# Search strategies for supermassive stars in young clusters and application to nearby galaxies

A. Kuruvanthodi, D. Schaerer, M. Messa, A. Adamo, C. Usher, C.

Charbonnel, R. Marques-Chaves

► To cite this version:

A. Kuruvanthodi, D. Schaerer, M. Messa, A. Adamo, C. Usher, et al. Search strategies for supermassive stars in young clusters and application to nearby galaxies. Astronomy & Astrophysics - A&A, 2023, 674, pp.A140. 10.1051/0004-6361/202245695. hal-04894670

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# Search strategies for supermassive stars in young clusters and application to nearby galaxies

A. Kuruvanthodi<fnref n="1" />, D. Schaerer<fnref n="1" />,<fnref n="2" />, M. Messa<fnref n="1" />,<fnref n="3" />, A. Adamo<fnref n="3" />, C. Usher<fnref n="3" />, C. Charbonnel<fnref n="1" />,<fnref n="2" />, and R. Marques-Chaves<fnref n="1" />

Received 15 December 2022 / Accepted 3 March 2023

## ABSTRACT

**Context.** Supermassive stars (SMSs) with masses $M \ge 10^3-10^4 M_\odot$ formed by runaway collisions in young, massive, and dense star clusters have been invoked as a possible solution to the problem of the presence of multiple stellar populations and peculiar abundance patterns observed in globular clusters (GCs). However, no such objects have been observed so far.

**Aims.** We aim to develop observational strategies to search for SMSs hosted within young massive clusters (thought to be the precursors of GCs) using both photometric and spectroscopic observations. Such strategies could be applicable in a relatively general fashion.

**Methods.** We used theoretical predictions of the spectra of SMSs and SMS-hosting clusters, together with predictions from standard simple stellar populations to examine their impact on color-color diagrams and on individual optical spectral lines (primarily hydrogen emission and absorption lines). As a first step, we applied our search strategies to a sample of about 3000 young star clusters (YSCs) from two nearby galaxies with multiband observations from the HST and optical integral-field spectroscopy obtained with MUSE on the Very Large Telescope.

**Results.** We focus on models for SMSs with large radii (corresponding to $T_{eff} \le 7000$ K), which predict strong Balmer breaks, and construct proper color-color diagrams to select the corresponding SMS-hosting cluster candidates. We show that the spectrophoto-metric properties of these latter are similar to those of normal clusters with ages of a few hundred million years. However, the cluster SEDs show signs of composite stellar populations due to the presence of nebular lines ($H\alpha$ and others). Examining the photometry, overall SEDs, and the spectra of approximately 100 clusters with strong Balmer breaks, we find several objects with peculiar SEDs, the presence of emission lines, or other peculiar signatures. After careful inspection of the available data, we do not find good candidates of SMS-hosting clusters. In most cases, the composite spectra can be explained by multiple clusters or H II regions inside the aperture covered by the spectra, by contamination from a planetary nebula or diffuse gas, or by improper background subtraction. Furthermore, most of our candidate clusters are too faint to host SMSs.

**Conclusions.** We demonstrate a strategy to search for SMSs by applying it to a sample of YSCs in two nearby galaxies. Our method can be applied to larger samples and also extended to higher redshifts with existing and upcoming telescopes, and therefore should provide an important test for GC-formation scenarios invoking such extreme stars.

**Key words.** stars: general – globular clusters: general – galaxies: star clusters: general – stars: massive – stars: abundances

## 1. Introduction

The ubiquitous presence of multiple stellar populations (MSPs) with unique spectroscopic and photometric properties in Galactic and extra-galactic globular clusters (GCs) is one of the major unsolved problems in modern astronomy (Piotto et al. 2007; Charbonnel 2016; Bastian & Lardo 2018; Gratton et al. 2012, 2019; Milone & Marino 2022). Instead of a simple population of coeval stars formed from a chemically homogeneous protocluster cloud, individual GCs associated with the Milky Way and with several galaxies of the Local Group host stars formed with large variations of their content of C, N, O, Na, and Al, with Mg also varying in the most massive and/or most metal-poor Galactic GCs (Cohen 1978; Peterson 1980; Carretta et al. 2009, 2010, 2017; Mészáros et al. 2015, 2020; Pancino et al. 2017; Schiavon et al. 2017; Wang et al. 2017; O'Malley & Chaboyer 2018; Mucciarelli et al. 2009; Schiavon et al. 2013; Dalessandro et al. 2016; Niederhofer et al.

2017; Gilligan et al. 2019; Milone et al. 2020; Vanaraj et al. 2021; Leath et al. 2022; Larsen et al. 2022). Evidence for the presence of MSPs with similar characteristics is also found in intermediate-age (down to ~2 Gyr) massive star clusters in the Magellanic Clouds (Hollyhead et al. 2017, 2019; Saracino et al. 2020; Martocchia et al. 2020, 2021; Asa'd et al. 2022; Cadelano et al. 2022; Salgado et al. 2022). While the epoch when the clusters formed is therefore not critical for MSPs to be present, the mass of the cluster is. The MSPs were indeed never found in open clusters, and they are present only in old and intermediate-age star clusters that are presently more massive than approximately a few times $10^4-10^5 M_\odot$, with the more massive clusters showing more extended spreads in light elements, including He (Carretta et al. 2010; Bragaglia et al. 2012, 2017; Carretta 2019). This implies that the MSP-formation phenomenon was not restricted to the early Universe and that it is potentially still happening today in sufficiently massive star clusters that can be considered as

<footnote n="1">¹ Department of Astronomy, University of Geneva, Chemin Pegasi 51, 1290 Versoix, Switzerland
e-mail: adarsh.kuruvanthodi@unige.ch</footnote>

<footnote n="2">² CNRS, IRAP, 14 avenue E. Belin, 31400 Toulouse, France</footnote>

<footnote n="3">³ The Oskar Klein Centre, Department of Astronomy, Stockholm University, AlbaNova 10691, Stockholm, Sweden</footnote>
the modern counterparts of proto-GCs, regardless of their host galaxy.

It is now well accepted that the observed abundance varia-
tions among MSPs and the associated photometric patterns result
from the very fast and early contamination of the proto-star clus-
ters with the products of hot H-burning (~75 MK; Prantzos et al.
2007, 2017) from short-lived stellar members. Different poten-
tial polluters were proposed, each of them implying a differ-
ent scenario for the formation and the chemical and dynamical
evolution of the GCs and their stars. Several arguments are in
favor of supermassive stars (SMSs) being the most viable pol-
luter candidate. As shown by Denissenkov & Hartwick (2014),
SMS models with masses of between a few times 10³ and
a few times 10⁴ M☉ reach the required H-burning temper-
ature to activate the CNO cycle and the NeNa and MgAl
chains very early on the main sequence, explaining the
C-N, O-Na, and Mg-Al anticorrelations and variations of the
Mg isotopic ratios very well while He is still low, in agree-
ment with the low ΔY observed in the large majority of star
clusters hosting MSPs. Instead, scenarios involving the ejecta
from AGB stars (Ventura et al. 2001; D’Ercole et al. 2012), mas-
sive binaries (de Mink et al. 2009; Bastian et al. 2013), or fast-
rotating massive stars (Decressin et al. 2007; Krause et al. 2013;
Chantereau et al. 2016) predict excessive He abundance vari-
ations among the MSPs and struggle to reproduce the other
abundance patterns. Other major difficulties, such as the mass-
budget or the gas-expulsion problems that plague the other sce-
narios (Prantzos & Charbonnel 2006; Schaerer & Charbonnel
2011; Renzini et al. 2015; Krause et al. 2016, 2020; Larsen et al.
2014, 2018), are easily overcome in the MSP formation sce-
nario proposed by Gieles et al. (2018). Here, SMS form and con-
tinue to be rejuvenated through runaway collisions induced by
high gas inflow ($\dot{M} \gtrsim 10^5 M_\odot \text{Myr}^{-1}$) in proto-star clusters host-
ing at least $\sim 10^6$ protostars. These conditions are not limited to
the early Universe, and are insensitive to the metallicity of the
proto-star cluster, meaning that the Gieles et al. (2018) model
can explain the presence of MSPs in both old and intermediate-
age massive star clusters.

