# On the Origin of Fast Rotating Stars.
I. Photometric calibration and results of AO-assisted $\mli{BVRI}$+H$\alpha$
imaging of NGC 330 with SAMI/SOAR

Felipe Navarete SOAR Telescope/NSF’s NOIRLab, Avda Juan Cisternas 1500,
1700000, La Serena, Chile  Pedro Ticiani dos Santos Universidade de São Paulo,
Instituto de Astronomia, Geofísica e Ciências Atmosféricas,
Rua do Matão 1226, Cidade Universitária São Paulo-SP, 05508-090, Brazil  Alex
Cavaliéri Carciofi Universidade de São Paulo, Instituto de Astronomia,
Geofísica e Ciências Atmosféricas,
Rua do Matão 1226, Cidade Universitária São Paulo-SP, 05508-090, Brazil  André
Luiz Figueiredo Universidade de São Paulo, Instituto de Astronomia, Geofísica
e Ciências Atmosféricas,
Rua do Matão 1226, Cidade Universitária São Paulo-SP, 05508-090, Brazil

###### Abstract

$\mathrm{H}\alpha$ emission is a clear indicator of circumstellar activity in
Be stars, historically employed to assess the classical Be star (CBe)
population in young open clusters (YOCs). The YOC NGC 330 in the Small
Magellanic Cloud exhibits a large known fraction of CBe stars and was selected
for a pilot study to establish a comprehensive methodology for identifying
$\mathrm{H}\alpha$ emitters in the Magellanic Clouds, encompassing the entire
B-type spectral range. Using the SOAR Adaptative Module Imager (SAMI), we
investigated the stellar population of NGC 330 using multi-band
$\mli{BVRI}$+$\mathrm{H}\alpha$ imaging. We identified $\mathrm{H}\alpha$
emitters within the entire V-band range covered by SAMI/SOAR observations
($V\lesssim 22$), comprising the complete B-type stellar population and
offering a unique opportunity to explore the Be phenomenon across all spectral
sub-classes. The stellar radial distribution shows a clear bimodal pattern
between the most massive (B5 or earlier) and the lower-mass main-sequence
objects (later than B6) within the cluster. The former is concentrated towards
the cluster center (showing a dispersion of $\sigma=4.26\pm 0.20$ pc), whereas
the latter extends across larger radii ($\sigma=10.83\pm 0.65$ pc), indicating
mass stratification within NGC 330. The total fraction of emitters is $4.4\pm
0.5\%$, notably smaller than previous estimates from flux- or seeing-limited
observations. However, a higher fraction of $\mathrm{H}\alpha$ emitters is
observed among higher-mass stars ($32.8\pm 3.4\%$) than within lower-mass
($4.4\pm 0.9\%$). Consequently, the putative CBe population exhibits distinct
dynamical characteristics compared to the bulk of the stellar population in
NGC 330. These findings highlight the significance of the current observations
in providing a complete picture of the CBe population in NGC 330.

instrumentation: adaptive optics, stars: activity, stars: early-type, stars:
emission-line, Be, stars: fundamental parameters, stars: massive, stars:
rotation, (galaxies:) Magellanic Clouds

††facilities: SOAR(SAMI)††software: Astropy (Astropy Collaboration et al.,
2013, 2018), SciPy (Virtanen et al., 2020), IDL

##  1 Introduction

Massive stars are known for their intense radiation, strong stellar winds, and
sometimes the presence of circumstellar material. These factors can
occasionally lead to the emergence of emission lines (mainly hydrogen) in
these stars’ spectra. Examples include luminous blue variables (LBVs) and
Herbig Ae/Be stars, which encompass massive evolved stars and intermediate-
mass pre-main-sequence stars, respectively. Studying the $\mathrm{H}\alpha$
emission in these massive stars provides essential insights into their
physical properties, evolutionary stages, and circumstellar environments.

In particular, the primary focus of this paper revolves around Classical Be
stars (hereafter CBe stars), which earned their name due to the presence of
hydrogen emission lines (particularly $\mathrm{H}\alpha$) in their spectra.
CBes are fast-rotating variable stars exhibiting mass ejection episodes from
their less-bound equator and decretion disks governed by viscosity (Rivinius
et al., 2013). The presence of $\mathrm{H}\alpha$ emission lines in CBes is
not merely used to confirm their classification; from spectroscopic studies,
the strength and variability of these lines can provide insights into the
dynamics and evolution of the disk, as well as the effects of processes such
as mass loss, binary interactions, density waves, etc. In principle, the term
Be star can be applied to any star with a B spectral type and emission lines.
However, even though this term was indeed a source of confusion in the past,
more recently, a taxonomically unique nomenclature was developed that
distinguishes CBes from other emission B stars, e.g., B[e] supergiants, Ae/Be
stars (Porter & Rivinius, 2003).

It has been long recognized that the variability of these stars is remarkably
diverse, encompassing a wide range of amplitudes and time scales. For
instance, short-term, low-amplitude periodicity from non-radial pulsations are
intrinsic to these objects (e.g., Rivinius et al. 2003), and the disk build-up
and dissipation phases can extend from days – with outbursts producing
detectable flickers (Labadie-Bartz et al., 2022) – to many years, such as
$\kappa$ Draconis (Klement et al., 2022), while ranging from tens of
milimagnitudes to more than one magnitude in the visible range. Some systems
have also shown periodicity in their long-term variability, such as $\omega$
CMa (Ghoreyshi et al., 2021) and HD 6226 (Richardson et al., 2021), while
others appear remarkably stable, such as $\beta$ CMi (see, e.g., Fig. B.1 from
Rubio et al. 2023). However, the prevailing scenario is likely unpredictable,
leading to intricate and varied light curves. (e.g., Labadie-Bartz et al.,
2018).

Fast rotation is a fundamental ingredient for the existence of CBe stars. To
date, there are three proposed scenarios to explain the presence of such
extreme rotators: $i)$ CBe stars are born as fast rotators (Bodenheimer,
1971); $ii)$ CBe stars are spun up by mass and angular momentum transfer from
a binary companion (e.g., Pols et al. 1991, Shao & Li 2014); and $iii)$ CBe
stars begin their life as slow to moderate rotators, increasing their surface
rotation rates along the main sequence (MS) (e.g., Ekström et al. 2008, Georgy
et al. 2013). The first two scenarios imply that fast rotation is already
present at or close to the Zero Age Main Sequence (ZAMS), while the third one
favors a higher incidence of CBe stars towards the end of their MS evolution.
It is important to note that these scenarios are not mutually exclusive, and a
combination of these processes could contribute to the formation of CBe stars.
Discriminating the relative prevalence of each scenario is a key step toward a
fuller understanding of the stellar evolution of massive stars, particularly
on the impact of binarity/multiplicity effects on the stellar evolution.

Several works have attempted to tackle this problem by studying CBe stars in
young open clusters (YOCs) using ground-based observations. Studying the ratio
of CBe stars to the total B star population – referred to as the Be/(B+Be)
fraction – in clusters of varying ages is a valid approach to unraveling the
formation mechanisms of rapidly rotating stars; however, so far,
methodological issues have hampered definite conclusions. One complication is
that different works employ different methodologies, making comparisons
between results difficult and often leading to conflicting conclusions. For
instance, Keller et al. (1999) found that the incidence of CBe stars increases
toward the MS turnoff, favoring the evolutionary channel, while Martayan et
al. (2006) found several CBe stars of lower masses close to the ZAMS, which
favors either the “born as fast rotators” or “binary evolution” scenarios.
Additionally, many authors do not adequately consider significant effects that
impact CBe star observations, such as gravity darkening and weak
$\mathrm{H}\alpha$ emitters. The last factor is often associated with tenuous
disks that can lead to SED with H$\alpha$ emission that fills only partially
the absorption profile. These CBe stars with weak disks are quite common (e.g.
Vieira et al., 2017) and often difficult to account for as CBes.

Milone et al. (2018) was the first study to effectively mitigate the
resolution challenges of previous seeing-limited, ground-based observations.
Their analysis was based on high-angular resolution and well-calibrated Hubble
Space Telescope (HST) photometry of different young clusters in the SMC and
LMC, including observations in the $\mathrm{H}\alpha$ filter with sufficient
depth to sample $\mathrm{H}\alpha$ emitters corresponding to mid-to-late
B-type stars.

Previous studies of CBe stars in stellar clusters estimated the Be/(B+Be)
fraction as a function of metallicity ($Z$) (e.g., Martayan et al. 2006,
Martayan et al. 2007) showing evidence that this number grows from about a
tenth in the Galaxy to $\approx 35\%$ in the Large Magellanic Cloud (LMC) and
can be even higher in the Small Magellanic Cloud (SMC) (Martayan et al.,
2010), suggesting a strong $Z$-dependency of the Be phenomenon.

This paper is the first of a planned series to present consistent ground-based
observations of YOCs with different ages and metallicities. This first
publication aims to describe the technical details of data observation,
reduction, and calibration pipelines while also showing the ability of
adaptive optics imaging at the 4-m class SOAR telescope to resolve dense cores
and provide photometric completeness for the entire B spectral type in the
SMC. Furthermore, a preliminary analysis of the YOC NGC 330 is presented.

The paper is structured as follows. Section 2 presents a brief review of NGC
330 and its significance in CBe research. Section 3 describes the observations
and subsequent reduction procedures. As follows, Sect. 4 details the
photometric calibration procedure and the comparison with external catalogs.
Finally, the photometric results and initial analysis of the NGC 330
observations are presented in Sect. 5, and the main conclusions are discussed
in Sect. 6.

##  2 NGC 330

NGC 330 is a young open cluster located at $\alpha=00$h $56$m $17.6$s and
$\delta=-72^{\circ}\,27\arcmin\,47\arcsec$ (J2000, Rafelski & Zaritsky 2005),
within the Small Magellanic Cloud (SMC). NGC 330 was chosen for this pilot
study due to its relatively large CBe content. It was the subject of intense
scrutiny in the last decades, with some stars being photometrically documented
over sixty years ago in a survey conducted by Arp (1959). The first detection
of CBes in NGC 330 was done by Feast (1972) by spectroscopically measuring the
equivalent width of the $\mathrm{H}\alpha$ line ($\lambda$=6562.8 Å). Emission
line stars, particularly active CBe stars, can be identified using color index
information based on the narrow-band $\mathrm{H}\alpha$ filter and another
filter encompassing the nearby continuum. For NGC 330, such methodology was
first introduced by Grebel & Richtler (1992), providing a significant
breakthrough in detecting CBes associated with the YOC. Their Fig. 2
summarizes the adopted classification method through a (H$\alpha-y$, $b-y$)
color-color diagram constructed from broad-band Strömgren $by$ filters and a
custom narrow-band $\mathrm{H}\alpha$ filter, where active CBes with
sufficiently dense disks deviate from the expected MS location. Later, Bessell
& Wood (1993) validated the methodology adopted by Grebel & Richtler,
observing NGC 330 using $\mli{VRI}$+$\mathrm{H}\alpha$ filters.

NGC 330 observations have provided substantial support for various subsequent
discoveries. These include a detailed analysis of blue stragglers and evolved
stars, comparing photometry with the available evolutionary models at that
time (Grebel et al., 1996). Additionally, the application of photometric
separation between CBes and normal B-type stars in clusters from the LMC and
SMC, including NGC 330, was further explored in works by Keller et al. (1999)
and Iqbal & Keller (2013). Other studies delved into the relationship between
CBe incidence and metallicity, as discussed in Martayan et al. (2006) and
Martayan et al. (2007). Moreover, investigations on stellar variability using
OGLE II data were conducted by Schmidtke et al. (2008). More recently,
(Bodensteiner et al., 2020) reported the first results from AO-assisted
integral-field MUSE spectroscopic observations of the densest region of NGC
330, resolving and classifying a flux-limited sample of B and Be stars and
providing an age estimate of the cluster in range of 35 to 40 Myr. At the same
time, Patrick et al. (2020) reported an independent assessment of the age of
NGC 330 as 45$\pm$5 Myr based on the analysis of the evolved red supergiant
population of the cluster.

##  3 Observations and Data Reduction

Kron-Cousins $\mli{BVRI}$+$\mathrm{H}\alpha$ imaging observations were carried
out at the 4.1-m SOAR telescope (Chile) on January 5th, 2019. We used the SOAR
Adaptive Module (SAM, Tokovinin et al., 2016), a GLAO system using a Rayleigh
laser guide star at $\sim$7 km from the telescope to correct the effects of
ground-layer atmospheric turbulence. SAM provides corrected images to its
internal CCD detector, SAMI (4k $\times$ 4k CCD), operating in a 2 $\times$ 2
binned mode, resulting in a plate scale of 91 mas pixel-1 over a field-of-view
(FOV) of $\sim$3$\farcm$1 $\times$ 3$\farcm$1 on the sky.

