11institutetext:  European Southern Observatory, Karl-Schwarzschild-Strasse 2,
85748 Garching bei München, Germany
11email<EMAIL_ADDRESS>22institutetext: Universitäts-Sternwarte München,
Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679 München, Germany
33institutetext: Dipartimento di Fisica e Astronomia ”Augusto Righi” Viale
Berti Pichat 6/2, Bologna, Italy 44institutetext: Department of Physics and
Astronomy, Rice University, 6100 Main St - MS 108, Houston, TX 77005, USA
55institutetext: Centre for Extragalactic Astronomy, Department of Physics,
Durham University, South Road, Durham DH1 3LE, UK 66institutetext: Institute
for Computational Cosmology, Department of Physics, University of Durham,
South Road, Durham DH1 3LE, UK 77institutetext: Dipartimento di Fisica,
Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy
88institutetext: Universität Heidelberg, Zentrum für Astronomie, Institut für
Theoretische Astrophysik, Albert-Ueberle-Straße 2, 69120 Heidelberg, Germany
99institutetext: Universität Heidelberg, Interdisziplinäres Zentrum für
Wissenschaftliches Rechnen, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
1010institutetext: INAF-Istituto di Astrofisica e Planetologia Spaziali, Via
del Fosso del Cavaliere 100, I-00133, Rome, Italy 1111institutetext:
Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191, Gif-
sur-Yvette, France

# The population of young low-mass stars in Trumpler 14††thanks: Based on
observations collected at the European Southern Observatory under ESO
programme 097.C-0137.

Dominika Itrich 1122 Leonardo Testi 33 Giacomo Beccari 11 Carlo F. Manara 11
Megan Reiter 44 Thomas Preibisch 22 Anna F. McLeod 5566 Giovanni Rosotti 77
Ralf Klessen 8899 Sergio Molinari 1010 Patrick Hennebelle 1111

(Received / Accepted)

Massive star-forming regions are thought to be the most common birth
environments in the Galaxy and the only birth places of very massive stars.
Their presence in the stellar cluster alters the conditions within the cluster
impacting at the same time the evolution of other cluster members. In
principle, copious amounts of ultraviolet radiation produced by massive stars
can remove material from outer parts of the protoplanetary disks around low-
and intermediate-mass stars in the process of external photoevaporation,
effectively reducing the planet-formation capabilities of those disks. Here,
we present deep VLT/MUSE observations of low-mass stars in Trumpler 14, one of
the most massive, young, and compact clusters in the Carina Nebula Complex. We
provide spectral and stellar properties of 717 sources and based on the
distribution of stellar ages derive the cluster age of $\sim$1 Myr. The
majority of the stars in our sample have masses $\leqslant$1 $M_{\odot}$, what
makes our spectroscopic catalogue the most deep to date in term of masses, and
proves that detailed investigations of low-mass stars are possible in the
massive but distant regions. Spectroscopic studies of low-mass members of the
whole Carina Nebula Complex are missing. Our work provides an important step
forward towards filling this gap and set the stage for follow-up investigation
of accretion properties in Trumpler 14.

###### Key Words.:

stars: formation, pre-main sequence, low-mass – ISM: HII regions – open
clusters and associations: individual: Trumpler 14, Carina Nebula Complex

##  1 Introduction

Star formation takes place in both, low-mass and massive complexes of
molecular clouds. The latter is considered to be a more common star-forming
environment in the Galaxy (e.g., Miller & Scalo, 1978; Lada & Lada, 2003;
Winter et al., 2018). Those giant regions form hot and massive OB stars, which
can significantly affect the formation and evolution of less massive cluster
members. Copious amounts of ionising far- (FUV) and extreme-ultraviolet (EUV)
photons, as well as an enormous volume of ejected mass via outflows or strong
stellar winds, can create a so-called negative feedback. By injecting large
amounts of energy into the surrounding medium, massive stars ionise and
disperse the natal molecular cloud producing expanding Hii regions (e.g.,
Freyer et al., 2003; Krumholz et al., 2011; Winter et al., 2018) and remove
the matter from circumstellar disks that could otherwise be used to form a
planetary system (e.g., Adams et al., 2004; Anderson et al., 2013; Facchini et
al., 2016; Eisner et al., 2018; Winter & Haworth, 2022). On the other hand,
expanding shock and ionisation fronts can also compress molecular clouds and
in that way trigger the formation of new stars (positive feedback, e.g.,
Gritschneder et al., 2010; Haworth & Harries, 2012). There is a strong
evidence that the formation of the Solar System took place in such a large
cluster and was heavily influenced by close-by massive stars (e.g., Adams,
2010; Pfalzner et al., 2015). It is therefore of great importance to
understand how the presence of massive stars in the cluster influences the
intrinsic star formation, particularly of low-mass stars, as well as the
initial mass function (IMF), star formation efficiency, or the planet
formation capacity.

Despite the importance of understanding the global picture of star formation,
a substantial part of the investigation was so far focused on nearby ($<$300
pc), and therefore low-mass, star-forming regions (Manara et al., 2022). While
they are very important to construct and test a theory of formation of Sun-
like stars, those studies neglect the role of the cluster environment. The
closest massive region, the Orion Nebula, although providing excellent first
examples of photoevaporating disks (“proplyds”, O’Dell et al., 1993), might
not be representative of the most extreme environments where most of the stars
in the Galaxy are forming (Smith, 2006).

The greatest problem of studying massive star-forming regions is that they are
all relatively far away from us ($>$1 kpc) and usually suffer from high
extinction. These two factors significantly hinder the characterisation (and
even detection) of individual members of these complexes, especially those
less massive and fainter. Since the stellar content of any cluster is
dominated by low-mass stars, lack of those objects can essentially impact
results of studies of massive star-forming regions, as well as their
interpretation. Moreover, low-mass stars are more vulnerable to the harsh
environment than the massive ones (see e.g., Whitworth & Zinnecker, 2004;
Almendros-Abad et al., 2023). Environmental conditions like high UV radiation
impacts also the capability of protoplanetary disks around young stars to form
planets (e.g., Throop & Bally, 2005; Anderson et al., 2013; Facchini et al.,
2016; Winter et al., 2018; Parker, 2020; Winter et al., 2020; Qiao et al.,
2023).

Another observational problem that often accompanies the studies of massive
regions is a bright and variable emission from the surrounding Hii region.
Assessment of this emission in most cases cannot be done globally but requires
the knowledge of the local variation of this emission. This issue is
particularly profound when studying emission lines from the young stars, e.g.,
tracing accretion, winds, or jets. Stellar spectrum is contaminated with the
nebular emission what can lead to potentially incorrect conclusions. Due to
that reason, fiber-fed spectroscopy is not a good approach to study star-
forming regions. A significantly more efficient way to obtain local and
wavelength-dependent sky emission is to employ integral field spectroscopy
(IFU) instruments. Current instrumentation offers several IFU spectrographs
with medium to high spectral and spatial resolution (e.g., ERIS, MUSE, KMOS at
the Very Large Telescopes, or GMOS, NIFS at the Gemini Telescopes, Allington-
Smith et al., 2002; McGregor et al., 2003; Bacon et al., 2010; Sharples et
al., 2013; Davies et al., 2023). They allow obtaining position-dependent
spectra of sources of interest as well as surrounding background and with that
characterising faint objects in distant regions.

The Carina Nebula Complex (CNC) is one of the biggest sites of star formation
and one of the most massive Hii regions in our Galaxy. It is located in the
plane of the Galactic Disk at a distance of 2.35 kpc from the Sun (Shull et
al., 2021; Göppl & Preibisch, 2022), which makes it the closest analog of a
typical environment in which stars form. Most if not all the clusters within
the CNC are located at similar distances with very small distance dispersion
of 1-2% (Smith, 2006; Cantat-Gaudin et al., 2018; Maíz Apellániz et al., 2020;
Göppl & Preibisch, 2022; Berlanas et al., 2023). Low interstellar extinction
towards the region (e.g., Walborn, 1995; Hur et al., 2023) makes it an even
more suitable target for observational studies of massive clusters in the
optical wavelengths. However, it was noticed that the reddening law towards
the CNC is anomalous ($R_{\rm V}$ = 4–5, e.g., Smith, 2002) combined with the
variable intracluster extinction (by $\sim$9 mag Tapia et al., 2003; Rowles &
Froebrich, 2009; Preibisch et al., 2012). Additionally, the CNC is located
close to the galactic plane, what causes serious problems with contamination
of the field stars (both foreground and background).

The CNC contains more than 5$\times$104 stars (Povich et al., 2019) with a
total mass of $\sim 37000\leavevmode\nobreak\ M_{\odot}$ (Preibisch et al.,
2011a) immersed in a massive Hii region. While part of the CNC population is
spread over a wide area characterised by a low stellar density regime, most of
the star formation is confined in a number of star clusters, with Trumpler
(Tr) 14, 15, and 16 being the most massive ones. These clusters host the
greatest concentrations of O-type stars, which are expected to highly
influence the evolution of their low-mass neighbours. There are at least 74
O-type stars in the CNC (Smith, 2006; Berlanas et al., 2023), including some
of the most massive stars known: prototypical O2 (HD 93129A in Tr 14) and O3
(in Tr 14 and Tr 16) stars, luminous blue variable $\eta$ Carinae (in Tr 16),
as well as several Wolf-Rayet stars (Walborn, 1973; Walborn et al., 2002;
Smith, 2006).

Current observational campaigns of the Carina Nebula focused mostly on massive
or intermediate-mass stars. Photometric studies included optical, near
infrared (NIR), and X-ray observations. More than 100 stars in Tr 14 and Tr 16
were observed by Feinstein et al. (1973) down to G-type stars which allowed
the authors to obtain distance values to the clusters close to the most recent
ones. DeGioia-Eastwood et al. (2001a) investigated over 500 stars in Tr 14 and
Tr 16 with optical photometry detecting stars down to $\sim$1 $M_{\odot}$.
Tapia et al. (2003) presented the optical and NIR photometry of 4150 stars in
the Carina Nebula with mass limit of 2 $M_{\odot}$. Multi-wavelength
observations (optical + NIR) were also analysed by Beccari et al. (2015) who
built spectral energy distributions (SEDs) of 356 stars, obtained their
stellar parameters (down to $<$0.4 $M_{\odot}$) and estimated their mass
accretion rates. Optical photometry of stars in Tr 14, Tr 16, and Collinder
232 was analysed by Carraro et al. (2004) down to $\sim$1 $M_{\odot}$. Hur et
al. (2012) showed visual CCD photometry of the two most massive clusters in
CNC and investigated their stellar content together with IMF with the limit of
1.5 $M_{\odot}$. They recently extended this catalogue by deep photometry of
135 000 stars down to 0.2 $M_{\odot}$ in $I$-band assuming the CNC age of 7
Myr (Hur et al., 2023).

NIR photometry of massive and intermediate-mass stars was published by Ascenso
et al. (2007) together with a study of the mass function. Povich et al. (2011)
investigated mid-IR excess of $\sim$1400 young stars in Carina based on
Spitzer observations. Extensive, wide-field, and deep NIR photometry of CNC
from VISTA and HAWK-I of more than 600 000 sources down to $<$0.1 $M_{\odot}$
was published by Preibisch et al. (2011a, b, 2014). Later, Zeidler et al.
(2016) investigated their NIR excess. These surveys were often cross-matched
with the deep X-ray imaging of the Chandra Carina Complex Project (CCCP, Broos
et al., 2011; Townsley et al., 2011), which identified $\sim$14 000 sources
and help confirming the youth of low-mass Carina stars. The survey was
preceded by study of Tr 16 with Chandra by Albacete-Colombo et al. (2008) and
XMM-Newton observations of early-type stars Antokhin et al. (2008).

Individual, high-mass members of the Carina Nebula were classified first
photometrically (Walborn, 1973; Massey & Johnson, 1993; Walborn, 1995), then
spectroscopically (Levato & Malaroda, 1982; Morrell et al., 1988; Walborn et
al., 2002; Vaidya et al., 2015; Maíz Apellániz et al., 2016; Preibisch et al.,
2021; Berlanas et al., 2023). The first spectroscopic properties of massive,
intermediate-mass, and solar-like stars in Tr 14 and Tr 16 were obtained in
the Gaia-ESO survey by (Damiani et al., 2017), who used high-resolution
(R$\sim$17 000) observations from FLAMES/Giraffe spectrometer at the ESO Very
Large Telescope (VLT) to characterise more than 1000 stars and to portray
characteristics of those two clusters.

The photometric and spectroscopic works listed above are not a comprehensive
list of all studies of the CNC. However, up to date no spectroscopic surveys
targeting stars below 1 $M_{\odot}$ were conducted in the Carina Nebula
leaving the most important part of the region uncharacterised. The aim of this
work is to fill this gap and provide a spectroscopic catalogue of low-mass
stars in one of the main clusters in the Carina Nebula, Trumpler 14.

Tr 14 is the most compact and youngest among the three main clusters in the
CNC. Its structure was recognised to consist of a dense core ($r$ of
0.5′–0.9′corresponding to 0.3–0.6 pc at the distance of 2.35 kpc) and an
extended halo population of possibly slightly older age (4′–7.8′corresponding
to 2.7–5.2 pc Tapia et al., 2003; Ascenso et al., 2007; Kharchenko et al.,
2013). Its age was estimated to be $\sim$1 Myr (Penny et al., 1993; Vazquez et
al., 1996; DeGioia-Eastwood et al., 2001a; Carraro et al., 2004); 2 Myr
younger than Tr 16 (Walborn, 1995; Smith & Brooks, 2008). It contains $\sim$20
O-type (Shull et al., 2021; Berlanas et al., 2023) and several tens B-type
stars. As a result, its ultraviolet luminosity is $\sim$20 times higher than
$\Theta^{1}$Ori C in the Orion Nebula (Smith, 2006; Smith & Brooks, 2008).
High UV field, high cluster density and mass, young age, and low reddening
towards the cluster make Tr 14 a perfect target to investigate the role of
environment on star formation.

Here, we present the optical photometry and spectroscopy of young, low-mass
stars in Tr 14. We define the methodology to detect those faint sources,
extract their spectra, assess contamination from the sky emission, and conduct
the spectral classification. Subsequently, we describe how the stellar
properties are obtained. We conclude our work with a more global outlook on
the Tr 14’s properties. This study will be followed up by the detailed
characterisation of accretion properties of the young stars presented here.