The major challenges in finding SMSs at high redshift are
the difficulties in observing a proto-GC and in differentiating the
SMS signatures from the integrated spectrophotometric proper-
ties of its host cluster. Several studies have inferred the expected
number density of proto-GCs and possible ways to find them
with the *James Webb* Space Telescope (JWST; see Renzini
2017; Pozzetti et al. 2019) assuming the simple stellar popu-
lation (SSP) concept. A few proto-GC candidates have been
observed with the help of gravitational lensing (Vanzella et al.
2019; Claeysens et al. 2023) but further follow-up studies are
required to better constrain their nature. More candidates are
expected to be found in new high-resolution near-infrared (NIR)
observations with JWST.

In the local Universe, some young massive star clusters
(YMCs; >10⁴ M☉), which are compact ($r_{core}$ < few parsecs), dense
(ρ_{core} ≥ 10³ M☉ pc⁻³), and bounded, are expected to be progenitors
of GCs (see review by Portegies Zwart et al. 2010; Krumholz et al.
2019). Apart from their metallicity, their physical properties seem
to be very close to what we expect from a progenitor of present-
day GCs (Krause et al. 2016). If the formation of those objects
is similar to that of proto-GCs, then YMCs might be the best
place to search for SMSs, as attempted for the first time in this
study for large samples of extra-galactic clusters that have been
identified from high-resolution, multi-band observations taken
with the *Hubble* Space Telescope (HST). We develop and apply
strategies to search for SMSs using multi-band photometry and

additional spectroscopic data when available. These strategies
are based on the spectrophotometric properties of SMSs and
SMS-hosting clusters predicted by Martins et al. (2020) follow-
ing the Gieles et al. (2018) scenario. Martins et al. (2020) predict
that SMSs with large radii are very bright in the optical bands,
and dominate over the total cluster flux. Such bloated SMS mod-
els (Gieles et al. 2018; Hosokawa et al. 2013) can have spectral
properties similar to an A-type star with conditions leading to a
strong Balmer break, which is not predicted by standard stellar
and atmospheric models (Martins et al. 2020). Such unique fea-
tures make those SMS-hosting clusters quite distinct from the
normal clusters and suggest a way to distinguish them from other
objects. On the other hand, the spectrophotometric properties of
compact SMSs are similar to those of young massive stars (O or
B type stars), making these types of SMS-hosting clusters dif-
ficult to differentiate from normal young clusters. We therefore
focus on the bloated SMS models in this study.

To apply these search strategies, we use HST observations
undertaken as part of the Legacy ExtraGalactic UV Survey
(LEGUS; see Calzetti et al. 2015) and their publicly released
cluster catalogs<fnref n="1" /> (Adamo et al. 2017), and another independent
study for the galaxy M83 (Bastian et al. 2012; Adamo et al.
2015; Della Bruna et al. 2022a). These are complemented by
other observations, including HST narrow-band Hα photometry
and integral-field spectroscopic observations taken with Multi
Unit Spectroscopic Explorer (MUSE) on the Very Large Tele-
scope (VLT).

Our paper is organized as follows. The data and data extrac-
tion are discussed in Sect. 2. In Sect. 3, we recall the main
properties and predictions of the SMSs and SMS-hosting cluster
models that our approach is based on, and present and discuss
criteria to select clusters hosting SMS. In Sect. 4 we discuss a
practical application of the approach to NGC 628 and M83, and
further investigations of the selected candidates. The difficulties
and further possibilities are discussed in Sect. 5. Our main con-
clusions are summarized in Sect. 6.

## 2. Observational data

The LEGUS survey covers approximately 50 galaxies in the
nearby Universe (see Calzetti et al. 2015) and provides HST
imaging in five bands spanning a wavelength range from 2750
to 8140 Å. To demonstrate and apply our strategies to search for
SMSs, we focus on massive star clusters in the nearby galaxies
NGC 628 and M83, for the following main reasons: (1) Both
of are spiral galaxies with “sufficient” star formation rates, such
that young star clusters (YSCs) are still forming in these galax-
ies. (2) They are relatively well studied, and multi-band clus-
ter catalogs are available. (3) Both galaxies host a large num-
ber of star clusters in which we can search for SMSs. Finally,
(4) Spectroscopic Integral Field Unit (IFU) observations are also
available for these galaxies. The catalogs used in this study are
from Adamo et al. (2017) for NGC 628, and from Bastian et al.
(2012), Adamo et al. (2015) and Della Bruna et al. (2022a) for
M83. These combine data from two different pointings in both
galaxies. The YSC catalogs of NGC 628 span an age range of 1
Myr to 3 Gyr with a median age of around 14 Myr and a mass
range of 433 M☉ to 3.2 × 10⁶ M☉ with a median mass around
4.5 × 10³ M☉. Similarly, the clusters of M83 span an age range
of 1 Myr to 10 Gyr with a median age of around 45 Myr and a
mass range of 246 M☉ to 4.5 × 10⁶ M☉ with a median mass of

<footnote n="1">¹ Publicly available at https://archive.stsci.edu/prepds/legus/.</footnote>
<table><caption>**Table 1.** Overview of the selected galaxies (morphological type and distance are adapted from Calzetti et al. (2015) and NED) and their cluster population.</caption><thead><tr><th>Galaxy</th><th>Morphological type</th><th>Distance Mpc</th><th>Number of class 1 &amp; 2 clusters</th><th>Number of clusters close to A2 SMS+cluster</th><th>Number of clusters close to B3 SMS+cluster</th><th>Number of massive clusters (Mass >10<sup>5</sup> M<sub>☉</sub>)</th></tr></thead><tbody><tr><td>NGC 628</td><td>SAc</td><td>9.9</td><td>849</td><td>88</td><td>48</td><td>30</td></tr><tr><td>M 83</td><td>SABc</td><td>4.9</td><td>2282</td><td>223</td><td>—</td><td>83</td></tr></tbody></table>

around $5.5 \times 10^3$ M$_{☉}$. The cluster masses are estimated assuming the Kroupa (2001) initial mass function (IMF).

LEGUS cluster catalogs classify the clusters into four different categories according to their morphology in the F555W band (Adamo et al. 2017). Class 1 is a more symmetric and compact cluster, Class 2 is a concentrated cluster with some level of asymmetry, Class 3 is a system with multi-peak PSF and a diffuse morphology (considered as stellar associations), and Class 4 is a spurious detection. According to this classification, Class 3 and Class 4 objects can be foreground or background, or insecure sources. Apart from the F435W/F438W, F555W, and F814W bands, all the Class 1 and 2 objects are detected in F275W, F336W, or both. We therefore select only Class 1 and Class 2 with photometry available for all five bands for further analysis$^2$. A summary of the galaxies and their cluster populations is listed in Table 1.

Near-ultraviolet(NUV)-optical broadband aperture photometry for clusters in NGC 628 was performed by Adamo et al. (2017). We complemented broad-band data with HST archival observations of Hα emission using F658N narrowband images (observations taken as part of the Program 10402, PI: R. Chandar). We performed standard aperture photometry on Hα images using the python package photutils (Bradley et al. 2020) and applying the same apertures and annuli used for the photometry on LEGUS broad-band observations, that is, a main aperture of 0.16" (3.2 pixels) and a background annulus of between 0.28" (5.6 pixels) and 0.32" (6.4 pixels). We performed an aperture correction estimated from isolated clusters in the image by deriving their total flux within an aperture of 0.8" (16 pixels), with background annuli of between 0.84" (16.8 pixels) and 0.88" (17.6 pixels). Cluster broad band aperture photometry in M83 was performed and described by Adamo et al. (2015, for the M83 disk) and by Della Bruna et al. (2022a, for the M83 center). In this case, we use the already available Hα photometry performed by Della Bruna et al. (2022a). Throughout the entire paper, we refer to magnitude values in the AB magnitude system.

Finally, we also use spectroscopic observations of NGC 628 and M83 using the VLT-MUSE (Bacon et al. 2010) spectrograph in the wavelength range 4350–9300 Å. We used a 1'×1' field of view (wide field mode) with 0.2" pixel-size observations for NGC 628 (Emsellem et al. 2022) and M83 (Della Bruna et al. 2022b,a).

For NGC 628, we downloaded the unsmoothed PHANGS MUSE mosaic from the Canadian Advanced Network for Astro-

nomical Research (CANFAR) website$^3$. To extract spectra, in each wavelength slice we performed aperture photometry for the selected star clusters using an aperture of two-thirds of the PSF (point spread function) full width at half maximum (FWHM) and a background annulus of between two and three times the FWHM, assuming a FWHM of 0.92" for the smoothed mosaic.

