11institutetext: Istituto Nazionale di Astrofisica (INAF) – Osservatorio
Astronomico di Palermo, Piazza del Parlamento 1, 90134 Palermo, Italy
11email<EMAIL_ADDRESS>
22institutetext: Universidad de Rio Negro, Sede Atlántica - CONICET, Viedma
CP8500, Río Negro, Argentina
33institutetext: Instituto de Astrofísica e Ciências do Espaço, Faculdade de
Ciências, Universidade de Lisboa, Ed. C8, Campo Grande, 1749-016 Lisbon,
Portugal
44institutetext: European Southern Observatory, Karl-Schwarzschild-Strasse 2,
D-85748 Garching bei München, Germany
55institutetext: Department of Physics and Chemistry, University of Palermo,
Palermo, Italy
66institutetext: Donostia International Physics Center (DIPC), Paseo Manuel de
Lardizabal, 4, E-20018 Donostia-San Sebastián, Guipuzkoa, Spain;
77institutetext: IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao,
Spain;
88institutetext: Astrophysics Research Institute, Liverpool John Moores
University, IC2 Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF,
UK
99institutetext: Space Sciences, Technologies and Astrophysics Research (STAR)
Institute, University of Liège, Quartier Agora, 19c, Allée du 6 Aôut, B5c,
B-4000 Sart Tilman, Belgium
1010institutetext: Instituto de Astrofísica de Canarias, E-38205 La Laguna,
Tenerife, Spain
1111institutetext: Departamento de Astrofísica, Universidad de La Laguna,
E-38206 La Laguna, Tenerife, Spain
1212institutetext: Departamento de Astrofísica, Centro de Astrobiología,
(CSIC-INTA), Ctra. Torrejón a Ajalvir, km 4, Torrejón de Ardoz, E-28850
Madrid, Spain
1313institutetext: School of Physical Sciences, The Open University, Walton
Hall, Milton Keynes MK7 6AA, UK
1414institutetext: Institute of Astronomy, University of Cambridge, Madingley
Road, Cambridge CB3 0HA, UK
1515institutetext: Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer
de Can Magrans s/n, E-08193, Barcelona, Spain
1616institutetext: Institut d’Estudis Espacials de Catalunya (IEEC), Carrer
Gran Capitá 2-4, E-08034 Barcelona, Spain
1717institutetext: Center for Astrophysics $|$ Harvard & Smithsonian, 60
Garden Street, Cambridge, MA 02138, USA
1818institutetext: Department of Astronomy, University of Florida, P.O. Box
112055, Gainesville, FL 32611-2055, USA
1919institutetext: Istituto Nazionale di Astrofisica (INAF) - Osservatorio
Astronomico di Roma, Via Frascati 33, I-00078 Monte Porzio Catone, Italy
2020institutetext: Universität Heidelberg, Zentrum für Astronomie, Institut
für Theoretische Astrophysik, Albert-Ueberle-Str. 2, D–69120 Heidelberg,
Germany
2121institutetext: Physics and Astronomy Department Galileo Galilei,
University of Padova, Vicolo dell’Osservatorio 3, I-35122 Padova, Italy
2222institutetext: Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
2323institutetext: Departamento de Física Aplicada, Facultad de Ciencias,
Universidad de Alicante, Carretera de San Vicente s/n, E-03690, San Vicente
del Raspeig, Spain
2424institutetext: Dipartimento di Fisica e Astronomia, Università di Bologna,
Via Gobetti 93/2, Bologna I-40129, Italy;
2525institutetext: Istituto Nazionale di Astrofisica (INAF) - Osservatorio di
Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti 93/3, Bologna
I-40129, Italy
2626institutetext: Space Telescope Science Institute, 3700 San Martin Dr,
Baltimore, MD, 21218, USA
2727institutetext: School of Physics & Astronomy, University of St Andrews,
North Haugh, St Andrews KY16 9SS, UK
2828institutetext: Istituto Nazionale di Astrofisica (INAF) – Osservatorio
Astrofisico di Catania, Via Santa Sofia 78, I-95123 Catania, Italy
2929institutetext: Université Côte d’Azur, Observatoire de la Côte d’Azur,
CNRS, Laboratoire Lagrange, F-06300 Nice, France; Université Grenoble Alpes,
CNRS, IPAG, F-38000 Grenoble, France
3030institutetext: Astrophysics Group, Keele University, Keele, Staffordshire
ST5 5BG, United Kingdom
3131institutetext: University of Split, Faculty of Science, Department of
Physics, Rudera Boškovića 33, 21000, Split, Croatia
3232institutetext: Johns Hopkins University, 3400 N. Charles Street,
Baltimore, MD 21218, USA
3333institutetext: Department of Astronomy, University of Massachusetts, 710
North Pleasant Street, Amherst, MA 01003, USA
3434institutetext: AURA for the European Space Agency (ESA), ESA Office, Space
Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
3535institutetext: The William H. Miller III Department of Physics &
Astronomy, Bloomberg Center for Physics and Astronomy, Johns Hopkins
University, 3400 N. Charles Street, Baltimore, MD 21218, USA
3636institutetext: Department of Astronomy, University of Texas at Austin,
Austin, TX 78712, USA
3737institutetext: Centre for Astrophysics and Supercomputing, Swinburne
University of Technology, PO Box 218, Hawthorn VIC 3122, Australia
3838institutetext: Department of Physics & Astronomy, University College
London, Gower Street, London WC1E 6BT, UK
3939institutetext: Astronomisches Rechen-Institut, Zentrum für Astronomie der
Universität Heidelberg, Mönchhofstr. 12–14, 69120 Heidelberg, Germany

# EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended
Westerlund 1 and 2 Open Clusters Survey††thanks: Table A.1 is only available
in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr
(130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.

M. G. Guarcello 11 E. Flaccomio 11 J. F. Albacete-Colombo 22 V. Almendros-Abad
11 K. Anastasopoulou 11 M. Andersen 44 C. Argiroffi 1155 A. Bayo 44 E. S.
Bartlett 44 N. Bastian 667788 M. De Becker 99 W. Best 3636 R. Bonito 11 A.
Borghese 10101111 D. Calzetti 3333 R. Castellanos 1212 C. Cecchi-Pestellini 11
J. S. Clark 1313 C. J. Clarke 1414 F. Coti Zelati 15151616 F. Damiani 11 J. J.
Drake 1717 M. Gennaro 26263535 A. Ginsburg 1818 E. K. Grebel 3939 J. L. Hora
1717 G. L. Israel 1919 G. Lawrence 37373838 D. Locci 11 M. Mapelli 20202121 J.
R. Martinez-Galarza 1717 G. Micela 11 M. Miceli 1155 E. Moraux 2222 K. Muzic
33 F. Najarro 1212 I. Negueruela 2323 A. Nota 2626 C. Pallanca 24242525 L.
Prisinzano 11 B. Ritchie 1313 M. Robberto 26263232 T. Rom 22223131 E. Sabbi
2626 A. Scholz 2727 S. Sciortino 11 C. Trigilio 2828 G. Umana 2828 A. Winter
2929 N. J. Wright 3030 P. Zeidler 3434

###### Abstract

Context. With a mass exceeding several $10^{4}$ M⊙ and a rich and dense
population of massive stars, supermassive young star clusters represent the
most massive star-forming environment that is dominated by the feedback from
massive stars and gravitational interactions among stars.

Aims. In this paper we present the ”Extended Westerlund 1 and 2 Open Clusters
Survey” (EWOCS) project, which aims to investigate the influence of the
starburst environment on the formation of stars and planets, and on the
evolution of both low and high mass stars. The primary targets of this project
are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.

Methods. The project is based primarily on recent observations conducted with
the _Chandra_ and JWST observatories. Specifically, the _Chandra_ survey of
Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a
total exposure time of 1 Msec. Additionally, we included 8 archival _Chandra_
/ACIS-S observations. This paper presents the resulting catalog of X-ray
sources within and around Westerlund 1. Sources were detected by combining
various existing methods, and photon extraction and source validation were
carried out using the ACIS-Extract software.

Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the
9420 initially provided to ACIS-Extract, reaching a photon flux threshold of
approximately $2\times 10^{-8}$ photons cm${}^{-2}\,$s-1. The X-ray sources
exhibit a highly concentrated spatial distribution, with 1075 sources located
within the central 1 arcminute. We have successfully detected X-ray emissions
from 126 out of the 166 known massive stars of the cluster, and we have
collected over 71000 photons from the magnetar CXO J164710.20-455217.

###### Key Words.:

Galaxies: star clusters: individual: Westerlund 1; Stars: formation; X-rays:
stars

##  1 Introduction

The star formation rate and the properties of the most common star-forming
environments in galaxies vary over time. When considering cosmological
timescales, the star formation rate is known to reach its peak at
approximately z$\sim$2–3 and then gradually decline (e.g., Hopkins & Beacom,
2006; Dunlop, 2011; Madau & Dickinson, 2014). In the local Universe, mergers
play a dominant role in shaping the star formation process in galaxies (Rieke
& Rujopakarn, 2011) as they influence the overall properties of the
interstellar medium. Such interactions happen frequently, and various studies
have demonstrated that interacting galaxies undergo periods of intense star
formation (e.g., Larson & Tinsley, 1978; Smith & Struck, 2010) because of the
considerable impact interactions have on the stars formation process, for
instance from the enhancement of the star cluster formation rate due to close
encounters (e.g. in the Magellanic Clouds) and the ram pressure stripping
enhancing star formation (e.g., jellyfish galaxies). Noticeable examples are
the nearby interacting galaxies M51 and M82, where we observe extreme star
formation taking place in very massive young clusters with masses reaching
several times $10^{5}\,$M⊙ (known as super star clusters; de Grijs et al.,
2001, 2003b, 2003a). Generally, these highly massive star clusters constitute
the dominant star-forming environments in starburst galaxies and are likely
prevalent during the peak era of cosmic star formation (e.g., Figer, 2008;
Adamo et al., 2020).

In the Milky Way, current estimates of the star forming heavily rely on the
methods employed. For example, Robitaille & Whitney (2010) derived a range of
0.68–1.45 M${{}_{\odot}}\,$yr-1 based on the population of young stellar
objects identified in the _Spitzer_ /IRAC survey of the Galactic plane GLIMPSE
(Benjamin et al., 2003). On the other hand, Licquia & Newman (2015) applied a
hierarchical Bayesian statistical method to previous analyses and determined a
star formation rate of about 1.6 M⊙/yr. For comparison, recent estimates of
the star formation rate in M51 range from 4.8 M${{}_{\odot}}\,$yr-1 (from a
158$\mu m$ map of the galaxy Pineda et al., 2018) to 2.7 M${{}_{\odot}}\,$yr-1
(from combined UV+optical spectral energy distribution fitting; Eufrasio et
al., 2017), while in M82 star formation rates of 2-4 M${{}_{\odot}}\,$yr-1
were observed (de Grijs et al., 2001). Nevertheless, all these studies
indicate that our Galaxy does not currently have a high star formation rate.
Consequently, it is not surprising that the Milky Way lacks a prominent
population of super star clusters with masses exceeding 104 M⊙. In order of
distance from the Sun, the most massive clusters known are Westerlund 1 (2.6-5
kpc; Aghakhanloo et al., 2020, Clark et al., 2005), Westerlund 2 ($\sim$4.2
kpc; Vargas Álvarez et al., 2013), NGC 3603 (7.6 kpc; Melena et al., 2008),
the Arches and Quintuplet clusters (both at $\sim$8.5 kpc; Figer et al., 2002,
Figer et al., 1999), Mercer 81 (11 kpc; Davies et al., 2012), and Mercer 30
(12 kpc; de la Fuente et al., 2016). Similar regions in terms of mass, but
with with a low stellar density, are the Cygnus OB2 association (1.4 kpc; Rygl
et al., 2012) and the W3 complex (about 2 kpc; Hachisuka et al., 2006).
Slightly older supermassive star clusters (10-20 Myrs) are found in the
Scutum-Crux arm (about 6 kpc from the Sun; Figer et al., 2006; Davies et al.,
2007; Clark et al., 2009). Despite their limited number, these super star
clusters hold significant importance as they enable the study of star and
planet formation, as well as early stellar evolution, in a star-forming
environment that was characteristic of epochs when the Milky Way had higher
rates of star formation than today and most of the field stars in our Galaxy
formed.

In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey
(EWOCS) project, which is focused on studying star and planet formation and
early stellar evolution in compact starbursts, using Westerlund 1 and 2 as
first science cases. In particular, this paper focuses on the catalog of X-ray
sources detected in the deep _Chandra_ observations of Westerlund 1. The paper
is organized as follows: We present Westerlund 1 and the EWOCS project in
Sect. 2. The EWOCS observations are described in Sect. 3, the procedure for
source detection is described in Sect. 4 and that of source validation and
extraction in Sect. 5. The final catalog of the X-ray sources in Westerlund 1
is described in Sect. 6.