##  2 Data

###  2.1 Observations and data reduction

Observations were carried out in 2016 with the Multi Unit Spectroscopic
Explorer (MUSE), a second generation integral field unit (IFU) instrument on
the VLT in Paranal, Chile (Bacon et al., 2010), under the programme ID
097.C-0137 (PI: A. Mc Leod). MUSE covers the wavelength range of 4650–9300 Å
with a spectral resolution $R\sim 4000$ (sampling of 1.25 Å). Observations
were performed without adaptive optics in Wide Field Mode (WFM) with spatial
sampling of 0.2$\arcsec$ and a total field of view of $1\arcmin\times
1\arcmin$. A wide region around Tr 14 including the core of the cluster and
the surrounding molecular cloud, was covered with 22 pointings with a total
integration time per pointing of 39 min. In the ESO archive, there are also
available “short” exposures of total integration time of 15 sec, designed for
observations of the brightest stars, which we do not use here because we are
investigating only the low-mass content of Tr 14. The goal of the project was
not only to capture the cluster members, but also to study the kinematics of
the gas in the pillar-like structures north-east and south-west from Tr 14.
The observations were designed to have small spatial overlap between
individual pointings, and with that smoothly cover the whole area. Each of the
pointings was observed three times with a 90∘ rotation dither pattern to
better remove instrument artefacts. Observational logs are presented in
Appendix A.

Observations were reduced using the dedicated ESO pipeline v. 2.8.3
(Weilbacher et al., 2020) embedded in the EsoReflex environment (Freudling et
al., 2013). The pipeline provides wavelength and flux calibrated IFU cubes.
The standard stars used for calibration are listed in Appendix A together with
the observing conditions. Calibrated exposures were combined into the 3D data
cubes, one per field, that were used for the analysis presented in this paper.

Figure 1: Trumpler 14 cluster studied in this work. Grey sky image from HAWK-I
$H$-band observations (Preibisch et al., 2011a, b) shows the whole region with
the light grey grid of MUSE pointings and stars studied in this work marked as
red circles. The five panels above and on the right show selected MUSE
$I$-band images. The panel inside consists a mosaic of four MUSE pointing of
the Tr 14 center. Their numbers are indicated in the panels. Positions of the
stars on MUSE images are marked with empty grey circles. The bar on the lower
right corner of the HAWK-I image indicates the projected distance of 0.5 pc at
the assumed distance of 2.35 kpc towards Tr 14 (Göppl & Preibisch, 2022).

###  2.2 Identification of sources and extraction of spectra

In addition to producing the 3D data cubes, the ESO pipeline allows the user
to extract photometric images, among other ones, in the standard Johnson-
Cousins bands. We use these images as reference to guide the selection of
bona-fide sources for the extraction of spectra from the IFU cubes. We use
SExtractor (Source–Extractor111https://sextractor.readthedocs.io/, Bertin, E.
& Arnouts, S., 1996) to perform the source identification on the photometric
images. SExtractor is a free software designed to perform aperture photometry
on astronomical images, suited also for crowded regions. It estimates and
subtracts the background emission assuming its smooth variation. We tested the
background estimation varying the size of the mesh cell and found that the
size of 16 pixels gives the best performance in terms of recovering large
gaseous features on the sky and at the same time not creating artificial ones.
The same pixel size is used throughout the aperture photometry and extraction
of the spectra. We in fact anticipate here that the latter is done by
performing aperture photometry on each individual slice of the MUSE cube at
the position of the bona-fide sources identified on the $I$-band images.

We first perform the identification of the sources on the $I$-band images,
which we use as the reference. We employed a fixed aperture size of 5 pixels
in diameter and the background mesh size of 16 pixels. Hence using the
SExtractor we create a catalogue which includes for each source the X and Y
position in the MUSE CCD reference frame together with I-band aperture
magnitudes. Based on “identification” image, we run the SExtractor in double
image mode on all photometric images obtaining magnitudes from other bands,
namely $R$ and $V$. This is possible as all the images have identical
dimensions being all extracted from the same IFU cube. With that we create the
initial photometric catalogue of 5428 objects with $I$-band magnitude
measurements.

We used the same approach to extract spectra from the MUSE cubes of each
source detected in the $I$-band images. Upfront, we slice MUSE datacubes with
MissFITS222https://www.astromatic.net/software/missfits/ (Marmo & Bertin,
2008) into individual images, one per spectral element. Then, we run
SExtractor on each slice and estimate flux for each source within the same
aperture as for photometric images. Measured fluxes per spectral element are
then combined into a single spectrum for each target. In the same way we
extract wavelength-dependent flux uncertainties and sky spectra. Both are
later used to evaluate goodness of stellar spectra.

####  2.2.1 Coordinates correction

We transform astrometric coordinates of stars extracted from the MUSE cubes to
the coordinate system of the recently released Gaia DR3 catalogue (Gaia
Collaboration et al., 2022). We first perform a match between the catalogues
with a large separation limit (1-2″), separately for each MUSE pointing. We
estimate median offsets of right ascension and declination for every pointing
and adopt them as coordinate corrections. Absolute corrections range between
1.46″ and 5.75″ for right ascension, and between 0.08″ and 2.98″ for
declination. We list corrections and show distributions of offset for each
pointing in Appendix B. We apply the corrections to coordinates of our stars
and list them in Table 1.

Consecutively, we match our catalogue with corrected coordinates once again
with Gaia (Gaia Collaboration et al., 2016, 2022). We find 1902 counterparts
within the separation of 0.5″. In Appendix B we show the distribution of
separations between Gaia and MUSE and argue the selection of the separation
limit. Based on this distribution we also find that the accuracy of astrometry
of our stars is of $\sim$0.1″.

####  2.2.2 Identification of spurious sources

Before analysing the sample we remove from the catalogue spurious sources,
which may be due to low signal to noise, confusion near the very bright stars,
and contamination from the structures in the nebular emission.

Due to different atmospheric conditions the sensitivity of different pointings
is uneven. Additionally, some images contain bright stars whose luminosity
dominates at the images making the detection of the faint sources in their
vicinity challenging. We first use flags issued by SExtractor on photometric
measurements to exclude potentially incorrect magnitudes. Those flags mark
cases when neighbouring source likely bias estimation, when the light from the
object has been deblended, when the position of the object is too close to the
edge of the image, when one or more pixels were saturated, or when the
photometry process was corrupted333The full description of SExtractor flags is
available on the website at
https://sextractor.readthedocs.io/en/latest/Flagging.html#flags-def. With this
approach, we remove 21% of the sources from the catalogue. We additionally
only accept stars with the photometric uncertainty in $I$-band of less than
0.1 mag. We remove photometric measurements not fulfilling those criteria in
other bands. This procedure leaves 3082 sources in our catalogue.

The Carina Nebula is an Hii region, remarkably bright in some atomic lines
(H$\alpha$, H$\beta$, OI, HeI, etc.). In particular, small, compact gas
concentrations can mimic light from the stars having stellar-like point spread
function (PSF). We performed visual inspection of the I-band images comparing
them to the other broad-band MUSE images, as well as to the HAWK-I H-band
image (Preibisch et al., 2011a, b), identifying all possible “spurious”
detections that are not present in other images; we flag them accordingly and
remove from the catalogue.

We pay particular attention to the images affected by the presence of nearby
saturated stars. Their light is spread on the pixels around their PSF on the
CCD detector. This artificially changes the local background making the
measurement of the stellar flux falling on those regions unreliable.
Additionally, we identify elongated spikes near those bright stars, due to the
diffraction pattern of the secondary mirror support. Combined, those effects
significantly hinder the analysis of fainter stars in the closest
neighbourhood of the bright ones. Based on visual inspection, we identify
stars where light is not separated spatially on I-band MUSE images from the
bright stars, flagged them as ,,illuminated” and remove from the final
photometry catalogue leaving 2727 stars.

####  2.2.3 Detections in overlapping pointings

Edges of some neighbouring pointings overlap causing double detection of the
same stars in our photometry catalogue. After correcting coordinates, we
defined a threshold separation of 0.5$\arcsec$ within which we looked for
stars present in two (or more) pointings. We find 55 pairs of doubly observed
targets. We exclude from the catalogue those sources that have worse signal-
to-noise ratio (snr) of spectrum around 7500 Å. We show comparisons of spectra
between two detection in the Appendix C.

####  2.2.4 Background emission

All the images of Carina Nebula, as an Hii region, suffer from bright and
highly variable background emission. The presence of a strong background with
flux variations of the order of one stellar PSF makes the estimation of the
local background in the vicinity of the stars very uncertain. Hence, the
aperture photometry from which the stellar spectra are built, can be very
imprecise and unreliable. During the stellar flux extraction (Sec. 2.2),
background emission was estimated by SExtractor assuming it is varying
smoothly across the field. To make sure that the photometry is robust, we
estimate the local background variation for each star in our catalogue based
on the standard deviation (std) of the background estimates for stars within a
radius of 20″. We adopt the threshold of 3$\sigma$, where $\sigma$ is the
standard deviation, and remove all photometric measurements where the stellar
flux is below the threshold. In Appendix D we discuss the applied definition
in depth. The final number of stars with well defined and reliable $I$-band
magnitudes is 804 (Figure 1).

####  2.2.5 Magnitude correction

To check the flux calibration we compare the MUSE photometry with the optical
photometry from the Wide Field Imager (WFI) at the MPG/ESO 2.2m telescope
published by Beccari et al. (2015). The catalogues were matched adopting a
0.5″maximum separation radius between the stars from the two catalogs. We find
613 common stars in the two catalogs. We perform the comparison of magnitudes
for each field and band separately. For the $I$-band the corrections vary
between 0.16 and 1.28 mag depending on the MUSE pointing with the mean value
of 0.55 mag. This is mainly due to the fact that each MUSE field was observed
in very different weather conditions. All corrections are provided in Appendix
E. We discard $B$-band magnitudes as highly uncertain for our faint stars. We
provide in the Table 1 the photometry of the sources extracted from the MUSE
images with the magnitudes corrected to match the WFI ones.

As a next step, we investigate the distribution of the magnitudes. We show the
observed luminosity function for $I$, $R$, and $V$-bands from MUSE
observations in Appendix E. The distribution of $I$-band magnitudes peaks at
$\sim$18 mag and falls to $\sim$21 mag. If we adopt the cluster age of 1 Myr
(Smith & Brooks, 2008), the distance to the cluster of 2.35 kpc (Göppl &
Preibisch, 2022), and extinction of 2.3 mag (see Sec. 3), those magnitudes
will correspond to the stellar masses of $\sim$0.8 and $\sim$0.14 $M_{\odot}$
according to the theoretical evolutionary models of Baraffe et al. (2015).
Even though we do not correct luminosity function for completeness, those
rough mass estimates show depth of our catalogue.

####  2.2.6 Cross-match with other photometry catalogs

To complete our catalogue with information from other wavelength ranges, in
addition to the Gaia DR3 and WFI, we cross-match the MUSE catalogue with VISTA
(Preibisch et al., 2014), HAWK-I (Preibisch et al., 2011a, b), Spitzer (Povich
et al., 2011), and Chandra (Preibisch et al., 2011b; Townsley et al., 2011)
observations. For consistency, we define the same maximum separation of 0.5″
for all the catalogues. In Appendix B we explain the use of this separation
limit. We find 658, 766, 26, and 309 stars in common between MUSE and VISTA,
HAWK-I, Spitzer, and Chandra, respectively. We present in Table 1 the example
of the catalogue together with flags indicating the presence of the
counterpart in any other catalogue. The full content of the catalogue is
available online.

We emphasise that we adopt a very conservative approach and apply severe
photometric quality thresholds and checks to select only bona-fide stars with
high quality spectra. In doing so we are aware that a number of real stars
which have not passed our photometric quality criteria might have been removed
from the final catalogue. In fact, a large number of these stars do have a
counterpart in one or more of the catalogues used to complement the MUSE
photometry. Among discarded sources are 841 Gaia, 212 WFI, 913 VISTA, 1809
HAWK-I, 2 Spitzer, and 120 Chandra counterparts. We are aware that within this
limitation our catalogue is not complete in terms of cluster members. We
report the list of probable members with uncertain photometry due to the
background contamination in Table 5 and assess the completeness in the next
section.

###  2.3 Completeness of the catalog

Figure 2: The distribution of $J$-band magnitudes from HAWK-I in the MUSE
field (Preibisch et al., 2011a, b). The dark berry histogram shows all HAWK-I
measurements taken in the same area that was covered by MUSE. The violet
distribution presents point source detections from Sec. 2.2.6, (upper panel)
and in combination with the one excluded due to the high background variation
and foreground stars (lower panel). In both panels, the grey line shows
completeness of our catalogue defined as a ratio of the number of stars in a
given magnitude bin (0.5 mag wide) in our catalogue and in the HAWK-I
catalogue.

The goal of this work is to have a high quality spectroscopic sample of low-
mass members of Tr 14. In order to achieve this goal we apply a number of
quality cuts to the photometric catalogue (Sec. 2.2.4), which can affect the
interpretation of our results.

To better understand the limitations of our work, we estimate the completeness
by comparison to the photometric catalogue from HAWK-I (Preibisch et al.,
2011a, b). Figure 2 shows distribution of $J$-band magnitudes observed by
HAWK-I in the exact same region as covered by our MUSE pointings (dark berry
histogram). The stars in common between the two catalogues are shown in
violet. With the grey line we show the ratio between the stars retrieved in
our catalogue and the number of stars observed by HAWK-I per magnitude bin of
0.5 mag. The ratio gives us a rough estimate of the completeness of our
catalogue. The upper panel shows only those stars for which three sigma level
of background variation did not exceed $I$-band flux measured with MUSE. Their
$J$-band magnitudes range from 12.5 to 19.0 mag, corresponding at the low-mass
end to 0.065 $M_{\odot}$ at 1 Myr (Baraffe et al., 2015). Assuming that the
HAWK-I catalogue is complete down to $\sim$21 mag in $J$-band (Preibisch et
al., 2011a), we can adopt this ratio as the rough estimate of the completeness
of our catalogue. Based on this assumption, we reach 50% level of completeness
at $\sim$15.5 mag corresponding to 0.8 $M_{\odot}$ at 1 Myr. The 30%
completeness level is achieved at $\sim$16.5 mag corresponding to $\sim$0.4
$M_{\odot}$ at 1 Myr. As we indeed see later in Sec. 3.2 or 4.2, our deep
observations allow us to detect and characterise very low-mass stars in Tr 14.
However, due to our conservative approach to the background emission (Sec.
2.2.4), the final sample is highly incomplete in the low end of mass spectrum.

In the lower panel of Figure 2 we include the “full MUSE” sample consisting
the one with robust $I$-band MUSE photometry and the one discarded due to the
highly variable background emission. Here, flagged or uncertain MUSE
photometry sources (Sec. 2.2.2) were not included. We see immediately that
with our approach we removed mostly faint, low-mass objects. The “full”
catalogue extends to the $\sim$21 $J$-band magnitude (0.018 $M_{\odot}$ at 1
Myr adopting the evolutionary models of Baraffe et al., 2015) and reaches 50%
level of completeness at $\sim$18.5 mag, corresponding to 0.085 $M_{\odot}$ at
1 Myr. The 30% completeness level is achieved at $\sim$19 mag (0.065
$M_{\odot}$).