For M83, we used the spectra from Usher et al. (in prep.). For each MUSE pointing, we used PampelMUSE (Kamann et al. 2013) to fit a Moffat PSF as a function of wavelength to bright point sources. For each wavelength slice and each star cluster, we fit a linear combination of a constant background and the fitted Moffat PSF within a region of two times the PSF FWHM. Spectra from different pointings of the same star cluster were combined by scaling by the exposure time.

# 3. Theoretical models and predicted observational signatures of SMSs and SMS-hosting clusters

## 3.1. SEDs of clusters with and without SMS

The observable features of an SMS-hosting cluster depend on the combination of the spectral energy distributions (SEDs) of the SMS themselves (determined by their physical parameters, such as temperature, surface gravity, etc.), the SED of the cluster (young) stellar population, and the SED of the surrounding H II region.

### 3.1.1. SMS models

We adopt the same parameters and properties for the SMS models as in Martins et al. (2020) and use the corresponding predictions of their atmospheric models for spectral synthesis. These SMS models belong to two different categories (see Table 2). In the first category (series A), these latter authors assumed two effective temperatures (7000 K and 10 000 K, with respectively log g = 0.5 and 0.8) that are close to the expected temperature range for a cool SMS (Haemmerlé et al. 2018) and in agreement with the formation scenario described by Gieles et al. (2018). For each temperature, Martins et al. (2020) computed synthetic spectra for two different luminosities ($10^8$ and $10^9$ L$_{☉}$), and thereby series A consists of four models (A1–A4) covering a large mass range (~2.5 × $10^3$ to ~5.4 × $10^4$ M$_{☉}$). The second category of models consists of two series (B and C) for which Martins et al. (2020) assumed a SMS mass of $10^4$ M$_{☉}$ (series B) and $10^3$ M$_{☉}$ (series C) and calculated the other physical properties (temperature, luminosity, and radius) according to the mass–luminosity and mass–radius relations adopted by Gieles et al. (2018) and extrapolated from massive star studies. The M–L relation reads $L = 2.8 \times 10^6 L_{☉} M/(100 M_{☉})$ for SMSs that are close to the Eddington limit. The large uncertainties in the M–R

<footnote>$^2$ While observations using F275W band were not available for M83, and clusters are classified into two different categories. Both class 1 and class 2 type clusters in the LEGUS classification are indicated as class 1 and the other two classes as class 2 in M83 (Adamo et al. 2015; Della Bruna et al. 2022a). We therefore considered only the class 1 objects in M83 for further analysis.</footnote>

<footnote>$^3$ https://www.canfar.net/storage/vault/list/phangs/RELEASES/PHANGS-MUSE/DR1.0/DATACUBES</footnote>
<table><caption>**Table 2.** Properties of different SMS models considered for the analysis (adopted from Martins et al. 2020).</caption><thead><tr><th>ID</th><th>T<sub>eff</sub><br>[K]</th><th>log L<br>[L<sub>☉</sub>]</th><th>log g</th><th>M<br>[M<sub>☉</sub>]</th><th>R<br>[R<sub>☉</sub>]</th><th>M<sub>F555W</sub></th></tr></thead><tbody><tr><td>A1</td><td>7000</td><td>8.0</td><td>0.5</td><td>5395</td><td>6723</td><td>-13.6</td></tr><tr><td>A2</td><td>7000</td><td>9.0</td><td>0.5</td><td>53 956</td><td>21 506</td><td>-13.6</td></tr><tr><td>A3</td><td>10 000</td><td>8.0</td><td>0.8</td><td>2585</td><td>3340</td><td>-13.2</td></tr><tr><td>A4</td><td>10 000</td><td>9.0</td><td>0.8</td><td>25 848</td><td>10 580</td><td>-13.4</td></tr><tr><td>B1</td><td>137 000</td><td>8.4</td><td>5.5</td><td>10 000</td><td>30</td><td>-6.4</td></tr><tr><td>B2</td><td>43 000</td><td>8.4</td><td>3.5</td><td>10 000</td><td>301</td><td>-9.6</td></tr><tr><td>B3</td><td>13 600</td><td>8.4</td><td>1.5</td><td>10 000</td><td>3006</td><td>-13.1</td></tr><tr><td>C1</td><td>77 000</td><td>7.4</td><td>4.5</td><td>1000</td><td>30</td><td>-8.3</td></tr><tr><td>C2</td><td>43 000</td><td>7.4</td><td>3.5</td><td>1000</td><td>95</td><td>-9.8</td></tr><tr><td>C3</td><td>24 000</td><td>7.4</td><td>2.5</td><td>1000</td><td>305</td><td>-11.3</td></tr></tbody></table>

**Notes.** The final column represents the absolute AB magnitude in the F555W band for those SMSs whose mass is rescaled to $10^3 M_☉$ (assuming $L \propto M$).

relation are accounted for by varying the $\delta = \frac{\log(R/30)}{M/100}$ parameter ($\delta = 0, 0.5$, and $1$ respectively in the models B1-C1, B2-C2, and B3-C3; in the case of models A1 to A4, the corresponding $\delta$ resulting from the assumed parameters equals 1.35, 1.05, 1.45, and 1.06 respectively).

As shown by Gieles et al. (2018), the higher $\delta$ is, the larger the cross-section of the collisions between the SMS and normal stars, which favors the mass growth of the SMS, and the cooler the effective temperature of the SMS. Additionally, Martins et al. (2020) found that compact and hot SMSs are difficult to differentiate from normal young clusters (SSPs) without SMS. On the other hand, these authors showed that the spectral properties of more extended and therefore cooler SMSs (with a surface temperature of around 7000–10 000 K) will be similar to those of a superluminous A-type star whose presence strongly alters the overall cluster SEDs, rendering it quite distinct from normal young stellar populations. In this study, we therefore investigate the three SMS models named A2, A4, and B3 from Martins et al. (2020) in more detail; these have relatively large radii, which is needed to maintain a high accretion rate, and provide the best detectability signatures.

### 3.1.2. Cluster models

To create the synthetic SEDs, a SMS is assumed to form within a cluster of mass $5 \times 10^3 M_☉$ (which corresponds to $10^6$ stars) with a Kroupa-like IMF (Kroupa 2001). The properties of the SMS are related to those of the cluster in the core of which it is formed; the relations are given by the model of Gieles et al. (2018). Following Martins et al. (2020), we take cluster (with an age of 2 Myr) and nebular (H II region) models to create the integrated SMS+cluster spectrum. We examined SMS models both at low (~1/100 of solar) and solar metallicity, yielding small differences in the spectral range of interest here. As the SMS dominates the spectrum, this also implies that the combined SMS+cluster colors depends only weakly on metallicity.

For comparison, we also use the physical properties estimated from the SED fits using the SSP models. For NGC 628, Adamo et al. (2017) used Yggdrasil (Zackrisson et al. 2011) models with Geneva stellar tracks and solar metallicity $Z = 0.02$ to fit observed cluster SEDs, while for M 83, Stochastically-

lighting-up-galaxy (SLUG) models (see da Silva et al. 2012; Krumholz et al. 2015b) were used to fit observed SEDs (Adamo et al. 2015; Della Bruna et al. 2022a). In our analysis, we consider Yggdrasil models based on Padova-AGB tracks (SSPs generated using Starburst99) (Leitherer et al. 1999; Vázquez & Leitherer 2005) with different covering factors $f_{cov}$ ($f_{cov} = 0$ correspond to models without nebular emission, $f_{cov} = 1$ to maximum nebular emission, and $f_{cov} = 0.5$ to 50% loss of ionizing photons). For all SEDs, we either computed or took the Yggdrasil synthetic photometry in the five HST filters available for the LEGUS galaxies (F275W, F336W, F435W, F555W, and F814W) for comparison with observations.