##  2 Westerlund 1 and the EWOCS project

Westerlund 1 is located at RAJ2000=16h47m04s and dec.J2000=-45∘51′05′′,
corresponding to Galactic coordinates l=339.55∘ and b=-00.40∘. The cluster was
discovered by Westerlund (1961) through observations made with the 26-inch
Uppsala-Schmidt telescope at Mt. Stromlo Observatory in Australia. From these
initial observations, it became evident that Westerlund 1 is a very massive
cluster. Today, it is considered to be the most massive young cluster known
within the Milky Way, with mass estimates ranging from approximately
5$\times$104 M⊙ to over 105 M⊙ (Clark et al., 2005; Brandner et al., 2008;
Gennaro et al., 2011; Lim et al., 2013; Andersen et al., 2017).

Despite over 60 years of studies and observations of Westerlund 1, the tension
regarding the parameters of this distinctive cluster remains unresolved. This
is primarily due to its compact nature and the significant extinction that has
long hindered the ability to resolve its low-mass stars.

The distance to the cluster has been a subject of long-standing debate. The
initial estimate by Westerlund (1961) was of 1.4 kpc. However, the same
authors later presented a more distant estimate of 5 kpc based on photographic
observations in the $VRI$ bands (Westerlund, 1968). The first study utilizing
CCD imaging of the cluster (Piatti et al., 1998) reported a distance estimate
of 1.0$\pm$0.4 kpc. However, this estimate was based on the incorrect
assumption that all cluster members were on the main sequence.

Several authors have made distance estimates for Westerlund 1 based on the
analysis of its rich population of massive stars. For example, Clark et al.
(2005) based their estimate on six yellow hypergiants (YHGs), assuming that
these stars have the standard luminosity for this class of objects
(log(L/L⊙)$\sim$5.7; Smith et al., 2004), and adopting an extinction of
AV=11m, resulting in a distance range between 2 kpc and 5.5 kpc. A similar
value was found by Crowther et al. (2006) through infrared analysis of WN and
WC stars. Koumpia & Bonanos (2012) derived a distance of 3.7$\pm$0.6 kpc from
the analysis of the dynamics and geometry of the eclipsing binary W13. By
comparing the cluster locus in color-magnitude diagrams with suitable
isochrones, Brandner et al. (2008) determined a distance of 3.55$\pm$0.17 kpc,
while Gennaro et al. (2011) found a distance of 4.0$\pm$0.2 kpc, and Lim et
al. (2013) reported a distance of about 3.8 kpc. An independent estimate
(3.9$\pm$0.7 kpc) was provided by Kothes & Dougherty (2007) using the radial
velocity of HI clouds in the direction of the cluster, assuming they were
physically connected to Westerlund 1.

More recently, _Gaia_ data have been extensively utilized to measure the
distances of star clusters, providing precise values up to distances of about
1 kpc (Gaia Collaboration et al., 2016). However, for more distant clusters,
careful analysis and assumptions are required to obtain reliable distance
measurements. Consequently, it is not surprising that different estimates of
the distance to Westerlund 1 have emerged from authors who have analyzed
_Gaia_ data. Aghakhanloo et al. (2020) conducted a Bayesian analysis of _Gaia_
data along the line of sight to Westerlund 1 and obtained a mean cluster
parallax of 0.35${}^{+0.07}_{-0.06}$ mas, which corresponds to a distance of
2.6${}^{+0.6}_{-0.4}$ kpc and is in tension with the previous estimate of
approximately 0.19 mas provided by Clark et al. (2020). Focusing on known
members of Westerlund 1, Davies & Beasor (2019) found a distance of
3.9${}^{+1.0}_{-0.64}$ kpc. More recently, Negueruela et al. (2022) carried
out a detailed determination of candidate members in Westerlund 1 using _Gaia_
Early Third Data Release (EDR3; van Leeuwen et al., 2021) data and obtained a
distance of 4.23${}^{+0.23}_{-0.21}$ kpc, suggesting that the cluster is
located in the Norma arm. A similar estimate from the _Gaia_ /EDR3 was
obtained by Navarete et al. (2022).

Given the uncertainty surrounding the distance to Westerlund 1, it is not
surprising that estimates of the cluster’s age provided by different authors
also vary significantly. Age estimates in the range of 3.2 to 5 million years
have been derived using isochrone fitting on the high-mass sequence and
arguments based on the diverse population of massive stars, including Wolf-
Rayet (WR) stars, YHGs, and red supergiants (RSGs; Clark et al., 2005;
Crowther et al., 2006; Brandner et al., 2008; Ritchie et al., 2010; Gennaro et
al., 2011; Koumpia & Bonanos, 2012; Kudryavtseva et al., 2012; Mackey et al.,
2015). These authors found a relatively narrow age spread, with an upper limit
of 0.4 million years indicating that Westerlund 1 likely formed in a single
burst of star formation (Kudryavtseva et al., 2012). However, some of these
estimates are based on arguments that strictly apply to single stars, whereas
it is known that the binary fraction among the massive members of Westerlund 1
is very high (Crowther et al., 2006). More recent studies suggest a more
complex star formation history and a slightly older age (Aghakhanloo et al.,
2020; Beasor et al., 2021; Navarete et al., 2022; Negueruela et al., 2022). In
particular, arguments based on spectral energy distribution fitting and the
luminosity of individual RSGs support an age estimate exceeding 10 Myrs
(Beasor et al., 2021; Navarete et al., 2022), although this estimate is in
tension with other properties of the cluster.

Figure 1: Contours of the pre-EWOCS and EWOCS _Chandra_ observations of
Westerlund 1 overlaid on the combined ACIS event file (left panel) and on an
image in the $Ks$ band obtained with the FourStar infrared camera mounted on
the Magellan 6.5 m telescopes (right panel).

There is a general consensus in the literature regarding other important
properties of Westerlund 1, including its high extinction, large mass, and
notably, its impressive population of massive stars. The significant
extinction toward Westerlund 1 has been acknowledged since the initial
publication on this cluster, where an approximate visual extinction of
AV$\sim$12m has been found (Westerlund, 1961). Subsequent estimates range from
10m to 13m of visual extinction (Negueruela et al., 2010; Lim et al., 2013;
Damineli et al., 2016). There is some disagreement regarding the extinction
law in the direction of Westerlund 1: While according to Negueruela et al.
(2010) it follows the standard law in the $VRI$ bands, Lim et al. (2013) and
Damineli et al. (2016) suggested a steeper extinction law in the near-IR
(RV=2.50$\pm$0.04).

The most remarkable characteristic of Westerlund 1 is its large population of
massive stars (Clark et al., 2005; Ritchie et al., 2009; Clark et al., 2020),
which includes 24 WR stars (Clark & Negueruela, 2002; Negueruela & Clark,
2005; Skinner et al., 2006; Groh et al., 2006; Crowther et al., 2006), the
luminous blue variable (LBV) Wd1-243 (Clark & Negueruela, 2004), ten YHGs with
spectral classes ranging from A5Ia+ to F8Ia+ (Clark et al., 2005)111A
different classification for six YHGs has recently been presented by Beasor et
al. (2023), two blue stragglers (Clark et al., 2019), four RSGs (Wright et
al., 2014b), seven blue hypergiants (BHGs), and over 100 bright OB supergiants
dominated by spectral classes O9-B1 (Negueruela et al., 2010). Most of these
sources are concentrated in the inner region of the cluster, spanning
approximately 1 arcminute, with only a few more isolated massive stars, such
as WR77.

In particular, Westerlund 1 hosts examples of every known transitional
evolutionary phase between H-rich OB supergiants and H-depleted WR stars. This
makes the cluster a unique target for studying massive stars and,
specifically, for understanding how binarity and mass loss impact the
evolutionary paths of these stars and how the initial stellar masses are
linked to the types of compact objects that form at the end of their
evolution. Winds and mass loss in these stars have been extensively studied
with radio and millimeter-continuum observations, which have detected
individual bright sources, such as W9, surrounded by extended nebulae,
providing evidence of intense mass loss in the past (up to several
10${}^{-4}\,$M⊙ per year, Dougherty et al., 2010; Fenech et al., 2018; Andrews
et al., 2019). These short-lived and episodic mass-loss events appear to be
necessary to explain the diversity of evolved massive stars in Westerlund 1.

Westerlund 1 is rich in binary systems. A high binary fraction has been
identified in massive stars through spectroscopic (Ritchie et al., 2022),
radio (Dougherty et al., 2010), infrared (Crowther et al., 2006), and X-ray
(Skinner et al., 2006; Clark et al., 2008, 2019) observations. For instance,
the WR population of Westerlund 1 has an estimated binary fraction of at least
70% (Crowther et al., 2006; Clark et al., 2008). Isolated stars are primarily
found among the mid-B to F hypergiants, with the exception of the LBV star
W243, whose binarity is supported by interferometric (Clark et al., 2019),
X-ray (Mahy et al., 2022), and spectroscopic (Ritchie et al., 2009)
observations.

This harsh environment is expected to have effects on the star formation
process, the evolution and dispersal of protoplanetary disks, and the
formation and early evolution of planets and their atmospheres. While no
studies to date have been able to identify the population of protoplanetary
disks in Westerlund 1 and explore the feedback provided by the starburst
environment on their evolution and dispersal, several authors have attempted
to quantify the cluster’s initial mass function (IMF) to investigate possible
deviations from the universal law. An IMF consistent with the Salpeter (1955)
law has been found by Brandner et al. (2008) in the 3.4–27 M⊙ range, by
Gennaro et al. (2011) extrapolated in the 0.5–120 M⊙ range, and Andersen et
al. (2017) down to 0.15 M⊙ in the outer cluster, while a shallower IMF slope
was found by Lim et al. (2013), integrated in the 0.08-85 M⊙ range.

###  2.1 Previous X-ray observations

X-ray observations of young clusters provide valuable diagnostics for
selecting pre-main-sequence (PMS) stars independently of the presence of
circumstellar disks (e.g., Montmerle, 1996), down to low stellar masses (e.g.,
Getman et al., 2005; Barrado et al., 2011). Additionally, in a cluster rich in
massive stars with a very compact configuration, X-ray observations can reveal
a plethora of processes and physical mechanisms that play an important role in
the evolution of massive stars (Seward et al., 1979; Berghoefer et al., 1996).
It is also worth mentioning that only the _Chandra_ X-Ray Observatory
(Weisskopf et al., 2002) can currently provide the high spatial resolution
required to resolve individual X-ray faint sources in a crowded cluster like
Westerlund 1. Given the designs of future X-ray missions currently in
development, such observations will likely be challenging for quite some time
after the _Chandra_ era.

Both _Chandra_ and XMM have been used in the past to observe Westerlund 1. The
initial observations performed with Chandra reached a depth of approximately
58 ksec (P.I. Skinner) and resolved numerous X-ray sources (Skinner et al.,
2006; Muno et al., 2006; Clark et al., 2008). Skinner et al. (2006) focused on
the WR stars and their spectral properties, detecting 12 out of 24 known stars
and finding strong evidence for the existence of very hot plasma in the
circumstellar environment in the two brightest objects (W72/A and WRB),
strongly suggesting the presence of a colliding winds in these binary systems;
Muno et al. (2006) studied the diffuse X-ray emission and its dominating hard
spectral component, which was later confirmed by Kavanagh et al. (2011) from
48 ksec XMM/Newton observations. These authors detected a strong Fe 6.7 keV
line in the diffuse emission spectrum, indicating its thermal nature. Clark et
al. (2008) found that 46 known high-mass members of Westerlund 1 were detected
in X-rays, and they supposed that the remaining $\sim$60 X-ray sources
detected in these images are likely PMS stars with masses $\leq$1.5 M⊙.

Since its discovery by Muno et al. (2006), the magnetar CXO J164710.2-455216
(CXOU J16) in Westerlund 1 — the brightest X-ray source in the cluster — has
garnered significant attention. Dedicated observations using XMM-Newton and
_Chandra_ /ACIS-S have accumulated a total exposure of 273.14 ksec (P.I.s
Israel, Muno and Schartel) and 94.65 ksec (P.I.s Israel and Rea),
respectively. A typical property of this class of pulsars is their frequent
bursts and recurrent outbursts. In fact, three distinct outbursts from CXOU
J16 have been observed in the past 17 years (Borghese et al., 2019). The first
one occurred in September 2006 and was triggered by a short burst that
released an energy of approximately $10^{39}\,$erg in the 15-150 keV band
(Krimm et al., 2006). It was followed by a second outburst in September 2011
(Israel et al., 2011), during which the pulsar exhibited a peculiar behavior:
The pulse profile evolved from a single peak in the pre-outburst phase to an
energy-dependent tri-peaked profile post-outburst. The overall spectrum
evolved from a single blackbody to a more complex shape that was well modeled
by including an additional hotter blackbody component. The most recent
outburst was again triggered by a short burst detected by the _Swift_ Burst
Alert Telescope in May 2017 (D’Ai et al., 2017). During these intense outburst
activities, the magnetic field strength was estimated to range from
7$\times$10${}^{13}\,$G (a value typical for low-field magnetars, Perna &
Pons, 2011) to $\sim$10${}^{14}\,$G (An et al., 2013; Israel et al., 2007).