Individual, long-exposure $\mli{BVRI}$ images were taken using a three-point
dither pattern, separated by 15″ in the E–W direction, with exposure times of
60 s per frame, totaling 180 s per filter. For $\mathrm{H}\alpha$, three
individual exposures of 240 s were obtained (totaling 12 min). Observations
included short exposures to avoid saturation of the brightest stars in the
FOV. The short exposures were taken in a two-point dither pattern separated by
15″ in the E–W direction, with exposure times of 5 s per frame, totaling 10 s
per filter. Table 1 summarizes the SAMI observations.

Table 1: Log of the SAMI observations for NGC 330 made on January 5th, 2019.

Filter | MJD | $\mathrm{N_{exp}}$ | $t_{\mathrm{exp}}$ | Airmass | Atm. Seeing
---|---|---|---|---|---
|  |  | (s) |  | (″)
$B$ | 58488.05261(50) | 3 | 60 | 1.47 | 0.54
$B$ | 58488.05462(06) | 2 | 5 | 1.47 | 0.53
$V$ | 58488.04946(50) | 3 | 60 | 1.46 | 0.50
$V$ | 58488.04823(06) | 2 | 5 | 1.46 | 0.47
$R$ | 58488.05661(50) | 3 | 60 | 1.47 | 0.55
$R$ | 58488.05536(06) | 2 | 5 | 1.47 | 0.51
$I$ | 58488.05968(50) | 3 | 60 | 1.48 | 0.49
$I$ | 58488.06229(07) | 2 | 5 | 1.49 | 0.50
$\mathrm{H}\alpha$ | 58488.06650(19) | 3 | 240 | 1.50 | 0.54
$\mathrm{H}\alpha$ | 58488.06316(06) | 2 | 5 | 1.49 | 0.59

Notes: The mean MJD of the observations are provided, and the errors on the
last two decimal places are indicated within the parenthesis. The mean
atmospheric seeing was obtained from the DIMM monitor installed at Cerro
Pachón.

###  3.1 Data Reduction

The data was processed using the SAMI PyRAF-based PySOAR
pipeline111https://noirlab.edu/science/programs/ctio/instruments/sam/user-
guides/reducing-your-sam-images.. Initially, the pipeline creates master bias
and master flat-field templates for each filter. Subsequently, the raw images
are corrected for overscan, bias-subtracted, and flat-fielded.

The astrometric solution and distortion correction of the field were obtained
by comparing the field with reference stars in the USNO-A2 catalog using
SExtractor and Scamp (Bertin et al., 2002), leading to positional errors
smaller than 0$\farcs$15\. Finally, the individual images were average-
combined using Swarp (Bertin et al., 2002).

Figure 1 presents false-color RGB maps using the long-exposure
$\mli{BVRI}$+H$\alpha$ images. The left panel shows the $\mli{BVI}$ images,
exhibiting a few reddened sources in the field. The right panel shows the
$\mli{BR}$+$\mathrm{H}\alpha$ images. It is possible to identify an extended H
ii-like structure to the NW direction of NGC 330, and very red sources
associated with a strong H$\alpha$ emission.

Figure 1: False-color SAMI images of NGC 330 based on the long-exposure
frames. Left: $\mli{BVI}$ image (blue: $B$, green: $V$, red: $I$). Right:
$BR$H$\alpha$ image (blue: $B$, green: $R$, red: H$\alpha$). Both images have
a 3$\farcm$1 $\times$ 3$\farcm$1 field-of-view, centered at $\alpha=00$h $56$m
$20.0$ s and $\delta=-72^{\circ}\,27\arcmin\,51\farcs 67$ (J2000). North is
up, and east is to the left.

###  3.2 PSF photometry

We extracted the stellar photometry using an automated PSF fitting procedure
based on the IDL StarFinder algorithm (Diolaiti et al., 2000).

We used relatively isolated and bright sources to construct the PSF of each
$\mli{BVRI}$+$\mathrm{H}\alpha$ image. Examples of the resulting PSF template
for the $\mli{BVI}$ images are presented in Fig. 2. The PSF models exhibit an
extended weak tail towards positive $x$-axis offsets, a common consequence of
the divergence of the tip-tilt loop, according to the instrument manual222SAM
Operator’s Manual in
https://noirlab.edu/science/programs/ctio/instruments/sam/support-staff..

Table 2 summarizes the results from the PSF fitting for each filter, showing
the extraordinary performance of the AO-assisted observations, achieving
angular resolutions as sharp as 0$\farcs$33 in the $\mathrm{H}\alpha$ filter.

Figure 2: PSF models for the SAMI $\mli{BVI}$-band images for NGC 330. Left
panel: two-dimensional profile of the PSF overlaid by the FWHM (red contour),
and the radii containing 95% (orange) and 99% (blue) of the enclosed fluxes,
respectively. Right: radial profile of the PSF. The vertical dashed lines
indicate the FWHM (red), and the radii containing 95% (orange) and 99% (blue)
of the enclosed flux. Table 2: Parameters of the PSF model for SAMI
observations and the peak and limiting magnitude for each filter.

Filter | FWHM | $N_{\ast}$ | $N_{\ast}$ | 1-$\sigma$ | $m_{\mathrm{peak}}$ | $m_{\mathrm{lim}}$ | $\sigma$
---|---|---|---|---|---|---|---
| (″) | (short) | (long) | (ADU) | (mag) | (mag) | (mag)
B | 0.40 | 1262 | 4820 | 1.86 | 21.3 | 22.5 | 0.06-0.14
V | 0.38 | 2101 | 7057 | 2.19 | 21.7 | 23.4 | 0.03-0.18
R | 0.35 | 3255 | 9464 | 3.40 | 22.2 | 24.2 | 0.03-0.30
I | 0.31 | 1840 | 7876 | 3.58 | 21.7 | 22.8 | 0.04-0.26
H$\alpha$ | 0.33 | 424 | 5715 | 2.05 | 22.0 | 23.6 | 0.09-0.21

Notes: The FWHM was measured for the PSF of each filter. $N_{\ast}$
corresponds to the number of sources detected above a 1-$\sigma$ limit in the
short and long exposure frames. $\sigma$ corresponds to the range of magnitude
uncertainties for each filter.

The identification and extraction of the fluxes of the point-like sources were
performed by adopting a total of three iterations, considering 3-, 2-, and
1-$\sigma$ thresholds, and a list of positions ($x,y$) and instrumental fluxes
(in ADU) was obtained for each image. The ($x,y$) positions were transformed
into sky coordinates (RA and Dec) using the astrometric information stored in
the header of the images. The instrumental fluxes were corrected to the
exposure time of 1 s, and instrumental magnitudes $bvri$+h$\alpha$333By
definition, lower case and capital letters denote instrumental and calibrated
magnitudes, respectively. were evaluated using a zero point of 25.0 mag.

Figure 3 presents the residuals between the magnitudes extracted from short
and long exposure lists for the $I$-band. The short and long exposure lists
were merged, and a final catalog per filter was created as follows. We
evaluated a relative zero point (ZP) between the magnitudes from the short and
long lists, that is

$m_{\lambda,\rm short}=m_{\lambda,\rm long}+\mathrm{ZP}_{\lambda}$

where the ZP per filter are: $\mathrm{ZP}_{b}\,=\,0.036(12)$ mag,
$\mathrm{ZP}_{v}\,=\,0.015(12)$ mag, $\mathrm{ZP}_{r}\,=\,0.063(23)$ mag,
$\mathrm{ZP}_{i}\,=\,0.146(26)$ mag, and
$\mathrm{ZP}_{h\alpha}\,=\,-0.094(25)$ mag. The ZPs were estimated from the
data points that are relatively brighter but not saturated in each filter, as
indicated by the vertical dashed blue lines in Fig. 3. Sources saturated on
the long-exposure images (corresponding to instrumental magnitudes brighter
than 12.0, 13.5, 13.4, 13.7, and 13.7 mag in $\mli{BVRI}$+$\mathrm{H}\alpha$
filters, respectively) were retrieved from the short-exposure list. Fainter
sources were obtained from the long-exposure list. We adopted the mean
instrumental magnitude value for all the other detections identified in both
lists. Finally, the individual filters were cross-matched one by one, assuming
a maximum separation of 0$\farcs$3, resulting in a final list of 10220 entries
with detections in at least one filter, and 4430 entries with magnitudes
detected in all five filters.

Figure 3: Distribution of residuals between the instrumental magnitudes from
short- and long-exposure images for the $I$-band filter. The zero-point offset
between short- and long-exposure magnitudes (ZP=0.145$\pm$0.026 mag, indicated
by the horizontal dashed black line) was estimated from the points located
within the vertical dashed blue lines. Saturated sources ($\lesssim 13.5$ mag)
were retrieved from the short-exposure list only.

##  4 SAMI photometry

###  4.1 Photometric calibration

We implemented a _stellar template fitting_ methodology for the photometric
calibration of the SAMI $\mli{BVRI}$+$\mathrm{H}\alpha$ photometry, following
a similar procedure adopted for the _Southern Photometric Local Universe
Survey_ (S-PLUS, Almeida-Fernandes et al., 2022). The method consists of
calibrating the instrumental magnitudes using a library of synthetic
photometry, calculated with a grid of atmospheric stellar models and an
external photometric reference catalog covering the same region of the sky.
The complete calibration process was developed in Python, using functions from
the AstroPy and SciPy libraries. The following sequence outlines the process:

  1. 1.

A list of sources with available magnitudes in the external and the SAMI
catalogs is used as input. The external reference catalog serves as a source
of pseudo-standard stars.

  2. 2.

The photometric spectral energy distribution (SED) of every star from the list
is fitted using the synthetic library, finding a representative model. As
atmospheric models provide surface fluxes instead of absolute fluxes, the
fitting is performed using a set of color indices (e.g., $g-r$, $r-z$, etc.);

  3. 3.

A mean magnitude difference (representing every filter from the external
catalog) between the best model and the corresponding star is determined;

  4. 4.

The SAMI magnitudes are then predicted using the stellar model. The residuals
between the predicted and instrumental magnitudes are used to infer a
photometric ZP for every filter;

  5. 5.

A final ZP of every filter is estimated based on the residuals obtained in
item (4), as presented in Fig. 4, and applied for every star in the SAMI
catalog.

One of the main advantages of this approach is the avoidance of transformation
equations (especially for narrow-band filters). Moreover, it treats extinction
as a separate and independent parameter, mapped by convolving the synthetic
spectra with a range of $R_{V}$ and $E(B-V)$ values.

In this method, the ZP system inevitably aligns with the external catalog.
Therefore, the spectral coverage of the external catalog must be similar to or
broader than that of the observations, as a necessary condition for obtaining
a precise photometric calibration.

We used the synthetic spectral library of Coelho (2014), which provides model
SEDs ranging from 0.13 to 10 µm, with resolutions of
$\Delta\log\lambda=8\times 10^{-4}$ and a wide range of stellar parameters:
effective temperature ($T_{\mathrm{eff}}$) from 3,000 to 25,000 K, surface
gravity from $\log(g)=-0.5$ to $+5.5$ (in steps of 0.5 dex), and metallicity
($Z$) from $Z=0.0017$ to 0.049 in a custom set of 12 chemical mixtures (for
more details, see Table 1 of Coelho 2014).

We adopted the SkyMapper DR1.1 (Wolf et al., 2018) as the external reference
catalog, combining an excellent photometric coverage of the southern
hemisphere in the SLOAN/SDSS $uvgriz$ filters, providing magnitudes in the AB
system and covering a broader spectral range than our observations.

We cross-matched the SAMI coordinates with SkyMapper, using a maximum radius
threshold of 0$\farcs$3 between the catalogs. This resulted in a total of 204
common sources in both catalogs, out of which 82 exhibit magnitudes detected
in all six $uvgriz$ filters.

The library of synthetic photometry was constructed as follows. Each spectrum
of the atmospheric library was reddened by following the Cardelli et al.
(1989) extinction law with a fixed value of $R_{V}=3.1$, and assuming 22
different $E(B-V)$ values ranging between 0 and 1.0 mag. Next, the reddened
spectra were convolved with the transmission curves of the filters from both
the external catalog and the SAMI sets. This process generated a list of 11
magnitudes ($\mli{BVRI}+$H$\alpha$ \+ $uvgriz$) for each synthetic spectrum.