Qualitatively, as illustrated by Martins et al. (2020), synthetic SEDs of SMS and young cluster (2 Myr) models show that the flux from the SMS dominates at $\lambda \gtrsim 3000$ Å for the A2 model, and at $\lambda \gtrsim 1200$ Å for the A4 SMS model. In addition, the A2 model shows a strong Balmer break in absorption. As we show in the following subsection and in Sect. 4, these two features of A2 SMS-hosting clusters can be used to identify them. On the other hand, the presence of a SMS with properties of the B3 model does not lead to easily distinguishable features in the SED, and hence such SMSs might be difficult to find. Finally, although the A4 SMS model has a relatively low $T_{eff}$, it produces a Balmer break in emission due to nonlocal thermodynamic equilibrium (NLTE) effects, which is not expected in normal cool stars. The fact that normal young clusters can also produce this feature (also due to nebular continuum emission) makes it hard to distinguish A4 SMS from normal clusters. Despite this, we consider the three different SMS models mentioned above for our investigation.

## 3.2. Theoretical colors of SMSs and SMS-hosting clusters

Using the five HST filters available for the LEGUS galaxies, we examined different color–color plots to see which combinations could maximize differences between normal cluster models (SSPs), an SMS alone, and clusters-hosting SMS (SMS+cluster). Interesting color–color plots showing the location of SSP models of different ages, SMS models, and clusters-hosting SMS are illustrated in Fig. 1.

Generally, the SMS models show colors that are quite similar to those of SSPs in most color–color plots. This similarity is particularly striking for the B3 and A4 SMS models, whose colors resemble those of young clusters (typically ages $\le 6$ Myr). However, we notice that the coolest SMS (A2) is significantly offset from SSPs; for example, in $m_{F336W} - m_{F435W}$ versus $m_{F275W} - m_{F336W}$, shown in the top panel of Fig. 1. Furthermore, the A2 model is found in a location where relatively old clusters (~200–600 Myr) are found, although both the SMS and its surrounding cluster are truly young ($\le 2–5$ Myr; Gieles et al. 2018). This implies that searches for such SMSs should not be restricted to clusters that appear to be young as judged by their color–color combinations or based on analyses using “normal” simple stellar population models.

The physical cause of this behavior is simple. The F275W, F336W, and F435W bands straddle the Balmer break. As the A2 SMS has a strong Balmer break (due to its cool temperature and NLTE effects) it is red in $m_{F336W} - m_{F435W}$ and hence resembles SSPs of advanced age where the Balmer break is strong (as A-type stars dominate the light at ages of ~200–600 Myr). Furthermore, as the flux of A2 dominates at these wavelengths, the integrated colors (SMS+cluster) remain relatively unchanged. A $m_{F336W} - m_{F435W}$ versus $m_{F275W} - m_{F336W}$ color–color selection—which probes the Balmer break—therefore
<figure><img src="image_2.png" /></figure>

**Fig. 1.** Theoretical color–color diagrams showing the effect of SMS hosted in young clusters compared to normal SSPs. Top: $m_{F336W} - m_{F435W}$ vs. $m_{F275W} - m_{F336W}$ color–color diagram. Bottom left: $m_{F435} - m_{F555W}$ vs. $m_{F275W} - m_{F336W}$ color–color diagram. Bottom right: $m_{F435W} - m_{F555W}$ vs. $m_{F336W} - m_{F435W}$ color–color diagram. Yggdrasil models with solar metallicity and different covering factors are shown as blue ($f_{cov} = 1$) and yellow ($f_{cov} = 0$) lines. After 10 Myr, the $f_{cov}$ is not relevant because the cluster is expected to be gas free. Therefore, models with different $f_{cov}$ produce the same color indices and are therefore seen as a single brown line. The young cluster model from Martins et al. (2020) is shown as a large green dot. Different SMS+Cluster and SMS models are shown in red (A2), blue (A4), and magenta (B3) triangles and stars, respectively. For the cluster and cluster+SMS models, the transparent symbols are models without including the nebular emission while the dark ones are with nebular emission. The arrow in the top right corner shows the reddening vector. The length of the reddening vector corresponds to $E(B-V) = 0.2$ with the Milky Way extinction law (Cardelli et al. 1989). All magnitudes and colors are given in the AB magnitude system.

appears as the most promising one to find young clusters hosting an A2-like SMS. Additional information should then be used to further test for the presence of SMS. These additional features of A2-like SMS hosting clusters are described below (see Sect. 4) following a presentation of the practical applications of the proposed color–color selection.

The $m_{F435W} - m_{F555W}$ versus $m_{F336W} - m_{F435W}$ color–color selection also probes the Balmer break (see Fig. 1, bottom right). However, old clusters (ages ≫3 Gyr) with high extinction can be scattered over the selection region, which would then be contaminated by GCs (see Sect. 4). Therefore, if available, the use of UV bands is preferred to select A2-like SMS candidates.

Finally, to distinguish B3-like SMS candidates, we use a $m_{F435W} - m_{F555W}$ versus $m_{F275W} - m_{F336W}$ color–color selection (see Fig. 1, bottom left), because the model was quite far from the SSP models and maximizes the sample. However, we caution that this distinction is primarily due to relatively strong emission lines ([O III] λλ4959,5007, Hβ) in our cluster model, which

lead to a redder $m_{F435W} - m_{F555W}$ color than the SSP models of Zackrisson et al. (2011). This is therefore not a robust selection criterion for B3-like SMSs, and again echoes the fact that such hot SMSs are difficult to distinguish.

### 3.3. Expected V band magnitude of SMS-hosting clusters

Even though the color–color plots provide a qualitative way to isolate A2-like SMS hosting clusters from a bigger sample of star clusters, this method ignores the importance of absolute quantities like the mass or magnitude. To illustrate this point, we show the predicted F555W magnitude of all SMS models of Martins et al. (2020) as a function of distance in Fig. 2. We note that the SMS models shown here span a wide range of parameters, with masses from 1000 $M_\odot$ to ~54 000 $M_\odot$, luminosities $log(L/L_\odot) = 7.4–9.0$, and effective temperatures $T_{eff} = 7000–137 000$ K (see Table 2). Although the SMS mass is a priori unknown, nucleosynthesis constraints from observed
<figure><img src="image_3.png" /><figcaption>**Fig. 2.** F555W band magnitude vs. distance. Top: SMS models in (Martins et al. 2020). A series of SMS models are shown in red, each with a different line style: solid (A1), dashed (A2), dash-dotted (A3), and dotted (A4). Similarly, B series models are shown in green: solid (B1), dashed (B2), and dash-dotted (B3), and C series models are shown as blue: solid (C1), dashed (C2), and dash-dotted (C3). The brightest clusters in 32 LEGUS galaxies are shown as blue filled dots. The brightest clusters in this study are indicated as red (NGC 628) and orange (M 83) filled dots. Bottom: A series and B series models are rescaled to the minimum mass of $10^3 M_{\odot}$. The indicators are the same as in the top figure.</figcaption></figure>

abundance patterns in GCs provide a lower limit of ~1000 $M_{\odot}$ for the SMS in the runway collision formation scenario (Gieles et al. 2018; Prantzos et al. 2017). We therefore also plot the predicted magnitudes for all the SMS models after rescaling them to this minimum SMS mass, assuming a linear mass–luminosity relation, which is a good approximation for very massive stars (See Fig. 1 in Martins et al. 2020).

The most striking point of Fig. 2 is the high brightness of the A2 SMS, which ranges from $m_{F555W} \sim 18$ to 13 for masses of $10^3 M_{\odot}$ to $5.4 \times 10^4 M_{\odot}$ at a distance of 20 Mpc. From those computed by Martins et al. (2020), this is the coolest model ($T_{\text{eff}} = 7000$ K) and therefore the brightest one in the visual domain (F555W). Hotter SMSs are significantly fainter in F555W, and the faintest models have magnitudes $m_{F555W} \sim 23$ at $d = 20$ Mpc. Figure 2 can be used to estimate the minimum brightness of SMS candidates or SMS-hosting clusters. For convenience, we list the absolute magnitudes $M_{F555W}$ of the models (all rescaled to the minimum SMS mass of 1000 $M_{\odot}$) in Table 2.