The significant difference between the two distributions (“MUSE” sample with
robust $I$-band photometry and “full MUSE” sample affected by the background
emission) shows the possible impact of the adopted procedure on the final
results and the estimated global properties of Tr 14. Since the deep NIR
photometric observations can contain significant fraction of contamination
from background sources, especially in the faint end (see the discussion in
Sec. 3.3 in Preibisch et al. (2011a) and in Sec. 2.3 in Preibisch et al.
(2011b)), we do not correct our analysis for the incompleteness. We assume
that our study is complete at the level of 50% for stars more massive than 0.8
$M_{\odot}$ and at the level of 30% for stars more massive than 0.4
$M_{\odot}$.

Table 1: catalogue of low-mass in Trumpler 14 stars analysed with MUSE
observations.

ID | coordinates |  $I$-band |  $R$-band |  $V$-band | snrI,bkg | snrR,bkg | snrV,bkg | possible_frg_bkg | gaia_flag | wfi_flag | VISTA_flag | hawki_flag | spitzer_flag | chandra_flag | NIR excess | SpT | $T_{\mathrm{eff}}$ | $A_{\rm{V}}$ | $r_{750}$ | $\log{(L_{\mathrm{bol}})}$ | $M_{\mathrm{*,PARSEC}}$ | $M_{\mathrm{*,B15S00}}$ | AgePARSEC | AgeB15S00
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (h:m:s d:m:s) | (mag) | (mag) | (mag) |  |  |  |  |  |  |  |  |  |  |  |  | (K) | (mag) |  | $L_{\odot}$ | ($M_{\odot}$) | ($M_{\odot}$) | (Myr) | (Myr)
F01N009 | 10:44:09.93 -59:29:11.72 | 20.49$\pm$0.12 | – | – | 3.96 | – | – | False | None | False | True | True | False | False | True | M5.0${}^{+1.6}_{-0.7}$ | 3125${}_{-201}^{+103}$ | 2.70${}_{-1.07}^{+1.22}$ | 0.08${}_{-0.07}^{+0.55}$ | -1.05${}_{-0.85}^{+0.51}$ | 0.38 | 0.18 | 6.2 | 2.3
F01N010 | 10:44:08.38 -59:29:12.03 | 17.37$\pm$0.09 | 18.11$\pm$0.09 | 19.01$\pm$0.08 | 17.26 | 4.18 | 5.00 | False | Good | True | True | True | False | False | False | K4.0${}^{+0.6}_{-0.6}$ | 4561${}_{-110}^{+108}$ | 1.20${}_{-0.43}^{+0.41}$ | 0.00${}_{-0.00}^{+0.56}$ | -0.32${}_{-0.36}^{+0.34}$ | 1.02 | 0.99 | 13.0 | 19.8

444The first column gives IDs of the detected sources, the second one lists
coordinates. The third, fourth, and fifth columns give apparent magnitudes in
$I$, $R$, and $V$-band, respectively. The sixth, seventh, and eighth columns
provide signal-to-noise of the flux with respect to the background variation
in a given band, as indicated by the lower script (see Sec. 2.2.4 for
details). The ninth marks possible foreground or background stars (see Sec.
3.1 for definitions). The next five columns flag matches with other catalogs:
Gaia (Gaia Collaboration et al., 2022), WFI (Beccari et al., 2015), VISTA
(Preibisch et al., 2014), HAWK-I (Preibisch et al., 2011a, b), Spitzer (Povich
et al., 2011), and Chandra (Preibisch et al., 2011a; Townsley et al., 2011).
The following indicates if the star has an NIR excess as defined by Zeidler et
al. (2016). In the consecutive nine columns are given stellar parameters:
spectral type, effective temperature, visual extinction, constant veiling at
7500 Å, bolometric luminosity, and stellar mass and stellar age estimated from
PARSEC (Bressan et al., 2012) and Baraffe et al. (2015) / Siess et al. (2000)
tracks, as indicated by the subscript. A full version of this table will be
available at the CDS upon publication. The first few rows are shown as an
example.

##  3 Stellar population

###  3.1 Identification of foreground stars

To exclude possible contamination from foreground and background stars we use
accurate Gaia astrometry for our sources. We first perform a number of quality
checks on the matched objects. We first exclude all stars that have goodness
of fit parameter RUWE $>1.4$ (Lindegren, 2018), astrometric_gof_al $>5$
(Lindegren et al., 2021), parallax over error lower than 5, and uncertainty of
the proper motion above 20%. We flag them as object with poor Gaia astrometry,
gaia_flag=‘poor’. We find 175 good objects out of the 794 Gaia counterparts.
None of them is flagged as a non-single star or a duplicated object,
reassuring us about the good quality of the astrometry. All of them have 5- or
6-parameter solution. We select fore- and background stars based on parallaxes
corrected for bias, as described in Lindegren et al. (2021). This correction
is possible only for stars with $G$-band magnitude between 5 and 21, and for
the effective wavenumber (for 5-parameter solution) or the pseudocolour (for
6-parameter solution) between 1.24 and 1.72 $\mu$m-1. Wavenumbers are
calculated using calibrated BP/RP spectra, while pseudocolour is an
approximate colour of the source based on its astrometric solution utilising
the chromaticity of the instrument.

We illustrate the distribution of corrected parallaxes of stars with good Gaia
astrometry in Figure 3. The Gaussian profile fit to the distribution is
centred at $\varpi=0.43$ mas and has a width of $\sigma=0.04$ mas. The
centroid parallax corresponds to the distance of 2.35 kpc, in very good
agreement to the findings of Göppl & Preibisch (2022). We follow their
procedure to identify fore- and background stars. We define the background
stars as those, whose 3$\sigma$ extend of the parallax value (i.e. parallax
value plus its error) is smaller than the $\varpi_{\rm{min}}$
($\varpi+3\sigma_{\varpi}<\varpi_{\rm{min}}$), while foreground stars as those
with 3$\sigma$ extend (i.e. parallax value minus its error) higher than
$\varpi_{\rm{max}}$ ($\varpi-3\sigma_{\varpi}>\varpi_{\rm{max}}$). We adopt as
$\varpi_{\rm{min}}$ and $\varpi_{\rm{max}}$ values corresponding to range of
parallaxes defined by the width of the Gaussian distribution (0.43$\pm$0.04
mas), further corresponding to the distance range of (2.61 kpc, 2.13 kpc). Out
of 175 ’good’ Gaia counterparts we identify 0 background stars and 24
foreground stars. However, if we take into account all possible Gaia matches
with corrected and positive parallaxes and possibly high astrometry
uncertainties (784 stars), then for the same parallax ranges we find 35
possible foreground stars and 10 possible background stars. We remove from our
catalogue 24 foreground stars with robust astrometry and flag remaining 21
stars as possibly contaminated (fore- or background) stars (possible_frg_bkg).
Summarising, we find 794 Gaia counterparts, including 175 with good
astrometry; 24 of them are foreground stars. At the end our catalogue contains
780 sources.

Figure 3: Distribution of corrected parallaxes (light blue histograms) with
fitted normal distribution (purple line). Dashed-dotted lines mark 1$\sigma$
width of the fitted distribution and applied ranges for excluding fore- and
background stars.

###  3.2 Colour–magnitude diagram

We first present the colour-magnitude diagrams (CMDs) based on corrected MUSE
photometry. Figure 4 shows two CMDs based on (V-I) and (R-I) colours from
MUSE, exclusively, and one based on $I$-band magnitude from MUSE and $J$-band
magnitudes from HAWK-I or VISTA. We also plot PARSEC
v1.2S555http://stev.oapd.inaf.it/cmd theoretical isochrones with black solid
lines (Bressan et al., 2012; Chen et al., 2014) reddened by $A_{\rm{V}}$=2.6
mag, best matching our observations (see also Sec. 3.4), using extinction law
of Cardelli et al. (1989) and $R_{\mathrm{V}}$=4.4 (Hur et al., 2012). We
apply a distance modulus of 11.86 mag, equivalent of the distance to Tr 14
(Göppl & Preibisch, 2022). We show tracks for 0.3, 0.7, 1, and 3 $M_{\odot}$
stars with dotted lines. Our observational CMDs already demonstrate that,
despite very conservative quality control, our MUSE data allows us to sample
stars in Tr 14 with robust $I$-band photometry down to $\sim
0.3\leavevmode\nobreak\ M_{\odot}$. We note, however, that due to the decrease
of snr at shorter wavelengths, number of robust $R$ and $V$-band magnitudes is
smaller than in $I$-band, and at the same time the number of very low-mass
stars detected in those bands reduced.

Ascenso et al. (2007) used high resolution near-IR data to study the core of
Trumpler 14. Based on their photometry they found a global visual extinction
towards Tr 14 of $A_{\rm{V}}$=2.6$\pm$0.3 mag and a sparse foreground
population with $A_{\rm{V}}$ of 1.4 mag. Additionally to the isochrones
reddened by the visual extinction matching our observations, we show also in
Fig. 4 the location of the Zero Age Main Sequence (ZAMS, grey solid line)
reddened by the visual extinction of a sparse population (1.4 mag). The
authors suggested that this population of older stars comes from the nearby
young clusters. In our CMDs we see indication of two separate populations, one
concentrated around 1 Myr isochrone, and the other following ZAMS. We note
similar, two-population CMDs of more massive stars in the work of Carraro et
al. (2004) (see their Fig. 5). We will examine this feature with spectral
classification in the following sections.

Figure 4: Colour–magnitude diagrams from MUSE broad-band filters images in $V$
and $I$ (right panel), $R$ and $I$ magnitudes (middle panel), and $I$ and $J$
magnitudes (left panel). $J$-band magnitudes are from VISTA and HAWK-I
instruments. Shown are only data points with $I$-band magnitudes above
3$\sigma$. Solid lines show PARSEC isochrones from 0.2 to 20 Myr and ZAMS,
dotted lines show isomasses of 0.3, 0.7, 1, and 3 $M_{\odot}$, as labeled
(Bressan et al., 2012). Isochrones were reddened by the average extinction
$A_{\rm{V}}$ = 2.6 mag measured from MUSE spectra (see Sec. 3.4).
Additionally, we plot the ZAMS reddened by $A_{\rm{V}}$=1.4 mag with grey
lines.

###  3.3 Spectral classification

The goal of this paper is to characterise the low-mass members of Trumpler 14
and provide a catalogue of their stellar parameters. As shown in Fig. 4, our
dataset samples a wide range of stellar masses and colours, and thus spectral
types. Hence, we split the procedure of spectral classification into two cases
and give the detailed description in the forthcoming sections. We note that
our procedure is comparable to the one adopted by Fang et al. (2021) in the
study of the Trapezium cluster.

We base the spectral classification on Class III templates observed with
VLT/X-Shooter and published by Manara et al. (2013, 2017). The list of
templates is provided in Appendix F. Those sources where previously studied in
the literature and their spectral types are well known. We note here that they
all have a negligible extinction $A_{\rm{V}}$$<$0.3 mag. We will refer to the
Class III templates as “templates” later in the text. We degraded the
templates spectra (with natal resolution of $R\sim 7500$–18200) to the MUSE
resolution convolving them with a Gaussian kernel and then re-sampled on the
common for the both instruments spectral range ($\sim$5500–9350 Å). The
comparison between the spectra is done in the aforementioned range after
normalising to the flux at 7500 Å, $f_{750}$.

####  3.3.1 M-type stars

The spectra of M-type stars have a characteristic shape in the optical range
due to the presence of TiO and VO absorption bands. The depth of those
features changes with the spectral sub-type and increases with later stellar
types.

In this work, only spectra that have sufficient signal-to-noise (snr$>$10) are
used and classified. From the whole sample of spectra we pre-select those,
that might be of M-type based on spectral indices from Riddick et al. (2007),
Jeffries et al. (2007) and Oliveira et al. (2003) (TiO feature at 7140 Å) and
Herczeg & Hillenbrand (2014) (TiO 7140, 7700, 8465 Å). We require that at
least half of the indices suggest an M-type spectrum. We remove from the
spectra prominent emission and absorption lines to prevent confusion in the
fitting to the templates. Spectral classification is performed together with
the estimation of the visual extinction, $A_{\rm{V}}$, and veiling at 7500 Å,
$r_{750}$. We veil and redden templates using the Cardelli extinction law
(Cardelli et al., 1989) and a pre-defined grids of $A_{\rm{V}}$ and $r_{750}$
values. The extinction is sampled with a step of 0.1 mag between 0.0 and 7.0
mag, while the veiling is assumed to change between 0.0 and 1.9 with a step of
0.02. The average extinction towards Tr 14 was found to be 2.6$\pm$0.3 mag
(Ascenso et al., 2007), thus we do not expect huge variation of $A_{\rm{V}}$
for cluster members. The adopted sampling of the extinction and veiling is
smaller than the typical uncertainty of these parameters assessed later.

We minimise the value of a reduced $\chi^{2}$-like metric, defined as

$\chi^{2}_{\rm{red}}=\frac{1}{N}\sum_{i}\frac{(O-T)_{i}^{2}}{err_{i}^{2}}$ (1)

to find the best combination of spectral type, $A_{\rm{V}}$, and $r_{750}$.
The $O$ is the observed spectrum, $T$ is the fitted template, $err$ defines
the extracted uncertainty of the observed spectrum per spectral bin $i$, and
$N$ is the number of degrees of freedom (number of all spectral bins
subtracted by three free parameters). Figure 5 shows an example of the result
from the fitting procedure, whereas in the Appendix G we show the
corresponding $\chi^{2}_{\rm{red}}$ maps. We notice that the worst fits
usually have marginal values of $A_{\rm{V}}$ and $r_{750}$. In total, we
classify 269 M-type stars.

To asses the uncertainty of the estimated parameters, we run the fitting again
keeping each time one of the parameters fixed at the best value. We draw the
1–$\sigma$ curves on the $\chi^{2}_{\rm{red}}$ maps between each two
parameters. Examples are shown in Fig. 21. The maximum and minimum values
within 1$\sigma$ from the best fit of two parameters are indicated by the
extreme points of the 1–$\sigma$ curve. With this procedure we get two pairs
of uncertainties for each parameter. We combine them taking the minimum. The
lower and upper uncertainties are reported together with the best-fit values
in the Table 1. The uncertainties of the spectral types obtained in this way
are on average 2-3 sub-classes, also confirmed by the visual goodness of the
fit to the spectra. We note that due to the uneven sampling of spectral types,
the $\chi^{2}_{\rm{red}}$ maps do not represent the true
$\chi^{2}_{\rm{red}}$. We also emphasise that our method of error assessment
introduces a bias towards the values close to the borders of the adopted
ranges and causes underestimation of the uncertainty on that side. Therefore,
uncertainties for parameter values close to the border should be treated with
caution.