The application of the _stellar template fitting_ procedure is divided into
external and internal calibration steps, explained as follows.

####  4.1.1 External calibration

The external calibration procedure compares the external catalog with each
atmospheric model by computing eight color indices based on the SkyMapper
filter set (e.g., $u-v$, $g-i$, etc). The best match between the synthetic
library and the catalog is selected through a $\chi^{2}$ minimization process,
where the $\chi^{2}$ value is computed from the contribution of every color
index ($C_{i}$) in the form:

$\chi^{2}=\sum_{\mathrm{i=1}}^{8}\left(\frac{\mathrm{C_{i,model}}-\mathrm{C_{i,ext}}}{\mathrm{e_{C_{i,ext}}}}\right)^{2},$
(1)

where $\mathrm{e_{C}}$ is the uncertainty of the color index given by
$\mathrm{e_{C}}=(\mathrm{C1}^{2}+\mathrm{C2}^{2})^{1/2}$, where $\mathrm{C1}$
and $\mathrm{C2}$ represent the magnitudes of $\mathrm{e_{C}}$. The best-
fitting model configuration for a specific source is determined by the minimum
value of $\chi^{2}$ among all possible models considered for that source.

To filter out unrealistic matches between the external catalog and the models,
we introduced a parameter termed the _mean photometric offset_
($\mu_{\Delta}$) and its corresponding error ($\sigma_{\mu_{\Delta}}$),
explained as follows. For each target, we computed the difference between the
magnitude from the external catalog ($m_{\mathrm{ext}}$) and the one from the
best-fitted model ($m_{\mathrm{best\,model}}$) as:

$\Delta
m_{i}=m_{i,\mathrm{ext}}-m_{i,\mathrm{best\,model}}\;\,\mathrm{for}\,\,i\in
uvgriz\,,$ (2)

Following the definition of $\mu_{\Delta}$ and $\sigma_{\mu_{\Delta}}$ as the
mean and standard deviation of $\Delta m_{i}$ values across all six $uvgriz$
filters, we established that a suitable fit should display consistent $\Delta
m_{i}$ values for all filters. Consequently, $\sigma_{\mu_{\Delta}}$ should
approach zero. Hence, we only regarded fits as satisfactory for sources
exhibiting $\sigma_{\mu_{\Delta}}\leq 0.15$ mag.

The predicted magnitudes for each source, derived from the best model
magnitude value in the external catalog and applied to the SAMI filters
($m_{\mathrm{pred}}$) were evaluated as:

$m_{i,\mathrm{pred}}=m_{i,\mathrm{best\,model}}+\mu_{\Delta}\;\,\mathrm{for}\,\,i\in\mli{BVRI}\texttt{+}\mathrm{H}\alpha$
(3)

The photometric zero point offset for each filter
($\mathrm{ZP}_{\mathrm{ext},i}$) was inferred from the residuals between the
instrumental magnitude ($m_{\mathrm{inst}}$) and the predicted magnitude
($m_{\mathrm{pred}}$) of the sources from the external catalog:

$\mathrm{ZP}_{\mathrm{ext},i}=m_{i,\mathrm{inst}}-m_{i,\mathrm{pred}}\;\,\mathrm{for}\,\,i\in\mli{BVRI}\texttt{+}\mathrm{H}\alpha.$
(4)

The outcome of Eq. (4) is a distribution of ZP values, as presented in Fig. 4.
For each filter, the distribution exhibits a defined peak containing the bulk
of the sources and an extended tail of outliers toward positive values. An
outlier-resistant Gaussian fit was performed on each histogram, and the mean
external ZP and its error ($\sigma_{\mathrm{ZP}}$) correspond to the Gaussian
$\mu$ and $\sigma$, respectively. Given that the fitting procedure excludes
outliers, the associated error is relatively low (e.g., see the last plot for
the $\mathrm{H}\alpha$ filter).

Figure 4: Distribution of residuals between the observed and synthetic model
magnitudes of the external reference catalog. The external photometric zero-
point (ZP) was estimated through an outlier-resistant Gaussian fitting
procedure. The ZP and the 1-$\sigma$ error bars (indicated at the title of
each plot) are shown as the filled and dashed vertical lines, respectively.

Finally, the calibrated SAMI magnitudes ($m_{\rm ext}$) and their errors
($\sigma_{\rm ext}$) were obtained by applying the fitted ZPs as:

$\left.\begin{array}[]{cc}m_{i,\mathrm{ext}}&=m_{i,\mathrm{inst}}-\mathrm{ZP}_{i}\\\
\sigma_{i,\mathrm{ext}}&=\sqrt{\sigma_{i,\mathrm{inst}}^{2}+\sigma_{\mathrm{ZP}_{i}}^{2}}\end{array}\right\\}\;\,\mathrm{for}\,\,i\in\mli{BVRI}\texttt{+}\mathrm{H}\alpha,$
(5)

In principle, Eq. (5) yields suitable calibrated magnitudes for scientific
purposes. However, the photometric calibration can be improved through an
internal calibration step, as explained below.

####  4.1.2 Internal calibration

The internal calibration is very similar to the previous procedure but uses
the entire externally calibrated SAMI catalog as input, replacing the external
reference catalog. As a consequence, this step is significantly time-
consuming. However, the internal calibration provides two important
byproducts: $i)$ Validation of the external calibration procedure for SAMI
magnitudes and improvement in photometric calibration, particularly for
filters without a direct counterpart in the external catalog (e.g. narrow-band
filters); and $ii)$ Obtaining extinction and atmospheric parameters from the
best-fitted model for all sources in the externally calibrated photometric
catalog. Instances where internal calibration improves photometric results are
typically linked to multi-band observations utilizing several narrow-band
filters, such as those in the S-PLUS survey (Almeida-Fernandes et al., 2022).
In addition, the second byproduct provides a complementary and independent
result from the improvement of the photometry, which can be used in a broader
range of applications.

In short, each source is matched against the synthetic magnitude library, and
a $\chi^{2}$ minimization procedure is obtained for five color indices based
on the broad-band $\mli{BVRI}$ filters, following a similar approach as
outlined in Eq. (1). The _internal mean photometric offset_
($\mu_{\Delta,\mathrm{int}}$) and its error
($\sigma_{\mu_{\Delta,\mathrm{int}}}$) were evaluated in the same way as the
external calibration procedure. In this case,
$\sigma_{\mu_{\Delta,\mathrm{int}}}$ serves as an indicator of the quality of
fit between the calibrated magnitudes and their corresponding counterparts in
the synthetic photometric library: values closer to zero signify well-fitted
models, while larger values indicate poorer fits. Then, the internally-
calibrated magnitudes ($m_{\mathrm{pred}}$) of the source are calculated as:

$m_{i,\mathrm{pred}}=m_{i,\mathrm{best\,model}}+\mu_{\Delta,\mathrm{int}}\;\,\mathrm{for}\,\,i\in\mli{BVRI}\texttt{+}\mathrm{H}\alpha.$
(6)

Similarly to the external calibration method, an internal zero-point offset
($\mathrm{ZP}_{\mathrm{int}}$) can be evaluated from the distribution of the
residuals between $m_{i,\mathrm{inst}}$ and $m_{i,\mathrm{pred}}$, as
presented in Fig. 5. For successful calibrations, all
$\mathrm{ZP}_{\mathrm{int}}$ values are expected to be close to zero, and
therefore, no internal calibration is necessary. For cases where the ZP of a
filter is larger than its error, the internal calibration process is a
necessary step, providing a better constraint on that region of the SED. In
such cases, the internal ZPs need to be accounted for in the calibration
process as follows:

$\left.\begin{array}[]{cc}m_{i,\mathrm{int}}&=m_{i,\mathrm{ext}}-\mathrm{ZP}_{\mathrm{int},i}\\\
e_{i,\mathrm{int}}&=\sqrt{e_{i,\mathrm{ext}}^{2}+e_{i,\mathrm{ZP}_{\mathrm{int}}}^{2}}\end{array}\right\\}\;\,\mathrm{for}\,\,i\in\mli{BVRI}\texttt{+}\mathrm{H}\alpha.$
(7)

Figure 5: Distribution of residuals between the observed and synthetic model
magnitudes of the SAMI magnitudes (internal calibration). The $y$-axis is
shown on a logarithmic scale. A full description of the plots is given in Fig.
4.

Indeed, Fig. 5 illustrates that histograms of the broad-band $\mli{BVRI}$
filters are centered around zero with relatively small errors ($\lesssim 0.01$
mag). This observation signifies the successful application of the photometric
calibration to the SAMI photometry. As previously mentioned, the internal
calibration does not improve the overall photometric results presented in this
work. However, its extinction and stellar parameter byproducts are presented
as a relevant result for further works.

Unlike the other filters, the zero point of the $\mathrm{H}\alpha$ filter
exhibits both the largest deviation from zero (ZP = 0.056 mag) and the largest
error ($\sigma_{\mathrm{ZP}}=\pm 0.083$ mag). Given that the
$\mathrm{H}\alpha$ filter serves as an indicator of stellar activity processes
(including disk emission from CBe stars), we do not expect it to have the same
dispersion observed in the broad-band $\mli{BVRI}$ filters. In fact, the
$\mathrm{H}\alpha$ residuals exhibit a bimodal distribution where most of the
sample is centered at zero, and a smaller fraction is concentrated around $-3$
mag. Such distribution indicates the bulk of $\mathrm{H}\alpha$ fluxes is
consistent with the synthetic models, as expected for normal stars, but a
significant number of sources exhibit $\mathrm{H}\alpha$ fluxes larger than
predicted by the synthetic models. This is an important output from the
internal calibration method, allowing us to identify the sources with
$\mathrm{H}\alpha$ excess.

###  4.2 Calibrated SAMI magnitudes

Table 3 presents the calibrated SAMI photometric results obtained from the
external calibration procedure (Sect. 4.1.1), together with the stellar
parameters from Coelho (2014), delivered by the internal calibration (Sect.
4.1.2). The uncertainties of the calibrated magnitudes range from 0.03 to 0.30
mag for the $\mli{BVRI}$ filters, and from 0.02 to 0.19 mag for the
$\mathrm{H}\alpha$ filter. The full list of the photometric results is
available online.

Table 3: Calibrated $\mli{BVRI}+\mathrm{H}\alpha$ SAMI photometry for NGC 330,
the associated physical parameters from the internal calibration method and
the photometric classification of the source.

ID | RA | Dec | Nfilt | $B$ | $V$ | $R$ | $I$ | $H\alpha$ | $E_{B-V}$ | $T_{\mathrm{eff}}$ | $\log(g)$ | Fe/H | $\alpha$ | $\sigma_{\mu_{\Delta,int}}$ | Type
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (deg) | (deg) |  | (mag) | (mag) | (mag) | (mag) | (mag) | (mag) | (K) | (dex) | (dex) |  | (mag) |
1 | 14.070568 |  $-$72.463074 | 5 | 12.494(64) | 12.619(29) | 12.815(40) | 13.048(51) | 12.769(21) | 0.000 | 9250 | 2.0 |  $-$0.5 | 0.4 | 0.0002 | MS
2 | 14.094029 |  $-$72.476657 | 5 | 12.523(64) | 12.535(29) | 12.652(40) | 12.834(51) | 12.636(21) | 0.000 | 7750 | 2.0 | 0.0 | 0.0 | 0.0048 | MS
3 | 14.014281 |  $-$72.485452 | 5 | 12.671(64) | 12.339(29) | 12.180(40) | 12.167(51) | 12.123(21) | 0.000 | 6250 | 4.5 |  $-$1.0 | 0.4 | 0.0133 | MS
4 | 14.103593 |  $-$72.461670 | 5 | 12.741(64) | 12.920(29) | 13.164(40) | 13.460(51) | 13.104(21) | 0.025 | 13000 | 4.0 | 0.0 | 0.0 | 0.0007 | MS
5 | 14.091106 |  $-$72.464351 | 5 | 12.972(64) | 13.050(29) | 13.207(40) | 13.426(51) | 13.220(21) | 0.025 | 10000 | 1.5 |  $-$1.0 | 0.4 | 0.0046 | MS
6 | 14.065419 |  $-$72.462967 | 5 | 13.017(64) | 13.107(29) | 13.284(40) | 13.484(51) | 13.300(21) | 0.000 | 8500 | 1.5 |  $-$1.0 | 0.0 | 0.0013 | MS
7 | 14.071939 |  $-$72.460710 | 5 | 13.032(64) | 13.116(29) | 13.274(40) | 13.484(51) | 13.305(21) | 0.025 | 10000 | 1.5 |  $-$1.0 | 0.4 | 0.0016 | MS
8 | 14.086628 |  $-$72.476189 | 5 | 13.069(64) | 13.238(29) | 13.491(40) | 13.814(51) | 13.435(21) | 0.000 | 12250 | 4.5 | 0.2 | 0.4 | 0.0048 | MS
9 | 14.083651 |  $-$72.464272 | 5 | 13.120(64) | 13.220(29) | 13.426(40) | 13.682(51) | 13.536(21) | 0.050 | 12250 | 4.5 | 0.0 | 0.0 | 0.0014 | MS
10 | 14.087173 |  $-$72.462312 | 5 | 13.254(64) | 13.223(29) | 13.261(40) | 13.358(51) | 13.268(21) | 0.000 | 7000 | 1.0 |  $-$1.0 | 0.0 | 0.0100 | MS

