNR $>$ 10,
membership probability $\rm P_{M}>$ 0.95 %, Magnitude accuracy $\geq$ 0.6 mag,
distance to the IFU edge $\geq$ 5 and Reliability $R\geq$ 0.5. Thus, 156,871
stars meet all these criteria.

Finally, we do a first analysis of the metallicity distribution comparing it
to previous works and find that they are consistent with our findings and
calculate the median systematic LOS to be $\rm v_{los}=(232.99\pm
0.06)~{}km~{}s^{-1}$. A more detailed analysis of the metallicities as well as
the LOS velocity information will be presented in a separate subsequent paper.
In addition, a new HST catalog with proper motions photometry for millions of
stars covering most of the MUSE data is in preparation (Häberle et al. in
prep.). Combining both, the astrometric and spectroscopic catalog for $\omega$
Cen, will allow us to measure the ages of the stars and identify the
subpopulations of the cluster using photometry and metallicity information
(Clontz et al. in prep.). Moreover, using the spectroscopic data we can also
measure individual abundances by combining spectra of the same population and
directly measuring the absorption lines of different elements (Di Stefano et
al. in prep.), which will further constrain the multiple populations and their
formation scenario. Combining the information on the stellar populations and
kinematics of a large number of stars in $\omega$ Cen will provide a clear
picture of its formation history.

## Acknowledgments

The work is based on observations collected at the European Southern
Observatory under ESO program 105.20CG.001. We thank the ESO staff for their
excellent support. Also based on observations made with the NASA/ESA Hubble
Space Telescope, obtained from the data archive at the Space Telescope Science
Institute. STScI is operated by the Association of Universities for Research
in Astronomy, Inc. under NASA contract NAS 5-26555. This research made use of
NASA’s Astrophysics Data System. AS and CC acknowledge support from HST grant
GO-16777. We acknowledge funding from the Deutsche Forschungsgemeinschaft
(grant LA 4383/4-1 and DR 281/35-1) and from the German Ministry for Education
and Science (BMBF Verbundforschung) through grants 05A14MGA, 05A17MGA, and
05A20MGA. SK acknowledges funding from UKRI in the form of a Future Leaders
Fellowship (grant no. MR/T022868/1). We thank the anonymous referee for the
helpful and constructive comments.

In the Appendix, we include further information and elaborate on checks we
performed on our data.

##  Appendix A Data Conditions

Since our data were taken over an extended period of longer than a year, the
atmospheric conditions were also varying. In Table 3 we summarize the
conditions and observing date of the individual GO pointings used in this
analysis. We requested an airmass less than 1.4 and seeing below $0\farcs 8$,
which were almost always fulfilled.