Table 1: Pre-EWOCS observations of Westerlund 1. Obs.ID. | Instrument | Exposure | Roll Angle | RA | Dec | Date | P.I.
---|---|---|---|---|---|---|---
|  | ksec | degrees | J2000 | J2000 |  |
5411 | ACIS-S | 38.47 | 326 | 16:47:05.40 | -45:50:36.70 | 2005-06-18 | Skinner
6283 | ACIS-S | 18.81 | 25 | 16:47:05.40 | -45:50:36.70 | 2005-05-22 | Skinner
14360 | ACIS-S | 19.06 | 242 | 16:47:10.20 | -45:52:16.90 | 2011-10-23 | Israel
19135 | ACIS-S | 9.13 | 22 | 16:47:10.20 | -45:52:17.00 | 2017-05-25 | Rea
19136 | ACIS-S | 13.67 | 331 | 16:47:10.20 | -45:52:17.00 | 2017-06-16 | Rea
19137 | ACIS-S | 18.2 | 295 | 16:47:10.20 | -45:52:17.00 | 2017-07-10 | Rea
19138 | ACIS-S | 18.2 | 86 | 16:47:10.20 | -45:52:17.00 | 2018-02-24 | Rea
20976 | ACIS-S | 16.39 | 86 | 16:47:10.20 | -45:52:17.00 | 2018-02-25 | Rea

###  2.2 The EWOCS project

The pre-EWOCS _Chandra_ observations of Westerlund 1 have been analyzed by
Townsley et al. (2018) in the framework of the Second Installment of the
Massive Star-forming Regions Omnibus X-ray Catalog (MOXC2), identifying 1721
X-ray sources. This work has confirmed that Westerlund 1 is rich in X-ray
bright sources, even though its low-mass stellar content remained undetected
in the pre-EWOCS observations. According to these authors, the X-ray
luminosity limit in the broad band where half of the brighter population is
detected was log(Lx)=30.69, with Lx in erg/s, corresponding to a 1.5 M⊙
star222As stated by Townsley et al. (2018), the corresponding X-ray flux has
been calculated using PIMMS6 assuming a limit of five-counts detection on-
axis, for a source with an APEC thermal plasma with kT=2.7 keV and abundance
0.4$\times$Z⊙, which are typical values for a PMS star (Preibisch et al.,
2005)..

The need to unveil the low-mass population of Westerlund 1 has motivated the 1
Msec observation of Westerlund 1 (P.I. Guarcello) with the _Chandra_ Advanced
CCD Imaging Spectrometer (ACIS-I, Garmire et al., 2003), which, together with
a 18.9 hours Cycle 1 JWST/MIRI and NIRCam observation (program ID 1905, P.I.
Guarcello) and a 48 ksec NICER observation (P.I. Borghese) of CXOU J16,
constitutes the set of new observations of the EWOCS
project333https://Westerlund1survey.wordpress.com/. The main objective of
EWOCS is to use Westerlund 1 and 2 as a test cases for understanding how star
and planet formation, early stellar evolution, and the production of compact
objects occur in a starburst environment. Specifically, the project aims to
achieve the following objectives:

  * •

Unveil the low-mass stellar population of Westerlund 1 and 2, both in their
core and halo. X-ray observations are expected to be critically important for
selecting cluster members in the halo, where contamination from background and
foreground sources could affect membership determination based on photometric
data.

  * •

Determine the actual stellar content of the clusters, down to the low-mass
regime, mainly thanks to the JWST observations; calculate their IMF down to
the brown dwarf regime, and understand whether the starburst environment
impact the formation of low-mass and very-low mass stars.

  * •

Study the clusters properties, particularly age, age spread, morphology and
dynamics. The project aims to understand whether the clusters formed in a
single burst of star formation or through a process spanning several million
years, as well as how and if they will disperse.

  * •

Identify the disk-bearing population of the clusters, mainly though the JWST
observations. Combining this with the detection of disk-less stars from the
_Chandra_ /ACIS-I observations and modeling of disks dispersal, we will
finally assess how disks evolve and how planet formation proceeds in a
starburst environment.

  * •

If planets can form, understand how they evolve while immersed in such an
environment characterized by high local fluxes of UV and X-ray radiation and
relativistic particles.

  * •

Study how binarity and mass-loss affect the evolution of the massive stars in
the clusters, and how their initial mass is mapped into the type of compact
objects formed at the end of their evolution.

  * •

Determine whether binarity across stellar masses is different in a starburst
environment.

  * •

Study for the first time the status of CXOU J16 far from bursts, which will
allow us to estimate the intrinsic properties of the pulsar.

  * •

Search for the expected population of compact objects that have been suggested
to exist in Westerlund 1, since, under specific assumptions, up to $\sim$65
core-collapse supernovae could have already occurred in the cluster (Muno et
al., 2006; Brandner et al., 2008). Besides, Westerlund 1 is one of the few
known star clusters meeting the properties required for the formation of
intermediate mass black holes from runaway coalescence (Portegies Zwart et
al., 2004). As estimated by Clark et al. (2008), such objects, if present and
if currently accreting mass, should be observable with a very deep _Chandra_
observation.

  * •

Understanding how stellar winds from massive evolved stars can affect the ISM
to produce diffuse X-ray emission, whether this hot gas could affect star
formation throughout the region, and whether we can prove ongoing accumulation
of polluted material in the cluster core.

Figure 1 shows the contours of the pre-EWOCS and EWOCS observations of
Westerlund 1 and CXOU J16, plotted over the combined _Chandra_ event file and
a $K_{S}$ band image of the cluster and the surrounding area obtained with the
FourStar infrared camera mounted on the Magellan 6.5 m telescopes.

##  3 _Chandra_ observations and data reduction

The EWOCS survey also includes eight pre-EWOCS observations performed with
ACIS-S, two of which were pointed at Westerlund 1 and six at CXOU J16. These
observations were conducted between June 2005 and February 2018 (Table 1).
Additionally, 36 EWOCS observations were carried out with the ACIS-I detector
from June 2020 to August 2021. The aim point of each ACIS-I observation was
adjusted based on the nominal roll angle, as indicated in Table 2. This
adjustment was crucial to for avoiding gaps that cover the cluster core, the
pulsar, or some of the brightest massive members, while ensuring the cluster
remained within the inner arcminute. By adopting this design, we maximized the
benefits of the subarcsecond spatial resolution and sensitivity in the central
part of the ACIS-I detector to observe the cluster core, which is highly
compact and crowded.

Table 2: EWOCS observations Obs.ID. | Exposure | Roll Angle | RA | Dec | Date
---|---|---|---|---|---
| ksec | degrees | J2000 | J2000 |
22316 | 39.55 | 245 | 16:46:59.97 | -45:51:13.70 | 2020-10-04
22317 | 24.75 | 272 | 16:47:00.55 | -45:51:29.59 | 2021-08-14
22318 | 26.72 | 312 | 16:47:03.24 | -45:51:45.84 | 2020-06-25
22319 | 46.45 | 243 | 16:46:59.97 | -45:51:13.70 | 2020-10-09
22320 | 37.58 | 321 | 16:47:05.45 | -45:51:39.01 | 2020-06-20
22321 | 37.58 | 1 | 16:47:04.93 | -45:51:14.41 | 2020-06-02
22977 | 37.57 | 236 | 16:46:59.97 | -45:51:13.70 | 2020-10-22
22978 | 24.75 | 340 | 16:47:05.45 | -45:51:39.01 | 2021-06-12
22979 | 21.79 | 14 | 16:47:07.63 | -45:51:13.62 | 2021-05-28
22980 | 24.75 | 331 | 16:47:05.45 | -45:51:39.01 | 2021-06-16
22981 | 21.85 | 314 | 16:47:03.24 | -45:51:45.84 | 2021-06-24
22982 | 16.85 | 335 | 16:47:05.45 | -45:51:39.01 | 2020-06-13
22983 | 27.72 | 340 | 16:47:05.45 | -45:51:39.01 | 2021-06-09
22984 | 22.61 | 303 | 16:47:03.24 | -45:51:45.84 | 2021-07-02
22985 | 24.75 | 52 | 16:47:07.13 | -45:50:48.14 | 2021-05-01
22986 | 17.67 | 335 | 16:47:05.45 | -45:51:39.01 | 2020-06-11
22987 | 24.75 | 1 | 16:47:04.93 | -45:51:14.41 | 2021-06-04
22988 | 17.85 | 280 | 16:47:02.20 | -45:51:31.62 | 2021-07-27
22989 | 21.79 | 14 | 16:47:07.63 | -45:51:13.62 | 2021-05-27
22990 | 24.75 | 288 | 16:47:01.97 | -45:51:40.91 | 2020-07-17
23272 | 11.92 | 1 | 16:47:04.93 | -45:51:14.41 | 2020-06-03
23279 | 29.69 | 335 | 16:47:05.45 | -45:51:39.01 | 2020-06-12
23281 | 30.49 | 321 | 16:47:05.45 | -45:51:39.01 | 2020-06-21
23287 | 34.61 | 312 | 16:47:03.24 | -45:51:45.84 | 2020-06-26
23288 | 29.18 | 312 | 16:47:03.24 | -45:51:45.84 | 2020-06-26
24827 | 24.75 | 269 | 16:47:00.55 | -45:51:14.83 | 2021-08-21
24828 | 24.75 | 1 | 16:47:04.93 | -45:51:14.41 | 2021-06-04
25051 | 31.66 | 14 | 16:47:07.63 | -45:51:13.62 | 2021-05-28
25055 | 29.68 | 1 | 16:47:04.93 | -45:51:14.41 | 2021-06-05
25057 | 25.25 | 340 | 16:47:05.45 | -45:51:39.01 | 2021-06-13
25058 | 27.22 | 333 | 16:47:05.45 | -45:51:39.01 | 2021-06-10
25073 | 34.62 | 314 | 16:47:03.24 | -45:51:45.84 | 2021-06-25
25096 | 18.14 | 280 | 16:47:02.20 | -45:51:31.62 | 2021-07-29
25097 | 23.59 | 280 | 16:47:02.20 | -45:51:31.62 | 2021-07-30
25098 | 25.43 | 280 | 16:47:02.20 | -45:51:31.62 | 2021-08-01
25683 | 24.74 | 272 | 16:47:00.55 | -45:51:29.59 | 2021-08-15

The total exposure for the pre-EWOCS observations is 151.93 ksec, while for
the EWOCS observations it is 967.80 ksec. The exposure times for the
individual EWOCS observations range from 11.92 ksec (Obs.ID 23272) to 39.55
ksec (Obs.ID 22319), with a mean exposure of 26.33 ksec. The EWOCS
observations span over one year, providing a robust baseline for studying the
X-ray variability of the brightest sources. All EWOCS observations were
conducted using the ACIS-I detector in imaging mode, utilizing all four chips
(I0–I3). The observations were performed in the VERY FAINT mode, which employs
telemetry in 5$\times$5 pixel event islands for improved background
suppression444http://cxc.harvard.edu/cal/Acis/Cal_prods/vfbkgrnd/index.html.
When combined with the pre-EWOCS observations, the total time baseline exceeds
16 years, which is particularly valuable for studying certain sources in the
cluster, such as the magnetar. Figure 2 displays a composite RGB ACIS image of
Westerlund 1, where colors represent different photon energies (red: soft
band, green: medium band, blue: hard band). The image shows both the entire
EWOCS field and a central region of approximately $\sim$3′. In the right
panel, it is evident that the source density is high in the cluster core and
it reveals that the majority of faint sources are predominantly hard, likely
due to high absorption or since they have been observed during periods of
intense magnetic activity such as flares. The list of Chandra datasets used in
this paper, and obtained by the Chandra X-ray Observatory, are contained in
the Chandra Data Collection (CDC) 153 https://doi.org/10.25574/cdc.153

Figure 2: RGB images of the whole ACIS-I field (left panel) and the central
area (right panel) of the composite _Chandra_ images. Soft band (0.5-1.0 keV)
photons are marked in red, medium band (1.0-2.0 keV) photons in green, and
hard band (2-7.9 keV) photons in blue. The brightest source in the southeast
direction is CXOU J16. The two images were smoothed adopting a Gaussian kernel
with a radius of 2 pixels.