Notes: Only the first 10 rows of the table are shown. The full table is
available online. The columns are: (1) Index (2–3) Right ascension and
declination (in degrees, J2000); (4) Number of filters in which photometric
measurements are available. (5–9) $B$, $V$, $R$, $I$ and $\mathrm{H}\alpha$
magnitudes and their uncertainties on the last two decimal digits; (10) Total
color excess; (11) Effective temperature; (12) Stellar surface gravity; (13)
Stellar metallicity; (14) Stellar $\alpha$ exponent; (15) Internal mean
photometric offset error; (16) Photometric classification of the source: (F)
Foreground objects, (RGB) evolved stars consistent with $>100$ Myr PARSEC
isochrones, (MS) Main Sequence stars with no clear $\mathrm{H}\alpha$ excess,
(Ha) Stars with $\mathrm{H}\alpha$ excess and selected through Eq. 8, (wHa)
Stars associated with $\mathrm{H}\alpha$ $-R<0$, but not selected through Eq..
(8) (therefore, weak H-alpha emitters), (SG) bright objects compatible with
blue/red super giants ($B-I>0.5$ and $V<16$) (–) objects associated with
incomplete photometry (N${}_{filt}<5$) or that did not fall into any of the
previous classification types.

To compare the photometry with the expected brightness of the stars in the
SMC, we derived synthetic $\mli{BVRI}$+H$\alpha$ magnitudes of rotating
stellar models from O9 to A7-type MS stars. This was achieved by convolving
BeAtlas photospheric grid of models (Rubio et al., 2023), with the proper
transformations to place them on the AB system.

The photospheric BeAtlas spectrum is characterized by four parameters: the
stellar mass ($M$), the rotation rate $W$
($v_{\mathrm{rot}}/v_{\mathrm{orb}}$, Rivinius et al., 2013) the MS lifetime
fraction ($t/t_{\mathrm{MS}}$), and the stellar inclination angle with respect
to the line-of-sight ($i$).

To establish the correspondence between each spectral type (ST) to mass (M),
we adopted the spectral type versus Mass (ST-M) relation from Schmidt-Kaler
(1982) for B-type stars, with Adelman (2004) and Martins et al. (2005) for A-
and O-type stars, respectively. As an effort to obtain the potential magnitude
range for each ST, we set the rotation rate W to its maximum value ($W=0.99$),
as the largest range in brightness occurs when the star is critically rotating
and is observed either pole-on ($i=0^{\circ}$) or edge-on ($i=90^{\circ}$). As
for the stellar age, we computed $t/t_{\mathrm{MS}}$ under the assumption that
NGC 330 has an age of $t=35$ Myr (Bodensteiner et al., 2020). For stars
earlier than B3, the magnitude range was estimated considering objects at the
TAMS ($t/t_{\mathrm{MS}}=1.0$), as these objects cannot exist in the MS
considering the expected age of NGC 330 and the single stellar evolution
scenario.

Given that the BeAtlas spectra are dereddened and flux-calibrated for a 10 pc
distance, we adopted the values of $E(B-V)=0.11$ mag and $d=57.5$ kpc (Milone
et al., 2018), with the extinction law as described by Fitzpatrick (1999) with
$R_{V}=3.1$ mag. Contrary to the relatively unequivocal prediction of the
brightness of non-rotating stars, the adoption of rotating models at different
inclination angles of the stellar spin axis leads to a relatively wide range
of expected magnitudes for a given spectral type, with a non-zero intersection
between adjacent subtypes. Table 4 lists the expected magnitude range for
$\mli{BVRI}$+$\mathrm{H}\alpha$ filters for the spectral types O9, A0, A2, A7,
and all B subtypes.

Table 4: Expected magnitude range for normal O-, B- and A-type stars in the SMC, including the effects of fast rotation. ST | $B$ | $V$ | $R$ | $I$ | H$\alpha$
---|---|---|---|---|---
O9 | 12.9-13.8 | 13.2-14.0 | 13.4-14.2 | 13.8-14.5 | 13.5-14.2
B0 | 13.4-14.2 | 13.6-14.4 | 13.9-14.6 | 14.2-14.9 | 13.9-14.7
B1 | 14.7-15.5 | 14.9-15.7 | 15.2-16.0 | 15.5-16.3 | 15.3-16.0
B2 | 14.9-15.8 | 15.2-16.0 | 15.4-16.2 | 15.8-16.5 | 15.5-16.2
B3 | 15.4-16.2 | 15.7-16.4 | 15.9-16.7 | 16.2-16.9 | 16.0-16.7
B4 | 16.0-16.8 | 16.2-17.0 | 16.5-17.2 | 16.8-17.5 | 16.5-17.2
B5 | 16.7-17.5 | 16.9-17.7 | 17.2-17.9 | 17.5-18.2 | 17.2-18.0
B6 | 17.9-18.7 | 18.1-18.7 | 18.3-19.1 | 18.6-19.3 | 18.4-19.1
B7 | 18.5-19.4 | 18.7-19.5 | 18.9-19.7 | 19.1-19.9 | 19.0-19.7
B8 | 18.9-19.7 | 19.0-19.8 | 19.2-20.0 | 19.5-20.2 | 19.3-20.1
B9 | 19.3-20.2 | 19.4-20.2 | 19.6-20.4 | 19.9-20.6 | 19.7-20.5
A0 | 19.8-20.7 | 19.8-20.7 | 20.0-20.8 | 20.2-21.0 | 20.1-20.9
A2 | 20.4-21.4 | 20.4-21.4 | 20.6-21.5 | 20.8-21.6 | 20.7-21.6
A7 | 20.8-22.0 | 20.8-21.8 | 21.0-21.9 | 21.1-22.0 | 21.1-22.0

The distribution of the calibrated SAMI photometry per filter is presented in
Fig. 6. The magnitudes for all filters follow an IMF-like distribution with
maximum frequency at 21.3 (B), 21.8 (V), 22.2 (R), 22.0 (I), and 21.6
($\mathrm{H}\alpha$), which serves as a proxy for evaluating the photometric
completeness limit of the observations. The completeness of all filters is at
least one magnitude fainter than the expected limit for B-type stars (B9,
indicated by the green shaded area). The B and $\mathrm{H}\alpha$ filters
exhibit the shallowest completeness limit, roughly consistent with the
expected faintest brightness for A2 stars. This result highlights that the
adopted instrumental setup provides sufficient depth to properly identify all
OB and early A-type stars at the distance of the SMC.

Figure 6: Photometric completeness for the $\mli{BVRI}$+$\mathrm{H}\alpha$
filters of SAMI observations. Each histogram is sampled with a bin of 0.1 mag,
from 11.5 to 24 mag. The vertical dashed line indicates the peak of the
distribution. The brightest and faintest object detected on each filter is
indicated on the label. We show the expected magnitude intervals for B0
(blue), B9 (green), and A2 stars (orange) for each filter.

###  4.3 Comparison with published catalogs

We validated the outcomes of our photometric calibration, as detailed in Sect.
4.1, by cross-referencing the results with three previously published
catalogs: the Optical Gravitational Lensing Experiment (OGLE-II, Udalski et
al., 1998), the Magellanic Clouds Photometric Survey (MCPS, Zaritsky et al.,
2004), and the AO-assisted MUSE observations from Bodensteiner et al. (2020).
For the cross-matching procedure, we adopted a maximum separation of
0$\farcs$5 for the seeing-limited OGLE and MCPS positions and 0$\farcs$3 for
the AO-assisted MUSE positions, leading to a sample of 3230 (OGLE), 1341
(MCPS), and 250 (MUSE) sources with SAMI counterparts.

Figure 7 presents the spatial distribution of the sources of the SAMI catalog
and the published catalogs (red: OGLE; blue: MCPS; black: MUSE) along the RA
(top panel) and declination (bottom) directions. Far from the cluster’s
center, OGLE and MCPS exhibit a relatively constant distribution of sources in
both RA and DEC directions. An overdensity of OGLE sources is observed towards
the cluster’s central position, which is not evident for the MCPS, indicating
that OGLE has a better completeness towards NGC 330 than MCPS. MUSE
observations are limited for $V\leq 18.5$ mag objects, located within a
considerably smaller $\sim$1′$\times$1′ FOV around the cluster’s center.
Consequently, MUSE covers a limited area, capturing a relatively smaller
number of targets than the other catalogs.

Figure 7: Distribution of sources in the NGC 330 FOV from the SAMI catalog
(grey), and the external catalogs (red: OGLE, blue: MCPS, black: MUSE) in the
RA (top panel) and declination directions (bottom). The number of sources from
each catalog is indicated on the label. The vertical blue line indicates the
central coordinates of NGC 330.

Figure 8 displays the cumulative distribution function of the distance of the
nearest neighbor in each of the four catalogs. This metric represents the
likelihood of a single object in one catalog being matched with one or
multiple sources from another catalog. It is particularly significant when
comparing catalogs derived from seeing-limited observations (such as OGLE and
MCPS) with those from adaptive optics-assisted observations (like MUSE and
SAMI), particularly in crowded areas like the central region of the cluster.
This quantity also relates to the depth of the images, as fainter targets
detected in one catalog might be absent in another. Consequently, the
probability of cross-matching multiple objects from a higher-resolution
catalog (e.g., SAMI) with a single object from a catalog with a coarser
resolution increases as this distance gets larger. For instance, a single
bright object in the seeing-limited OGLE or MCPS catalogs can be resolved into
multiple, fainter objects detected in SAMI images. The minimum distance
corresponds to 1$\farcs$04 for MCPS, and 0$\farcs$40 for OGLE and MUSE. A
minimum separation of 0$\farcs$08 is observed for SAMI, indicating a
significant gain in resolution and depth from the AO-assisted observations.

Figure 8:  Comparison of the distance of the nearest neighbor from different
photometric catalogs: SAMI (filled grey curve), OGLE (dotted red), MCPS
(dashed blue), MUSE (filled blue). The curves represent the cumulative
distribution function of the quantity, starting at zero and progressing
towards one. The total number of objects in each respective catalog is
indicated on the plot. The minimum separation between the sources of each
catalog is indicated in the plot.

We now compare the calibrated $\mli{BVI}$ magnitudes with those from the OGLE
catalog to check the reliability of our photometric calibration. OGLE
magnitudes in the Vega system were converted to the AB system, and comparisons
were made for sources brighter than 20 mag in all the $\mli{BVI}$ filters. The
OGLE catalog was primarily selected given that, among the three published
catalogs, OGLE exhibits the deepest completeness of sources in the same FOV of
SAMI observations (Fig. 7) and displays a relatively small minimum separation
of closest neighbors (0$\farcs$4, Fig. 8). For completeness, the comparison
between SAMI photometry and the MCPS and MUSE catalogs is presented in
Appendix A.

The distribution of the residuals between SAMI and OGLE magnitudes are
presented in Fig. 9. The residuals are distributed around 0 mag with
1-$\sigma$ widths smaller than 0.4 mag in all filters. Despite the relatively
large widths, the comparison with OGLE gives the most symmetric results among
the three external catalogs. Two factors can explain the extended tails in the
distributions: $i)$ deblending of multiple sources, as we are comparing
photometry from AO-assisted observations with coarser seeing-limited catalogs;
and $ii)$ intrinsic variability among sources in the sample (e.g., CBes),
given the significant time gaps between the observations.

Figure 9: Distribution of residuals between $\mli{BVI}$ magnitudes from SAMI
and OGLE catalogs. Filled vertical lines indicate the median values of the
distributions, while the dashed line is placed at $x=0$. The median value and
1-$\sigma$ width (68%) of each distribution are indicated in the label.

The results from this section and Appendix A indicate that the adopted
calibration method is robust and consistent with the published catalogs,
providing calibrated AB magnitudes, ranging between $\sim$12 and $\sim$24 mag,
for all $\mli{BVRI}+$H$\alpha$ filters.