Figure 5: Example of a MUSE spectrum (red solid line) of an M-type star and
the matching spectral template (black dashed line). Both spectra are
normalised at 7500 Å.

####  3.3.2 K and late G-type stars

The prominent TiO and VO bands in the spectra of M-type stars fade away in
mid-K-type stars, while the overall shape of the spectrum flattens. We
identify hotter stars in our sample based on the equivalent widths (EWs) of
selected absorption lines; we list them in Table 8. We first calibrate the
change of the EWs as a function of spectral type using the Class III templates
(Sec. 3.3) assuming a linear correlation. For each line we adopt a single
value of the uncertainty of our calibration based on the fit’s uncertainty.
Additionally, for late K-type stars we use the spectral index TiO (7140 Å)
identified by Oliveira et al. (2003) and Jeffries et al. (2007) and add it to
a pool of previous estimates. The final spectral type is assigned as a
weighted mean of types from single EWs and indices. Similarly, the uncertainty
of the spectral type is a weighted mean of the uncertainties assigned to all
of the indices. A single index error is the root of the sum of the squared
uncertainties on individual EW measurements and EW calibrations. The resulting
values are listed in Table 1.

Once the spectral type is assigned, we perform an estimation of the extinction
and veiling following the same approach used to classify the M-type stars (see
Sec. 3.3.1). We fit to observed spectra the templates closest to the estimated
spectral types varying $A_{\rm{V}}$ and $r_{750}$. The best values are those,
for which the value of pseudo-$\chi^{2}_{\rm{red}}$, $\chi^{2}_{\rm{red,ps}}=$
$\chi^{2}_{\rm{red}}$/min$(\chi^{2}_{\rm{red}})$, is minimum. The
uncertainties of $A_{\rm{V}}$ and $r_{750}$ are estimated based on
$\chi^{2}_{\rm{red,ps}}$ maps, similar to the procedure described in Sec.
3.3.1. Example of a MUSE spectrum of a K-type star with the matched template
is shown in Fig. 6. We find 14 early M-, 339 K-, and 95 late G-type stars.

Figure 6: Example of the MUSE spectrum (red solid line) of the K-type star and
matching spectral template (black dashed line). Both spectra are normalised at
7500 Å.

We note that the non-homogeneous sampling of the templates can cause an error
on the estimates of stellar parameters that is hard to estimate properly (see
the examples of $\chi^{2}_{\rm{red}}$ maps in Appendix G). That applies not
only to the spectral types, but also for extinction and veiling. However, for
the lowest mass stars in our sample, the low snr dominates over any other
source of uncertainty. For this reason, we do not interpolate between spectral
types of templates to create a homogeneous grid. K- and G-type stars have on
average smaller uncertainties of the spectral classification than M-type
stars, since for these stellar types the estimate is based on absorption lines
and is independent of the density of the grid sampling. A possible source of
large error is the assumption of a linear correlation between the spectral
types and EWs. Those relations are usually quadratic (e.g., Cai Herczeg &
Hillenbrand, 2014) or higher-order polynomial (e.g., Oliveira et al., 2003;
Riddick et al., 2007). Overall, our estimations of spectral type are accurate
within 2-3 sub-classes.

###  3.4 Extinction corrected colour-magnitude diagrams

As described in Sec. 3.2, the MUSE data presented here allow us to sample the
stellar population in Tr 14 down to very low-mass stars. The observed CMDs
shown in Fig. 4 indicate the presence of two populations. Here, after the
accurate determination of the stellar parameters using the MUSE spectra (see
previous Section) we reevaluate this using the extinction values derived for
each individual star.

Figure 7: Distribution of $A_{\rm{V}}$ estimated for Tr 14 stars.
Additionally, we fitted the Gaussian function to estimate the centroid of the
distribution. Centroid, width of the distribution and median value in our
sample is indicated in the upper right part of the figure.

Based on measurements toward individual stars, we estimate the visual
extinction towards the Tr 14. The medium value of $A_{\rm{V}}$ is 2.60 mag. In
Fig. 7 we show the distribution of visual extinctions estimated in the
previous sections. The distribution has a Gaussian-like shape, the fitted
profile raises a centroid of 2.49 mag, consistent with the findings of Ascenso
et al. (2007) and slightly lower with respect to the value reported by Beccari
et al. (2015). Our distribution of $A_{\rm{V}}$ is quite broad with Gaussian
width of 1.04 mag. On average, the uncertainties of individual $A_{\rm{V}}$
estimates are $\sim 0.5$ mag. We conclude that our measurements are in line
with the literature values within uncertainties.

We use the estimated $A_{\rm{V}}$ to correct the observed magnitudes. We show
de-reddened colour-magnitude diagrams in Fig. 8 together with the isochrones
from the PARSEC v1.2S models (Bressan et al., 2012). The previously seen two
populations are no longer apparent when the new extinction correction is
applied, as expected for differently obscured populations (Ascenso et al.,
2007). This reassures us about the correctness of our procedure. The large
scatter of points remains, we will discuss possible reasons in the following
sections.

Figure 8: Colour–magnitude diagrams from MUSE broad-band filters images in $V$
and $I$ (left panel), $R$ and $I$ magnitudes (middle panel), and $I$ and $J$
magnitudes (right panel) corrected for individual extinction. $J$-band
magnitudes are from the VISTA and HAWK-I observations. Reddening vectors in
the lower left corners show reddening by a median value of $A_{\rm{V}}$
estimated for Tr 14. Solid lines show isochrones from 0.2 to 20 Myr (and
ZAMS), dotted lines show isomasses of 0.3, 0.7, 1, and 3 $M_{\odot}$, as
labeled (Bressan et al., 2012).

##  4 Physical parameters of the stars

###  4.1 Effective temperature and stellar luminosity

We derive the effective temperatures ($T_{\mathrm{eff}}$) of our stars based
on their spectral types. For M-type stars we use the SpT – $T_{\mathrm{eff}}$
scale from Luhman et al. (2003) and for earlier types, we apply the scaling
from Kenyon & Hartmann (1995) and interpolate linearly between the sub-
classes. Newer scales, like e.g., from Herczeg & Hillenbrand (2014), agree
well for low-temperature stars (types later K5). The scale adopted here
deviates for the hotter stars up to 380 K in case of K0 stars in comparison to
Herczeg & Hillenbrand (2014).

It has been shown in the literature that the $J$-band photometry is most
suitable in deriving bolometric correction for young stars. The spectral
energy distribution in these objects can be strongly affected by the presence
of NIR excess due to the ongoing mass accretion from a protoplanetary disk or
intrinsic differential extinction. Such effects can not be fully avoided but
are minimised using the $J$-band filter (e.g., Kenyon & Hartmann, 1995;
Luhman, 1999). Our bolometric luminosities are hence calculated using the
$J$-band photometry from VISTA (Preibisch et al., 2014) and HAWK-I (Preibisch
et al., 2011a, b). Whenever magnitudes from both catalogues are available for
a given star, we choose the one with smaller uncertainty. We first calculate
the bolometric magnitude ($M_{\mathrm{bol}}$) dereddening the observed
magnitudes by individual visual extinction determined from our spectral
classification (Sec. 3.3) and estimating its value in $J$-band using
extinction law from Cardelli et al. (1989), subtracting distance modulus and
adding bolometric correction with colours, as indicated by the equation:

$M_{\mathrm{bol}}=J-A_{\mathrm{J}}-{\rm DM}+({\rm BC}_{V}+(V-K)-(H-K)-(J-H))$
(2)

Values of the corrections and colours were taken from Kenyon & Hartmann
(1995). Finally, to obtain the bolometric luminosity in $L_{\odot}$, we
subtract from the previously estimated $M_{\mathrm{bol}}$ the solar bolometric
magnitude $M_{\mathrm{bol},\odot}=4.74$ (Cox, 2000):

$\log{(L_{\rm
bol}/L_{\odot})}=-0.4\cdot(M_{\mathrm{bol}}-M_{\mathrm{bol},\odot})$ (3)

The $L_{\rm bol}$ values thus calculated are listed in Table 1. There is only
$\sim$1% of spectroscopically classified stars in our catalogue which were not
matched with any source from the NIR catalogues and therefore do not have
estimated stellar parameters. This might be due to the fact that NIR
catalogues are not 100% complete.

The uncertainty of the stellar luminosity in our estimations is mostly driven
by two factors: uncertainty of $J$-band photometry adopted from the VISTA and
HAWK-I catalogs, and uncertainty of the extinction measured by us while
performing the spectral classification of the each star (Sec. 3.3). The latter
has significantly greater impact: typical uncertainty of the $J$-band
magnitudes used in this work is $\sim$0.03-0.05 mag, while the average
$A_{\rm{V}}$ error is $\sim 0.5$ mag, corresponding to $\Delta A_{\rm J}\sim
0.16$ mag.

###  4.2 HR diagram and stellar parameters

Figure 9: HR diagram for low-mass stars of Tr 14. Filled circles show data
points, empty squares are median values of the bolometric luminosity for each
spectral subclass with errorbars indicating 1-$\sigma$ percentiles.
Theoretical tracks from Bressan et al. (2012) are shown as solid black lines.
Grey dotted lines show tracks for 0.3, 0.7, 1, and 3 $M_{\odot}$ stars.

In Figure 9 we show the bolometric luminosity as function of effective
temperature. The stars detected with MUSE are shown with filled circles. The
open squares represent the median luminosities for each spectral type. We show
on the HR diagram the PARSEC v1.2S theoretical isochrones (Bressan et al.,
2012). We assign the stellar masses and ages by performing linear
interpolation between the tracks and isochrones. The resulting values are
listed in Tab. 1. For stars more luminous than predicted by the lowest age
isochrone we assign the boundary value of 0.1 Myr as a stellar age.

The HR diagram (Fig. 9) shows the presence of a large spread of luminosities
for sources with the same spectral type. Depending on the spectral type, the
spread ranges from 0.5 to 2.0 dex. Possible explanations of this behavior are
two-fold: observational and physical. Observational reasons for the spread
cover uncertainties in estimations of stellar luminosity and / or effective
temperature, as well as contamination from foreground sources. As we discussed
in Sec. 4.1, the main source of luminosity uncertainty is the extinction,
closely linked to the uncertainty of the spectral type (and thus
$T_{\mathrm{eff}}$) and veiling. On average, the luminosity values are
uncertain by $\sim$0.3 dex, temperatures by 300 K, and veiling by 0.1-0.3.
Given the large distance to Tr 14 (2.35$\pm$0.05 kpc, Göppl & Preibisch,
2022), we expect a significant contamination by foreground stars. In Sec. 3.1
we therefore used the Gaia DR3 catalogue to minimise this effect and remove
objects in the foreground of Carina Nebula. However, the limited number of
good astrometric measurements does not allow to identify all non-cluster
members. It is then not trivial to estimate the contribution of foreground
contamination to our results. This effect, combined with uncertainties in our
measurements, can explain a large part of the observed luminosity spread in
our HR diagram.

The physical sources of the luminosity spread include intrinsic age spread,
variability, binarity, dispersion in distance, and accretion history. Episodic
but vigorous accretion of low-mass objects at the very early stages of their
formation (Class 0 – Class I) can leave its imprint on their evolution for the
next few Myr (Baraffe et al., 2009). If most of the accreting kinetic energy
is radiated away, the structure of the stars will be more compact (i.e.,
stellar radius will be smaller) than of the non-accreting star of the same age
and mass. Short, intense and numerous accretion episodes do not leave enough
time for the object to relax to a larger radius for the newly acquired mass.
As a result, object has lower luminosity and seems to be older than non-
accreting of the same $T_{\mathrm{eff}}$. Baraffe et al. (2009) found that
episodic accretion at early stages of stellar evolution can well reproduce
luminosity spread equivalent to an age spread of $\sim$10 Myr observed in
Orion Molecular Cloud (Peterson et al., 2008). Moreover, the intrinsic spread
of accretion rates in the cluster might add to the luminosity spread. In their
estimates, Hartmann (2001) adopted arbitrarily an error of 0.1 in $\log{L}$
due to accretion (ignoring the effect of disk inclination). We use the
$J$-band photometry to minimise the excess luminosity caused by the accretion
(following Kenyon & Hartmann, 1995). We also included veiling in our spectral
classification. However, we made a very simplistic approach, where the veiling
is independent of the wavelength.

Another physical process, that has a great impact on the luminosity of young
stars is the photometric variability and to lesser extend, accretion
variability. Usually, photometric variability is relatively small (e.g.,
$\sim$0.2 mag in J, H, Ks bands, see Carpenter et al., 2001) and has a
timescale of less than a few days. It is very often assigned to the rotational
modulation of cool or hot spots. Variability related to accretion can span
wide range of amplitudes and timescales. Typically, changes in brightness are
lower than 1-2 mag and last few days (Fischer et al., 2023). However, some
extreme cases were also spotted. For example, Claes et al. (2022) recently
reported change by $\gtrsim$1.4 dex on accretion rate of XX Cha measured on UV
excess and by $\sim$0.5 dex measured on lines (including Pa$\beta$ in
$J$-band) over a period of 11 years. Previous studies of accretion variability
from photometry (e.g., Venuti et al., 2014) or spectroscopy (Costigan et al.,
2012, 2014) recorded variability $<$0.5 dex at different-time scales (years,
days, and minutes). If behaviour of XX Cha is more common for young stars than
thought so far, it could explain a significant fraction of observed luminosity
spread. The authors note also high photometric variability of the star in
optical bands ($>2$ mag in $B$-band to $\sim 0.5$ mag in $I$-band). Hartmann
(2001) in their Taurus study adopted a variability of 0.1 mag to explain an
observed luminosity scatter. While not negligible, this value alone cannot
explain our observations.

A different source of uncertainty, which impact is difficult to predict, is
the inclination of the accretion disk: stars with edge-on disks will appear
significantly redder than face-on ones. For instance, Alcalá et al. (2014)
suggested highly inclined disks as an explanation of the sub-luminosity of
four young stars in Lupus. After correction for disk obscuration by a factor
of 4–25 (corresponding to 0.4–1.4 dex) their accretion properties were well in
line with those from other sources in the region.