###  3.1 Data reduction

The _Chandra_ observations were analyzed using the ”pre-_ACIS_ Extract
workflow” procedure outlined in Townsley et al. (2003) and Broos et al.
(2010). This procedure utilizes various tools integrated within the _Chandra_
Interactive Analysis of Observations (CIAO) software (Fruscione et al., 2006).
We employed versions 4.13 of CIAO along with the CALDB 4.9.5 calibration
files.

The L1-to-L2 processing flow aims to generate calibrated _Chandra_ event files
from the L1 products provided by the _Chandra_ X-Ray Center (CXC). It includes
event energy calibration, refinement of event positions, and correction for
contamination caused by bad pixels and cosmic-ray afterglow. This workflow
utilizes a less aggressive bad pixel table compared to the one produced by
CIAO and it incorporates the $clean55$ algorithm for background reduction.
Additionally, cosmic-ray afterglows are removed, and the source point spread
function (PSF) is improved by disabling the random $\pm$0.25 pixel
randomization. The standard grade filter is applied to events, retaining only
$ASCA$ grades 0, 2, 3, 4, and 6. However, events are not filtered for the
standard _status=0_ requirement, which may result in the exclusion of a
significant number of reliable events.

Afterglows, which are groups of events appearing at the same location in
consecutive CCD frames, can often be mistaken for faint sources. To address
this, the CIAO tool _acis_detect_afterglow_ is typically employed to remove
afterglows. This tool applies a relatively aggressive cleaning approach,
eliminating several false positives. Another tool, _acis_run_hotpix_ , is less
aggressive but it may fail to detect afterglow series with fewer than ten
counts. In this L1-to-L2 procedure, a bifurcated workflow is adopted, where we
applied an aggressive cleaning to the files used for source detection and
validation, and a less aggressive cleaning for the files used in spectral
analysis.

The background light curves were examined to identify and exclude intervals
with intense and fluctuating background. This correction was required only for
Obs.ID 5411, as the background remained relatively stable throughout the other
observations.

The astrometry of the event files was corrected in three steps. In the first
step, we addressed the offset of each Obs.ID relative to Obs.ID 22319, which
is the deepest observation. We utilized _Wavdetect_ to identify the brightest
sources in each observation and cross-matched their positions with those
detected in the Obs.ID 22319 image. Subsequently, we employed the CIAO tools
_wcs_match_ and _wcs_update_ to update the astrometry for each observation. In
the second step, which was part of the L1-to-L2 workflow, we corrected the
astrometry of each event file using the _Gaia_ Third Data Release (DR3; Gaia
Collaboration et al., 2023) astrometric system. This process was repeated as
the third step, but using the brightest sources from the final list of
validated sources (Sect. 6).

Exposure maps were calculated using the standard CIAO tools implemented in the
pre-_ACIS_ Extract workflow for each observation in the broad (0.5–7.9 keV),
soft (0.5–1.0 keV), medium (1.0–2.0 keV), hard (2.0–7.9 keV), and very hard
(4.0–7.9 keV) bands, and subsequently combined. The resulting combined
exposure map in the broad band is displayed in Fig. 3, revealing a deep and
nearly uniform exposure in the central region. This region is sufficiently
large to encompass both the core of Westerlund 1 and a portion of the expected
halo of the cluster (as recently discovered, extended haloes are typically
associated with stellar clusters; Meingast et al., 2021; Prisinzano et al.,
2022).

Figure 3: Combined exposure map in the broad band.

##  4 Source detection

The strategy we employed for source detection aims to maximize the depth of
the EWOCS catalog, even in the core of Westerlund 1. This region presents
challenges due to source confusion and a bright, irregular background, making
the detection of faint sources a complex task (see Figure 4).

Figure 4: Inner region of Westerlund 1 observed with ACIS (left panel) in the
broad band and with HST (right panel) using the F160W filter. In the ACIS
image, source confusion and a high background intensity dominate the cluster
core.

Source detection is implemented using four different methods:

  * •

The wavelet-based algorithm _PWDetect_ (Damiani et al., 1997) is applied in
the broad, soft, medium, hard, and very hard energy bands. The detection
threshold we adopted roughly corresponds to 50 spurious sources. We excluded
the outermost regions where the selection resulted in a very large number of
false positives, resulting in 2306 detected sources.

  * •

The wavelet-based algorithm _Wavdetect_ (Freeman et al., 2002) is applied to
images in the broad, soft, medium, hard, and very hard energy bands. We set
the _sigmathreshold_ parameter equal to 10-4 and used only two small detection
scales, resulting in 2509 detected sources.

  * •

The maximum likelihood reconstruction method developed by Townsley et al.
(2006) is applied in the broad, soft, hard, and very hard energy bands. This
algorithm operates over small tiles across the observed field, making it more
sensitive to the spatial variation in the PSF and background and thus more
capable of detecting faint sources in crowded fields (Broos et al., 2010). The
reconstructed image is first calculated using the Lucy-Richardson algorithm
(Lucy, 1974), and then searched for peaks that identify the positions of point
sources. This method resulted in 7585 detected sources.

  * •

A time-resolved deployment of _PWDetect_ , described in more details in the
following, is performed over segments of 10 ksec of the observations. This
method is aimed at detecting faint and variable sources that may only be
significant during specific short time segments in which they were detected.
This method produced a list of 1147 detected sources.

Figure 5 shows a comparison of the spatial distribution of candidate sources
detected using the four methods. In all cases, the cluster appears highly
crowded, with the image reconstruction method being the only one capable of
detecting a large number of sources in the central region of Westerlund 1, as
expected.

Figure 5: Spatial distribution of candidate sources detected with the four
methods (from the top: _Pwdetect_ , _Wavdetect_ , image reconstruction, and
time-resolved Pwdetect). The left panels show the whole ACIS field, those on
the right the inner region. Different colors in the first and second rows mark
sources detected at different energy bands.

###  4.1 Time-resolved PWDetect

We devised a simple time-resolved detection method, tailored to faint
transient sources such as magnetically flaring low-mass stars. These may
remain undetected in the full dataset because of the high background, but may
be detected in a shorter time slice that includes the transient emission,
thanks to the enhanced source-counts/background contrast.

We started by considering 10 ks time slices from each observation segment.
Since exposure times are not multiple of 10 ks, the exposure time of the last
frame was forced to range between 7 ks and 17 ks. Moreover, in order to fully
capture transients that would otherwise be split between two frames, we also
considered intervals shifted in time by half a frame (5 ks).

The 44 EWOCS and pre-EWOCS observations were thus split into 194 frames: 106
were 10 ks long, while the duration of the remaining ones are quite uniformly
distributed between 5 and 16 ks. For each frame, event lists (and exposure
maps) were then extracted in the following five energy bands: 0.5-7.0 keV,
4.0-7.0 keV, 0.5-1.2 keV, 1.2-2.0 keV, and 2.0-7.0 keV, resulting in a total
of 970 event files.

We ran _PWDetect_ twice on each of these 970 event files, once to estimate the
background level and thus evaluate the significance thresholds to obtain the
desired number of spurious sources, and once more for the final detection. For
the first run we adopted a low significance threshold, 4.9$\sigma$, so to
detect as many sources as possible, but also resulting in several spurious
faint sources. The number of background photons was then estimated by
subtracting the detected source photons from the total; we then chose the
final detection threshold so to yields, on average, 0.1 spurious sources per
frame. This was derived from the appropriate significance versus background
curve provided by Damiani et al. (1997).

The final _PWDetect_ runs produced 944 lists of sources555For the observations
in standard ACIS-I configuration, detection was performed only on the most on-
axis CCD (CCD.ID=7). In 26 cases _PWdetect_ crashed or no sources were found.
We did not investigate these cases further for a total of 14178 sources, most
of which are, obviously, repeated detections of the same source in multiple
frames and/or bands. We started cleaning up this large sample by removing
$\sim$1600 extended sources, many of which were unresolved detections of
multiple point sources (extent parameter, as given by _PWDetect_ , larger than
2). We then screened for the remaining sources for possible cosmic rays
afterglow events: for each source we extracted photons from a circle with
radius twice the ”detection scale” provided by _PWDetect_. In 284 cases the
arrival times of all extracted photons were in subsequent 3.14s-long readout
frames, and the detection, a likely afterglow artifact was discarded.

All detection lists were cross-identified and merged in a final source list
using an iterative procedure: first we cross-identified and merged the first
two catalogs. The resulting catalog was then merged with the third original
catalog, and so on for all the 944 catalogs. Identifications were performed
searching the close spatial coincidences with identification radii of each
original detection taken as the 1$\sigma$ uncertainties as estimated by
_PWDetect_ (rounded up to 0.5 arcsec if smaller). The coordinates and
uncertainties or identification radii of merged sources were computed, at each
step, as the uncertainty-weighted means of the coordinates/radii of cross-
identified sources666Since most detections are not independent (they may share
the same photons because of energy band or overlapping time frames), we
computed weighted means only among values belonging to independent groups of
positions. Within each group of dependent detections we chose the coordinates
and radii of the source with the smallest positional uncertainty. At the end
of this process we are left with 1262 cross-matched sources.

Finally, we inspected all the final sources by eye, examining individual
detections in the original event file, and the positions in the _Hubble_ Space
Telescope (HST) H-band image (when available, in the field center) and images
from the Digitized Sky Survey (DSS) and the Two Micron All-Sky Survey (2MASS).
Some cross-identifications were adjusted and a number of ”sources,” which were
not merged by the automatic process above, where merged as they clearly
referred to the same star. The final list counts 1147 sources.

###  4.2 The merged list of candidate sources

At this stage, we generated a list of candidate sources that includes all the
sources detected using the adopted methods. Contamination of this list by
false positives is expected to be large, but we relied on the source-
validation step, described in the next sections, to prune the catalog from
these false and not significant sources.

The lists generated by the four detection methods were cross-matched by eye.
In cases where it was difficult to confidently determine the presence of one
or more nearby sources, we left those entries unmatched between the catalogs.
Additionally, we included in the input list the following sources that were
not detected by any of the aforementioned methods:

  * •

446 faint sources from the catalog presented by Townsley et al. (2018), which
are likely not detected in EWOCS observations because of the intrinsic
variability of young stars;

  * •

21 massive stars of Westerlund 1 from the list published by Clark et al.
(2020);

  * •

47 candidate sources added by eye corresponding to the positions of _Gaia_
sources in or nearby the cluster center.

The final list of candidate sources, which was used as input for the source
validation process in $ACIS$-Extract (AE), consists of 9420 sources.

##  5 Source extraction, validation, and photometry

Source validation and photometry were performed using the AE software in IDL
(Broos et al., 2010)777http://www.astro.psu.edu/xray/acis/acis_analysis.html,
which has been successfully employed in previous X-ray surveys including the
_Chandra_ Carina Complex Project (Townsley et al., 2011), the Massive Young
Star-forming Complex Study in Infrared and X-Rays (MYStIX) survey (Feigelson
et al., 2013), the three Massive Star-forming Regions Omnibus X-ray Catalog
(MOCX) data releases (Townsley et al., 2014, 2018, 2019), the _Chandra_ Cygnus
OB2 Legacy Survey (Wright et al., 2014a), and the Star Formation In Nearby
Clouds (SFiNCs) project (Getman et al., 2017). AE enables the extraction and
validation of sources across multiple observations, generating individual
source spectra and light curves. It utilizes various data analysis software
packages including CIAO, MARX (Davis et al., 2012),
HEASoft888https://heasarc.gsfc.nasa.gov/lheasoft, and the IDL Astronomy User’s
Library (Landsman, 1993).

Following the guidelines provided by the authors and available on the AE
website, we adopted a three-step procedure to compile the X-ray EWOCS catalog:

  * •

Initially, sources were extracted and validated using a parameter defined by
AE, which helps distinguish between genuine and false sources. This step was
repeated iteratively until no more false sources were identified and removed
(Sect. 5.1).

  * •

Subsequently, source positions were updated, followed by another round of
source validation process (Sect. 5.2).

  * •

Once the catalog reached a stable state, we performed the photometric
procedure, to extract source events comprehensively and calculate the primary
spectral and temporal properties for each source across multiple energy bands
(Sect. 5.3).

###  5.1 Source validation

The AE procedure assesses the local PSF at the given position of each source
and defines extraction regions based on the 1.5 keV local PSF, ensuring they
do not overlap with neighboring sources. In the case of close pairs, the
extraction region of the fainter source is progressively reduced to prevent
overlap until it reaches 40% of its original size. Once this threshold is
reached, if the two extraction regions still overlap, AE further reduces the
size of the brighter source until the regions no longer overlap. If overlap
persists even when both extraction regions are reduced to 40%, AE either
discards the specific observation or automatically removes the fainter source.