###  4.4 Identification of foreground sources from Gaia DR3

We took advantage of the astrometric stellar parameters from Gaia Data Release
3 (Gaia DR3, Gaia Collaboration et al., 2023) to identify and remove Galactic
foreground sources in the SAMI FOV. Initially, we cross-matched the SAMI
catalog with Gaia DR3, leading to a list of 2866 sources with Gaia
counterparts. Given our photometric completeness extending beyond Gaia DR3,
the faintest objects associated with a Gaia DR3 counterpart exhibit magnitudes
reaching $V\lesssim 22.0$ mag, about $\sim 1.5$ mag brighter than the faintest
objects detected by SAMI (cf. Table 2 and Fig. 6).

Subsequently, we implemented the following selection criteria:

  * •

Removal of sources associated with large Renormalized Unit Weight Error
values, $\mathrm{RUWE}>1.4$ (Lindegren et al., 2021), keeping only those
associated with a good astrometric solution;

  * •

Removal of sources exhibiting parallaxes with nominal values smaller than
1-$\sigma$; and

  * •

Selection of sources exhibiting parallax values $|\varpi|\geq 0.1$ mas, much
larger than the expected parallax value for the SMC,
$\omega_{\mathrm{SMC}}\approx 0.016$ mas, estimated from the distance of
$d_{\mathrm{SMC}}=62.44$ kpc (Graczyk et al., 2020).

Employing the above procedure resulted in 849 confirmed foreground objects
($\approx 8\%$ of the SAMI catalog), which were excluded from the results and
analysis presented in the next section.

##  5 Results

###  5.1 Photometric analysis of NGC 330

We used the calibrated $\mli{BVI}$ photometry, excluding foreground objects,
to construct the C-M diagram presented in Fig. 10. PARSEC (Bressan et al.,
2012) evolutionary tracks for ages ranging from 10 to 800 Myr are overlaid
with distinct colors to assist the analysis. The isochrones were scaled to the
distance of the SMC ($m-M=18.97$ mag, Milone et al. 2018) and a $A_{V}=0.2$
mag reddening vector, assuming the Cardelli et al. (1989) extinction law with
$R_{V}=3.1$, is overlaid.

Figure 10: Color-magnitude diagram based on the SAMI photometry for NGC 330.
PARSEC evolutionary tracks for ages between 10 and 800 Myr are overlaid in
different colors. Magenta $+$ symbols within the dotted lines are likely
associated with an old stellar population, consistent with the 250-800 Myr
isochrones. The black error bars indicate the typical errors of the points as
a function of the $y$-axis. The right panel shows a zoom-in view of the main
sequence, delimited by the black dashed lines in the left panel. The red arrow
indicates the direction of the reddening vector, assuming $A_{V}=0.2$ mag.

Most sources are located on the main sequence at $B-I\lesssim 0$ mag, while a
considerable fraction of targets exhibit redder colors ($B-I>0.3$ mag).
Sources brighter than $V=16$ mag are consistent with a population of main
sequence (for $B-V<0$ mag) and evolved objects ($B-V\gtrsim 0$ mag) with ages
between 20 and 60 Myr. The right panel shows that the top-brightest sequence
of stars is consistent with the 10 Myr isochrone (dark blue), assuming
$A_{V}=0.2$ mag (indicated by the reddening vector). Targets at $V\sim 15$ mag
and $B-I\sim 2$ mag are consistent with a relatively older population with
ages between 50 and 60 Myr (yellow isochrone). We also observe a relatively
large fraction of stars located to the right of the main sequence (see details
on the right panel), which are likely objects associated with
$\mathrm{H}\alpha$ excess at the expected position of CBe stars.

Fainter targets exhibiting larger $B-I$ values represent an older population
of evolved stars in the Red Giant Branch (RGB) phase and, therefore, are
clearly not associated with the young cluster. We identified 674 sources
fainter than $V=15.5$ mag and exhibiting $B-I>0.5$ mag (shown as magenta $+$
symbols). These sources were not filtered out based on their Gaia DR3
parameters, suggesting they are either foreground Galactic objects or field
stars from the SMC with poor astrometry (see Sect. 4.4) and will therefore be
omitted from further analysis. A mixture between young main sequence and older
stars leaving the main sequence is likely observed for $V\gtrsim 18$ mag,
making it difficult to disentangle different populations solely based on
color-criteria selections.

The same C-M diagram is presented in Fig. 11 (left), with each point color-
coded based on its H$\alpha-R$ color index, taking into advantage the
calibrated $\mathrm{H}\alpha$ and $R$ photometry. This color index is a
variation of the $R-$$\mathrm{H}\alpha$ index, often adopted as a proxy for
selecting $\mathrm{H}\alpha$ emitters in the SMC (e.g., Keller et al., 1999;
Iqbal & Keller, 2013), which may include stars undergoing the Be phenomenon,
Red Supergiants (RSGs), Blue Supergiants (BSGs), and possibly active young
stellar objects (YSOs). We further compare the expected $V$-magnitude range
for B0, B9, and A2 stars listed in Table 4 as shaded regions over the diagram.

Figure 11: (left) $V$ vs $B-I$ color-magnitude diagram of NGC 330 with SAMI
photometry. The points are color-coded using the H$\alpha-R$ color index. The
total number of sources with H$\alpha$ excess (H$\alpha-R<0$) is indicated on
the label. The number of old stars (located within the magenta dotted lines)
with H$\alpha$ excess is also indicated. The expected magnitude intervals for
B0 (blue), B9.5 (green), and A2 stars (red) are represented by the shaded
regions. The black error bars on the left indicate the typical errors of the
points as a function of the $y$-axis. (right) An inset of the color-magnitude
diagram highlighting the sources exhibiting H$\alpha$ excess. The points
associated with H$\alpha-R<0$ are color-coded, while points with H$\alpha-R>0$
are indicated as smaller grey dots. Red $\times$ symbols correspond to known
CBe stars from previous works, and blue circles indicate the H$\alpha$
emitters selected through the color selection criterion (see text). Magenta
$+$ symbols indicate stars in the RGB phase (unlikely members of NGC 330).

A total of 1419 sources exhibiting $\mathrm{H}\alpha$ excess (that is,
H$\alpha-R<0$ mag) are shown as green to blue points in the C-M diagram. The
visual inspection of the C-M diagram suggests four main groups of
$\mathrm{H}\alpha$ emitters:

  1. 1.

The bulk of $\mathrm{H}\alpha$ emitters (blue points) are located to the right
of the main sequence at $B-I<0$ mag, spread around the expected $V$-band
magnitudes for B-type stars (indicated by the blue and green regions) and
consistent with the expected loci of CBes (e.g., Keller et al. 1999 and Iqbal
& Keller 2013);

  2. 2.

Several $\mathrm{H}\alpha$ emitters are detected to the left of the main
sequence, aligning with the expected position of blue stragglers or mergers
(e.g., Dresbach et al. 2022); and

  3. 3.

A third group corresponds to red and evolved objects stars ($V>15.5$,
$B-I>0.6$) located within the RGB region defined in Fig. 10, for which 407 of
459 objects ($88.7\pm 4.4\%$) exhibit H$\alpha-R<0$. The behavior for more
evolved objects to exhibit a relatively large $\mathrm{H}\alpha$ excess
compared to typical MS stars has been previously observed in earlier studies
of NGC 330 (e.g., see Fig. 1 from Keller et al. 1999 and Fig. 2 from Iqbal &
Keller 2013) and other clusters (e.g., NGC 6752, Bailyn et al. 1996).

  4. 4.

We note a significant number of sources with a positive H$\alpha-R$ color in
the faintest region of the MS ($V\gtrsim 20$ mag). Considering the shallower
photometric completeness of the $\mathrm{H}\alpha$ filter ($\sim 21.7$ mag,
Fig. 6) in comparison to the $R$ filter ($\sim 22.2$ mag), it is possible that
these positive H$\alpha-R$ values could be a result of a signal-to-noise
effect.

###  5.2 Selection of $\mathrm{H}\alpha$ emitters

Previous studies (e.g., Keller et al., 1999; Iqbal & Keller, 2013) adopted
$R-$H$\alpha$ versus $V-I$ diagrams to identify active CBes in NGC 330. By
adopting a simple color selection criteria, they were able to separate objects
exhibiting clear $\mathrm{H}\alpha$ excess from normal stars, thus excluding
the bulk of main sequence stars and the cooler evolved objects. Although both
studies have made significant contributions to identifying CBe stars in the
SMC, their findings were limited by the following observational aspects:

  1. 1.

Their photometric analysis was based on seeing-limited observations
(1$\farcs$5–2$\farcs$0), not sufficient to disentangle and resolve the stellar
population in the innermost and crowded central region of the cluster;

  2. 2.

Both works limited their sample to relatively bright stars ($V<17.5$ mag for
Keller et al. 1999 and $V<18.0$ mag for Iqbal & Keller 2013);

  3. 3.

Arbitrary zero-points were adopted for the $R-$H$\alpha$ color index (so that
normal MS stars had $R-$$\mathrm{H}\alpha$$\approx 0$).

HST observations presented by Milone et al. (2018) were able to overcome the
coarser angular resolution of previous observations from Keller et al. (1999);
Iqbal & Keller (2013); however, their analysis did not show significant
$\mathrm{H}\alpha$ emission detected for $I$-band magnitude around $\sim 18$
mag (see their Fig. 2), corresponding to B6 stars at the distance of the SMC.

Leveraging the superior spatial resolution provided by the adaptive optics AO-
assisted SAMI observations with sufficient photometric depth in all broad-band
$\mli{BVRI}$ and narrow-band $\mathrm{H}\alpha$ filters, we have reevaluated
the color selection criteria utilized previously by Keller et al. (1999) and
Iqbal & Keller (2013). This reassessment was undertaken to validate our
ability to identify both known and new $\mathrm{H}\alpha$ emitters (most
probably active CBes) within NGC 330.

We first cross-matched the positions of known CBe stars with the SAMI catalog,
leading to a total of 70 unique objects, from which 47, 31 and 23 are from
Keller et al. (1999, K99), Iqbal & Keller (2013, I18), and Martayan et al.
(2007, M07), respectively (12 objects are in common with K99 and I13, while
four objects are unique from M07). They are indicated as red $\times$ symbols
in Figs. 11 (right) and 12.

Figure 12: H$\alpha-R$ vs. $V-I$ color-color diagram for NGC 330. Red $\times$
symbols correspond to known CBe stars from previous works (see text). Blue
circles indicate the H$\alpha$ emitters selected through the color selection
criterion defined by Eq. (8) and indicated by the dashed blue line. Magenta
$+$ symbols are likely stars in the RGB phase (not associated with NGC 330).
The black error bars indicate the typical errors of the points as a function
of the H$\alpha-R$ color.

The overall distribution of the points in Fig. 12 exhibits a clear
concentration of targets with positive H$\alpha-R$ values, consistent with
main sequence stars with $V-I\sim 0$ mag) and evolved red objects at
$V-I\gtrsim 0.5$ mag (which is also consistent with the position of most of
the sources classified as RGB sources). The sources exhibiting
$\mathrm{H}\alpha$ excess, however, have $V-I$ colors ranging from -2.0 (to
the left of the MS) to 1.0 mag (to the right of the MS). As expected, almost
all known CBe stars (red $\times$ symbols) are located at the top of the C-C
diagram, exhibiting negative H$\alpha-R$ values. Only three targets exhibit
H$\alpha-R\approx 0$ mag values: two are located within the MS objects, and
one is found within the RGB sequence at $V-I\approx 0.5$ mag.

To expand the selection of similar objects exhibiting $\mathrm{H}\alpha$
excess, we adopted the following color selection criterion:

$(\mathrm{H}\alpha-R)=-0.10\cdot(V-I)-0.18\,,$ (8)

indicated as the dashed blue line in Fig. 12, such that objects with
(H$\alpha-R$) smaller than the above criterion for a given $(V-I)$ are
considered to have $\mathrm{H}\alpha$ excess. This color selection criterion
identified 181 sources exhibiting $\mathrm{H}\alpha$ excess, represented by
the blue circles in the C-C diagram from Fig. 12. This criterion roughly lies
between the color selection criteria established by Keller et al.
(1999)444H$\alpha-R\approx-0.05\cdot(V-I)-0.33$, in AB magnitudes and Iqbal &
Keller (2013)555H$\alpha-R\approx-0.15\cdot(V-I)-0.04$, in AB magnitudes.
Moreover, it also considers the higher quality and the deeper photometric
depth achieved by SAMI observations compared to the previous works.