$2$ OB Date Average Airmass Average Seeing 1.1 17 February 2021 1.263 0.897
1.2 17 February 2021 1.246 0.777 1.3 17 February 2021 1.204 0.733 1.3666OB 1.3
was observed twice since it had a wrong offset causing a gap in our dataset. 2
September 2022 2.144 0.577 2.1 16 March 2021 1.102 1.203 2.2 16 March 2021
1.092 1.133 2.3 16 March 2021 1.087 1.357 3.1 16 March 2021 1.088 1.097 3.2 16
March 2021 1.093 1.127 3.3 16 March 2021 1.103 1.360 4.1 8 April 2021 1.096
0.433 4.2 8 April 2021 1.089 0.500 4.3 8 April 2021 1.086 0.470 5.1 14 March
2021 1.088 1.140 5.2 14 March 2021 1.094 1.110 5.3 14 March 2021 1.103 1.133
5.4 14 March 2021 1.116 1.273 6.1 8 April 2021 1.088 0.503 6.2 8 April 2021
1.093 0.527 6.3 8 April 2021 1.101 0.497 6.4 8 April 2021 1.113 0.547 7.1 18
May 2021 1.209 0.567 7.2 18 May 2021 1.180 0.547 7.3 18 May 2021 1.155 0.553
7.4 18 May 2021 1.135 0.450 8.1 18 May 2021 1.089 0.59 8.2 18 May 2021 1.086
0.573 8.3 18 May 2021 1.087 0.687 9.1 30 June 2021 1.088 0.883 9.2 30 June-1
July 2021 1.093 0.907 9.3 1 July 2021 1.101 1.147 9.4 1 July 2021 1.113 1.163
10.1 4 July 2021 1.106 0.937 10.2 4 July 2021 1.119 0.877 10.3 4 July 2021
1.119 0.843 10.4 4 July 2021 1.157 0.840 11.1 31 March 2022 1.295 0.62 11.2 31
March 2022 1.253 0.540 11.3 31 March 2022 1.217 0.50 11.4 31 March 2022 1.186
0.4340 12.1 9 February 2022 1.325 0.557 12.2 9 February 2022 1.279 0.677 12.3
9 February 2022 1.239 0.637 12.4 9 February 2022 1.206 0.700 13.1 9 February
2022 1.171 0.507 13.2 9 February 2022 1.148 0.703 13.3 9 February 2022 1.128
0.563 13.4 9 February 2022 1.113 0.693 14.1 9 February 2022 1.099 0.723 14.2 9
February 2022 1.091 1.020 14.3 9 February 2022 1.087 0.650 14.4 9 February
2022 1.085 0.780 15.1 10 February 2022 1.250 0.653 15.2 10 February 2022 1.215
0.727 15.3 10 February 2022 1.184 0.823 15.4 10 February 2022 1.159 0.597 16.1
10 February 2022 1.133 0.740 16.2 10 February 2022 1.117 0.600 16.3 10
February 2022 1.103 0.433 16.4 10 February 2022 1.094 0.897 17.1 27 February
2022 1.358 0.350 17.2 27 February 2022 1.308 0.307 17.3 27 February 2022 1.265
0.293 17.4 27 February 2022 1.228 0.250 18.1 27 February 2022 1.090 0.387 18.2
27 February 2022 1.086 0.413 18.3 27 February 2022 1.086 0.357 18.4 27
February 2022 1.089 0.520 19.1 27 February 2022 1.100 0.437 19.2 27-28
February 2022 1.147 0.463 19.3 28 February 2022 1.201 0.500 19.4 28 February
2022 1.173 0.627 20.1 28 February 2022 1.143 0.493 20.2 28 February 2022 1.125
0.397 20.3 28 February 2022 1.110 0.380 20.4 28 February 2022 1.100 0.380 21.1
28 February 2022 1.360 0.413 21.2 28 February 2022 1.087 0.453 21.3 28
February 2022 1.087 0.373 21.4 28 February 2022 1.091 0.307 22.1 2 March 2022
1.379 0.640 22.2 2 March 2022 1.326 0.517 22.3 2 March 2022 1.280 0.567 22.4 2
March 2022 1.241 0.877 23.1 2 March 2022 1.114 0.487 23.2 2 March 2022 1.102
0.493 23.3 2 March 2022 1.094 0.437 23.4 2 March 2022 1.089 0.463

Table 3: Observing Conditions

Note. — The observing conditions for all GO observations used in our work. OB:
the name/numbering of the individual pointings, Date: the date of observation,
average airmass: the mean airmass at the start of each of the three rotated
exposures, and average seeing: the mean seeing at the start of the three
rotated exposures for one OB. OB 1.3 was observed twice since the offset of
the pointing was not correct and created a gap in our continuous coverage.

##  Appendix B PampelMuse tests

We verify that slightly changing the PampelMuse setup, does not influence our
results for stars with SNR$>$ 10\. For these tests, we use two example
pointings where a different setting might have been more appropriate. First,
we use a round PSF, fixing the ellipticity to 0, for OB 15.3, since the free
Moffat PSF we generally use seems unnecessarily complex as it is round anyway.
For the second example, we use OB 21.2 and masked certain layers in the
wavelength range that appear to have something wrong with them, bad pixels
from the data reduction, since their values drop significantly compared to the
rest of the spectrum. The results show no significant difference in the spexxy
output for an SNR $>$ 10, even though the new setup should be better for these
two cases. Therefore, we keep the setup consistent for all OBs as described in
Section 3.1.

##  Appendix C Surface gravity log(g)

In this section of the Appendix we investigate the bias we have due to the
fixed log(g) parameter from one single isochrone for most stars (see Section
3.3).