The local background is determined within an optimized region surrounding the
source. For isolated sources, this region is delimited by an inner radius,
which is 1.1 times the radius encompassing 99% of the PSF, and an outer radius
large enough to collect at least 100 background events not associated with
nearby sources. AE adjusts the size of the background-extraction region to
ensure that Poissonian noise contributes no more than 3% to the background
uncertainty. However, in crowded regions, defining a region with 100 events
may not be feasible. In such cases, AE employs a different calculation that
incorporates the contribution from nearby bright sources and a model
accounting for the spatial variation of the background.

Source validation relies on a parameter provided by AE called _prob_no_source_
(PB), which represents the probability that there is no real source at a given
position. In our case, where multiple observations of a source are available,
AE calculates PB based on the extractions with the highest source
significance. To differentiate between valid and spurious sources, we applied
a threshold of PB=0.01, consistent with previous studies. Since the removal of
not valid sources could potentially impact the extraction region and
background of valid sources, the procedure is iterated until the catalog
reaches convergence and no further spurious sources are detected.

After the first iteration, we conducted a visual inspection of sources flagged
by AE as potentially resulting from the hook-shaped feature of the
PSF999http://cxc.harvard.edu/ciao/caveats/psf_artifact.html. This feature can
account for up to 5% of the source flux and its position is influenced by the
roll-angle, making it distinguishable from the actual source only in a few
cases where the real source is both on-axis and sufficiently bright. Figure 6
illustrates an example of a source (MOXC2) that was flagged by AE as a
potential PSF hook and subsequently removed after visual inspection.

Figure 6: Example of a source (label MOXC2) that was excluded as a potential
product of a PSF hook near a brighter source (label c10200). The green
contours outline the extraction regions of MOXC2 in all observations, while
the red polygons indicate the locations where the PSF hook may appear in each
observation, depending on the roll-angle.

AE also identifies sources that are expected to suffer from significant
pileup101010http://cxc.harvard.edu/ciao/why/pileup_intro.html (which is the
loss of information due to different incident photons registered as a unique
event by the detector). In our case, the only source affected by piled source
is the magnetar.

###  5.2 Positions update and visual review

For each source, AE calculates three different position estimates. The first
estimate is obtained by taking the mean value of the positions of the events
associated with the source (mean-data position). However, this estimate may be
inaccurate for large off-axis angles and in cases where there are significant
offsets between the true source position and the extraction region (which can
happen when the PSF is asymmetric). To obtain a more accurate estimate in
these cases, AE correlates the source PSF with the spatial distribution of
extracted events (PSF position). This calculation takes into account the
combination of several Obs.IDs by using the PSF calculated in each
observation. Both of these estimates can be influenced by nearby sources. In
crowded fields, a third estimate is provided by AE using the reconstructed
image of the source’s neighborhood. It identifies the position of the closest
peak in the reconstructed image. According to AE’s recommendations, the mean-
data position is used for on-axis sources, the PSF position is used for off-
axis sources, and the image reconstruction position is used for sources in
crowded regions. The repositioning of sources was performed twice, with each
step followed by a new sequence of iterations for source validation, as
described in the previous section.

Before conducting the visual review of validated sources, the astrometry of
both the X-ray sources and the main products file was corrected using the
_Gaia_ /DR3 astrometric system. After this step, and when catalog stability
was achieved again, we conducted a visual review of specific critical sources,
including very faint sources that could affect the size of the extraction
region of nearby bright sources and suspected afterglows. The decisions made
during the visual review were guided also by the presence of high-probability
optical and/or infrared counterparts. After the visual review, a new round of
source validation was performed.

###  5.3 Spectral extraction

After 21 iterations of the source validation process, the catalog reached
stability, with a total of 5963 validated X-ray sources. The final step
involved the extraction of X-ray events and the estimation of X-ray properties
in 17 energy bands, merging all available observations in a consistent manner.
In addition, AE generates light curves and spectra for each source, although
these will not be discussed in this paper. AE performs this calculation by
excluding observations where the sources are observed off-axis to improve the
overall signal-to-noise ratio. However, in our case, this correction was not
necessary due to the design of our survey. The calculated quantities include
source counts, net counts, photon flux in photon/cm2/s, and the quartiles of
photons energy.

Figure 7: Extraction regions of the validated sources across the entire merged
ACIS image (left panel), and extraction regions in the central area of
approximately $3^{\prime}$ in size (right panel).

Figure 7 depicts the spatial distribution of the validated sources in the
merged ACIS event files. In the left panel it is evident that there is a high
concentration of validated sources toward the center of the cluster, as well
as a significant number of sources surrounding the cluster core. This
indicates that we have detected stars associated with the extended halo of
Westerlund 1. This will be further investigated in upcoming papers of this
series, which will focus on source classification and the identification of
optical/infrared (OIR) counterparts. The right panel also highlights how this
survey has pushed to the limits of _Chandra_ in resolving individual stars
within such a densely populated stellar cluster with a bright and irregular
background. In fact, in the actual core of the cluster, where the background
is both intense and variable, a few tens of sources that were initially
included as input to AE were subsequently discarded during the validation
process (see Fig. 8). The limited number of validated sources in the central
region can be attributed to the intense background, and it is likely that many
of these discarded sources are indeed genuine X-ray sources. Although we did
not attempt to recover these stars, in future papers of this series their
candidate OIR counterparts will be analyzed in order to estimate the fraction
of real sources that we have excluded.

Figure 8: Extraction regions of the validated sources and positions of the
input candidate sources (crosses) within the central 1 arcmin region

##  6 The final catalog

It is informative to analyze the number of sources detected using the various
methods we employed and assess how many have survived the pruning process.
Table 3 presents the total number of input sources for each detection method,
as well as the fraction of these sources within 1′′ and 3′′ of a source in the
final catalog (source positions changed during the pruning process and thus an
exact position match was not possible). The image reconstruction method is the
only one that experienced significant pruning of the input catalog, as it
selects sources that are too faint according to the adopted PB threshold.
According to Table 3, and considering also that the number of sources in the
input _PWDetect_ list of candidate sources more distant than 3′′ from any
source in the Image reconstruction input catalog is low, but not negligible
(314, 688 for _Wavdetect_), it is evident that in complex fields like these,
deploying different detection methods is crucial for optimizing the number of
detected sources.

Table 3: EWOCS sources and detection methods. Detection method | Input N | within 1′′ | within 3′′
---|---|---|---
Image reconstruction | 7585 | 0.29 | 0.30
_PWDetect_ | 2306 | 0.87 | 0.92
_Wavdetect_ | 2509 | 0.77 | 0.82
Time resolved _PWDetect_ | 1147 | 0.77 | 0.82
Massive stars | 21 | 0.34 | 0.81
Townsley et al. (2018) | 446 | 0.48 | 0.66
Added by eye | 47 | 0.38 | 0.95

Given the design of the EWOCS survey and the compact nature of Westerlund 1,
it is not surprising that the majority of sources are observed at low off-axis
angles, as depicted in Fig. 9. Specifically, 63.7% of the sources (3485/5464)
are located within 1 arcminute from the field center, and 87.7% are within 3
arcminutes. Consequently, source positions are generally well-determined, with
a median position error of 0.17′′ and a 75% quantile position error of 0.27′′.
Position errors are estimated from the single-axis standard deviations of the
PSF inside the extraction region and the number of counts extracted. This
precision is crucial for the search of OIR counterparts and for dynamics
studies.

Figure 9: Distribution of the off-axis angles of the EWOCS X-ray sources.

As depicted in Fig. 10, the catalog is predominantly composed of faint
sources. In the broad band, the median value of the net counts is 12.9 counts.
There are 607 sources (10.2%) with fewer than 5 net counts and only 69 sources
(1.2%) with fewer than 3 counts. It is well known that the sensitivity of
ACIS-I decreases with the off-axis angle. This must be taken in consideration
when comparing the spatial distribution of X-ray sources detected with ACIS-I
to those detected with other instruments. Fig. 11 illustrates the spatial
distributions of EWOCS X-ray sources with fewer than 12.9 net counts and those
with more net counts. The former sample exhibits a higher concentration in the
center of the field, with only 37 sources having an off-axis angle larger than
7′. This region is considerably large compared to the size of Westerlund 1, so
studies based on the spatial distribution of cluster members would not be
significantly affected by the decline in sensitivity with the off-axis angle.

Given the design of the EWOCS observations and the intricate procedure we
employed for source detection and validation, it is not currently feasible to
provide a reliable estimate of catalog completeness without making strong and
unverified assumptions about cluster properties, its morphology, and both mass
and LX distributions. Instead, we prefer to discuss the achieved completeness
in future papers of this series, once the identification of OIR counterparts
and the determination of true cluster members have been accomplished. In
Appendix C, however, we present a simplified analysis of completeness based on
different assumptions regarding cluster morphology, along with simulations
conducted using the MARX simulator.

Figure 10: Distributions of source net counts in the broad, soft, medium,
hard, and very hard energy bands. The number of sources with more than 50
counts is indicated in the top-right corner of each panel. Figure 11: Spatial
distribution of EWOCS X-ray sources, sorted into two bins based on their net
counts in the broad band.

The distribution of the median photon energy for the EWOCS X-ray sources is
shown in Fig. 12. The median value of the distribution is 2.8 keV. In the case
of young stellar populations in clusters with low extinction, the median
photon energy serves as a reliable indicator of membership since the coronal
plasma temperature in young stars is typically higher than in older stars.
However, since interstellar absorption is significant in the direction of
Westerlund 1, it becomes challenging to differentiate between the absorbed
background population and the young stars within the cluster. However, the
secondary peak observed at energies below 2 keV in the Emed distribution could
potentially be attributed to a foreground population. Nevertheless, the
spatial distribution of these soft sources does not differ significantly from
that of the more energetic sources. Additionally, Fig. 12 includes a
comparison between the photon median energy distribution of the EWOCS X-ray
sources and the X-ray catalog published by Townsley et al. (2018) based on
pre-EWOCS observations, which clearly exhibits a peak below 2 keV. The evident
differences in the two distributions can be due to a combination of factors:
the presence of a large population of stars associated with Westerlund 1 in
the EWOCS catalog (which is a factor of $\sim$5 deeper in X-ray photon flux
compared to the catalog published by Townsley et al. 2018, considering the
faintest sources in the two catalogs), as well as the decline in sensitivity
in the soft band of the ACIS detector with the years, and the better
sensitivity toward soft events of the ACIS-S detector compared with ACIS-I.

Figure 12: Distribution of the median photon energy in the broad band for the
validated EWOCS X-ray sources (black) and the catalog published by Townsley et
al. (2018), in red.

The catalog also includes a measure of source flux provided by AE: the photon
flux (Fphotons), which is calculated as the ratio of the source net counts to
the product of the mean effective area and nominal exposure time (thus
expressed in units of photons cm${}^{-2}\,$s-1). A model-independent estimate
of the apparent source energy flux can be calculated as
1.602$\times$10${}^{-9}\times$E$\rm{}_{med}\times$Fphotons. The coefficient is
derived from the conversion between keV and erg, as determined by Getman et
al. (2010).

In Appendix A, we show ten rows of the X-ray EWOCS catalog, which is available
in full at the CDS. We have also made the output table produced by AE
available on the EWOCS website in its original IDL
format.111111https://westerlund1survey.wordpress.com/.

###  6.1 Specific sources

Not surprisingly, CXOU J16 is the brightest source in the EWOCS X-ray catalog,
with a total of 71601$\pm$268 net counts collected and a photon flux of
3.45$\times$10${}^{-4}\,$photons cm${}^{-2}\,$s-1. The source, which is
strongly piled-up, is quite isolated and produces a surrounding bright
background, with the closest source being at about 8 arcsec. The pulsar will
be analyzed in detail in future papers of this project.

As explained in Sect. 2, Westerlund 1 hosts a unique ensemble of massive stars
caught in different evolutionary stages. Understanding the mechanisms
responsible for the emission of X-rays and studying both binarity and the
circumstellar environment in these stars is of primary importance for EWOCS.
We visually inspected the X-ray counterparts of massive stars published by
Clark et al. (2020) and found 126 coincidences out of the 166 listed massive
stars. The results are listed in Table LABEL:tab_massive. In the vast majority
of cases, there was a clear one-to-one correspondence between the sources in
the two catalogs. There are a few uncertain cases, which can be easily
identified by repeated massive star IDs, EWOCS objects, or large separations.