Naturally, the adoption of Eq. (8) led to a much smaller number of objects
than by just selecting all sources exhibiting negative H$\alpha-R$ values
(1419, Fig. 11). In addition, it correctly identifies most of the known CBe
stars (67 of 70), excluding the majority of evolved objects to the right of
the MS (indicated as green $+$ symbols). The three known CBe stars not
selected by the color criterion of Eq. (8) are located within the MS locus.
This is expected, given the long-term variability of CBe stars. In a time
scale of a decade, some stars may have dissipated their disks (entirely or
partially) with a corresponding reduction of their $\mathrm{H}\alpha$ excess.

The right panel of Fig. 11 highlights the sources associated with negative
$\mathrm{H}\alpha$ $-R$ indices, and also shows the known CBe stars and the
objects selected through the color criterion from Eq. (8). The known CBe stars
are relatively bright objects ($V\lesssim 18$ mag), given the flux-limited
nature of the previous observations. The sources selected using Eq. (8) are
observed over the full range of $V$-band magnitudes (i.e., luminosities). A
total of 137 $\mathrm{H}\alpha$ emitters selected through the color criteria
exhibit $V<20.3$ mag, corresponding to stars earlier or equal to B9. The
remaining 44 sources exhibit $20.3<V\lesssim 22.5$ mag, as expected for lower
mass objects with spectral types ranging from early to mid-A stars.

The exact nature of these low-mass stars associated with $\mathrm{H}\alpha$
excess is difficult to assess. At least for some of them, the
$\mathrm{H}\alpha$ excess is spurious due to the larger photometric errors in
the $\mathrm{H}\alpha$ filter. However, eight sources exhibit positive $B-I$
indices, consistent with objects leaving the MS through the red-giant branch
(RGB).

According to the color selection criterion, most of the bright
$\mathrm{H}\alpha$ emitters ($V\leq 20.3$ mag) are located to the right of the
MS, together with most of the known CBe stars from previous works. About 16
$\mathrm{H}\alpha$ emitters (including two known CBe stars) are identified to
the left of the MS ($B-I\lesssim-1$ mag), corresponding to stellar mergers or
blue stragglers candidates. Only four $\mathrm{H}\alpha$ emitters are
associated with $B-I$ values larger than 0.5 mag, three are likely old RGB
sources, and the brightest one ($V=14.535\pm 0.026$ mag, #45 in Table 3)
corresponds to a known binary system associated with a cold supergiant
component (SMC5_002807, Martayan et al., 2007).

We compared the total number of 63 $\mathrm{H}\alpha$ emitters identified by
Milone et al. (2018, see their Fig. 2) showing F814W $\lesssim$ 18 mag with
the equivalent number of 83 $\mathrm{H}\alpha$ emitters from our selection
exhibiting $I$ $<$ 18 mag. The difference of 20 sources detected in SAMI
observations, but not in HST data, can be attributed to two main factors: $i)$
the shallower photometric completeness of HST observations; and/or $ii)$ the
intrinsic variability of the Be phenomenon over a 1.5-year scale. HST
observations date back to July 2017 (see their Table 1), while SAMI
observations are from January 2019 (Sect. 3).

###  5.3 Comparison with MUSE

The recent MUSE observations of the central region of NGC 330 ($\alpha=00$h
$56$m $16.8$s, $\delta=-72^{\circ}\,27\arcmin\,47\arcsec$,
FOV$\sim$63″$\times$63″) reported by Bodensteiner et al. (2020) offers an
excellent opportunity to compare spectroscopic and photometric results. The
identification of Be stars in the study by Bodensteiner et al. (2020) was
based on the analysis of the MUSE spectra, while the $V$-band magnitudes
adopted in their work were extracted from both ground-based and HST
photometric catalog.

First, we selected all the 1242 objects from the SAMI catalog that lie within
the MUSE FOV (from here on, it will be referred to as the “SAMI subsample”).
Fig. 13 presents the photometric completeness of this subsample, confirming
that it is also complete within the expected magnitude ranges for B-type stars
in all filters. For instance, the photometric completeness for the $V$ band is
at $V=20.94$ mag, about $\sim 2.5$ mag deeper than the $V=18.5$ mag limit
reached by Bodensteiner et al. (2020). A total of 334 sources with SAMI
photometry are brighter than $V=18.5$ mag (referred to as the “bright
subsample”), while 908 are fainter than the photometric limit adopted
throughout their analysis.

Figure 13: Same as Fig. 6 but for a smaller FOV of 1′$\times$1′ centered at
$\alpha=00$h $56$m $16.9$s, $\delta=-72^{\circ}27$′$48.7$″, and bins of 0.4
mag comprising the same magnitude range.

A cross-match between the SAMI catalog and the objects listed in Table D.1 of
Bodensteiner et al. (2020) resulted in 250 targets with measurements in all
five filters (henceforth “MUSE subsample”). From these, 73, 163, and 14 were
classified by Bodensteiner et al. as Be, normal B, and giants (RSG, BSG),
respectively.

To identify the $\mathrm{H}\alpha$ emitters within the MUSE FOV, we applied
the same selection criterion from Fig. 12 on the SAMI (1242 sources) and the
MUSE subsamples (250 sources). The results are presented in Fig. 14.

Figure 14: Same as Fig. 12 but for a smaller FOV of 63″$\times$63″ centered at
$\alpha=00$h $56$m $16.9$s, $\delta=-72^{\circ}27$′$48.7$″. Top panel: 1242
sources with SAMI photometry. Middle: flux-limited ($V\leq 18.5$ mag)
subsample of the SAMI sources. Bottom: 250 MUSE objects detected on the SAMI
catalog. Open blue circles correspond to the $\mathrm{H}\alpha$ emitters
selected through the color selection criterion of Eq. (8), shown as dashed red
lines. Open cyan circles correspond to non-Be MUSE objects exhibiting
$\mathrm{H}\alpha$ excess. Red $\times$ symbols indicate spectroscopic
confirmed CBe stars not showing $\mathrm{H}\alpha$ excess.

A total of 123 $\mathrm{H}\alpha$ emitters were selected among the 1242 SAMI
sources within the MUSE FOV, corresponding to $10\pm 1\%$666The fractional
errors shown throughout the manuscript were derived using a Poisson
distribution, i.e.,
$\sigma_{\mathrm{Be}}=N_{\mathrm{Be}}^{1/2}/N_{\mathrm{total}}$. of the
sample. This fraction is much smaller than the $32\pm 3\%$ reported by
Bodensteiner et al. (2020) based on a flux-limited sample of stars. The bright
subsample ($V<18.5$ mag) of SAMI sources provides a direct comparison with
their results. Here, a total of 87 $\mathrm{H}\alpha$ emitters were
identified. A fraction of $27\pm 3$% $\mathrm{H}\alpha$ emitters was observed
after the exclusion of 16 giant stars located on the right side of the diagram
($V-I>0.5$ mag, middle panel of Fig. 14). Finally, 63 CBe stars + 10 non-CBe
stars from the MUSE sample exhibited $\mathrm{H}\alpha$ excess from 250
targets. By excluding the giants located on the right side of the diagram
(14), we end up with a fraction of $31\pm 4\%$ of $\mathrm{H}\alpha$ emitters
for the MUSE samples, which is in good agreement with the findings from
Bodensteiner et al. (2020, $32\pm 3$%).

The analysis of the flux-limited SAMI subsample led to a similar fraction of
CBe stars ($27\pm 3$%) as that obtained from spectroscopic MUSE observations
($32\pm 3$%). Despite that, the deeper SAMI photometry allowed us to identify
a significant number of fainter $\mathrm{H}\alpha$ emitters, consistent with
late-type CBe stars candidates. As the population of normal stars increases
exponentially as a function of the mass (and the $V$-band magnitude), the
total fraction of active CBe stars with clear $\mathrm{H}\alpha$ emission
decreases toward late-B stars, reaching $10\pm 1$% when considering all stars
exhibiting $V\leq 22$ mag.

###  5.4 Fraction of $\mathrm{H}\alpha$ emitters versus normal stars

The C-M diagrams of Fig. 11 show that $\mathrm{H}\alpha$ emitters are found
over a wide range of luminosities ($12<V\lesssim 22.0$ mag). This range is
wider than that expected for B-type stars ($13.6\leq V\leq 20.2$ mag),
indicating the SAMI photometry is deep enough to identify all CBe stars
exhibiting strong enough $\mathrm{H}\alpha$ emission within NGC 330.

By taking advantage of the deeper photometric completeness of SAMI photometry,
we can now obtain a complete census of the fraction of $\mathrm{H}\alpha$
emitters stars versus normal MS stars associated with NGC 330. For the
analysis presented in this section, we selected a total of 3318 sources
exhibiting $B-I<0.5$ mag, i.e., excluding the bright evolved objects and the
RGB sources (see Fig. 10).

The next subsections present the analysis of the fraction of
$\mathrm{H}\alpha$ emitters as a function of $i)$ the distance from the center
of NGC 330, and $ii)$ the spectral type of B stars.

####  5.4.1 Radial distribution of $\mathrm{H}\alpha$ emitters in NGC 330

We investigated the surface density of $\mathrm{H}\alpha$ emitters as a
function of the distance from the cluster’s center (assuming as central
coordinates $\alpha=00$h $56$m $16.9$s,
$\delta=-72^{\circ}\,27\arcmin\,48\arcsec$). For reference and comparison, we
also computed the surface density of MS objects (sources exhibiting $B-I<0.5$
mag and not selected using Eq. (8), dividing them into higher- and lower-mass
MS stars with respect to $V\leq 18.0$ mag (corresponding to the transition
between B5 and B6 stars) to look for evidence of mass stratification within
the cluster. The distance of 57.5 kpc to the SMC was adopted (Milone et al.,
2018) to convert the angular projected distances from arcseconds to parsecs.

The resulting curves are presented in the top panel of Fig. 15, showing the
number of sources per parsec2, evaluated at concentric rings from 0 to 140″,
in steps of 5″ (solid lines). For comparison, the cumulative distribution
function (CDF) of the total number of stars as a function of the projected
distance is shown as the dashed lines in the same plot.

Figure 15: Top panel: Surface density (number of sources per area) of normal
MS stars (the filled blue curve indicates higher-mass objects associated with
$V\leq 18$ mag, and fainter, lower-mass objects by the filled black curve),
$\mathrm{H}\alpha$ emitters (filled red), and the total number MS and
$\mathrm{H}\alpha$ emitters (filled grey) as a function of the distance from
the center of NGC 330. The values were calculated for concentric rings around
the central coordinates of the cluster in steps of 5″. The dashed curves
indicate the cumulative distribution function of the quantities, while the
dotted curves indicate the distance corresponding to $\textrm{CDF}=0.5$. For
reference, the vertical filled black line indicates the 1$\farcs$33 cluster
radius from Glatt et al. (2010). Middle: The $\mathrm{H}\alpha$ emitter
fraction as a function of the distance from the center of NGC 330 (solid
line). The uncertainties are indicated by the error bars. For comparison, the
CDF for $\mathrm{H}\alpha$ emitters is indicated by the dashed curve. Bottom:
Three-dimensional Gaussian fit model to the surface density of
$\mathrm{H}\alpha$ emitters (red), higher- (blue) and lower-mass MS stars
(black). The best parameters for each curve ($N_{c}$, $\sigma$) are indicated
on the label.

The surface density of the sources with available SAMI photometry (filled grey
curve) shows a cusp pattern towards the center of the cluster, decreasing
towards larger radii. The CDF (dashed grey curve) reaches 50% at a radius of
16.8 pc ($\sim$60″), which is about 75% smaller than the radius of the cluster
reported by Glatt et al. (2010, indicated by the horizontal filled black
line). The lower-mass MS stars exhibit a similar surface density profile
(black curve), and the CDF of the total number of low-mass stars reaches 50%
at a projected distance of 17.2 pc (62″), roughly following the CDF of the
MS+$\mathrm{H}\alpha$ sample (in grey). The higher-mass MS stars (blue curve),
however, exhibit a much more compact distribution, indicating that massive
stars are preferably located within the inner region of the cluster (the CDF
reaches 50% at 6.4 pc (23″). Finally, the $\mathrm{H}\alpha$ emitters (red
curves) exhibit a similar distribution as that observed for the high-mass MS
stars, and its CDF reaches 50% at 6.6 pc (24″) distance. These results suggest
that the $\mathrm{H}\alpha$ emitters and the massive stellar populations are
likely confined within the inner region of the cluster.