Figure 15: Discrepancy between spectral parameters with free and fixed log(g)
(a) The one-to-one comparison between the [M/H] values, red line the 1 to 1
ratio, (b)-(e); The sigma deviations for [M/H], $\rm v_{los}$, $\rm T_{eff}$
and log(g). We divide the difference between the two results with the scale
error in our catalog, except for the log(g) where we take the spexxy error for
the free log(g) run. The dashed red line is at 0, the solid red lines at the 3
$\sigma$ limits, and the orange solid line is the median of all stars, while
the red shaded area is the SNR limit of 10.

###  C.1 Free logg

First, we investigate how allowing log(g) to vary freely for all stars during
the fit with spexxy, would change our results. For that, we look at a subset
of our data including RGB and MS stars, which gives us a complete
representation of the magnitude and SNR range.

The deviations between the free and fixed log(g) fit are shown in Fig. 15.
Most of the results are within the 3 $\sigma$ range for a SNR $>$ 10\. The
deviations at high SNR are because of the smaller errors at that level. We can
see that all parameters tend to get lower when the log(g) values are left
free, but not as significant for [M/H] and $\rm v_{los}$ where they almost all
stay within the 3 $\sigma$ range. This also proves that the log(g) parameter
does not affect the metallicity calculation strongly.

###  C.2 Metal rich stars

Figure 16: Metal rich. On the left plot, the one-to-one comparison of the
[M/H] is shown, with the red solid line being the 1 to 1 ratio. On the right
is the difference in log(g) between the two isochrones, with the dashed line
indicating no difference at all, the orange line the median difference of our
data, and the red shaded area the SNR limit of 10.

Since the cluster is known to have multiple populations, we know that one
isochrone for finding the log(g) is not ideal. To investigate the bias we have
because of that, we test one extreme population, the metal rich stars with
[M/H]$>-1$ dex, and use a different isochrone, more representative for them,
and assign them new log(g) values.

In Fig. 16 the [M/H] results are shown and the difference between the log(g).
In general, there seems to be just a small difference in log(g) even with a
different isochrone and a tight one-to-one correlation between the [M/H],
reassuring us that the exact isochrone used for the initial guesses and log(g)
values is not that significant.

###  C.3 Literature logg

Figure 17: Literature comparison log(g). We plot the Literature values against
the difference between Literature and our log(g) values.

Using the matching between Johnson & Pilachowski (2010); Johnson et al.
(2020); Mészáros et al. (2021) and our catalog, described in Section 4.8, we
also compare our surface gravity values with the literature. Almost all values
are for a fixed log(g) from the isochrone described in Section 3.3.

The log(g) of the matched stars are shown in Fig. 17. The measurements have a
mean offset between the Johnson & Pilachowski (2010); Johnson et al. (2020) of
0.18 dex and a scatter of 0.26 dex, with the literature values having slightly
lower log(g) values. With the Mészáros et al. (2021) values the mean offset is
0.04 dex and a scatter of 0.46 dex. This shows that even though our initial
isochrone is not a perfect match for all stars, because of multiple
populations and binaries, it still gives reasonable log(g) values since they
are comparable to previous studies. In addition, the metallicity values also
are within the expected literature range (see Section 4.8) even though log(g)
is fixed, hence this is another indication that there is no strong effect, as
already suggested in Husser et al. (2016); Kamann et al. (2016) and in Section
C.1, Section C.2.

##  Appendix D SNR test

To make sure that we have no bias in our metallicity and velocity measurements
for stars with different SNR, we performed another test, adding different
noise values to the spectra and redoing the spexxy fit.

We selected randomly 147 spectra with SNR above 28 (being not on the HB) and
added Gaussian noise, creating 3,999 spectra with SNR between 1 and the
original SNR. The difference between the original spexxy results and the new
ones with more noise increases as expected for lower SNR, and the output
errors also increase. The $\sigma$ difference as a function of the new SNR is
shown in Fig. 18. Almost all results are within the 3$\sigma$ range for SNR
$>$ 10 and we do not see any bias towards higher or lower values for lower
SNR.

The $\sigma$ difference is calculated using the error directly from spexxy, if
we also apply the error correction as described in Section 4.2, the difference
even decreases.

Figure 18: SNR test. The left plot shows on the y-axis the $\sigma$ difference
between the original result and the different [M/H] results after adding noise
to the spectra, and the x-axis is the new SNR with the added noise. Similar
for the right plot but for the $\rm v_{los}$ values. The light red shaded
areas indicate SNR below 10, the red solid horizontal lines are the 3$\sigma$
difference, the red dashed horizontal lines are at 0, and the orange solid
lines are the median values for our measurements as a function of SNR.