The brightest X-ray massive star in the EWOCS catalog is the SgB[e] star W9
(Clark et al., 2014), with nearly 8000 net counts collected in the broad band.
The intense X-ray brightness (L$\rm{}_{X}\sim$3.6$\times 10^{33}\,$erg/s) and
the hardness of the spectrum, as previously reported by Clark et al. (2008),
are consistent with the evidence of intense mass loss rate, estimated to be
around 10${}^{-5}\,$M⊙/yr (Andrews et al., 2019), and strong indications of
binarity (Ritchie et al., 2022). W9 is the brightest source in the cluster
also at radio wavelengths (Andrews et al., 2019), millimeter band (Fenech et
al., 2018), and it shows very bright mid-IR emission (Clark et al., 1998).

In terms of X-ray luminosity, W9 is followed by the post-binary blue straggler
W30 (O4-5Ia+ Clark et al., 2019, 2008), for which a putative orbital period of
approximately 6.2 days has been identified from a radial velocity series
analyzed by Ritchie et al. (2022). We have detected nearly 6000 net counts in
the broad band for W30. After W9 and W30, the list of sources with net counts
ranging between 190 and 5400 photons includes most of the known WR stars and
OB supergiant binary systems.

The deep EWOCS observations provide, for the first time, candidate X-ray
detections for some normal giant and subgiant stars, such as W50b and W1051.
The lack of detection in the pre-EWOCS observations has been explained as a
natural consequence of the lower intrinsic bolometric luminosity of these
stars compared to more evolved massive stars in the cluster (Clark et al.,
2019). The detection in the EWOCS observations supports this hypothesis. Faint
X-ray counterparts have also been found for the two YHGs W4 and W8 (with 22
and 73 net counts, respectively), whose nature has been recently discussed by
Beasor et al. (2023), who classified them as yellow supergiants. Additionally,
a faint counterpart has been detected for the BHG W1049 (with
$14.16^{20.4}_{8.4}$ net counts). For the first time, faint counterparts have
been found for the four O9.5II SB1 stars W1022, W1050, W1056, and W1060, as
well as for the B1.5II star W1048. We also confirm the relatively faint
($75.75^{85.7}_{65.8}$ net counts) and soft (median photon energy of 1.9 keV)
X-ray emission from the SB2 star (B0.5I+OB) W10, as previously reported by
Clark et al. (2008). Ritchie et al. (2022) attributed the X-ray properties of
this star to the possibility that the pre-EWOCS observations were made at a
phase where the wind collision zone was weak or obscured. However, given the
length of the EWOCS observations, it is more likely that these properties are
intrinsic to the star.

It is quite interesting that out of the 124 sources in our catalog with more
than 100 net counts, 94 do not readily match any known massive stars in the
cluster. This subset will be studied in detail in future works of this series
to determine their nature. It is intriguing that this sample does not seem to
follow the distribution of photon energy shown in Fig. 12. In fact, its photon
median energy distribution exhibits three distinct peaks: one below 2 keV
(which may be dominated by foreground stars), one between 2.5 keV and 3 keV
(compatible with cluster stars), and one between 3.8 keV and 4.3 keV (which
could be influenced by background sources or flaring low-mass cluster
members).

We also provide a list of positions for the unvalidated candidate X-ray
sources on the EWOCS website121212https://westerlund1survey.wordpress.com/.
This list will be cross-matched with existing optical and infrared catalogs of
Westerlund 1 to determine the fraction of rejected sources that could
potentially be true counterparts of cluster members. Likewise, identifying
optical and infrared counterparts will enable us to assess the level of
contamination and the fraction of expected spurious sources in the EWOCS X-ray
source catalog, as well as determine the completeness limit achieved by our
survey.

##  7 Conclusions

In this paper, we present the EWOCS project and a new list of X-ray sources in
the young supermassive star cluster Westerlund 1 and its surrounding area. The
EWOCS project aims to investigate the impact of the starburst environment on
the formation process of stars and planets, the dispersal of protoplanetary
disks, and the evolutionary pathway of massive stars.

Here we present the 1 Msec _Chandra_ /ACIS-I EWOCS observations of Westerlund
1, the workflow for data reduction, the procedure for source detection and
validation, and the spectral extraction of the validated sources. Initially,
we generated a preliminary list of 9420 candidate X-ray sources using the
image reconstruction method, _PWDetect_ , _WAVDETECT_ , and a specific
deployment of _PWDetect_ focused on identifying flaring stars that exhibited a
significant signal above the background for a brief duration. Additionally, a
few sources were manually added or obtained from existing catalogs of
Westerlund 1 sources. From these input sources, we compiled the EWOCS catalog
of X-ray sources in Westerlund 1 of 5963 sources successfully validated using
the IDL-based software AE.

The median value of net counts in the EWOCS X-ray catalog is approximately 13
counts, with about 10% of sources having fewer than 5 net counts detected in
the broad energy band. The distribution of the median photon energy of the
sources peaks at approximately 2.8 keV, with a contribution from unrelated
(foreground and background) sources that is challenging to distinguish from
the candidate cluster members. The brightest source in the catalog is the
magnetar CXO J164710.2-455216, with over 70000 net counts detected in the
broad band. It is followed by several massive stars in Westerlund 1, including
the SgB[e] star W9, the post-binary blue straggler W30, and some WR stars and
supergiants in binary systems. Out of the 166 known very massive stars in
Westerlund 1, we have identified a reliable X-ray counterpart for 126 of them.
Additionally, we have made the first detection of an extended and rich halo
surrounding the core of Westerlund 1, which will be crucial in assessing the
cluster’s true mass content, formation, and evolution.

###### Acknowledgements.

We acknowledge the referee for his/her careful reading of our paper and
suggestions. M.G.G. is also indebted to Leisa K. Townsley and Patrick S. Broos
for their valuable suggestions and advice on data reduction and ACIS
extraction. M. G. G., C. A., R. B., E. F., G. L. I., L. P., and S. S.
acknowledge the INAF grant 1.05.12.05.03. K.M. acknowledges support from the
Fundação para a Ciência e a Tecnologia (FCT) through the CEEC-individual
contract 2022.03809.CEECIND and research grants UIDB/04434/2020 and
UIDP/04434/2020. Support for this work was also provided by the National
Aeronautics and Space Administration through _Chandra_ Proposal 21200267
issued by the _Chandra_ X-ray Center, which is operated by the Smithsonian
Astrophysical Observatory for and on behalf of the National Aeronautics Space
Administration under contract NAS8-03060. I.N. is partially supported by the
Spanish Government Ministerio de Ciencia e Innovación (MCIN) and Agencia
Estatal de Investigación (MCIN/AEI/10.130 39/501 100 011 033/FEDER, UE) under
grant PID2021-122397NB-C22, and also by MCIN with funding from the European
Union NextGenerationEU and Generalitat Valenciana in the call Programa de
Planes Complementarios de I+D+i (PRTR 2022), project HIAMAS, reference
ASFAE/2022/017. M. G. G. and R. B. also acknowledge partial support from the
Grant INAF 2022 YODA; R. B. also from the project PRIN-INAF 2019
”Spectroscopically Tracing the Disk Dispersal Evolution”. The scientific
results reported in this article are based on observations made by the
_Chandra_ X-ray Observatory. M.M. acknowledges financial support from the
European Research Council for the ERC Consolidator grant DEMOBLACK, under
contract no. 770017, and from the German Excellence Strategy via the
Heidelberg Cluster of Excellence (EXC 2181 - 390900948) STRUCTURES.

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##  Appendix A Extract of the EWOCS X-ray Westerlund 1 sources catalog

Ten rows of the EWOCS catalog of the X-ray sources in Westerlund 1 are shown
here. The full catalog is available at the CDS.

Table 4: Ten rows extracted from the EWOCS catalog of the X-ray sources in Westerlund 1 Astrometry | Photometry |
---|---|---
EWOCS-X ID |  Catalog name(a) | $\alpha$ | $\delta$ | $\sigma_{\alpha}^{b}$ | $\sigma_{\delta}^{b}$ | $\Theta^{(c)}$ |  Ct |  Cs |  Cm |  Ch |  |
|  | J2000 | J2000 | arcsec | arcsec | arcmin | counts | counts | counts | counts |  |
3001 | 164704.14-454957.4 | 251.767277 | -45.832630 | 0.06 | 0.06 | 1.6 | 38 | 0 | 11 | 27 |  |
3002 | 164704.14-455100.2 | 251.767284 | -45.850057 | 0.06 | 0.06 | 0.8 | 32 | 1 | 11 | 20 |  |
3003 | 164704.15-455133.6 | 251.767302 | -45.859349 | 0.05 | 0.05 | 0.6 | 47 | 0 | 13 | 34 |  |
3004 | 164704.15-455118.1 | 251.767311 | -45.855035 | 0.05 | 0.05 | 0.6 | 50 | 0 | 11 | 39 |  |
3005 | 164704.16-455320.2 | 251.767343 | -45.888959 | 0.09 | 0.10 | 1.9 | 14 | 1 | 5 | 8 |  |
3006 | 164704.16-455002.9 | 251.767353 | -45.834155 | 0.10 | 0.10 | 1.6 | 7 | 0 | 2 | 5 |  |
3007 | 164704.16-455135.0 | 251.767366 | -45.859734 | 0.06 | 0.06 | 0.6 | 19 | 0 | 5 | 14 |  |
3008 | 164704.17-455010.5 | 251.767382 | -45.836274 | 0.08 | 0.08 | 1.4 | 23 | 0 | 5 | 18 |  |
3009 | 164704.18-455025.7 | 251.767450 | -45.840474 | 0.06 | 0.05 | 1.2 | 36 | 1 | 13 | 22 |  |
3010 | 164704.19-455126.4 | 251.767479 | -45.857345 | 0.07 | 0.07 | 0.6 | 27 | 0 | 10 | 17 |  |
Photometry
Cnet,t |  Cnet,s |  Cnet,m |  Cnet,h |  Emedian |  Fphotons,t |  Fphotons,s |  Fphotons,m |  Fphotons,h |  log(PB,best) |  |  |
counts | counts | counts | counts | keV |  photons cm${}^{-2}\,$s-1 |  photons cm${}^{-2}\,$s-1 |  photons cm${}^{-2}\,$s-1 |  photons cm${}^{-2}\,$s-1 |  |  |  |
25.9${}^{+7.2}_{-6.1}$ |  -0.5${}^{+1.8}_{NaN}$ |  8.1${}^{+4.4}_{-3.2}$ |  18.2${}^{+6.3}_{-5.1}$ | 3.22 |  1.25$\times$10${}^{-}7$ | NaN |  3.00$\times$10${}^{-}8$ |  8.68$\times$10${}^{-}8$ | -8.94 |  |  |
12.9${}^{+6.8}_{-5.7}$ |  0.7${}^{+2.3}_{-0.8}$ |  3.7${}^{+4.4}_{-3.3}$ |  8.4${}^{+5.6}_{-4.4}$ | 2.77 |  6.97$\times$10${}^{-}8$ |  2.32$\times$10${}^{-}8$ |  1.50$\times$10${}^{-}8$ |  4.49$\times$10${}^{-}8$ | -2.23 |  |  |
37.1${}^{+7.9}_{-6.8}$ |  -0.1${}^{+1.8}_{NaN}$ |  8.9${}^{+4.7}_{-3.5}$ |  28.2${}^{+6.9}_{-5.8}$ | 2.95 |  2.19$\times$10${}^{-}7$ | NaN |  3.93$\times$10${}^{-}8$ |  1.65$\times$10${}^{-}7$ | -15.2 |  |  |
19.1${}^{+8.3}_{-7.2}$ |  0.0${}^{+1.8}_{NaN}$ |  -0.1${}^{+4.5}_{-3.4}$ |  19.2${}^{+7.4}_{-6.3}$ | 4.15 |  8.95$\times$10${}^{-}8$ | NaN | NaN |  8.85$\times$10${}^{-}8$ | -5.1 |  |  |
7.4${}^{+4.8}_{-3.7}$ |  0.7${}^{+2.3}_{-0.8}$ |  3.2${}^{+3.4}_{-2.1}$ |  3.4${}^{+3.9}_{-2.7}$ | 2.02 |  4.15$\times$10${}^{-}8$ |  2.14$\times$10${}^{-}8$ |  1.36$\times$10${}^{-}8$ |  1.90$\times$10${}^{-}8$ | -6.61 |  |  |
3.1${}^{+3.7}_{-2.5}$ |  -0.1${}^{+1.8}_{NaN}$ |  0.9${}^{+2.6}_{-1.2}$ |  2.2${}^{+3.4}_{-2.1}$ | 2.24 |  2.49$\times$10${}^{-}8$ | NaN |  5.53$\times$10${}^{-}9$ |  1.80$\times$10${}^{-}8$ | -3.53 |  |  |
9.7${}^{+5.4}_{-4.3}$ |  -0.1${}^{+1.8}_{NaN}$ |  1.2${}^{+3.4}_{-2.1}$ |  8.6${}^{+4.8}_{-3.7}$ | 3.46 |  5.56$\times$10${}^{-}8$ | NaN |  5.34$\times$10${}^{-}9$ |  4.84$\times$10${}^{-}8$ | -2.92 |  |  |
11.1${}^{+5.9}_{-4.7}$ |  -0.2${}^{+1.8}_{NaN}$ |  0.9${}^{+3.4}_{-2.1}$ |  10.4${}^{+5.3}_{-4.2}$ | 4.99 |  5.31$\times$10${}^{-}8$ | NaN |  3.62$\times$10${}^{-}9$ |  4.87$\times$10${}^{-}8$ | -4.68 |  |  |
19.4${}^{+7.1}_{-6.0}$ |  0.6${}^{+2.3}_{-0.8}$ |  7.2${}^{+4.7}_{-3.6}$ |  11.6${}^{+5.8}_{-4.7}$ | 2.17 |  1.06$\times$10${}^{-}7$ |  2.04$\times$10${}^{-}8$ |  2.94$\times$10${}^{-}8$ |  6.27$\times$10${}^{-}8$ | -3.70 |  |  |
9.2${}^{+6.3}_{-5.2}$ |  -0.5${}^{+1.8}_{NaN}$ |  3.7${}^{+4.3}_{-3.1}$ |  6.0${}^{+5.2}_{-4.1}$ | 4.16 |  4.66$\times$10${}^{-}8$ | NaN |  1.44$\times$10${}^{-}8$ |  2.98$\times$10${}^{-}8$ | -2.60 |  |  |
Columns 1–11 are shown in the top table; columns 12–21 in the bottom table.
a: IAU designation.
b: single axis position error, representing only the random component of the
position uncertainty.
c: Off-axis angle.
Photometric quantities are given in broad ($t$), soft ($s$), medium ($m$), and
hard ($h$) bands.
CX indicate the total counts in the X band, CX,net the net counts.