Unresolved multiplicity has potentially a large impact on luminosity
distribution, especially for young clusters, where the multiplicity fraction
is observed to be higher than among the more evolved field stars (Duchêne &
Kraus, 2013; Zurlo et al., 2023). Multiplicity also scales with stellar mass,
from $\sim$25% for M-type stars to almost 100% for OB stars (Duchêne & Kraus,
2013; Zurlo et al., 2023). Zagaria et al. (2022) noted, that at lest 20% of
all stellar systems in Lupus, Chameleon I and Upper Scorpius with measured
disk masses and accretion rates are multiples. They all also have higher
observed accretion rates than isolated stars. Similarly, Zurlo et al. (2020)
found the fraction of binaries in Ophiuchus with separations from 9 to 1200 au
to be 18%, whereas in Coronae Australis that number was estimated to be
36.2$\pm$8.8% (separations between 17 and 780 au, Köhler et al., 2008) and in
Taurus is 37.4$\pm$4.6% (the same separation range, Leinert et al., 1993).
Unresolved multiples appear brighter with respect to the single stars in the
HR diagram mimicking younger age. Hartmann (2001) estimated this potential
shift of luminosities to be $\sim 0.2\leavevmode\nobreak\ \log{(L_{\odot})}$.

The individual distances to the cluster members might also add to the observed
spread. Here, we use the distance estimate of $2.35\pm 0.05$ kpc based on Gaia
EDR3 catalogue (Göppl & Preibisch, 2022) for all sources in the field. We
expect to include in that way both members of the Tr 14 and young stars from
the dispersed population of CNC. Tr 14 has a compact core of radius of
$\sim$0.6–0.7 pc with extended halo up to $\sim$3.4–5.3 pc (Ascenso et al.,
2007; Kharchenko et al., 2013), much less than the distance uncertainty of 50
pc (note, that Ascenso et al. (2007) assumed distance of 2.8 kpc to Tr 14,
here we re-scaled their results to 2.35 kpc). This error corresponds to an
uncertainty of 0.05 dex in luminosity and cannot explain the scatter of
estimated values. Similarly, the dispersion in distances to the different
clusters in Carina of 2% (Göppl & Preibisch, 2022) is too small to explain
observed scatter. Therefore, we neglect any impact from the distance spread on
the luminosity dispersion.

Summarising, we conclude that the luminosity spread is mostly caused by large
uncertainties of photospheric parameters, contamination of non-cluster
members, accretion and photospheric variability, and unresolved multiplicity.
Other parameters, like internal spread of stellar ages, accretion properties,
individual distances might play a role, but their impact is smaller.

###  4.3 Age of Trumpler 14

Figure 10: Fraction of stellar ages derived from HR diagram for stars with
$\log{(T_{\rm eff})}<3.73$. Filled orange histogram shows distribution for the
whole sample, while hatched red histogram represents the fraction distribution
after removing the extreme bars with respect to the total number of stars
within the new age range. The normal fit to the probability density
distribution converted into the fraction distribution for the visual purposes
is shown as a dark violet curve with mean value of $\log{\rm{(age)}}=5.96\pm
0.41$ corresponding to the 0.9${}^{+1.4}_{-0.6}$ Myr.

The YSOs plotted in Fig. 9 concentrate near the 1 Myr isochrone strongly
suggesting a young age of the cluster. Here, we look more closely into the
distribution of stellar ages in Tr 14.

Figure 10 presents the distribution of fraction of the stars within each age
bin in logarithmic scale. Only measurements for stars with $\log{(T_{\rm
eff})}<$3.73 are included in the distribution. Ages were estimated based on
PARSEC evolutionary tracks (Bressan et al., 2012, see Sec. 4.2). The lowest
stellar ages provided by the models are 0.1 Myr. Some of our sources lay above
this isochrone on HR diagram. Since we do not extrapolate stellar parameters
beyond theoretical models, those sources have a fixed age of 0.1 Myr causing
an artificial overdensity in the first bin of the age distribution in Fig. 10.
Therefore, to estimate the cluster age, we excluded from this analysis the
boundary bars. We fit the lognormal profile to the remaining distribution, as
shown in Fig. 10. The fit peaks at the logarithm of 5.96$\pm$0.03, which we
interpret as a cluster age, with the width of 0.41$\pm$0.02, which we adopt as
an uncertainty. In linear scale that corresponds to the age of Tr 14 of
0.9${}^{+1.4}_{-0.6}$ Myr.

We check how conclusion on the cluster age is impacted when using different
set of models. Therefore, we employ tracks from Baraffe et al. (2015) for low-
mass stars (spectral types later than K5), and since they are limited to the
solar-mass stars, for hotter stars we employ tracks from Siess et al. (2000).
We present HR diagram, stellar properties, and comparison between those two
set of tracks in Appendix H. Those stellar parameters ($M_{*}$ and age) are
also listed in Table 1 and 5. Use of different models changes values of
parameters for individual stars, but do not affect our conclusion on cluster
age. We perform the same exercise as described above for a distribution of
stellar ages based on Baraffe et al. (2015) / Siess et al. (2000) evolutionary
tracks. The normal fit indicates cluster age of $\log{\rm{(age)}}=6.16\pm
0.31$, corresponding to 1.4${}^{+1.5}_{-0.7}$ Myr, consistent within errors to
the previous estimate. Stellar, and hence cluster, ages around 1 Myr are
difficult to infer precisely. We adopt that the age of Tr 14 is $\sim$1 Myr.
This is a robust result (given uncertainties related to differences in models
and internal uncertainties of observations) since the estimate is not affected
by the choice of evolutionary tracks.

The large spread in the HR diagram seen in Tr 14 lead in the past to
conclusions of long, continuous star formation over last 10 Myr (DeGioia-
Eastwood et al., 2001b; Povich et al., 2019), 1–6 Myr (Tapia et al., 2003), or
5 Myr (Ascenso et al., 2007). While comparing different clusters in Carina,
Damiani et al. (2017) stated that Tr 14 is younger than Trumpler 16, similarly
to Smith & Brooks (2008) who found the age difference of 1-2 Myr between these
two clusters. More precise estimates indicate a Trumpler 14’s age of 2$\pm$1
Myr (Preibisch et al., 2011b). Rochau et al. (2011) found a recent
(1.0$\pm$0.5 Myr) starburst-like event and hint of the presence of an older (3
Myr) population in Tr 14, which might be part of the dispersed population of
CNC. Overall, our estimate is in line with general findings in literature. Our
measurements also show a large spread of isochronal ages, which is a direct
consequence of the luminosity spread. In the previous section (4.2) we listed
several possible sources responsible for the spread in luminosity within the
stellar population of Tr 14, with the uncertainty of the parameters estimated
during spectral classification expected to have the strongest impact. It is
important to note, that the aforementioned studies were mostly focused on
massive and intermediate-mass stars ($\gtrsim 1M_{\odot}$), while here we do
not analyse stars hotter than $\sim$5500 K.

Additionally to the spread, Fig. 9 shows also decrease in median luminosities
toward hotter stars and deviation from $\sim$1 Myr isochrone with the last
temperature bin above $\log{(T_{\rm eff})}\sim$3.73 exhibiting significant
drop in luminosity. This behaviour can be caused by our selection bias as we
focus on low-mass objects and do not identify in this work stars with spectral
classes earlier than G8. This might result in the apparent ‘older’ population
of hotter stars. Hartmann (2003) noted a similar trend in Taurus star-forming
region. Stars colder than 4350 K (corresponding to the masses below $\sim$1
$M_{\odot}$) had an age distribution strongly pointing to the values $<$2 Myr,
while hotter stars exhibited flat distribution spanning up to 22 Myr
(Hartmann, 2003, see their Fig. 1). If we divide the age distributions into
the same $T_{\mathrm{eff}}$ ranges, we do not see such a strong behavior, both
sub-samples peak around 1 Myr, although we note that the youngest stars
($\leqslant$0.15 Myr) are among those with $T_{\mathrm{eff}}$$<$4350 K.
Hartmann (2003) argued, that the flat distribution of hotter Taurus members is
due to the highly inaccurate positions of birth line for the more massive
stars, as well as non-member contamination. Similarly, Fang et al. (2017)
showed that cluster ages are higher when derived from luminosities and
temperatures of hotter stars. The behaviour hold for different theoretical
models and different young clusters. This effect can also impact our results.

Our observations span prominent, dense and compact cluster core
($r\sim$0.5′–0.9′, Ascenso et al., 2007; Kharchenko et al., 2013) and extended
area around. The widely dispersed population of Carina Nebula Complex members
(Feigelson et al., 2011; Zeidler et al., 2016) is mixed in our observations
with the Tr 14 members causing the apparent age spread. We investigate that
possibility below.

In Fig. 11 we mark the “core” area with radius 0.9′ and compare it to the
location of our sources. We do not detect many sources in the most central
area due to the spectral contamination. We investigate whether the stars
inside the core have different properties than the population at larger radii
from the cluster center. Figure 12 shows de-reddened CMDs where sources inside
(left panel) and outside (right panel) the radius of 0.9′ are marked with red
hexagons. The core population of Tr 14 is mostly concentrated around 1 Myr
isochrone. Although the extended, “halo”, population exhibits larger spread in
colours and ages, most of the stars are also located around 1 Myr isochrone.
There are more faint stars in the latter group which are affected by the
higher observational uncertainties. It is likely that the “halo” population is
a mixture of young Tr 14 members and the older widely distributed population
of the whole Carina Nebula Complex. Since the widely distributed population of
young stars in the CNC exhibits a range of ages between $<$1 Myr and $\sim$8
Myr (Preibisch et al., 2011a), it is not possible with the available data to
distinguish between Tr 14 members in the outer parts of the cluster and stars
from the distributed population.

We additionally check the spatial distribution of young stars using the Lii
6708 Å absorption line. In the Figures 11 and 12 the stars where Lithium was
detected are marked with blue crosses. We do not find any specific
concentration in the cluster of those stars but they all follow the $<$10 Myr
isochrones, as expected for Lithium-bearing stars. We note similar behaviour
for NIR excess or X-ray emitting sources (see Appendix I). We conclude that in
our dataset, where the most central core part is saturated and we can not
characterise most of the stars located there, the true, young members of Tr 14
are distributed evenly across the cluster. However, our sample contains also
number of stars from the widely distributed Carina population. We are not able
to distinguish between the true and apparent Tr 14 members nor to confirm the
cluster membership of older stars.

Figure 11: Locations of the Li 6708Å detections in the MUSE field blue
crosses). All stars studied here are marked with red dots, as in Fig. 1. The
dashed circle with radius of 0.9′ shows the core of the Tr 14, as defined by
Kharchenko et al. (2013). The background image in grey scale is the $H$-band
image from HAWK-I (Preibisch et al., 2011a, b). Figure 12: Colour-magnitude
diagrams for de-reddened $R$ and $I$-band magnitudes from MUSE. Red hexagons
mark stars within the core of Tr 14 (left, 0.9′, Kharchenko et al. (2013)) or
outside (right). The blue crosses indicate location of the Lithium-bearing
stars on the CMDs within and outside the core radius, respectively. Plotted
are the same tracks as in Fig. 8.

###  4.4 Mass distribution

Figure 13: Distribution of stellar masses in Tr 14 for stars with
$\log{(T_{\rm eff})}<3.73$. Top: filled histograms presents distribution of
masses for stars analysed in this paper. On top of it (hatched histogram) we
display the distribution of the probable members with uncertain photometry
removed from the analysis due to the high variability of the background
emission. As expected, most of the removed stars are faint, low-mass objects.
Bottom: fraction of stars in the final spectroscopic catalogue within each
mass bin relative to the combined catalogues of final sample and probable
members with uncertain photometry due to the variable background emission.
Bins are the same as in the upper panel.

Whether the environment can affect the initial mass function (IMF) of the
stellar cluster was investigated in multiple studies. For example, Damian et
al. (2021) studied low-mass stars in eight young clusters ($\sim$2-3 Myr)
observed in $J$ and $K$-band spanning wide range of FUV radiation levels,
cluster densities, and galactocentric distances. Their log-normal IMFs
(Chabrier, 2003) agreed well within each other peaking within the range
0.2–0.4 $M_{\odot}$ and not revealing any dependence on any of the three
environmental properties. On the other hand, De Marchi et al. (2010) suggested
that the present-day characteristic mass of the IMF is significantly
correlated with the dynamical age of the cluster.

There is no study dedicated to investigate the impact of high FUV field on the
IMF in the Carina Nebula. Only Rochau et al. (2011) tried to look at the mass
function in the closest vicinity of the massive stars in Tr 14, but they could
not draw any binding conclusions on their impact onto neighbouring stars.
Similarly, Rainot et al. (2022) studied low-mass companions in the vicinity of
seven O-type stars with VLT/SPHERE in $K$-band. Despite the found differences
between their IMF and the one from Rochau et al. (2011) or Chabrier (2003),
they could not robustly confirm if the presence of the massive stars impacts
their neighbouring companions or if the noticed differences are due to the
observational bias. Former IMF studies in Tr 14 (e.g., Ascenso et al., 2007;
Hur et al., 2012) were also based mostly on NIR photometry, up to date there
is no study employing spectroscopy in Tr 14 to investigate the stellar mass
distribution.

Our work focuses on low-mass stars with spectral type later than G8. Figure 13
presents the distribution of stellar masses estimated based on MUSE
observations in Tr 14 for stars with $\log{(T_{\rm eff})}$ below 3.73. The
shown masses range from 0.17 to 2.08 $M_{\odot}$. The presented distribution
is not an IMF as we did not correct for the photometric incompleteness. As we
discussed in Sec. 2.3, completeness of our catalogue is affected by crowdness
in the cluster core, presence of bright stars, and highly variable nebular
emission. According to the $J$-band magnitudes distribution in Fig. 2, we
reach 50% completeness level at 15.5 mag corresponding to 0.8 $M_{\odot}$ at 1
Myr (Bressan et al., 2012; Baraffe et al., 2015). However, if we include
detections excluded from our catalogue due to the variable background
emission, the 50% completeness level is already achieved at 18.5 mag
(equivalent of 0.1 $M_{\odot}$), demonstrating the depth and value of our MUSE
data. In the second panel of Fig. 13 we show the fraction of stars in mass
bins in the final (clean) catalogue in comparison to the sample without
applying the background cut (Sec. 2.2.4). In the mass range below $\sim$0.8
$M_{\odot}$ more than 50% detections are missing due to our conservative
approach to the background contamination. At the same time, none of the stars
with masses $\gtrsim$2.3 $M_{\odot}$ is removed due to the high background
variation. In Table 5 we list targets with uncertain photometry and their
stellar parameters, where available. Removing the lowest-mass stars from our
catalogue prevents us from constructing an IMF estimate and identifying the
characteristic mass of the Tr 14 population. More than half of the stars with
masses $<$0.8 $M_{\odot}$ are removed from the final catalog due the highly
variable background (Fig. 13) but the proper completeness analysis is beyond
the goal of this work. We note however, that when using combined set of
Baraffe et al. (2015) and Siess et al. (2000) evolutionary tracks, the
distribution of masses is similar, although stellar masses extend only up to
4.1 $M_{\odot}$. While the global picture of stellar mass distribution in Tr
14 is not affected by the choice of evolutionary models, the individual values
can be different even by a factor of few, especially for the least massive
objects. This illustrate how challenging it is to derive accurate properties
of young, low-mass stars.