For comparison with observations, we also show the observed magnitude of the brightest clusters from the full

LEGUS sample including 32 galaxies in Fig. 2. This shows that the brightest cluster in NGC 628 (M 83) is approximately ten (four) times fainter in the V-band than the minimum brightness expected for the cool SMS model (A2). Of course, this comparison neglects extinction, which—if significant—could increase the number of clusters reaching the minimum brightness limit of this SMS. In any case, most of our candidate SMS-hosting clusters do not reach this brightness limit. Taken at face value, these limits imply that effective searches for SMSs should combine both relative measurements, that is, the colors of the SED and quantities such as the absolute magnitude of the candidate clusters. Furthermore, it should be noted that the SMSs with large radii (i.e., low effective temperature), which are those that can be distinguished more easily from normal stellar populations, are also the brightest objects in the visible. On the contrary, the faintest SMSs are the hottest; their SEDs are predicted to more closely resemble those of the young clusters in which they are hosted, and they are therefore difficult to detect.

# 4. Selection and analysis of SMS-hosting cluster candidates

Although our sample does not host clusters as bright as the originally proposed SMS models, some of them are not too far from the rescaled 1000 $M_{\odot}$ SMS models, and we want to examine the potential candidates selected by our proposed color–color criteria in depth, and demonstrate and discuss the different steps we propose for searches for SMS in proto-GCs.

## 4.1. Color–color selection of SMS and SMS-hosting cluster candidates

To put our strategy into practice, we examined the clusters in the spiral galaxy NGC 628, which has around 415 Class 1 and 434 Class 2 clusters with photometry available in all five bands. The relevant color–color diagrams are shown in Fig. 3. We selected clusters close to the A2 and B3 models (using the above-mentioned color–color combinations) within two times the average photometric error of the sample and reddening limit. The reddening is estimated using the Milky Way extinction law (Cardelli et al. 1989) and assuming $E(B-V) = 0.2$ (which is the median extinction for clusters in NGC 628). Those selected clusters are within the magenta box in Fig. 3. There were around 88 clusters close to the A2 SMS+Cluster model and 48 close to the B3 SMS+Cluster model on NGC 628, as indicated in Table 1. We note that we do not consider stochastic effects on the IMF (da Silva et al. 2012; Krumholz et al. 2015b), because our targeted clusters are expected to be more massive than $10^{4-5} M_{\odot}$ and previous studies show that these effects are prominent when cluster mass is below $10^{3.5} M_{\odot}$ (Krumholz et al. 2015a).

The LEGUS catalogs provide the $E(B-V)$, age, and mass of the clusters estimated from the classical SED fit. The number of massive clusters ($>10^5 M_{\odot}$) according to this classical SED fit (i.e., without SMS) are shown in Table 1. There were 11 massive clusters in our selected sample and 5 more would be added if we were to assume higher extinction.

As F275W observations were not available for the M 83, we use the $m_{F435W}-m_{F555W}$ versus $m_{F336W}-m_{F435W}$ color–color diagram, which also probes the Balmer break. Additionally, observations were made with the F438W filter instead of F435W, but this has a negligible impact on our analysis. The observed clusters and the predicted colors are shown in Fig. 4. The shaded blue region in the color–color plots shows the location of sources
<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Location of clusters selected for further analysis from NGC 628 in color–color plots. Left: Color–color diagram used for the selection of clusters close to the A2 SMS+Cluster model. Right: Color–color plot for the selection of clusters close to the B3 SMS+Cluster model. Class 1 and Class 2 objects are shown in yellow points while clusters with mass >10⁵ M☉ are shown by green squares. Yggdrasil models with solar metallicity and different covering factors are shown as blue ($f_{cov} = 1$), black ($f_{cov} = 0.5$), and green ($f_{cov} = 0$) lines ($f_{cov}$ is important only at young ages (<10 Myr) and all three models will be the same at older ages and are therefore seen as a single black line). The model cluster is shown as a large green dot. Different SMS+Cluster and SMS models are shown in red (A2), blue (A4), and magenta (B3) triangles and stars, respectively. Clusters close to the A2/B3 SMS+Cluster models within the 2 × photometric error + reddening limit are shown in the magenta box. The reddening vector is shown in the top right corner of the plot. The length of the reddening vector corresponds to $E(B - V) = 0.2$ with the Milky Way extinction law (Cardelli et al. 1989). All the magnitudes and colors are given in the AB magnitude system.</figcaption></figure>

that can still be moved into our selection boxes if they have high extinction ($E(B-V)$ up to 1.0). Within our selection box, we find 223 clusters and only very few (5) massive clusters. However, if we allow higher extinction, our color criteria could be compatible with a larger number of massive clusters, which are found in the shaded area in Fig. 4. We therefore retain 30 massive clusters (>10⁵ M☉) as possible candidates for further inspection. As there was no proper way to identify the B3-like SMS-hosting clusters, these compact SMSs are not investigated in M 83.

Having selected clusters that could potentially host cool SMS from color–color plots, we now proceed to a more detailed analysis of these candidates using the full multiband photometry and spectroscopic information available. This serves in particular to illustrate some of the additional features that can, and should, be examined to bolster possible claims of the presence of SMSs.

## 4.2. SED fitting

To use all the available photometric data (5 broad bands) from the LEGUS catalogs and thus use more information than the three bands used for the color–color selection, we fitted the

observed SEDs to the theoretical SEDs of the A2 SMS+cluster model and to normal SSPs using the well-known models from Bruzual & Charlot (2003) for solar metallicity and considering the Calzetti attenuation law (Calzetti et al. 2000). The fits are made with a version of the *Hyperz* code – described in Schaerer & de Barros (2009) – which also includes nebular emission.

Out of the 88 preselected clusters in NGC 628, we find 7 that are a better fit to the A2 SMS+cluster model than to the SSP models according to the reduced $\chi^2$ values. The SED of one source (LEGUS ID 2838) in NGC 628 with comparable reduced $\chi^2$ values is shown in Fig. 5. Clearly, both SED fits nicely reproduce the observed fluxes and the two solutions cannot be distinguished on this basis. Nevertheless, we notice that the SMS model better reproduces the F275W band flux than the SSP models. We also caution that the reduced $\chi^2$ values are subject to subtle effects due to metallicity differences and the differences in the number of free parameters considered in both models (both age and extinction are free parameters in the case of SSP models while only extinction is the free parameter in the SMS scenario). In general, both models reproduce a strong Balmer break, which for the SSP is due to an advance in age (360 Myr) and due to
<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Color–color diagram used for the selection of clusters close to the A2 SMS+Cluster model in M 83. The symbols are the same as in Fig. 3.</figcaption></figure>

the A2 SMS in the second case. The main difference is that the SED including the SMS has emission lines, which are due to the presence of the young population surrounding the SMS. This latter young population contains massive stars producing nebular emission. Narrowband imaging or spectroscopy, which we discuss below, are needed to distinguish such cases.

We also examined SED fits using the hotter SMS model, that is, B3 SMS+cluster. In this case, we find no cluster for which the SMS+cluster SED provides a better fit than with standard SSP models. This is in line with our expectations, because the B3-like SMS has a smaller impact on the integrated SED than the cooler (A2-like) SMS.

### 4.3. Combining $H\alpha$ narrow and broadband photometry

To possibly support the presence of a cool, A2-like SMS in a young cluster, which is selected as it has colors similar to old (~200–600 Myr) clusters, the next step is to verify that the $H\alpha$ emission is associated with the cluster and hence confirms its young age. To do so, we use narrowband observations available for both NGC 628 and M 83. Combining the *F658N* (for NGC 628) or *F657N* (for M 83) narrowband images with *F555W* and *F814W* to construct continuum-subtracted images, we find one cluster with significant $H\alpha$ emission (LEGUS ID 2838) in NGC 628. The overall SED and postage stamps of this cluster are shown in Figs. 5–7.

The broadband SED of cluster 2838 shows a good fit to the A2 SMS+Cluster model; the flux in the *F275W* band is particularly well reproduced in the SMS+Cluster scenario (see Fig. 5). The reduced $\chi^2$ values for the SMS scenario (2.96) and SSP scenario (2.83) are comparable and make it hard to distinguish the best fit. The best SSP model gives an age of 360 Myr and mass of $1.6 \times 10^4 M_{\odot}$ for the cluster. Figure 6 illustrates the observed SED, including the excess in the $H\alpha$ filter and shows for comparison Yggdrasil SSP models at selected ages of between 1 Myr and 2 Gyr. As expected, in the blue part of the spectrum shortward of the Balmer break, the SED of the cluster resembles that of SSPs at ~300–400 Myr. However, at the longer wavelength, the SED including the SMS is bluer than that of clusters of this age, as can be seen by the steeper decrease in the flux between 4000 and ~9000 Å. We attribute this to the fact that the SMS+cluster SED is largely dominated by a single star here, whereas the SSP model contains stars with a range of effective temperatures, which “broadens” the SED. This finding implies that multiband observations covering a broad spectral range and with sufficient accuracy could also potentially help to identify the presence of an SMS. However, such differences can be degenerate with reddening and subtle effects of emissions.