##  Appendix E Catalog Columns

Table 4 lists all parameters given in the spectroscopic catalog described in
this paper. The entries in the catalog are sorted by increasing radius from
the center.

$3$ Column Name Description More Details Units MUSE Identifier of stars in
spectroscopic catalog RVel Line-of-sight velocity ($\rm v_{los}$) spexxy
output $\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ errsRVel Line-of-sight
velocity uncertainty ($\epsilon_{v_{los}}$) spexxy output
$\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ sRVel Scaling factor for
$\epsilon_{v_{los}}$ Section 4.2 e_RVel Scaled error $\rm v_{los}$ Section 4.2
$\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ prv Perspective rotation see
Section 4.7 and van de Ven et al. (2006)
$\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ prvRVel $\rm v_{los}$
corrected for perspective rotation see Section 4.7 and van de Ven et al.
(2006) $\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ Teff Effective
Temperature ($\rm T_{eff}$) spexxy output K errsTeff Effective Temperature
uncertainty ($\epsilon_{T_{eff}}$) spexxy output K sTeff Scaling factor for
$\epsilon_{T_{eff}}$ Section 4.2 e_Teff Scaled error $\rm T_{eff}$ Section 4.2
K loggfix Fixed surface gravity ($\rm log(g)$) Isochrone output (Section 3.3)
dex loggfree Fitted surface gravity ($\rm log(g)$) spexxy output dex MH
Metallicity ([M/H]) spexxy output dex MHadc Metallicity corrected for AD see
Section 4.5 dex errsMH Metallicity uncertainty ($\epsilon_{[M/H]}$) spexxy
output dex sMH Scaling factor for $\epsilon_{[M/H]}$ Section 4.2 e_MH Scaled
error [M/H] Section 4.2 dex SNR Signal-to-noise ratio (SNR) spexxy output ffit
Fixed or free log(g) in spexxy 0 free and 1 fixed edge Distance to OB edge
PampelMuse output pixel Magacc Relative accuracy of the recovered magnitude
PampelMuse output SpecFlag Extraction quality flag PampelMuse output Rel
Reliability Parameter $R$ Section 4.1 Num Number of times the star was
observed Section 4.3 Data Observing program star belongs to GTO, GO or both
(GO_GTO) Rad Radius from cluster center $\sqrt{\left((RA-
RA_{c})cos(Dec)\right)^{2}+\left(Dec-Dec_{c}\right)^{2}}$ deg RAdeg Right
Ascension Sarajedini et al. (2007); Anderson et al. (2008), deg Anderson & van
der Marel (2010) DEdeg Declination Sarajedini et al. (2007); Anderson et al.
(2008), deg Anderson & van der Marel (2010) 435mag Magnitude in the F435W
filter (Vega) Anderson & van der Marel (2010) mag 625mag Magnitude in the
F625W filter (Vega) Anderson & van der Marel (2010) mag 435magC F435W-band
photometry $\rm A_{V}$ and $\rm R_{V}$ Correction Applied mag 625magC
F625W-band photometry $\rm A_{V}$ and $\rm R_{V}$ Correction Applied mag e_435
RMS scatter single-exposure f435w Anderson & van der Marel (2010) mag e_625
RMS scatter of single-exposure f635w Anderson & van der Marel (2010) mag NBf #
of B images where star was found Anderson & van der Marel (2010) NRf # of R
images where star was found Anderson & van der Marel (2010) probRV Membership
probability radius and velocity (Section 4.4) probRVM Membership probability
radius, velocity and [M/H] Flag Our quality suggestions 1=True, 0=False, see
Section 4.7 HST10Flag HST quality flag for Anderson & van der Marel (2010)
1=reliable, 0=unreliable photometry/astrometry

Table 4: Catalog Columns

Note. — $\mathrm{R}A_{c}$ = 13:26:47.24 and $\mathrm{D}ec_{c}$ =-47:28:46.45
(Anderson & van der Marel, 2010). For the parameters edge, Magacc, SpecFlag
and Rel we provide the minimum (maximum for SpecFlag) value when combining
multiple measures, see Section 4.3.

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