The (in)variance of the IMF in the high FUV environment is also outside the
scope of this paper. Future work addressing this problem needs first to
resolve the completeness issue. Including more massive stars will allow
investigating the slope of the mass function in the high-mass end. More
sophisticated approach to the estimation of the background emission may allow
including significantly more low-mass stars and with that testing the breaking
point of the Kroupa-like IMF or characteristic mass of log-normal IMF. High-
spatial-resolution observations (e.g., with adaptive optics) of the very
center of Tr 14 can help resolving the inner core region. Brown dwarfs and
very low-mass members of Tr 14 can only be well spectroscopically
characterised by the NIR IFU instruments, like VLT/KMOS, VLT/ERIS,
JWST/NIRspec, or future ELT/HARMONI.

##  5 Summary and conclusions

In this work, we presented the first optical spectroscopic study of low-mass
stars in Tr 14 based on IFU observations from VLT/MUSE. We identified targets
and extracted photometry and spectra using SExtractor. We excluded from the
catalogue all sources with uncertain photometry. Specifically, the most
significant cut (of 1868 sources) was related to the highly variable in
spatial dimension emission of the Hii region in Carina Nebula. At the end, our
catalogue consists of 780 stars. We make available both catalogs, with robust
and uncertain photometry for possible future follow-up studies.

Most of our sources have photometric measurements from NIR (99%) and optical
(76%) catalogs, and almost 40% were detected in X-rays. We performed the
spectral classification using spectra of Class III stars from Manara et al.
(2013, 2017) as templates. Together with spectral type we estimated visual
reddening and constant veiling of 717 stars. We converted the spectral types
to the effective temperatures and used $J$-band photometry to calculate
bolometric luminosities. We placed our stars in the HR diagram and by the
comparison to the theoretical evolutionary tracks (Bressan et al., 2012) we
estimated the stellar masses and ages. Based on the distribution of stellar
ages we estimate the cluster age of $\sim$1 Myr. This result is maintained
even when using different evolutionary models (Siess et al., 2000; Baraffe et
al., 2015). Majority of our stars (51%) have mass below 1 $M_{\odot}$, while
the least massive object has estimated mass of 0.17 $M_{\odot}$.

Massive star-forming regions represent the most common environment in which
the stars form in the Galaxy. This environment differs from those seen in the
solar neighbourhood and therefore necessitates for extension of the studies of
the more distant regions. Those examinations are however challenging due to
the large distance to the cluster, often high extinction, and high stellar
crowding. This is particularly difficult for spectroscopic observations. Here,
we presented that those kind of explorations are feasible with IFU
spectrographs like VLT/MUSE. Low-mass stars are the most common in the Galaxy
but at the same time the most vulnerable to the environmental conditions.
Presented here stellar characteristics of the few hundreds of low-mass stars
provide a step into the better understanding of formation and early evolution
of low-mass stars in the massive cluster. This study set up a base for the
follow-up investigation of the protoplanetary disk population response to the
high FUV field in the cluster that will be presented in the consecutive paper.

###### Acknowledgements.

We thank the referee, Guido De Marchi, for a careful reading and for
insightful comments helping improving this manuscript. This work was partly
supported by the Italian Ministero dell’Istruzione, Università e Ricerca
through the grant Progetti Premiali 2012-iALMA (CUP C52I13000140001), by the
Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Ref no.
325594231 FOR 2634/2 TE 1024/2-1, by the DFG Cluster of Excellence Origins
(www.origins-cluster.de), by the Fondazione Cariplo, grant no. 2022-1217. This
project has received funding from the European Union’s Horizon 2020 research
and innovation program under the Marie Skłodowska- Curie grant agreement No
823823 (DUSTBUSTERS), from the European Research Council (ERC) via the ERC
Synergy Grant ECOGAL (grant 855130), and by the European Union (ERC, WANDA,
101039452 and ERC, DiscEvol, 101039651). Views and opinions expressed are
however those of the author(s) only and do not necessarily reflect those of
the European Union or the European Research Council Executive Agency. Neither
the European Union nor the granting authority can be held responsible for
them. This work has made use of data from the European Space Agency (ESA)
mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data
Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

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##  Appendix A Observational log

In Table 2 we provide basic information about weather conditions during
observations with “long” integration times (3$\times$13 min) and name of the
standard star used for flux calibration for each set. Due to the bad
atmospheric conditions some observations were repeated. We checked all
datasets and used those, which were described as better quality by the
Observatory. We include in the Table all observations made for the information
of the astronomical community.

Table 2: Observational log

pointing | coordinates | date | seeing | grade | calibration
---|---|---|---|---|---
| (h:m:s d:m:s) |  | (″) |  | standard
1 | 10:44:08.4 -59:29:39.9 | 28.02.2016 | 0.75 | A | GD108
2 | 10:44:00.7 -59:29:39.6 | 25.02.2016 | 0.92 | B | GD71
3 | 10:44:00.7 -59:30:39.3 | 25.02.2016 | 0.85 | B | GD71
4 | 10:44:08.3 -59:30:39.7 | 25.02.2016 | 0.86 | B | GD71
5 | 10:44:08.3 -59:31:39.0 | 25.02.2016 | 0.92 | A | GD153
6 | 10:44:00.6 -59:31:38.6 | 28.02.2016 | 0.90 | B | GD71
7 | 10:44:00.6 -59:32:38.4 | 25.02.2016 | 1.24 | B | GD108
8 | 10:44:08.2 -59:32:38.8 | 02.03.2016 | 0.89 | A | GD108
9* | 10:44:08.2 -59:33:38.1 | 25.03.2016 | – | C | –
9 | 10:44:08.2 -59:33:38.1 | 30.03.2016 | 1.01 | A | GD108
10* | 10:44:00.5 -59:33:37.7 | 25.03.2016 | – | C | –
10 | 10:44:00.5 -59:33:37.7 | 30.03.2016 | 1.07 | A | GD108
11 | 10:44:00.5 -59:34:37.3 | 28.03.2016 | 1.10 | A | GD108
12 | 10:44:08.1 -59:34:37.8 | 27.03.2016 | 1.58 | B | GD108
13* | 10:43:52.9 -59:32:37.8 | 27.03.2016 | 2.71 | C | –
13 | 10:43:52.9 -59:32:37.8 | 04.04.2016 | 0.53 | A | GD108
14* | 10:43:45.3 -59:32:37.3 | 27.03.2016 | 2.80 | C | –
14 | 10:43:45.3 -59:32:37.3 | 04.04.2016 | 0.50 | A | GD108
15* | 10:43:45.3 -59:33:36.8 | 27.03.2016 | 2.06 | C | –
15* | 10:43:45.3 -59:33:36.8 | 16.04.2016 | 0.66 | C | –
15 | 10:43:45.3 -59:33:36.8 | 17.04.2016 | 0.68 | B | GD108
16 | 10:43:52.9 -59:33:37.2 | 30.03.2016 | 1.48 | B | GD108
17 | 10:43:52.9 -59:34:36.9 | 30.03.2016 | 1.38 | B | GD108
18 | 10:43:45.2 -59:34:36.4 | 01.04.2016 | 0.79 | A | GD108
19 | 10:43:37.7 -59:33:36.2 | 01.03.2016 | 1.47 | B | LTT3218
20 | 10:43:30.0 -59:33:35.7 | 02.03.2016 | 1.33 | A | GD108
21 | 10:43:30.0 -59:34:35.3 | 02.03.2016 | 0.99 | A | GD108
22 | 10:43:37.6 -59:34:35.9 | 02.03.2016 | 1.15 | A | GD108

666 Each of the pointings were observed three times with a 90o dither pattern,
listed seeing is a mean value for each Observational Block (OB). Due to bad
weather conditions some pointings were repeated, those not used in this work
due to the low quality are marked with an asterisk (*). OB’s grades refer to:
A – fully within constraints, OB completed; B – mostly within constraints,
some constraint is $\sim$10% violated, OB completed; C - out of constraints,
OB must be repeated.

##  Appendix B Coordinates correction and cross-match with photometric
catalogs

We corrected MUSE coordinates using Gaia DR3 catalogue (Gaia Collaboration et
al. 2022). The applied corrections are median differences in right ascension
and declination between MUSE and Gaia. We show distribution of those
differences per each pointing in the Figure 14. Corrections, which need to be
added to the original MUSE coordinates, are listed in Table 3. They range in
absolute values between 1.46″and 5.75″for right ascension, and between
0.08″and 2.98″for declination with typical standard deviation of 0.15″for
right ascension and 0.08″for declination.

Figure 14: Distribution of differences in right ascensions and declinations
from MUSE and Gaia DR3 at each field. Table 3: Applied coordinate offsets.

pointing | $\Delta\alpha$ | $\Delta\delta$
---|---|---
| (″) | (″)
1 | -3.86 $\pm$ 0.15 | -0.08 $\pm$ 0.08
2 |  3.76 $\pm$ 0.19 |  2.50 $\pm$ 0.08
3 |  4.53 $\pm$ 0.15 |  0.26 $\pm$ 0.07
4 |  4.25 $\pm$ 0.17 |  0.65 $\pm$ 0.07
5 | -2.12 $\pm$ 0.15 |  1.41 $\pm$ 0.08
6 | -5.75 $\pm$ 0.16 | -0.59 $\pm$ 0.07
7 | -1.58 $\pm$ 0.14 |  1.57 $\pm$ 0.07
8 | -2.98 $\pm$ 0.15 |  0.28 $\pm$ 0.07
9 | -2.80 $\pm$ 0.14 |  1.64 $\pm$ 0.06
10 | -2.09 $\pm$ 0.13 |  1.75 $\pm$ 0.06
11 | -3.04 $\pm$ 0.14 |  1.49 $\pm$ 0.08
12 | -2.85 $\pm$ 0.21 |  1.59 $\pm$ 0.09
13 | -2.60 $\pm$ 0.14 |  1.25 $\pm$ 0.06
14 | -2.68 $\pm$ 0.15 |  1.58 $\pm$ 0.06
15 | -1.58 $\pm$ 0.15 |  2.30 $\pm$ 0.07
16 | -1.91 $\pm$ 0.18 |  2.98 $\pm$ 0.08
17 | -1.46 $\pm$ 0.16 |  1.86 $\pm$ 0.07
18 | -1.81 $\pm$ 0.12 |  1.40 $\pm$ 0.05
19 | -4.67 $\pm$ 0.15 |  1.91 $\pm$ 0.07
20 |  1.67 $\pm$ 0.13 |  1.18 $\pm$ 0.06
21 |  2.49 $\pm$ 0.08 |  1.48 $\pm$ 0.06
22 | -3.80 $\pm$ 0.14 |  2.11 $\pm$ 0.07
777Corrections calculated as a median difference between the Gaia and MUSE
coordinates. Corrections were added to MUSE coordinates.

After correcting MUSE coordinates we matched again our sources with Gaia to
examine the goodness of our astrometry and define the best matching radius
between different catalogs. Based on the bimodal distribution of separations
between corrected MUSE and Gaia coordinates in Figure 15, we found that the
best separation radius for cross-matching is 0.5″. Within it we find all true
counterparts and do not include false matches with larger separations. False
matches are caused by the crowding, especially large in the cluster center.
The same distribution shows that the uncertainty of our astrometry is
$\sim$0.1″.

Figure 15: Separations in arcsec between MUSE and Gaia DR3 stars in
logarithmic scale. MUSE catalogue here contains data points as of Sec. 2.2.1,
before removing uncertain photometry. Overplotted is the threshold separation
of 0.5$\arcsec$ used in this work. Figure 16: Proper motions of Gaia
counterparts. We show points with available proper motion measurements (grey
dots) and with good astrometry (dark blue circles) (see Sec. 2.2.6 for
details). Uncertainties of the latter points are smaller than the symbol
sizes. Foreground and possibly contaminated stars are excluded. For reference,
we also mark group proper motions from Berlanas et al. (2023) derived from
Gaia EDR3 astrometry of OB stars in Tr 14.

##  Appendix C Targets detected in more than one pointing

The pointing of observations were designed to overlap. Therefore, some stars
are detected multiple times in several pointings. After coordinates correction
we identify those targets performing coordinate matching within the catalogue.
We define the same separation limit of 0.5″, below which we assume that the
two detections correspond to the same object. We find separations in the range
from 0.09″ to 0.26″ with median of 0.20″ corresponding to the size of one
pixel. In Table 4 we list all the pairs of double detections.

In most of the cases the $I$-band magnitudes of both detections are consistent
within the uncertainties. That reassures us about the overall good inter-frame
calibration. We choose a signal-to-noise ratio in the vicinity of 7500 Å
(snr750) as a measure of the quality and use in the analysis the spectrum with
higher snr750. In Figure 17 we show few examples of comparisons between the
spectra of the two doubles. Corresponding snr750 are indicated in the legend
for each panel. The difference between the spectra is particularly visible in
the case of late-type stars. There, the blue part of the spectrum is very
vulnerable to the quality of the spectrum. In general, we see no trend between
the chosen spectra and weather conditions, although there is a slight
preference towards better seeing. We also note that stars located very close
to the detector’s edge were not detected by the SExtractor.

Table 4: Double detected sources.