### 4.4. Spectroscopy

In addition to narrowband imaging, which can detect the presence of emission lines from the cluster surrounding the SMS, optical spectroscopy can provide similar and potentially additional information that is useful in the quest for SMSs. To illustrate this, we use MUSE integral field observations of the two galaxies studied here.

#### 4.4.1. Emission lines

First, we examine cluster 2838 from NGC 628 already discussed above, whose extracted MUSE spectrum is shown in Fig. 8. The first challenge in this approach is spatial resolution, as already visible from the HST postage stamp of this cluster shown in Fig. 7. Clearly, the MUSE spectrum extracted for this region is a sum of multiple objects (two clusters, presumably), whose contributions are a priori difficult to evaluate. On the other hand, the continuum-subtracted HST $H\alpha$ image shows that cluster 2838 is the sole, or at least clearly dominating, source of $H\alpha$ emission in the MUSE aperture. Therefore, the observed $H\alpha$ emission in the MUSE data, and most naturally also [N II] $\lambda\lambda6548,6584$ emission, originates from 2838.

The estimated equivalent width of the $H\alpha$ emission is $22.5 \pm 1.6$ Å, which is relatively low. The typical $H\alpha$ equivalent width of an H II region surrounding a young stellar population (<5 Myr) can easily exceed 500 Å (and can reach a few thousand angstroms; Leitherer et al. 1999), while for the A2 SMS scenario this is expected to be around 200–400 Å (Martins et al. 2020). The smaller-than-expected estimates of EW($H\alpha$) makes it difficult to explain the properties of this cluster with the A2 SMS+Cluster scenario. We classify the spectrum of 2838 into category 2 clusters in Sect. 4.5.2 and discuss its origin.

#### 4.4.2. Balmer lines in absorption

Apart from $H\alpha$ emission due to ambient gas ionized by the young massive stars surrounding the SMS, spectra of clusters hosting a cool SMS are expected to show absorption features similar to those of an A-type star (see Martins et al. 2020).
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** SED fits of cluster 2838 with SSP models (left) and A2 SMS+Cluster models (right). The red crosses indicate the flux of the best-fit model in each band. The vertical error bar indicates the photometric uncertainty while the horizontal error bar indicates the bandwidth of the filter.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Observed SED of cluster 2838 using six HST bands with a reddening correction corresponding to $E(B-V) = 0.2$. Model SEDs of A2 SMS+Cluster and Yggdrasil models with different ages are also overplotted (flux in F658N/F657N narrow band is not shown for models).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Postage stamps of cluster 2838 in the MUSE white light (top left), HST F555W band (top right), the HST F658N image (bottom left), and the continuum-subtracted F658N ($H\alpha$) image (bottom right). The aperture (0.61") used to extract the spectra is shown in green and the background annulus (1.84" to 2.76") is shown in red. The targeted cluster 2838 is shown in magenta (0.32") and the nearby class 1 cluster (2835) is shown in yellow (0.32").</figcaption></figure>

However, the low S/N of our spectrum makes it hard to investigate these lines. Still, we suspect some absorption lines in the spectrum, such as $H\beta$ (4861.333 Å) and MgH (5176.7 Å). Zoomed in portion around the $H\beta$ line together with a Gaussian fit is also shown in Fig. 8. We therefore measured the equivalent width of the $H\beta$ line of cluster 2838 and other short-listed clusters in the sample (which are discussed in detail in the following sections). The result is shown in Fig. 9. We find typical equivalent widths of $EW(H\beta) \sim 2-14$ Å, except for 2838

with $EW(H\beta) = 19.7 \pm 4.1$ Å from the MUSE spectrum. From the HST F555W image, which shows one neighboring cluster (ID 2835 with an estimated age of ~14 Myr from the cluster catalog) with a similar magnitude within the MUSE aperture, we can correct the continuum flux and hence estimate the intrinsic EW ($H\beta) = 35.1 \pm 4.1$ Å of cluster 2838, assuming $EW(H\beta) = 4.31$ Å for the young cluster (see Fig. 9).
<figure><img src="image_10.png" /><figcaption>**Fig. 8.** MUSE spectrum (blue) and error spectrum (orange) of the candidate SMS-hosting cluster 2838 in NGC 628. Zooms onto the regions around $H\alpha$ and $H\beta$ are also shown in the figure. In the zoomed-in cutout around $H\beta$, a Gaussian fit is also shown in red.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Evolution of the equivalent width of the $H\beta$ absorption line (blue) with age. The equivalent widths of the $H\beta$ of observed clusters are shown as dots (NGC 628 and M 83) and a star (H6 from Brodie et al. (1998)) at the ages derived from SED fits with standard SSPs. The corrected $H\beta$ equivalent width of cluster 2838 is shown by a green triangle.</figcaption></figure>

The measured Balmer line equivalent widths are compared in the same plot to predictions from the recent HR-pyPopStar SSP models (Millán-Irigoyen et al. 2021), which include high-resolution spectral libraries. We used the spectral windows from Brodie et al. (1998) both for the synthetic and observed spectra. In some cases, we first subtracted nebular emission; for example for cluster 61328, which shows both nebular emission and stellar absorption. The model predicts a maximum equivalent width of EW($H\beta$) ≈ 12 Å in absorption around an age of 500 Myr, as expected because A-type stars will dominate the integrated cluster spectrum at this age. Apart from clusters 2838 (NGC 628), 2364 (NGC 628), and 40183 (M 83), the estimated equivalent widths are in relatively good agreement with the SSP model.

In Fig. 9, we also plot the measurement from Brodie et al. (1998), who reported a proto-GC candidate in NGC 1275 that shows strong Balmer lines and a large EW($H\beta$) = 14.77$^{+4.21}_{-4.54}$ Å, which could not be explained by standard SSP models at that time. These authors also point out that to fit the observations with Bruzual & Charlot (1993) models, it is necessary to assume an IMF that favors the formation of a large number of A-type stars. Similarly, other spectroscopic studies of proto-GC candidates show strong Balmer absorption lines, with EWs that could

not be reconciled with the synthesis models available at the time (see e.g., Zepf et al. 1995). However, our comparison with recent SSP models shows that such high equivalent widths are predicted at ages of ~300–500 Myr with normal IMFs.

We also compared the EW($H\beta$) and a measure of the Balmer Break<fnref n="4" /> of our SMS models with predictions from the HR-PyPopstar (Millán-Irigoyen et al. 2021) SSP models and models of individual stars with $log g = 4.5$ from Coelho (2014), which is shown in Fig. 10. From the computations of Martins et al. (2020), the expected EW($H\beta$) ~ 4 Å of the A2 SMS is relatively low for its low effective temperature ($T_{eff}$ = 7000 K), when compared to normal stars of similar $T_{eff}$. This figure shows that joint measurements of the Balmer break and the stellar $H\beta$ absorption should in principle allow us to distinguish bloated SMSs (with properties similar to those of A2) from normal stellar populations.