##  Appendix B EWOCS X-ray counterparts of the massive stars in Westerlund 1

Table LABEL:tab_massive shows the EWOCS X-ray counterparts of the massive
stars in Westerlund 1 listed in Clark et al. (2020).

Table 5:  Known massive stars in the EWOCS X-ray catalog ID | Spectral type | Catalog name |  Cnet,t |  Fphotons,t | Sep.
---|---|---|---|---|---
|  |  | counts |  photons cm${}^{-2}\,$s-1 | arcsec
W9 | sgB[e] | 164704.13-455031.3 | $7975.3_{7885.7}^{8065.8}$ |  3.7$\times$10-5 | 0.2
W30 | O4-5Ia | 164704.10-455039.2 | $5930.2_{5852.8}^{6008.4}$ |  2.7$\times$10-5 | 0.2
W72 | WN7b | 164708.35-455045.4 | $5412.8_{5338.8}^{5487.5}$ |  4.5$\times$10-5 | 0.3
WRB | WN7o | 164705.36-455104.8 | $3046.2_{2990.6}^{3102.4}$ |  1.4$\times$10-5 | 0.1
WRU | WN6o | 164706.53-455039.1 | $1996.9_{1952.0}^{2042.3}$ |  9.6$\times$10-6 | 0.1
W44 | WN9h | 164704.19-455107.2 | $1221.9_{1186.5}^{1257.6}$ |  5.6$\times$10-6 | 0.3
W239 | WC9d | 164705.20-455225.0 | $903.2_{873.0}^{933.7}$ |  6.0$\times$10-6 | 0.0
W53 | OBIa+OBIa | 164700.38-455131.8 | $515.5_{492.4}^{538.7}$ |  2.5$\times$10-6 | 1.0
W36 | OBIa+OBIa | 164705.07-455055.2 | $514.7_{491.0}^{538.7}$ |  2.4$\times$10-6 | 0.4
WRO | WN6o | 164707.65-455236.0 | $387.6_{367.7}^{407.7}$ |  2.5$\times$10-6 | 0.1
WRN | WC9d | 164659.91-455525.6 | $375.2_{355.3}^{395.2}$ |  2.2$\times$10-6 | 0.4
W27 |  O7-8Ia+ | 164705.14-455041.4 | $340.1_{320.8}^{359.6}$ |  1.5$\times$10-6 | 0.1
W13 |  B0.5Ia++OB | 164706.44-455026.1 | $258.0_{241.4}^{274.7}$ |  1.2$\times$10-6 | 0.1
WRW | WN6h | 164707.61-454922.1 | $243.0_{227.1}^{259.1}$ |  1.3$\times$10-6 | 0.3
WRJ | WN5h | 164702.47-455059.9 | $233.4_{217.5}^{249.5}$ |  1.1$\times$10-6 | 0.1
W14c | WN5o | 164706.09-455022.4 | $192.9_{178.1}^{207.8}$ |  9.2$\times$10-7 | 0.3
W24 | O9Iab | 164702.15-455112.6 | $191.7_{177.2}^{206.4}$ |  9.3$\times$10-7 | 0.2
W43c | O9Ib | 164703.75-455058.5 | $188.5_{173.8}^{203.3}$ |  1.0$\times$10-6 | 0.2
1041 | O9.5Iab | 164704.45-455109.4 | $170.4_{156.2}^{184.8}$ |  7.9$\times$10-7 | 1.0
WRX | WN5o | 164714.13-454832.0 | $154.2_{141.3}^{167.3}$ |  8.6$\times$10-7 | 0.3
WRG | WN7o | 164704.00-455125.1 | $146.8_{133.8}^{159.9}$ |  6.8$\times$10-7 | 0.0
W50b | O9III | 164701.21-455027.6 | $136.2_{124.1}^{148.4}$ |  7.4$\times$10-7 | 1.0
W38 | O9Iab | 164702.88-455046.2 | $118.9_{106.9}^{130.9}$ |  5.6$\times$10-7 | 0.3
W37 | O9Ib | 164706.01-455047.5 | $118.1_{106.1}^{130.2}$ |  5.5$\times$10-7 | 0.1
W35 | O9Iab | 164704.20-455053.7 | $110.3_{98.5}^{122.3}$ |  5.9$\times$10-7 | 0.2
W25 | O9Iab | 164705.77-455033.4 | $108.4_{96.9}^{120.1}$ |  5.1$\times$10-7 | 0.1
W232 | B0Iab | 164701.43-455235.2 | $104.7_{94.1}^{115.3}$ |  6.4$\times$10-7 | 0.4
W6a | B0.5Iab | 164703.04-455023.7 | $98.5_{87.9}^{109.2}$ |  4.6$\times$10-7 | 0.1
W17 | O9Iab | 164706.23-455049.3 | $96.7_{85.7}^{107.7}$ |  4.8$\times$10-7 | 0.1
W74 | O9.5Iab | 164707.07-455013.0 | $93.7_{83.5}^{104.0}$ |  4.9$\times$10-7 | 0.0
W15 | O9Ib | 164706.62-455029.6 | $92.1_{81.7}^{102.5}$ |  4.5$\times$10-7 | 0.0
W47 | O9.5Iab | 164702.61-455117.8 | $89.0_{78.5}^{99.5}$ |  4.4$\times$10-7 | 0.3
W57c | WN7o | 164701.59-455145.2 | $88.9_{78.9}^{98.9}$ |  5.3$\times$10-7 | 0.2
WRI | WN8o | 164700.87-455120.6 | $86.6_{76.6}^{96.6}$ |  4.0$\times$10-7 | 0.1
WRQ | WN6o | 164655.54-455134.5 | $86.6_{76.9}^{96.3}$ |  5.6$\times$10-7 | 0.4
1027 | O9.5Iab | 164701.02-455007.0 | $85.6_{75.8}^{95.5}$ |  4.2$\times$10-7 | 0.7
1051 | O9III | 164706.98-454940.1 | $79.5_{70.0}^{88.9}$ |  4.6$\times$10-7 | 0.2
1056 | O9.5II | 164708.69-455101.7 | $76.3_{66.9}^{85.8}$ |  3.7$\times$10-7 | 0.6
W10 | B0.5I+OB | 164703.34-455034.6 | $75.8_{65.8}^{85.7}$ |  3.5$\times$10-7 | 0.3
W8a | F8Ia+ | 164704.83-455025.5 | $73.7_{63.9}^{83.6}$ |  3.4$\times$10-7 | 0.8
W1 | O9.5Iab | 164659.39-455046.7 | $69.8_{60.9}^{78.8}$ |  3.4$\times$10-7 | 1.2
WRD | WN7o | 164706.25-455126.4 | $69.3_{59.8}^{78.8}$ |  3.1$\times$10-7 | 0.1
W62a | B0.5Ib | 164702.52-455138.0 | $69.1_{60.0}^{78.1}$ |  4.0$\times$10-7 | 0.2
W65 | O9Ib | 164703.88-455146.5 | $67.9_{58.9}^{76.9}$ |  3.7$\times$10-7 | 0.2
WRV | WN8o | 164703.79-455038.7 | $66.8_{57.8}^{75.9}$ |  4.9$\times$10-7 | 0.1
1037 | O9.5II | 164702.84-455006.4 | $64.8_{56.1}^{73.3}$ |  3.2$\times$10-7 | 0.1
W28 | B2Ia | 164704.66-455038.5 | $63.2_{53.1}^{73.3}$ |  2.9$\times$10-7 | 0.1
W61b | O9.5Iab | 164702.56-455141.9 | $61.3_{52.5}^{70.0}$ |  3.1$\times$10-7 | 0.3
1030 | O9.5Iab | 164701.67-455258.0 | $60.1_{51.9}^{68.4}$ |  3.4$\times$10-7 | 0.3
1040 | O9-9.5I-III | 164704.59-455008.1 | $59.9_{51.7}^{68.0}$ |  4.0$\times$10-7 | 1.0
1061 | O9-9.5III | 164709.61-455040.4 | $59.7_{51.3}^{68.1}$ |  3.1$\times$10-7 | 1.3
W84 | O9.5Ib | 164659.03-455028.3 | $57.0_{49.1}^{64.8}$ |  4.4$\times$10-7 | 0.1
1064 | O9.5Iab | 164711.50-455000.0 | $56.4_{48.3}^{64.5}$ |  2.9$\times$10-7 | 0.6
W241 | WC9 | 164705.96-455208.3 | $56.3_{48.2}^{64.3}$ |  3.9$\times$10-7 | 0.9
1060 | O9.5II | 164709.19-455048.4 | $56.2_{47.8}^{64.5}$ |  2.8$\times$10-7 | 0.1
1036 | O9.5Ia | 164702.78-455212.7 | $55.8_{47.8}^{63.8}$ |  3.8$\times$10-7 | 0.3
1004 | OeBe star | 164653.44-455300.3 | $53.9_{45.9}^{61.8}$ |  2.7$\times$10-7 | 0.8
1058 | O9III | 164708.89-455124.5 | $53.7_{45.8}^{61.6}$ |  3.3$\times$10-7 | 0.1
W56b | O9.5Ib | 164658.87-455145.9 | $52.5_{44.9}^{60.1}$ |  4.8$\times$10-7 | 0.2
W29 | O9Ib | 164704.40-455039.9 | $51.5_{43.5}^{59.5}$ |  3.7$\times$10-7 | 0.1
1023 | O9III | 164700.14-455110.3 | $49.7_{42.0}^{57.8}$ |  2.3$\times$10-7 | 1.0
W53 | OBIa+OBIa | 164700.55-455132.0 | $47.6_{39.4}^{56.3}$ |  2.3$\times$10-7 | 0.7
1034 | O9.5Iab | 164702.52-455148.3 | $47.4_{40.1}^{55.3}$ |  2.9$\times$10-7 | 0.1
1063 | O9III | 164710.74-454947.8 | $46.8_{39.5}^{54.6}$ |  2.3$\times$10-7 | 0.6
1005 | B0Iab | 164654.28-455154.8 | $43.8_{37.0}^{51.3}$ |  2.7$\times$10-7 | 0.4
1047 | O9.5II | 164706.12-455232.2 | $43.4_{36.4}^{51.0}$ |  2.9$\times$10-7 | 0.2
W41 | O9Iab | 164702.70-455057.1 | $43.0_{35.7}^{50.8}$ |  2.3$\times$10-7 | 0.2
1033 | O9-9.5I-III | 164702.37-455234.2 | $42.8_{36.1}^{50.1}$ |  2.7$\times$10-7 | 0.2
1018 | O9.5Iab | 164658.28-455057.0 | $41.8_{35.1}^{49.1}$ |  2.5$\times$10-7 | 0.4
W11 | B2 | 164702.24-455046.8 | $41.4_{34.1}^{49.2}$ |  1.9$\times$10-7 | 0.2
1040 | O9-9.5I-III | 164704.54-455009.0 | $36.0_{29.8}^{42.8}$ |  2.4$\times$10-7 | 0.3
1038 | O9III | 164703.49-454857.1 | $34.8_{28.3}^{41.9}$ |  1.7$\times$10-7 | 1.1
1007 | O9-9.5III | 164654.90-455005.8 | $34.5_{28.3}^{41.2}$ |  2.1$\times$10-7 | 0.5
W243 | LBV | 164707.50-455229.0 | $33.7_{27.5}^{40.4}$ |  2.4$\times$10-7 | 0.7
1043 | O9.5II-III | 164704.56-455059.5 | $32.3_{25.8}^{39.2}$ |  2.2$\times$10-7 | 0.2
W86 | O9.5Ib | 164657.15-455010.0 | $30.3_{24.6}^{36.5}$ |  1.8$\times$10-7 | 0.1
W61a | B0.5Ia | 164702.27-455141.7 | $28.6_{22.0}^{35.6}$ |  1.5$\times$10-7 | 0.2
W46b | O9.5Ib | 164703.67-455120.5 | $28.5_{21.4}^{36.2}$ |  1.3$\times$10-7 | 0.9
1066 | O9III | 164712.60-455055.6 | $28.3_{22.8}^{34.4}$ |  2.0$\times$10-7 | 1.2
1050 | O9.5II | 164706.77-454955.2 | $26.4_{20.8}^{32.6}$ |  1.3$\times$10-7 | 0.0
WRH | WC9d | 164704.23-455120.2 | $26.3_{19.3}^{33.9}$ |  1.2$\times$10-7 | 0.1
1029 | O9-9.5III | 164701.50-454950.1 | $25.5_{19.9}^{31.6}$ |  1.2$\times$10-7 | 0.6
W46a | B1Ia | 164703.90-455119.9 | $24.5_{17.2}^{32.4}$ |  1.1$\times$10-7 | 0.4
W21 | B0.5Ia | 164701.10-455113.7 | $24.4_{18.3}^{31.0}$ |  1.1$\times$10-7 | 0.1
W5 | WN10/B0.5Ia+WRS | 164702.98-455018.5 | $23.7_{18.2}^{29.7}$ |  1.2$\times$10-7 | 1.0
1055 | B0Ib(+O?) | 164707.82-455147.1 | $23.1_{17.8}^{28.8}$ |  1.9$\times$10-7 | 1.2
W4 |  F3Ia+ | 164701.54-455037.1 | $22.3_{16.6}^{28.6}$ |  1.0$\times$10-7 | 1.3
1065 | B0Ib | 164711.60-454922.6 | $22.2_{16.8}^{28.2}$ |  1.1$\times$10-7 | 0.2
1048 | B1.5 | 164706.28-455104.0 | $21.4_{16.5}^{26.9}$ |  1.7$\times$10-7 | 0.3
W34 | B0Ia | 164704.39-455047.3 | $21.3_{13.6}^{29.4}$ |  1.0$\times$10-7 | 0.1
W228b | O9Ib | 164658.13-455301.2 | $21.1_{16.4}^{26.5}$ |  1.5$\times$10-7 | 0.9
1059 | O9III? | 164709.08-455320.7 | $21.1_{16.3}^{26.4}$ |  1.4$\times$10-7 | 0.3
W43c | O9Ib | 164703.70-455057.7 | $21.0_{15.6}^{27.0}$ |  2.1$\times$10-7 | 0.8
1044 | O9-9.5III | 164705.56-454951.8 | $19.8_{14.6}^{25.5}$ |  1.0$\times$10-7 | 0.3
W43b | B1Ia | 164703.52-455056.6 | $19.8_{13.2}^{26.8}$ |  1.1$\times$10-7 | 0.1
1059 | O9III? | 164709.11-455319.4 | $18.7_{14.2}^{23.7}$ |  1.4$\times$10-7 | 1.3
1042 | O9.5II | 164704.66-455206.8 | $17.9_{13.0}^{23.3}$ |  1.3$\times$10-7 | 1.1
W2a | B2Ia | 164659.77-455051.8 | $17.3_{12.3}^{22.8}$ |  8.1$\times$10-8 | 0.9
1024 | O9.5Iab | 164700.78-455102.0 | $16.6_{11.8}^{21.9}$ |  8.6$\times$10-8 | 0.6
W50b | O9III | 164701.11-455026.6 | $16.5_{11.5}^{22.0}$ |  8.7$\times$10-8 | 0.7
W228b | O9Ib | 164658.02-455301.1 | $16.3_{12.0}^{21.0}$ |  1.2$\times$10-7 | 0.3
W243 | LBV | 164707.62-455228.4 | $15.9_{11.4}^{21.1}$ |  1.2$\times$10-7 | 0.7
W1 | O9.5Iab | 164659.20-455045.4 | $15.8_{11.0}^{21.2}$ |  7.9$\times$10-8 | 1.4
W4 | F3Ia+ | 164701.35-455036.5 | $15.6_{10.5}^{21.2}$ |  7.4$\times$10-8 | 0.8
1032 | O9-9.5III | 164702.32-455017.1 | $15.3_{10.4}^{20.7}$ |  7.3$\times$10-8 | 0.7
1016 | O9-9.5III | 164658.09-455247.1 | $15.2_{10.7}^{20.2}$ |  8.2$\times$10-8 | 0.2
W54 | B0.5Iab | 164703.14-455131.2 | $14.7_{9.30}^{20.7}$ |  6.9$\times$10-8 | 1.2
1014 | O9-9.5III | 164657.81-455119.3 | $14.4_{10.1}^{19.3}$ |  8.7$\times$10-8 | 0.4
1010 | O+O? | 164655.99-455210.1 | $14.4_{10.2}^{19.2}$ |  8.7$\times$10-8 | 0.7
1015 | O9III | 164657.97-455141.0 | $14.2_{10.3}^{18.6}$ |  1.5$\times$10-7 | 0.3
1049 | B1-2Ia+ | 164706.66-454738.8 | $14.2_{8.4}^{20.4}$ |  8.5$\times$10-8 | 0.3
1031 | O9III | 164701.90-455056.1 | $14.0_{9.8}^{18.6}$ |  9.9$\times$10-8 | 0.2
1043 | O9.5II-III | 164704.63-455059.4 | $13.1_{8.6}^{18.1}$ |  1.2$\times$10-7 | 0.7
W23a | B2Ia+BI? | 164702.56-455108.8 | $12.9_{7.1}^{19.2}$ |  6.0$\times$10-8 | 0.1
W63a | B0Iab | 164703.41-455157.4 | $12.7_{8.3}^{17.6}$ |  9.0$\times$10-8 | 0.3
W55 | B0Ia | 164658.40-455131.1 | $12.5_{8.5}^{17.0}$ |  8.9$\times$10-8 | 0.0
1012 | O9-9.5III | 164656.95-455055.6 | $12.4_{8.3}^{17.1}$ |  7.1$\times$10-8 | 0.3
W238 | B1Iab | 164704.41-455227.7 | $12.1_{7.8}^{17.1}$ |  7.5$\times$10-8 | 0.1
1046 | O+O? | 164705.98-454955.4 | $11.6_{7.3}^{16.6}$ |  5.6$\times$10-8 | 1.4
1045 | O9.5II | 164705.83-455155.1 | $11.6_{8.0}^{15.8}$ |  1.0$\times$10-7 | 0.2
W75 | M4Ia | 164708.96-454958.7 | $11.6_{7.3}^{16.4}$ |  6.3$\times$10-8 | 0.4
1021 | O9-9.5III | 164658.77-455432.0 | $11.5_{6.8}^{16.8}$ |  6.2$\times$10-8 | 0.1
1013 | O+O? | 164657.54-455231.0 | $11.5_{7.4}^{16.2}$ |  6.4$\times$10-8 | 0.6
1035 | O9-9.5III | 164702.67-455151.2 | $11.3_{7.1}^{16.1}$ |  7.6$\times$10-8 | 0.4
1046 | O+O? | 164706.09-454957.7 | $11.1_{6.8}^{15.9}$ |  5.4$\times$10-8 | 1.3
1017 | O9-9.5III | 164658.24-455033.8 | $10.8_{6.7}^{15.5}$ |  6.0$\times$10-8 | 0.1
W20 | M5Ia | 164703.11-455218.9 | $8.8_{5.1}^{13.3}$ |  5.4$\times$10-8 | 0.3
1028 | O9-9.5 | 164701.32-455137.5 | $8.7_{4.5}^{13.6}$ |  4.5$\times$10-8 | 0.6
1054 | O9-9.5 | 164707.64-455141.1 | $8.0_{5.0}^{11.7}$ |  8.3$\times$10-8 | 0.3
W78 | B1Ia | 164701.48-454957.4 | $7.8_{4.0}^{12.2}$ |  3.8$\times$10-8 | 0.6
W373 | B0Iab | 164657.72-455320.0 | $7.7_{4.1}^{11.9}$ |  4.6$\times$10-8 | 0.1
1026 | O9-9.5III | 164701.01-454948.8 | $7.0_{3.3}^{11.3}$ |  3.5$\times$10-8 | 0.5
W71 | B2.5Ia | 164708.57-455049.8 | $5.5_{2.1}^{9.4}$ |  4.5$\times$10-8 | 1.5
1020 | O9-9.5+O? | 164658.49-455228.4 | $5.2_{2.5}^{8.5}$ |  3.7$\times$10-8 | 1.3
1008 | O9.5II | 164655.45-455154.2 | $5.1_{2.1}^{8.7}$ |  3.3$\times$10-8 | 0.1
1062 | O+O? | 164710.65-455047.2 | $5.0_{1.9}^{8.7}$ |  3.2$\times$10-8 | 0.9
1022 | O9.5II | 164659.88-455025.1 | $4.6_{1.6}^{8.1}$ |  3.0$\times$10-8 | 0.5
1045 | O9.5II | 164705.86-455154.2 | $4.4_{2.1}^{7.5}$ |  4.8$\times$10-8 | 0.8
W29 | O9Ib | 164704.47-455039.5 | $4.3_{1.4}^{7.8}$ |  4.8$\times$10-8 | 0.7