Selected double | Discarded double |
---|---|---
ID | snr750 |  $I$-band | ID | snr750 |  $I$-band | separation
|  | (mag) |  |  | (mag) | (″)
2_14 | 17.02 | 19.87 $\pm$ 0.02 | 1_2 | 12.36 | 19.95 $\pm$ 0.02 | 0.22
1_29 | 63.08 | 17.808 $\pm$ 0.002 | 2_33 | 62.55 | 17.784 $\pm$ 0.003 | 0.20
1_35 | 79.62 | 17.121 $\pm$ 0.001 | 2_39 | 44.84 | 17.694 $\pm$ 0.003 | 0.22
1_55 | 6.53 | 21.09 $\pm$ 0.05 | 2_66 | 3.64 | 21.07 $\pm$ 0.06 | 0.26
1_62 | 13.81 | 20.04 $\pm$ 0.02 | 2_69 | 10.24 | 20.06 $\pm$ 0.02 | 0.20
1_90 | 8.61 | 20.65 $\pm$ 0.03 | 2_135 | 7.14 | 20.61 $\pm$ 0.04 | 0.17
2_162 | 77.77 | 16.459 $\pm$ 0.001 | 1_118 | 71.39 | 16.763 $\pm$ 0.001 | 0.25
2_177 | 8.00 | 20.43 $\pm$ 0.03 | 1_140 | 7.90 | 20.27 $\pm$ 0.02 | 0.18
3_4 | 6.80 | 20.70 $\pm$ 0.05 | 4_2 | 5.09 | 20.53 $\pm$ 0.04 | 0.22
3_84 | 5.18 | 20.75 $\pm$ 0.05 | 4_45 | 4.27 | 20.78 $\pm$ 0.05 | 0.20
3_184 | 15.78 | 19.39 $\pm$ 0.02 | 4_116 | 14.32 | 19.39 $\pm$ 0.01 | 0.22
7_12 | 18.22 | 19.69 $\pm$ 0.08 | 10_280 | 11.33 | 19.77 $\pm$ 0.03 | 0.26
8_23 | 27.06 | 19.34 $\pm$ 0.01 | 7_33 | 20.22 | 19.46 $\pm$ 0.06 | 0.20
13_140 | 51.00 | 17.94 $\pm$ 0.01 | 7_164 | 21.99 | 18.41 $\pm$ 0.02 | 0.17
7_222 | 20.56 | 19.72 $\pm$ 0.08 | 8_122 | 8.48 | 19.75 $\pm$ 0.01 | 0.25
8_127 | 23.12 | 19.11 $\pm$ 0.01 | 7_237 | 15.69 | 19.12 $\pm$ 0.05 | 0.18
8_182 | 53.25 | 18.544 $\pm$ 0.004 | 7_376 | 35.47 | 18.62 $\pm$ 0.03 | 0.22
8_1 | 6.40 | 20.79 $\pm$ 0.03 | 9_7 | 5.29 | 20.75 $\pm$ 0.04 | 0.26
10_48 | 10.51 | 20.41 $\pm$ 0.05 | 9_19 | 8.79 | 19.98 $\pm$ 0.02 | 0.26
10_86 | 47.456 | 18.16 $\pm$ 0.01 | 9_43 | 42.22 | 18.235 $\pm$ 0.004 | 0.22
10_100 | 15.94 | 19.60 $\pm$ 0.03 | 9_54 | 14.83 | 19.56 $\pm$ 0.01 | 0.26
10_126 | 18.29 | 19.45 $\pm$ 0.02 | 9_67 | 16.14 | 19.45 $\pm$ 0.01 | 0.26
10_232 | 73.77 | 17.308 $\pm$ 0.003 | 9_144 | 65.14 | 17.383 $\pm$ 0.002 | 0.17
10_266 | 15.93 | 19.66 $\pm$ 0.03 | 9_180 | 11.07 | 19.65 $\pm$ 0.01 | 0.25
16_39 | 50.09 | 17.51 $\pm$ 0.01 | 10_22 | 42.31 | 17.560 $\pm$ 0.004 | 0.15
16_43 | 73.70 | 16.008 $\pm$ 0.002 | 10_27 | 73.43 | 15.965 $\pm$ 0.001 | 0.24
16_68 | 34.34 | 18.12 $\pm$ 0.01 | 10_65 | 28.41 | 18.01 $\pm$ 0.01 | 0.25
10_72 | 79.62 | 17.696 $\pm$ 0.005 | 16_79 | 35.85 | 17.84 $\pm$ 0.01 | 0.18
10_87 | 80.83 | 17.716 $\pm$ 0.005 | 16_89 | 46.28 | 17.77 $\pm$ 0.01 | 0.20
16_98 | 20.65 | 18.99 $\pm$ 0.02 | 10_102 | 19.55 | 18.96 $\pm$ 0.01 | 0.25
10_140 | 50.56 | 18.02 $\pm$ 0.01 | 16_149 | 40.08 | 18.07 $\pm$ 0.01 | 0.24
10_165 | 92.15 | 16.245 $\pm$ 0.001 | 16_183 | 73.15 | 16.267 $\pm$ 0.002 | 0.25
10_255 | 28.86 | 18.721 $\pm$ 0.012 | 16_256 | 25.06 | 18.72 $\pm$ 0.02 | 0.18
12_67 | 89.56 | 14.873 $\pm$ 0.001 | 11_76 | 85.15 | 14.9120 $\pm$ 0.0002 | 0.20
11_104 | 7.77 | 20.37 $\pm$0.03 | 17_99 | 5.86 | 20.47 $\pm$ 0.06 | 0.18
13_3 | 28.83 | 18.50 $\pm$ 0.01 | 16_284 | 27.22 | 18.11 $\pm$ 0.01 | 0.21
13_4 | 6.61 | 20.65 $\pm$ 0.07 | 16_286 | 5.07 | 20.41 $\pm$ 0.09 | 0.23
16_6 | 96.93 | 16.546 $\pm$ 0.002 | 13_6 | 88.40 | 16.39 $\pm$ 0.001 | 0.22
13_29 | 11.36 | 20.26 $\pm$ 0.05 | 14_53 | 10.03 | 20.36 $\pm$ 0.03 | 0.24
14_140 | 11.75 | 19.98 $\pm$ 0.02 | 13_144 | 10.61 | 20.12 $\pm$ 0.04 | 0.19
14_301 | 16.92 | 19.78 $\pm$ 0.02 | 13_361 | 8.05 | 19.28 $\pm$ 0.02 | 0.14
16_2 | 69.07 | 16.325 $\pm$ 0.002 | 15_5 | 47.33 | 16.138 $\pm$ 0.001 | 0.15
16_57 | 13.90 | 19.47 $\pm$ 0.04 | 15_59 | 5.67 | 19.49 $\pm$ 0.03 | 0.18
16_241 | 45.60 | 18.11 $\pm$ 0.01 | 15_350 | 23.01 | 17.86 $\pm$ 0.01 | 0.09
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18_177 | 37.29 | 18.65 $\pm$ 0.01 | 17_112 | 24.83 | 18.57 $\pm$ 0.01 | 0.15
18_246 | 10.48 | 20.34 $\pm$ 0.04 | 22_142 | 6.51 | 20.10 $\pm$ 0.06 | 0.23
20_23 | 6.83 | 20.42 $\pm$ 0.05 | 19_24 | 5.19 | 20.36 $\pm$ 0.09 | 0.17
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20_65 | 16.53 | 19.69 $\pm$ 0.02 | 19_60 | 11.32 | 19.59 $\pm$ 0.05 | 0.16
20_80 | 15.67 | 19.55 $\pm$ 0.02 | 19_76 | 11.60 | 19.54 $\pm$ 0.04 | 0.16
19_84 | 53.84 | 17.62 $\pm$ 0.01 | 20_95 | 51.17 | 17.623 $\pm$ 0.004 | 0.24
20_113 | 68.79 | 17.776 $\pm$ 0.004 | 19_100 | 40.30 | 17.82 $\pm$ 0.01 | 0.13
21_22 | 6.49 | 20.42 $\pm$ 0.02 | 22_14 | 6.15 | 20.38 $\pm$ 0.08 | 0.19

888Table is separated into two part: left part lists ID, snr at 750 nm, and
$I$-band magnitude for measurements used in the analysis, while right part
lists the same properties of the discarded measurements. Magnitudes are
corrected to match those from WFI catalogue (Beccari et al. 2015).
Additionally, last column shows separation between the two measurements. One
MUSE pixel has width of 0.2″.

Figure 17: Examples of spectra observed twice. Spectra were normalised to the
flux at 7500 Å. Label indicates source identifier and its snr around 7500 Å
used to decide which spectrum to keep for the analysis.

##  Appendix D Assessment of the background variability

Figure 18: Left: distribution of number of sources within a separation of
20″from a given star. Right: distribution of the standard deviation (std) of
background emission estimated in $I$-band from the individual measurements
within 20″ from the given star. Table 5: Parameters of stars removed from the
catalogue due to the high background variation.

ID | coordinates |  $I$-band |  $R$-band |  $V$-band | snrI,bkg | snrR,bkg | snrV,bkg | possible_frg_bkg | gaia_flag | wfi_flag | VISTA_flag | hawki_flag | spitzer_flag | chandra_flag | NIR excess | SpT | $T_{\mathrm{eff}}$ | $A_{\rm{V}}$ | $r_{750}$ | $\log{(L_{\mathrm{bol}})}$ | $M_{\mathrm{*,PARSEC}}$ | $M_{\mathrm{*,B15S00}}$ | AgePARSEC | AgeB15S00
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (h:m:s d:m:s) | (mag) | (mag) | (mag) |  |  |  |  |  |  |  |  |  |  |  |  | (K) | (mag) |  | $L_{\odot}$ | ($M_{\odot}$) | ($M_{\odot}$) | (Myr) | (Myr)
F01N008 | 10:44:07.40 -59:29:11.60 | 19.29$\pm$0.01 | 20.80$\pm$0.04 | 22.01$\pm$0.04 | 2.42 | 0.36 | 0.37 | False | Poor | True | True | True | False | False | False | M3.0${}^{+0.6}_{-0.0}$ | 3415${}_{-89}^{+0}$ | 0.00${}_{-0.00}^{+0.17}$ | 0.02${}_{-0.00}^{+0.05}$ | -1.09${}_{-0.22}^{+0.17}$ | 0.60 | 0.33 | 23.6 | 6.8
F01N011 | 10:44:11.86 -59:29:12.11 | 20.94$\pm$0.03 | – | – | 1.10 | – | – | False | None | False | True | True | False | False | True | M4.0${}^{+3.5}_{-1.7}$ | 3270${}_{-475}^{+248}$ | 3.50${}_{-0.95}^{+1.02}$ | 0.00${}_{-0.00}^{+0.58}$ | -0.99${}_{-1.75}^{+0.52}$ | 0.48 | 0.23 | 8.9 | 2.3

999The first column gives IDs of the detected sources, the second –
coordinates. The third, fourth, and fifth columns give apparent magnitudes in
$I$, $R$, and $V$-band, respectively. The sixth, seventh, and eighth columns –
signal-to-noise of the flux with respect to the background variation in a
given band, as indicated by the lower script (see Sec. 2.2.4 for details). The
ninth marks possible foreground or background stars (see Sec. 3.1 for
definitions). The next five columns flag matches with other catalogs: Gaia
(Gaia Collaboration et al. 2022), WFI (Beccari et al. 2015), VISTA (Preibisch
et al. 2014), HAWK-I (Preibisch et al. 2011a, b), Spitzer (Povich et al.
2011), and Chandra (Preibisch et al. 2011a; Townsley et al. 2011). The
following indicates if the star has an NIR excess as defined by Zeidler et al.
(2016). In the consecutive nine columns are given stellar parameters: spectral
type, effective temperature, visual extinction, constant veiling at 7500 Å,
bolometric luminosity, and stellar mass and stellar age estimated from PARSEC
(Bressan et al. 2012) and Baraffe et al. (2015) / Siess et al. (2000) tracks,
as indicated by the subscript. A full version of this table will be available
at the CDS upon publication. The first few rows are shown as an example.

SExtractor provides estimates of stellar fluxes, magnitudes, and sky emission
at the positions of the stars. It assumes smooth variation of the sky emission
across the whole image. The tool does not provide uncertainty of the
background estimation. Since some parts of the cluster covered by our
observations are very crowded and sky emission exhibits prominent gaseous
structures, local variation of the sky emission might not be smooth.
Therefore, we employ another strategy to assess the quality of stellar
magnitudes and spectra.

We look at the variation of the background emission estimated for each target
by SExtractor within the defined area around each star. We checked that the
circle with the radius of 20″ is a large area enough to cover satisfactory
number of neighbouring sources, and at the same time, small enough to cover
only “local” area. Left panel of Figure 18 shows how many neighbouring sources
for each star is within the radius 20″. The distribution peaks at 40-50
neighbours giving a satisfactory large statistics. We calculate the standard
deviation (std) of the sky emission within this area for every star in our
catalogue. Right panel of the Fig. 18 shows the distribution of the std
measured in flux units of erg s-1 cm-2 Å-1. We use such defined variability to
select a robust photometry: we discard measurement of the stellar flux that is
below the threshold of three sigma (here $\sigma$=std). We initially perform
this exercise in $I$-band, as the presence of this magnitude is our definition
of detection, and repeat for $R$ and $V$-bands. Since our stars have late
spectroscopic types, they appear fainter in bluer bands, therefore, there are
fewer photometric measurements in $R$ and $V$-bands than in the $I$-band. That
can be noticed in our CMDs in Fig. 4 and 8. We note that our approach is very
conservative: spectra of some of the removed targets from the final catalogue
have high enough snr for spectral classification. For this reason, we list in
Table 5 sources removed due to the uncertain photometry in $I$-band caused by
the high background variation. We include in the Table uncertain photometry
from all bands. The columns “snrI,bkg” “snrR,bkg” and “snrV,bkg” show ratios
between stellar flux and background variation in a given band, and therefore
can be used as indicators of photometric certainty.

##  Appendix E MUSE photometry

The MUSE $I$, $R$, and $V$-band images in flux units were produced by
collapsing the 3D MUSE cubes within the corresponding wavelength range and
applying the filter transmission curve embedded in the ESO reduction pipeline
(Weilbacher et al. 2020). We performed the aperture photometry with SExtractor
extracting stellar fluxes from the images and converting them to magnitudes
using Vega zero points written in the headers by the pipeline. Even though our
observations were flux calibrated using standard stars, we found that our
magnitudes deviate from those measured with Wide Field Imager by Beccari et
al. (2015) (described below). As those measurements are well calibrated, we
correct MUSE magnitudes so they match those from WFI. We define a correction
as a difference between MUSE and WFI magnitudes and subtract it from MUSE
photometry. Corrections for each field and each band are listed in the Table
6. In $I$-band they range from 0.29 mag in field No. 5 to 1.27 mag in field
No. 15. We also check whether a colour term is present in MUSE photometry.
Fig. 19 shows an example of this examination with the result of no colour term
between $I$ and $R$-bands.

The highest values of corrections are in fields No. 15, 12, and 19 ($\gtrsim
1.0$ mag). Pointings No. 12 and 19 have the worst seeing from all used
observations, which may explain the difference in the estimated flux. No. 12
suffers additionally from the presence of two very bright stars in the center
of the field, whose brightness impact all neighbouring stars in the image,
possibly to a larger extent than assumed in this work. No. 15 is one of the
most crowded pointings, although it does not cover the very center of the Tr
14. The presence of few bright stars and prominent extincted feature in the
lower right corner of the field might be another explanation of the large
magnitude difference. If, as the result, the background estimation from the
SExtractor is incorrect, that would lead to the uncertain stellar photometry.
Weather conditions were moderate (thin clouds) which might also have affected
the observations.

The uncertainty of magnitude corrections, measured as a standard deviation of
magnitude differences, is $\sim$0.1 mag for most of the pointings. It also
usually increases towards bluer bands. However, smaller number of available
magnitudes in bluer bands due to the high background variability can cause
underestimation of those uncertainties. Overall, the offset of the MUSE
magnitudes seem to be relatively constant within the pointing. We add linearly
correction uncertainties to the magnitude uncertainties of our sources and
report them in the catalogues (Tab. 1 & 5).