The middle panel of Fig. 15 shows the fraction of $\mathrm{H}\alpha$ emitters,
i.e., $\mathrm{H}\alpha$/(MS+$\mathrm{H}\alpha$), as a function of the
distance to the cluster’s center. The data suggests a significant increase in
the proportion of $\mathrm{H}\alpha$ emitters towards the center, in agreement
with the surface density results above. About 50% of all $\mathrm{H}\alpha$
emitters and $>50\%$ of the higher-mass MS stars are concentrated within a
circle of 6.6 pc (24″) radius, whereas only $\sim 10\%$ of the lower-mass MS
objects are found within the same area. Such distinct distribution between
higher- and lower-mass objects corresponds to a clear evidence of mass
segregation within NGC 330.

The stellar surface density measurements can be used to infer the physical
properties of the cluster. For example, they provide valuable information
about the structure, density profile, and dynamical characteristics, offering
insights into the formation and evolution of stellar systems and populations.
Taking the analysis a step further, we transformed the surface density
information mentioned earlier into volume density. This conversion assumes
that the stars exhibit a spatial distribution following a three-dimensional
Gaussian distribution, as detailed in Appendix B). For this analysis, we can
estimate the stellar density at the center of the cluster (in stars pc-3) and
the characteristic scale (i.e., standard deviation, $\sigma$) of the stellar
population (in pc).

The bottom panel of Fig. 15 presents the observed stellar density of the MS
stars and $\mathrm{H}\alpha$ emitters as a function of the projected distance
from the center of the cluster, together with the best three-dimensional
Gaussian fit. We observe a reasonably good fit for all datasets for $r\lesssim
15$ pc, indicating that the model can reproduce the observed spatial stellar
distribution. This simple model better fits the observed dataset with greater
accuracy when compared to, e.g., simplified King profiles often adopted for
young stellar clusters (e.g. Bonatto & Bica, 2009; Hetem & Gregorio-Hetem,
2019). Therefore, adopting this profile is encouraging and warrants testing
with other young stellar clusters. The characteristic scale for the lower-mass
MS stars is $\sigma=10.83\pm 0.65$ pc, while the $\sigma$ values are
relatively shorter for the higher-mass and $\mathrm{H}\alpha$ emitters
($4.26\pm 0.20$ and $3.80\pm 0.13$ pc, respectively). These results show
unequivocally that the $\mathrm{H}\alpha$ emitters and the most massive stars
are preferably located in a more compact region from the center of the
cluster. At the same time, low-mass MS objects are observed towards larger
distances.

In addition, the central density for high-mass MS and $\mathrm{H}\alpha$
emitters corresponds to $N_{c}=(35.9\pm 0.30)\cdot 10^{-2}$ pc-3 and $(26.9\pm
0.17)\cdot 10^{-2}$ pc-3, respectively, while the density of lower-mass MS
stars is relatively lower, $N_{c}=(17.5\pm 0.16)\cdot 10^{-2}$ pc-3. These
estimates quantitatively support $i)$ the existence of a significant mass
stratification within NGC 330, and $ii)$ that $\mathrm{H}\alpha$ emitters are
preferably found towards the inner region of the cluster.

####  5.4.2 Fraction of $\mathrm{H}\alpha$ emitters as a function of the
Spectral Type

We further investigated the fraction of $\mathrm{H}\alpha$ emitters as a
function of the $V$-band magnitude (i.e., spectral type) to assess its
distribution vs. stellar mass within NGC 330 and in the adjacent stellar
field. We defined two sub-samples of normal MS stars and $\mathrm{H}\alpha$
emitters exhibiting with $B-I<0.5$ mag (therefore excluding older objects).
This selection led to 3397 highly probable members located within the radius
of NGC 330, $r={1.33\arcmin}$ (Glatt et al., 2010). In an effort to examine
the B-type stars associated with $\mathrm{H}\alpha$ emission, we selected a
subset of 858 sources exhibiting $V$-band magnitudes within the range expected
for B0-B9 stars (from Table 4. Additionally, 1631 sources were identified at
greater distances from the cluster’s center, which are more likely to be field
stars. We adopted the Main Sequence Turn Off point (MSTO) as $V=15.92$ mag (in
AB magnitudes) from Iqbal & Keller (2013), equivalent to the age of NGC 330
estimated as $\log(\textrm{age})=7.4$ dex ($\sim 25$ Myr) from Glatt et al.
(2010). The results are presented in Fig. 16.

Figure 16: Top panels: Distribution of normal MS stars and $\mathrm{H}\alpha$
emitters as a function of the $V$-band magnitude. From left to right, we show
the total number of stars within a 1$\farcs$33 radius from the center of NGC
330, the B-type star candidates in NGC 330, and the total number of stars in
the field ($r>1\farcs 33$). The expected magnitude intervals for B0 (blue), B9
(green), and A2 stars (red) are indicated by the shaded regions. The vertical
filled blue line indicates the MSTO ($V=15.92$) for NGC 330, and the vertical
dashed black lines divide the sample into higher- (HM) and lower-mass stars
(LM) using $V=18.0$ mag as reference. The values on the legend correspond to
the number of sources brighter than $V=18.0$, and the total number of sources,
respectively. Bottom: the ratio of $\mathrm{H}\alpha$ emitters a function of
the $V$-band magnitude for the same subsamples presented in the top panel. The
upper axis indicates the mean $V$-band magnitude for each spectral type listed
in Table 4. The ratio of $\mathrm{H}\alpha$ emitters for the HM and LM
subsamples are indicated on each panel. The error bars correspond to the
fractional errors for each bin.

The top left panel of Fig. 16 presents the distribution of the normal MS stars
(blue bars) and $\mathrm{H}\alpha$ emitters (red) as a function of their
$V$-band magnitude. For comparison, the associated spectral sub-types are also
indicated in the plots, using the mean value of the magnitudes listed in Table
4. The sources are distributed across a wide range of brightness ($12\leq
V\leq 22.5$), covering the entire magnitude interval expected for B-type
stars. While the number of normal MS objects increases towards late-type
objects following a power law (i.e., IMF-like), the distribution of
$\mathrm{H}\alpha$ emitters peaks at $V$ between 15.5 and 18 mag (B1-B5
stars), and the bulk of $\mathrm{H}\alpha$ emitters is slight offset towards
fainter magnitudes than the MSTO for NGC 330. A total of 152
$\mathrm{H}\alpha$ emitters are observed within the entire $V$-band magnitude
range, corresponding to a fraction of 4.4$\pm$0.5% of $\mathrm{H}\alpha$
emitters ($\mathrm{H}\alpha$/[$\mathrm{H}\alpha$ +MS]) with $V\lesssim 22.5$
mag.

The bottom left panel of Fig. 16 shows the fraction of $\mathrm{H}\alpha$
emitters as a function of the $V$-band magnitude. As observed on the top
panel, the largest fraction of $\mathrm{H}\alpha$ emitters is also found for
$V$-band magnitudes between 15 and 18 mag, consistent with B1-B5 stars. The
distribution reaches a peak of $60\pm 14\%$ at $V\sim 15.5$ mag, corresponding
to early B-type objects (B1-B3) close to the MSTO, in agreement with findings
from previous seeing-limited results from Iqbal & Keller (2013).

The fraction of $\mathrm{H}\alpha$ emitters decreases to values smaller than
10% for $V>18$ mag (i.e., for spectral sub-types later or equal to B6).
Despite the smaller fraction observed towards fainter objects, the total
number of sources with $\mathrm{H}\alpha$ excess (top panel) is remarkable,
indicating a considerable number of late-B type stars exhibiting
$\mathrm{H}\alpha$ emission, a result absent in previous works due to the
relatively faint nature of such objects. To properly compare our statistics
with previous works, we adopted $V=18.0$ mag (corresponding to B5-B6 stars) as
a limit to estimate the fraction of $\mathrm{H}\alpha$ emitters for higher-
and lower-mass stars (indicated as HM and LM in the legend of the figure).
Such division led to a fraction of $31.9\pm 3.3\%$ of $\mathrm{H}\alpha$
emitters for stars more massive than B5-B6, and $1.8\pm 0.2\%$ for lower mass
objects.

A similar behavior is observed when restricting the analysis towards the
expected magnitudes for B-type stars ($13.6\leq V\leq 20.2$, from Table 4), as
indicated by the middle panels in Fig. 16. For such sub-sample, the
$\mathrm{H}\alpha$ emitter fraction reaches a peak of $60\pm 15\%$ for B2
stars at the limit of the MSTO, decreasing towards late-type objects. The
fractions are slightly larger than observed for the full sample (left panel),
reaching $32.8\pm 3.4\%$ and $4.4\pm 0.9\%$ for the higher- and lower-mass
samples, respectively. The higher fraction of $\mathrm{H}\alpha$ emitters
towards the more massive stellar population agrees with the previous results
from Bodensteiner et al. (2020), while the lower fraction towards lower-mass
objects is an interesting new result, indicating a small but significant
fraction of active stars towards the lower mass limit of B-type stars. The
decrease of the CBe fraction with decreasing mass has been pointed out by
several authors (e.g., Keller et al., 1999; Iqbal & Keller, 2013; Bodensteiner
et al., 2020; Hastings et al., 2021); however, this is the first time a non-
zero fraction of $\mathrm{H}\alpha$ emitters is actually observed at the
lower-mass limit of the B-type population in the SMC. In particular, Hastings
et al. (2021) observed a sudden decrease in the CBe fraction beyond spectral
types later than B5 in NGC 330 (e.g., see their Fig. 3). We argue that may be
influenced by the flux limitations of their $\mathrm{H}\alpha$ observations
(based on HST photometry from Milone et al. 2018).

For completeness, the top right panel of Fig. 16 presents the distribution of
$\mathrm{H}\alpha$ emitters and MS stars for the field stars. The MS stars
exhibit a similar IMF-like distribution as observed on the top left panel,
with very few bright (e.g., massive) objects exhibiting $V<18$ mag. This is
expected as massive stars (at the top of the IMF) are less likely to be
isolated stars, i.e., unbound to the cluster. Only 22 of the 1631 sources at
larger radii from NGC 330 are $\mathrm{H}\alpha$ emitters. While most of them
are fainter than $V=21$ mag, only four are brighter than $V=18$ mag.
Consequently, low-count statistics at the high-mass end likely affect the
fraction of $\mathrm{H}\alpha$ emitters, as indicated by the bottom right
panel of Fig. 16. The integrated high-mass fraction ($11.8\pm 5.9\%$) is about
three times lower than observed towards NGC 330, while the fraction remains at
$\sim$1% values for the lower-mass objects.

##  6 Discussion and Conclusions

Although previous studies have investigated the B content of NGC 330 with
high-angular resolution observations (e.g., Milone et al. 2018, Bodensteiner
et al. 2020), this work represents the first study combining high-angular
resolution with sufficient photometric depth to investigate the stellar
population up to early A-type ($V\approx 22$ mag) in both broad-
$(\mli{BVRI})$ and narrow-band ($\mathrm{H}\alpha$) filters. The unprecedented
quality of AO-assisted SAMI/SOAR observations allowed us to resolve the
stellar population of NGC 330 at scales of $\gtrsim 0\farcs 1$ in all five
filters, and to identify $\mathrm{H}\alpha$ emitters throughout the entire
B-type stellar population, providing an excellent opportunity to investigate
the Be phenomenon and the occurrence of CBe stars across all spectral sub-
classes.

We first established a photometric calibration based on a _stellar template
model fitting_ methodology to calibrate all $\mli{BVRI}$+H$\alpha$ filters of
the SAMI catalog, delivering photometric errors smaller than 0.3 mag for
sources at the 23-mag limit using less than a hundred known objects. As a
direct consequence of using stellar template models, we also obtained the
corresponding stellar parameters for each object, and these findings will be
utilized in an upcoming publication.

The astrometric information from the Gaia DR3 catalog was used to identify and
filter out 849 foreground objects in the line-of-sight of NGC 330. In
addition, using a simple inspection of PARSEC evolutionary tracks, we
identified 674 old Red Giant Branch stars that are unlikely to be associated
with the young stellar cluster, removing them from further analysis. The
online version of Table 3 presents the classification of the full SAMI
catalog.

Through the adoption of a color selection criterion based on color indices, we
successfully identified 181 $\mathrm{H}\alpha$ emitters within the NGC 330
field. Among these sources, 137 are brighter than $V<20.2$ mag, corresponding
to stars equal to or earlier than B9. This count surpasses by a factor of two
the previously reported number of $\mathrm{H}\alpha$ emitters in literature,
based on similar selection criteria (Keller et al., 1999; Iqbal & Keller,
2013). The remaining 44 $\mathrm{H}\alpha$ emitters correspond to fainter,
lower-mass objects within the magnitude range of $20.2<V\lesssim 22.5$ mag.