##  Appendix C Estimate of catalog completeness

The resulting completeness of our survey depends not only on the total
exposure, but also on source crowding and the bright and irregular background.
A full understanding of completeness will only be possible after the
identification and classification of the OIR counterparts of the X-ray sources
in order to distinguish between cluster members and sources in the foreground
and background. However, we conducted some simple simulations using MARX,
which, despite being based on strong assumptions, can provide some hints about
completeness.

In order to simulate the cluster population, since the true shape of the IMF
of Westerlund 1 is still a subject of debate, particularly in the low-mass
regime, we made the assumption that the cluster IMF follows the law proposed
by Kroupa (2001), which is applicable to most known young stellar clusters. We
understand that the starburst environment can influence the distribution of
stellar masses, leading to different mass functions. However, at this level of
approximation, this is considered a secondary effect. To accommodate the
compact morphology of the cluster, we assumed that cluster members are
distributed according to a Gaussian function with a full width at half maximum
of 4 arcminutes. Therefore, we did not account for the asymmetric morphology
of Westerlund 1, as suggested by previous authors (e.g., Gennaro et al. 2011).
Additionally, we assumed a total cluster mass of 45000 solar masses,
encompassing stars with masses as low as 0.08 solar masses.

To convert the mass distribution into an LX distribution, we utilized the LX
versus mass distribution derived from the _Chandra_ Orion Ultradeep Project
(COUP) conducted in the Orion Nebula Cluster (Preibisch & Feigelson 2005),
accounting for its observed spread. We chose this distribution because the
COUP survey provides the most complete X-ray observation of a young stellar
cluster. However, it should be noted that this distribution may not accurately
represent the population of Westerlund 1 due to differences in age and the
presence of a distinct massive stellar population in this cluster. To account
for this massive stellar population, we simply added the massive sources
identified by Clark et al. (2005) with their corresponding measured LX values
to the simulated cluster population. Additionally, we normalized the COUP LX
versus mass distribution to account for the decline in stellar X-ray
luminosity with age (Preibisch & Feigelson 2005), and we used the specified
values for cluster distance and absorption to convert luminosity into flux.

We simulated a 1 Msec ACIS-I observation of this fake cluster, taking into
account instrumental
background131313https://cxc.harvard.edu/cal/Acis/detailed_info.html, and
performed source detection using _Wavdetect_ (thus not accounting for the
source validation procedure we adopted with AE). By comparing the input and
output lists of sources, we determined that the completeness in the 0.8-2
solar mass range is approximately 40% within the central 4 arcminute region,
decreasing by approximately 10% in the inner 1 arcminute region. For more
massive stars, the estimated completeness is around 85% regardless of the
distance from the cluster center. It is important to note that this is a
preliminary estimation of the completeness of the EWOCS X-ray catalog, which
will be further validated through the identification of OIR counterparts and
source classification.