Table 6: Photometric corrections.

# | $I$ | $R$ | $V$
---|---|---|---
| (mag) | (mag) | (mag)
1 | 0.47 $\pm$ 0.09 | 0.57 $\pm$ 0.08 | 0.58 $\pm$ 0.08
2 | 0.43 $\pm$ 0.11 | 0.42 $\pm$ 0.12 | 0.41 $\pm$ 0.15
3 | 0.36 $\pm$ 0.12 | 0.34 $\pm$ 0.18 | 0.37 $\pm$ 0.21
4 | 0.52 $\pm$ 0.06 | 0.58 $\pm$ 0.07 | 0.55 $\pm$ 0.07
5 | 0.29 $\pm$ 0.22 | 0.26 $\pm$ 0.12 | 0.22 $\pm$ 0.18
6 | 0.43 $\pm$ 0.14 | 0.47 $\pm$ 0.11 | 0.46 $\pm$ 0.11
7 | 0.44 $\pm$ 0.07 | 0.52 $\pm$ 0.11 | 0.56 $\pm$ 0.14
8 | 0.37 $\pm$ 0.25 | 0.42 $\pm$ 0.25 | 0.42 $\pm$ 0.17
9 | 0.49 $\pm$ 0.15 | 0.58 $\pm$ 0.14 | 0.62 $\pm$ 0.13
10 | 0.46 $\pm$ 0.11 | 0.53 $\pm$ 0.08 | 0.55 $\pm$ 0.06
11 | 0.44 $\pm$ 0.18 | 0.48 $\pm$ 0.36 | 0.48 $\pm$ 0.41
12 | 1.07 $\pm$ 0.05 | 1.18 $\pm$ 0.05 | 1.17 $\pm$ 0.08
13 | 0.37 $\pm$ 0.27 | 0.42 $\pm$ 0.31 | 0.41 $\pm$ 0.15
14 | 0.47 $\pm$ 0.08 | 0.54 $\pm$ 0.10 | 0.49 $\pm$ 0.13
15 | 1.27 $\pm$ 0.09 | 1.33 $\pm$ 0.06 | 1.31 $\pm$ 0.06
16 | 0.77 $\pm$ 0.11 | 0.86 $\pm$ 0.14 | 0.91 $\pm$ 0.15
17 | 0.65 $\pm$ 0.10 | 0.74 $\pm$ 0.13 | 0.75 $\pm$ 0.21
18 | 0.16 $\pm$ 0.19 | 0.20 $\pm$ 0.10 | 0.18 $\pm$ 0.09
19 | 0.93 $\pm$ 0.37 | 1.01 $\pm$ 0.02 | 1.05 $\pm$ 0.02
20 | 0.50 $\pm$ 0.03 | 0.58 $\pm$ 0.04 | 0.62 $\pm$ 0.06
21 | 0.54 $\pm$ 0.02 | 0.61 $\pm$ 0.05 | 0.65 $\pm$ 0.12
22 | 0.62 $\pm$ 0.27 | 0.72 $\pm$ 0.36 | 0.75 $\pm$ 0.06
101010Corrections are defined as mean differences between MUSE and WFI
(Beccari et al. 2015) magnitudes. Provided uncertainties are standard
deviations of the difference between MUSE and WFI magnitudes.

Figure 19: Difference between MUSE and WFI (Beccari et al. 2015) $I$-band
photometry as a function of MUSE colour $R-I$. Every panel represents separate
field, as indicated in the upper right corner. Grey dashed line shows mean
difference between $I$-band magnitudes applied to MUSE photometry as magnitude
correction.

We show the resulting distributions of the corrected MUSE magnitudes in Figure
20. The distribution of $I$-band magnitudes peaks at 18.01 mag, $R$-band –
17.60 mag, and $V$-band – 17.58 mag. The number of magnitudes in each band
decreases bluewards from 780 in $I$-band, through 294 in $R$-band, to 223 in
$V$-band.

Figure 20: Distribution of corrected MUSE magnitudes. colours indicate
different photometric bands as stated in the upper left corner of the figure.
Dashed lines show the turn-over point of the distributions located at: 18.01
mag ($I$-band), 17.60 mag ($R$-band), 17.58 mag ($V$-band).

##  Appendix F Spectral templates

Here, we list all Class III stars and their properties used in spectral
classification as spectral templates (Table 7). Spectral types for those stars
later than K5 were obtained based on depth of molecular absorption bands (TiO,
VO and CaH) and few photospheric lines (e.g., NaI, CaI, MgI, etc.) present in
optical part of the spectra (Manara et al. 2013). Earlier $K$-type stars were
identified using the spectral indices introduced by Herczeg & Hillenbrand
(2014), while $G$-type stars were identified based on the difference at 5150 Å
of continuum estimated between 4600 and 5400 Å, and 4900 and 5150 Å (Herczeg &
Hillenbrand 2014). Effective temperatures ($T_{\mathrm{eff}}$) were derived
from spectral types using relations from Luhman et al. (2003) for $M$-type
objects and Kenyon & Hartmann (1995) for $K$\- and $G$-type stars. Most of the
templates have none or negligible extinction ($A_{\mathrm{V}}<0.5$ mag, Manara
et al. 2017); spectra were dereddened before analysis assuming the extinction
law from Cardelli et al. (1989) and $R_{\mathrm{V}}=3.1$. All the details of
the data reduction, calibration, and spectral classification are provided in
the original papers.

Table 7: Properties of Class III stars used as spectral templates.

Object | SpT |  $T_{\mathrm{eff}}$ (K) | Reference
---|---|---|---
RXJ1508.6-4423 | G8.0 | 5520 | 2
RXJ1526.0-4501 | G9.0 | 5410 | 2
HBC407 | K0.0 | 5200 | 2
RXJ1515.8-3331 | K0.5 | 5050 | 2
PZ99J160550.5-253313 | K1.0 | 5000 | 2
RXJ0457.5+2014 | K1.0 | 5000 | 2
RXJ0438.6+1546 | K2.0 | 4900 | 2
RXJ1547.7-4018 | K3.0 | 4730 | 2
RXJ1538.6-3916 | K4.0 | 4590 | 2
RXJ1540.7-3756 | K6.0 | 4205 | 2
RXJ1543.1-3920 | K6.0 | 4205 | 2
SO879 | K7.0 | 4060 | 1
TWA6 | K7.0 | 4060 | 1
Tyc7760283_1 | M0.0 | 3850 | 1
TWA14 | M0.5 | 3780 | 1
RXJ1121.3-3447_app2 | M1.0 | 3705 | 1
RXJ1121.3-3447_app1 | M1.0 | 3705 | 1
CD_29_8887A | M2.0 | 3560 | 1
Sz122 | M2.0 | 3560 | 1
TWA15_app2 | M3.0 | 3415 | 1
TWA7 | M3.0 | 3415 | 1
TWA15_app1 | M3.5 | 3340 | 1
Sz94 | M4.0 | 3270 | 1
Sz121 | M4.0 | 3270 | 1
SO797 | M4.5 | 3200 | 1
SO641 | M5.0 | 3125 | 1
Par_Lup3_2 | M5.0 | 3125 | 1
SO925 | M5.5 | 3060 | 1
SO999 | M5.5 | 3060 | 1
Sz107 | M5.5 | 3060 | 1
Par_Lup3_1 | M6.5 | 2935 | 1
LM717 | M6.5 | 2935 | 2
J11195652-7504529 | M7.0 | 2880 | 2
LM601 | M7.5 | 2795 | 2
CHSM17173 | M8.0 | 2710 | 2
TWA26 | M9.0 | 2400 | 1
DENIS1245 | M9.5 | 2330 | 1
111111References: (1) Manara et al. (2013); (2) Manara et al. (2017).

##  Appendix G Spectral classification

In this Appendix, we list spectral indices used for spectral classification of
K- and late G-type stars, as well as we explain more in detail estimation of
uncertainties based on $\chi^{2}_{\rm red}$ maps.

Indices were defined, calibrated, and tested on Class III spectra listed in
the Table 7. Each spectral index is defined as an equivalent width of a given
line or a line ratio of the two. Table 8 shows our indices together with their
weights. The final spectral type is a weighted average of indices. Indices
with values outside the applicable range of spectral types (indicating type
earlier than G8 or later than M0) were excluded from the average to avoid
extrapolation. We required at least 3 valid indices to estimate the spectral
type. Additionally, we included in our list the index from Oliveira et al.
(2003); Jeffries et al. (2007), TiO 7140Å. It is applicable only to the stars
with spectral type later than K5.

Extinction and veiling at 7500Å, as well as spectral type for M-type stars,
were estimated based on $\chi^{2}_{\rm red}$ maps. Figure 21 shows the
examples of such maps for an M-type star, and Figure 22 for an K-type star. At
each time, we examine the distribution of $\chi^{2}_{\rm red}$ in relation to
a given two out of three variables in our problem (spectral type, SpT; visual
extinction, $A_{\rm{V}}$, and constant veiling at 7500 Å, $r_{750}$). Hence,
for M-type stars, there are three $\chi^{2}_{\rm red}$ maps for each star. For
K-type stars, where uncertainties of the spectral type are assigned
differently, there is only one $\chi^{2}_{\rm red}$ map constructed based on
the Class III template closest with the SpT to the SpT of a given star. The
best set of parameters’ values is indicated by the minimum value of the
$\chi^{2}_{\rm red}$. The 1-sigma contours drawn on top of the distributions
are the basis for the uncertainty estimates. We adopt the projections of the
contours onto the axis as the uncertainties of the given parameters. Fig. 21
and 22 show 1-sigma contours, and additionally also 2-, and 3-sigma ones, for
reference.

Estimating uncertainties based on our $\chi^{2}_{\rm red}$ distributions is
itself prone to the uncertainty. The sampling of spectral templates used for
classification is not even causing discontinuous, step-like shape of 1-sigma
contours. We do not propagate errors outside the range of adopted values for
our parameters. As a result, when the best value is close to the edge if this
range, one of the uncertainties will be underestimated. We observe high
degeneracy between veiling and extinction, as well as high uncertainty of the
value of the veiling, especially in hotter stars. Therefore, our veiling
estimates might be inaccurate and we recommend to treat them as the rough
indications of the presence of the veiling and its prominence.

Table 8: Indices used for spectral classification of K- and late G-type stars.

Index | weight | G8 | G9 | K0 | K1 | K2 | K3 | K4 | K5 | K6 | K7 | M0 | Uncertainty | Source
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
NaI 5890Å | 2.0 | 1.424 | 1.971 | 2.519 | 3.066 | 3.613 | 4.160 | 4.708 | 5.255 | 5.802 | 6.349 | 6.896 | 0.112 | This work
CaI 6162Å | 1.0 | 0.850 | 1.029 | 1.207 | 1.386 | 1.564 | 1.743 | 1.921 | 2.099 | 2.278 | 2.456 | 2.635 | 0.033 | This work
CaI 6103Å | 1.0 | 0.323 | 0.358 | 0.393 | 0.428 | 0.463 | 0.498 | 0.533 | 0.567 | 0.602 | 0.637 | 0.672 | 0.018 | This work
NaI 8183Å | 1.0 | 0.279 | 0.325 | 0.372 | 0.418 | 0.465 | 0.511 | 0.558 | 0.604 | 0.651 | 0.697 | 0.743 | 0.008 | This work
NaI 8195Å | 1.0 | 0.357 | 0.412 | 0.468 | 0.523 | 0.578 | 0.634 | 0.689 | 0.744 | 0.800 | 0.855 | 0.910 | 0.016 | This work
CaI 8690Å | 2.0 | 0.315 | 0.358 | 0.401 | 0.444 | 0.487 | 0.530 | 0.573 | 0.616 | 0.659 | – | – | 0.016 | This work
MgI 8806Å | 1.75 | 0.665 | 0.713 | 0.761 | 0.809 | 0.857 | 0.905 | 0.954 | 1.002 | 1.050 | – | – | 0.029 | This work
MgII 8824Å | 2.25 | 0.230 | 0.263 | 0.296 | 0.329 | 0.362 | 0.395 | 0.428 | 0.460 | 0.493 | 0.526 | 0.559 | 0.010 | This work
KI 7665Å/7699Å | 1.0 | 2.531 | 2.442 | 2.354 | 2.265 | 2.177 | 2.088 | 2.000 | 1.912 | 1.823 | 1.735 | 1.646 | 0.111 | This work
CaII 8663Å/CaI 8690Å | 1.75 | 3.639 | 3.447 | 3.256 | 3.065 | 2.873 | 2.682 | 2.490 | 2.299 | 2.108 | 1.916 | 1.725 | 0.189 | This work
MgI 8806Å/MgII 8824Å | 1.25 | 2.834 | 2.722 | 2.611 | 2.499 | 2.387 | 2.276 | 2.164 | 2.052 | 1.941 | 1.829 | 1.717 | 0.137 | This work
TiO 7140Å | 1.5 | – | – | – | – | – | – | – | -2 | -1.5 | -1 | 0 | 0.1 | Jeffries et al. (2007)
Oliveira et al. (2003)

121212Indices listed here are equivalent widths and their ratios, as indicated
by the index name. Values were obtained from linear fitting of equivalent
widths to spectral types. Listed uncertainties represent the uncertainty of
this fit. The final spectral type is a weighted average of corresponding
spectral types to each index and their weights. Indices and weights were
calibrated on the Class III spectra listed in the Tab. 7.

Figure 21: The $\chi^{2}_{\rm red}$ maps corresponding to the fit presented in
Fig. 5. Top: $\chi^{2}_{\rm red}$ as a function of spectral type and visual
extinction. Bottom: $\chi^{2}_{\rm red}$ as a function of spectral type and
veiling. The yellow star marks the best-fit position in the parameter space.
Contours represent 1, 2, and 3$\sigma$ levels. Figure 21: (cont.) The
$\chi^{2}_{\rm red}$ as a function of veiling and extinction. The yellow star
marks the best-fit position in the parameter space. Contours represent 1, 2,
and 3$\sigma$ levels. Figure 22: The $\chi^{2}_{red}$ map as a function of
veiling and extinction corresponding to the fit presented in Fig. 6. The
yellow star marks the best-fit position in the parameter space. Contours
represent 1, 2, and 3$\sigma$ levels.

##  Appendix H Stellar parameters

Selection of stellar evolutionary models impact values of derived stellar
parameters. In Section 4.2 we constructed HR diagram and employed PARSEC v1.2S
tracks (Bressan et al. 2012) to estimated masses and ages of Tr 14 members.
Here, we investigate how the choice of tracks impact our results on cluster
properties. We use tracks developed for young stars from Siess et al. (2000)
and Baraffe et al. (2015). The latter are dedicated to low- and very-low mass
stars and therefore do not cover star more massive than $\sim$1 $M_{\odot}$.