We conducted a comparison between the AO-assisted SAMI observations and the
recent HST observations reported by Milone et al. (2018). They identified 63
$\mathrm{H}\alpha$ emitters consistent with main-sequence objects in NGC 330.
Even with their analysis relying on high-angular resolution observations, they
are constrained to $\mathrm{H}\alpha$ emitters exhibiting $I$ $\sim$ 18 mag,
roughly equivalent to B6 objects. We conducted a direct comparison using a
flux-limited sample of objects exhibiting $I$ $<$ 18 mag on the SAMI/SOAR
photometric catalog (Table 3), resulting in a total of 83 $\mathrm{H}\alpha$
emitters. This population is 30% larger than that reported by Milone et al.
(2018).

Similarly, we compared our SAMI observations with those reported by
Bodensteiner et al. (2020) based on MUSE observations. Our focus was on the
identical sky region, and we restricted our sample to match their magnitude
limit ($V<18.5$ mag). Based on spectroscopic classification, Bodensteiner et
al. identified a total of 82 stars (2 Oe and 80 Be) leading to a Be fraction
of Be/(B+Be) = $32\pm 3\%$. Using our adopted color selection criterion (Eq.
8), we identified 87 stars in our magnitude-limited sample, leading to a
fraction of $\mathrm{H}\alpha$ emitters of $27\pm 3\%$, in good agreement with
the previous study.

Further comparison was made with the previous seeing-limited works of Keller
et al. (1999) and Iqbal & Keller (2013), who analyzed the fraction of CBe
stars for a flux-limited sample of objects exhibiting $V<17$ mag. Keller et
al. (1999) reported that the fraction of CBe stars reaches a maximum of 80% at
$V$ between 15.0 and 15.5 mag (consistent with B1-B2 objects), decreasing
towards fainter objects. Their findings are very similar to the results
presented in Fig. 16. In addition, Iqbal & Keller (2013) found the fraction of
$\mathrm{H}\alpha$ emitters peaks at the MSTO ($V\sim 16$ mag), at 40% (see
their Fig. 4). Although their fraction is smaller than observed from the SAMI
observations (see below), our observations also match the peak of CBe stars
closer to the MSTO (cf. their Fig. 4). The existence of stars above the MSTO
can only be explained by binary interaction or rapid rotation, therefore
explaining the significantly large fraction of CBe stars for stars earlier
than B2-B3. This finding is consistent with the results of Georgy et al.
(2013), who estimated an increase in the MS lifetime by factors of up to 35%
depending on the initial rotation and mass of a star (at solar metallicity),
with a potential extension of up to 60% for SMC metallicities (Z=0.002).

Our comprehensive sample enables us to construct a detailed perspective of the
$\mathrm{H}\alpha$-emitting population in NGC 330. We demonstrate that
$\mathrm{H}\alpha$ emitters are found across a broader range of magnitudes
than that expected for B stars, signifying that $\mathrm{H}\alpha$ emitters
are found across the late O up to A spectral subtypes.

An analysis of the radial spread of the stars in the cluster revealed that the
surface density distribution of normal MS stars is clearly bimodal: the
higher-mass stars (arbitrarily defined as the ones brighter than $V=18$ mag,
roughly earlier than B6) are concentrated in the inner part of the cluster. In
contrast, the lower-mass ones are spread over a much larger volume.
Furthermore, the $\mathrm{H}\alpha$ emitting stars are spatially correlated
with the higher-mass ones. From the above, and further supported by Fig. 16,
two important conclusions may be drawn: $1)$ the $\mathrm{H}\alpha$ emitters
are much more frequent among the higher-mass subsample, reaching a peak value
of almost 60% for B2 stars; $2)$ the stellar content of the cluster clearly
displays mass stratification, with the higher-mass ones (presumably also with
a high binary content, e.g., Sana et al. 2014) occupying a much smaller
effective volume. The current analysis offers a more robust confirmation of
mass stratification within NGC 330 compared to earlier space-based HST
observations indicating similar evidence (e.g., Sirianni et al. 2002;
Gouliermis et al. 2004).

When the whole main-sequence population is considered (removing the stars with
$B-I>0.5$ mag), we found a $\mathrm{H}\alpha$/($\mathrm{H}\alpha$+MS) ratio of
$4.4\pm 0.5\%$. This is much lower than the fraction of CBe stars reported by
Keller et al. (1999, $34\pm 8\%$) and Iqbal & Keller (2013, 16.6%). The reason
is apparent from Fig. 16, which shows that the total number of stars rises
quickly towards later spectral types while the number of $\mathrm{H}\alpha$
emitters drops sharply. When we restrict the analysis to the B-stars (middle
panels of Fig. 16), the fraction increases to $14.0\pm 1.3\%$, but is still
much lower than the magnitude-limited estimates from the previous works. The
fraction of $\mathrm{H}\alpha$ emitters significantly increases when
restricting the analysis towards the stars brighter than $V=18$ mag
(corresponding to B5-B6 stars), showing $\mathrm{H}\alpha$ fractions around
32%, which is consistent with the fraction of CBe stars reported by
Bodensteiner et al. (2020, $32\pm 3\%$).

The photometric analysis presented in this work is biased towards
$\mathrm{H}\alpha$ emitters with relatively strong H$\alpha-R$ excess (Fig.
12). Such $\mathrm{H}\alpha$ excess may unequivocally be associated with CBes
that were active at the time of the observations and, thus, possessed large
and dense disks. Conversely, we expect that weak $\mathrm{H}\alpha$ emitters
or quiescent CBe stars with proper spectroscopic classification from
Bodensteiner et al. (2020) are generally not selected by the color criterion.
Indeed, ten of the CBe stars classified by those authors do not satisfy Eq. 8
(indicated as red $\times$ symbols in Fig. 14). In contrast, ten of their
B-type stars are clear $\mathrm{H}\alpha$ emitters in our sample (indicated as
open cyan circles in the same figure).

Despite the large dispersion on the fraction of $\mathrm{H}\alpha$ emitters as
a function of mass, a significant number of individual $\mathrm{H}\alpha$
emitters are observed over the entire range of magnitudes shown in Fig. 16. On
the premise that $\mathrm{H}\alpha$ emission is a strong indicator of CBe
activity, this evidence shows that CBe stars exist regardless of their main
sequence lifetime fraction ($t/t_{\mathrm{MS}}$), supporting that the Be
phenomenon observed in NGC 330 is unlikely to be mainly ruled by evolutionary
phases (such as core contraction), in agreement with the findings from Iqbal &
Keller (2013); Keller et al. (1999).

Even though the telltale signature of the Be phenomenon is $\mathrm{H}\alpha$
emission, estimating the $\mathrm{Be}/(\mathrm{B}+\mathrm{Be})$ fraction using
only photometry is a challenging task, as there are many foreseeable
situations in which CBe stars will not display a detectable $\mathrm{H}\alpha$
$-R$ color excess. For instance, during the early (late) stages of disk
construction (dissipation) the line emission can be too weak. Also, some CBe
stars only develop tenuous disks at times (e.g., Vieira et al., 2017).
Finally, many CBes are seen without any traces of disks for extended periods
of time. One classical example is $\delta$ Sco, which was considered a normal
B-type star for over a century, but grew a disk in the year 2000 that lasts to
this day (Suffak et al., 2020).

From the above, it follows that the real
$\mathrm{Be}/(\mathrm{B}+\mathrm{Be})$ fraction will always be higher than the
observed $\mathrm{H}\alpha$ emitter fraction in young clusters. One way to
improve estimates of the CBe content is to consider observations at different
epochs. For instance, when considering the MUSE objects with available SAMI
photometry from Fig. 14, ten spectroscopically classified CBe stars do not
show $\mathrm{H}\alpha$ excess. In contrast, 63 CBe stars and ten B stars are
identified as $\mathrm{H}\alpha$ emitters. When considering all these 83
objects, the lower limit of the $\mathrm{Be}/(\mathrm{B}+\mathrm{Be})$
fraction would slightly rise from $31\pm 4\%$ to $35\pm 4\%$.

In the following paper of this series, a new methodology will be presented,
taking into account the complexities of CBe stars to create realistic stellar
populations and their ensuing photometry to obtain a much better estimate of
the CBe content of NGC 330, without the known biases outlined above.

We thank the referee for the useful comments and suggestions that led to a
much improved version of this manuscript. The work of F. N. is supported by
NOIRLab, which is managed by the Association of Universities for Research in
Astronomy (AURA) under a cooperative agreement with the National Science
Foundation. P. T. acknowledges support from CAPES (grant
88887.604774/2021-00). A. C. C. acknowledges support from CNPq (grant
311446/2019-1) and FAPESP (grants 2018/04055-8 and 2019/13354-1). A. F.
acknowledges support from CAPES (grant 88882.332925/2019-01) and FAPESP (grant
2023/06539-0). This work made use of the computing facilities of the
Laboratory of Astroinformatics (IAG/USP, NAT/Unicsul), whose purchase was made
possible by the Brazilian agency FAPESP (grant 2009/54006-4) and the INCT-A.
Based on observations obtained at the Southern Astrophysical Research (SOAR)
telescope, which is a joint project of the Ministério da Ciência, Tecnologia e
Inovações (MCTI/LNA) do Brasil, the US National Science Foundation’s NOIRLab,
the University of North Carolina at Chapel Hill (UNC), and Michigan State
University (MSU).

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##  Appendix A Comparison between SAMI photometry and external catalogs

For completeness of the results exhibited in Sect. 4.3, the comparison between
the SAMI photometry and the external catalogs from MCPS and MUSE is presented
as follows.

###  A.1 MCPS

We compared the calibrated $\mli{BVI}$ magnitudes with those from the MCPS
catalog for sources brighter than 20 mag for all filters. The residuals
between SAMI and MCPS magnitudes are presented in the left panel of Fig. 17.

The residuals peak around 0 mag, exhibiting an extended tail towards positive
values. Therefore, the 1-$\sigma$ widths of the distributions are relatively
larger than those observed for OGLE (see Fig. 9). According to Fig. 8, the
minimum distance of the nearest neighbor for MCPS is 1$\farcs$04, the largest
value observed among all the other photometric catalogs, suggesting that a
single and bright object in MCPS is likely resolved into multiple and fainter
objects in SAMI observations, explaining the positive residuals as observed in
Fig. 17.

Figure 17: Left panel: Residuals between SAMI and MCPS photometry. Right
panel: Residuals between SAMI and MUSE photometry. The full description of the
plots is given in Fig. 9.

###  A.2 MUSE

The right panel of Fig. 17 presents the residuals between the $\mli{BVRI}$
magnitudes from SAMI and MUSE photometry. The synthetic MUSE photometry was
obtained by extracting the one-dimensional spectrum of the objects and
convolving them with the SAMI filter transmissions. The distribution of the
photometric residuals exhibits a systematic negative offset towards the bluest
filters, ranging from $-0.241$ mag for the $I$-band to $-0.89$ mag to the
$B$-band. Given that the comparison between OGLE (Sect. 4.3) and MCPS
(Appendix A.1) do not exhibit any systematic divergence, we speculate that a
zero-point correction on the flux-calibrated MUSE datacube can be the cause of
such large offsets.

##  Appendix B A three-dimensional Gaussian Model for the Stellar Density

The formula for a 3D Gaussian function in cylindrical coordinates is given by:

$n(r,\phi,z)=N_{\rm
c}\cdot\exp\left(-\frac{r^{2}}{2\sigma_{r}^{2}}-\frac{z^{2}}{2\sigma_{z}^{2}}\right)\,,$
(B1)

where it was assumed, for simplicity, symmetry around the $z$-axis. $N_{c}$ is
the density of stars (stars $\rm pc^{-3}$) at the cluster’s center. Further
assuming that the observer is placed along the $z$-axis, and that the standard
deviations along the $r$ and $z$ directions are the same (i.e.,
$\sigma_{r}=\sigma_{z}=\sigma$), we have that the observed superficial density
of stars, $\Sigma(r)$ (in pc-2), at a distance $r$ from the cluster’s center
is

$\Sigma(r)=\int_{-\infty}^{\infty}n(r,\phi,z)dz\int_{0}^{2\pi}d\phi=(2\pi)^{3/2}N_{\rm
c}\cdot\sigma\cdot\exp\left(-\frac{r^{2}}{2\sigma^{2}}\right)\,.$ (B2)