### 4.5. Consolidation of findings: Clusters with peculiar features and their probable nature

We investigated the spectra of SMS candidate clusters that are within the selection box and show $H\alpha$ emission in NGC 628, and all the massive clusters (>10⁵ $M_{\odot}$) in M 83 within the selection box and its extension to high $E(B-V)$. We investigated the Balmer lines covered by the MUSE spectra ($H\beta$ and $H\alpha$). Based on the $H\alpha$ line strength, we classified the analyzed cluster spectra into four different categories. The first category has a cluster that shows very strong signatures of $H\alpha$ emission (EW($H\alpha$) > 100 Å) and $H\beta$ in emission. In the second category, the clusters show moderate $H\alpha$ emission with an EW($H\alpha$) of ~5–100 Å. In this case, $H\beta$ can be either weakly in emission or in absorption. The clusters in category 3 show very weak $H\alpha$ emission, and $H\beta$ in absorption. The remaining cluster spectra (category 4) include some GCs, some normal clusters of a few hundred million years old, and some very low-S/N spectra for which further investigation is not possible. There are significant numbers of GCs in our shortlisted sample for the spectroscopy follow-up because these are located in the high $E(B-V)$ region in the $m_{F435W}-m_{F555W}$ versus $m_{F336W}-m_{F435W}$ diagram. GCs, or

<footnote n="4">⁴ Here we use the ratio of the mean flux longward and shortward of the break, that is $F_{\lambda}(4000-4100)$ and $F_{\lambda}(3500-3600)$.</footnote>
<figure><img src="image_12.png" /></figure>

**Fig. 10.** Predicted stellar Hβ absorption line strength EW(Hβ) vs a measure of Balmer Break. The red, blue, and magenta triangles show the A2, A4, and B3 SMS models, respectively. The SSP models with an age range of 0.1 Myr–15 Gyr are shown with the red line. Models of individual main sequence stars with log g = 4.5 and varying T<sub>eff</sub> are shown as dots color-coded according to temperature.

in general, category 4 clusters, are out of the scope of this study. We cross-checked all the clusters in M 83 with supernovae (SN; Long et al. 2022) and planetary nebula (PN; Della Bruna et al. 2022a) catalogs and confirmed that the observed Hα emission is associated with the cluster itself, and does not emanate from a known SN or PN. We now discuss the properties of clusters in different categories in detail.

4.5.1. Cluster with strong Hα emission

As mentioned before, cluster 61328 is young in nature given that
it shows strong Hα emission together with [N II] and Hβ in emis-
sion (see Fig. 11). The estimated EW(Hα) is 152.8 ± 22.7 Å and
EW([N II] λ6584) = 31.4 ± 3.5 Å. These values are much smaller
than the typical YSC-hosting regions but are close to the expec-
tations from the SMS scenario (Martins et al. 2020). The esti-
mated EW(Hβ) is 53.4 ± 7.5 Å and F<sub>Hα</sub>/F<sub>Hβ</sub> ≈ 3.5, which indi-
cates significant extinction with E(B − V) ≈ 0.19, or A<sub>V</sub> ≈ 0.77
assuming the Calzetti attenuation law (Calzetti et al. 2000).

The other prominent emission lines in the spectrum are the
[S II] lines at 6716.4 and 6730.8 Å, the [O III] line at 5006.8 Å,
and He I at 5875.6 Å. Although all the Balmer lines within the
MUSE coverage are in emission, there are signatures of a few
absorption lines (see the zoomed portion of Fig. 11). We detect
the Na 5896 Å line in absorption although with low S/N and par-
tially affected by the residuals of a bright sky emission.

Combining spectroscopic and photometric information indi-
cates a composite nature for this cluster. According to the SED
fits (using SSPs), the median age is around 1.9 Gyr with the first
quartile of the PDF around 700 Myr (Della Bruna et al. 2022a),
as it also shows a Balmer break (the m<sub>F336W</sub> - m<sub>F438W</sub> color
of the break is 0.91 ± 0.09 mag). Most likely there is a coin-
cidence between the position of this cluster and an H II region
but because of the old age of the cluster, it was treated as a
chance line-of-sight overlap and is not considered to have a phys-
ical connection by Della Bruna et al. (2022a). Alternatively, the
spectral properties and SED information could also be in agree-
ment with our SMS scenario. However, the SMS scenario faces

<figure><img src="image_13.png" /></figure>

**Fig. 11.** MUSE spectrum of the candidate SMS-hosting cluster 61328 in M 83. A zoomed-in portion of the region between 5600 and 6100 Å is shown within the figure.

some difficulties. Most importantly, the cluster is much fainter
(m<sub>F555W</sub> = 20.98) than expected (see Martins et al. 2020, and
below). Furthermore, the extinction measured from the Balmer
decrement is not sufficient to reconcile the observed colors with
intrinsic model colors, which indicates some inconsistency in the
SED. Apart from that, the emission in the extracted cluster spec-
trum is identical to the background, suggesting that the emission
lines could be the result of poor extraction.

4.5.2. Clusters with moderate Hα emission

The clusters in this category include cluster 2838 (NGC 628), discussed above, and clusters 2364 (NGC 628), 6943 (M 83), 40 183 (M 83), and 70545 (M 83). These show significant Hα emission but are weaker than cluster 61328, with EW(Hα) ranging from ~ 6 to 33 Å. The [N II] λλ6548,6584 lines are also weak. The Hβ line is in emission for clusters 2364 and 70 545, while it might be in absorption (or the absorption component might dominate) or absent in the other clusters. As in the case of cluster 2838, the low S/N of the spectra makes it hard to investigate the Hβ line for several clusters. Cluster 70545 shows a clear detection of the [S II] λλ6717,6731 lines, clusters 2838 and 2364 show a weak detection, and the remaining clusters show no [S II] λλ6717,6731 line emission. The clusters in M 83 show a strong NaD line in absorption, while this is absent in clusters in NGC 628. The other major absorption lines are CaII triplets, which are present in all the clusters.

The age of the clusters ranges from 300 Myr to 4.8 Gyr
according to the SED fits and the SEDs of all the clusters
are reasonably well fitted both with standard SSP models and
with SMS+Cluster models (see Fig. 5 for an example). In
the continuum-subtracted images, the clusters 2838, 6943, and
40183 show centrally concentrated Hα emission, while nearby
H II regions are found in the other two cases, which could explain
the emission lines from these clusters.

In summary, several clusters in this group show the features
expected for a young cluster hosting a cool, A2-like SMS. In
particular, cluster 2838 shows both a very strong Balmer break
– which could originate from the SMS – and nebular emission,
which would indicate the presence of young massive stars sur-
rounding the SMS. Such a combination of apparently young
## 5.2. Normal versus highly embedded clusters

The LEGUS cluster catalog and M83 catalog used in our work contain clusters selected from white-light images (a combination of four or five filters from F275W to F814W). Furthermore, for NGC 628, we selected only clusters detected in all five filters, including the bluest one (F275W), which is not available for M83. This could lead to a bias against very young and strongly reddened clusters with SMSs, which would be undetected in the blue filter(s). From the SED fits (using classical SSP spectra), we find extinctions in the range $E(B-V) \sim 0-1$, with a median of 0.17 (0.89) for the clusters in NGC 628 (M83), that is, no high extinction. On the other hand, if SMS-hosting clusters were significantly reddened and showed a strong Balmer break, then these objects may not be detected in the F275W band and perhaps not even in the F336W band.

The formation scenario of Gieles et al. (2018) for SMSs in proto-GCs foresees this in very gas-rich environments, which could indeed be associated with large amounts of dust and therefore be heavily extinction. However, the model does not make any quantitative prediction for the expected extinction, which could presumably depend on many unknown factors, including the chemical composition (metallicity) of the gas. To the best of our knowledge, there have not yet been any high-resolution studies of very extinction clusters in the two galaxies investigated here. There are ongoing studies exploring the dust-obscured star formation and star clusters with JWST (Kim et al. 2023), but a detailed investigation of the massive embedded clusters has not yet been published. A search for young embedded clusters with HST NIR filters in the LEGUS galaxy NGC 1313 revealed that cluster catalogs based on NUV-optical (like the ones used in this study) may miss up to 40% of young (<7 Myr) clusters (Messa et al. 2021). Future studies with JWST (such as the JWST-FEAST program) will remove this selection bias, and extending searches for SMS-hosting clusters to highly obscured, massive, and compact star-forming regions could be of interest for future studies.

## 5.3. Other possibilities to find SMSs and future work

The strategy presented here to search for the presence of SMSs in proto-GCs and to test the formation scenario proposed by Gieles et al. (2018) can in principle be extended to much larger samples of clusters and to galaxies over a wide range of redshifts. We now briefly discuss such an extension and speculate on other possibilities to search for SMSs or their descendants.

### 5.3.1. SMSs at high redshift

Given the extreme brightness of SMSs, the detection of individual SMSs should be feasible out to very high redshifts with JWST and possibly other facilities (see e.g., Surace et al. 2018, 2019; Martins et al. 2020). Indeed, these models predict that SMSs with luminosities in the range of $log(L/L_\odot) \sim 9-9.3$ (corresponding to masses of the order of a few times $10^4 M_\odot$) have magnitudes up to $m_{AB} \sim 28-30$ in the near-IR at redshifts of $z \sim 5-12$ (the absolute AB magnitude is $\sim -18$ mag), which is within the reach of present-day telescopes.

Gravitational lensing can clearly facilitate such studies, because of the gain it provides in the amplification of unresolved sources and effective spatial resolution, which could help to identify compact young clusters, as demonstrated for example in the pioneering work of Vanzella et al. (2017, 2019), and Bouwens et al. (2021). With multiband photometry from NIR-

CAM/JWST covering the UV, Balmer break, and rest-optical domain, a similar strategy to the one used here should now become applicable at high redshift, as already pointed out by Martins et al. (2020). For first results on high-z star cluster observations with JWST, see for example Vanzella et al. (2022) and Claeysens et al. (2023).

### 5.3.2. Searches for SMSs at other wavelengths

From the predictions of Martins et al. (2020), it seems to be difficult to recognize the presence of SMSs surrounded by a cluster of young massive stars in the UV domain, because the latter dominate the emission in this part of the spectrum. This is also the main factor that motivated us to focus on the rest-optical domain in the present study. Whether SMSs have distinctive features above $\ge 1$ microns remains to be determined. The emission from protostars begins to dominate in the IR regime (Lada 1987; Molinari et al. 2008), which is not included in Martins et al. (2020). The IR-submillimeter regime could also be of interest because a fraction of YMCs are expected to be embedded in the early phase (Messa et al. 2021) and they are only detected in these wavelengths. However, further work is needed to examine whether or not SMSs can be detected using observations of this kind.

Nowak et al. (2022) proposed that SMSs should have accretion disks around them, where the conditions would be appropriate to have masers, which could be observable as so-called kilomasers. These authors modeled the kilomaser spectrum of the nuclear super star cluster W1 in NGC 253 using hydrodynamical simulations. According to these authors, W1 is a potential cluster to host an SMS because its estimated mass is around $4 \times 10^5 M_\odot$ and its age is within 1–2 Myr (Gorski et al. 2019), which is above the minimum mass required to form an SMS and within the expected lifetime of SMSs (Gieles et al. 2018). Their simulations with a $4000 M_\odot$ SMS accurately reproduced the observed maser spectra and pointed out the potential to use kilomasers to identify the SMS-hosting cluster. Follow-up studies of this and other objects could therefore be an interesting alternative method to search for SMSs.

### 5.3.3. Searches for the end stages of SMSs

Observing the end stages of SMSs could be another possibility to identify the existence of such extreme stars. Although the end stages are not yet well modeled, there are a few suggested possibilities. One possibility is that SMSs suffer from various types of instability, such as gravitational, pulsational, and general relativistic (Schwarzschild & Härm 1959; Chandrasekhar 1964; Yungelson et al. 2008; Inayoshi et al. 2013), and completely dissolve into the intracluster medium without showing any direct traces. Another possibility is that SMSs experience pair instability and directly collapse into a black hole (Heger & Woosley 2002; Yungelson et al. 2008). Apart from this, the possibility of a superluminous supernova cannot be completely ruled out. Recently, Nagele et al. (2022) predicted that population III SMSs within the mass range of $(2.6-3.0) \times 10^4 M_\odot$ will undergo a general relativistic instability supernova (GRSN). Also, Moriya et al. (2021) predict the mass range to be around $5.5 \times 10^4 M_\odot$ for GRSNe, which is exactly the mass assumed for the A2 SMS in our scenario. These latter authors also predict that these events can be observed with magnitudes of $m_{AB} \sim 29$ at redshifts up to 15 with JWST. How these predictions for Pop III SMSs can be generalized to SMSs of nonzero metallicity for our
case remains to be examined, but they may provide a good start-
ing point to speculate about their end stages.

**6. Conclusions**

Supermassive stars are of great interest because they could
for example provide the seeds of supermassive black holes
in the early Universe (see e.g., Haemmerlé et al. 2020), and
could play a key role in shaping the chemical and photomet-
ric properties of MSPs in massive star clusters, both young and
old (see Denissenkov & Hartwick 2014; Prantzos et al. 2017;
Gieles et al. 2018). Their formation pathway via runaway col-
lisions is supported by numerical simulations and is indepen-
dent of the formation redshift of their massive host star clus-
ter, meaning that they may exist in both the local and distant
Universe. Depending on the radius (and therefore the effec-
tive temperature) of the SMS in particular, the presence of
these extreme stars in the center of young clusters can lead
to peculiar and distinguishable observational features in their
integrated spectra and SEDs. The most favorable cases are
cool SMSs (T<sub>eff</sub> < 10 000 K), which are predicted to domi-
nate the rest-optical emission of the SMS+cluster system, and
can show very strong Balmer breaks in their integrated spec-
tra (see Martins et al. 2020). Motivated by recent theoretical
predictions of spectra and SEDs of SMSs, by the possibility
that such peculiar objects could be observed with existing and
upcoming facilities (see Surace et al. 2018, 2019; Martins et al.
2020), and by the recent discoveries of proto-GC candidates
at high-redshift (e.g., Vanzella et al. 2017, 2019; Bouwens et al.
2021), we investigated search strategies for proto-GCs hosting
a SMS, focusing first at low redshift. We applied this strategy
to relatively nearby galaxies with HST multiband imaging (from
Adamo et al. 2017, 2015) and spectroscopic integral field obser-
vations obtained with MUSE at the VLT for the first time. Our
main results can be summarized as follows:

- The expanded SMS-hosting clusters show optical colors resembling those of relatively old clusters (~200–600 Myr), despite the fact that they only harbor very young stars (~1–5 Myr). The additional presence of nebular emission lines and/or strong UV emission from the young stars surrounding the central SMS –which are signs of composite spectra– should then be the major distinguishing feature between such “exotic” objects and normal clusters.

- We show that, in principle, color-color diagrams probing the Balmer break, together with Hα photometry and/or spectroscopy and the analysis of the overall SEDs, could potentially allow us to distinguish such peculiar stellar populations (a young cluster hosting a cool SMS) from normal stellar populations. Joint measurements of the Balmer break and the stellar Hβ absorption could also help us to identify SMSs with low T<sub>eff</sub>.

- We applied the proposed search strategy to a sample of more
than approximately 3000 clusters in NGC 628 and M 83
identified from the HST multiband survey (Adamo et al.
2017, 2015). From the color-color diagrams, we identified
about 100 sources (candidates) with strong Balmer breaks.
We then carefully examined the SEDs and spectra of these
objects to search for indications of composite spectra. In
the MUSE IFU spectra, several (21 sources) show signs of
young populations and/or emission lines. In the majority of
cases (13 sources), the emission lines can be attributed to the
presence of multiple clusters or a nearby H II region falling
within the resolution of the MUSE aperture, as judged by
HST broad- and narrowband (Hα) imaging. Following these

inspections, 8 cases (2 clusters from NGC 628 and 6 from
M 83) are left unexplained.

- Qualitatively, these 8 identified clusters show the expected properties of young clusters (producing optical emission lines) hosting a cool SMS (T<sub>eff</sub> ≲ 10 000 K), which produces a strong Balmer break. However, the luminosities of these objects, both in the emission lines (Hα) and in the continuum, are significantly fainter than expected in the presence of a SMS, even considering a minimum mass of ~1000 M<sub>☉</sub> for such objects. From a detailed analysis of all available observations, we conclude that these composite spectra and SEDs are most likely due to a superposition of relatively old clusters with emission from a faint H II, a planetary nebula, diffuse or shocked gas, or from improper background subtraction.

Our search strategy can be applied to much larger samples
of objects and in principle out to very high redshifts. Future
searches should focus on bright clusters (ideally with absolute
V band magnitudes brighter than M<sub>V</sub> ≲ −13) in particular
and also examine strongly obscured clusters, which could cor-
respond to the gas-rich young phase during which the putative
SMS forms.

It is the hope that the strategies presented in this study and
the first practical applications will trigger future studies to search
for the presence of SMSs in proto-GCs and possibly elsewhere
in the Universe.

Acknowledgements. We are thankful to F. Martins for providing some of the supermassive star models and for all the fruitful discussions and suggestions. We thank the anonymous referee also for useful comments and suggestions which helped us to improve the overall presentation of the results. This work was supported by the Swiss National Science Foundation. A.A. acknowledges support from the Swedish Research Council (Vetenskapsrådet project grants 2021-05559).

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