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A dearth of young and bright massive stars in the Small Magellanic Cloud.

AbstractMassive star evolution at low metallicity is closely connected to many fields in high-redshift astrophysics, but poorly understood. The Small Magellanic Cloud (SMC) is a unique laboratory to study this because of its metallicity of 0.2 Zsol, its proximity, and because it is currently forming stars. We used a spectral type catalog in combination with GAIA magnitudes to calculate temperatures and luminosities of bright SMC stars. By comparing these with literature studies, we tested the validity of our method, and using GAIA data, we estimated the completeness of stars in the catalog as a function of luminosity. This allowed us to obtain a nearly complete view of the most luminous stars in the SMC. When then compared with stellar evolution predictions. We also calculated the extinction distribution, the ionizing photon production rate, and the star formation rate. Our results imply that the SMS hosts only 30 very luminous main-sequence stars (M > 40 Msol; L > 10^5 Lsol), which are far fewer than expected from the number of stars in the luminosity range 3*10^4 20 Msol, stars in the first half of their hydrogen-burning phase are almost absent. This mirrors a qualitatively similar peculiarity that is known for the Milky Way and Large Magellanic Cloud. This amounts to a lack of hydrogen-burning counterparts of helium-burning stars, which is more pronounced for higher luminosities. We argue that a declining star formation rate or a steep initial mass function are unlikely to be the sole explanations for the dearth of young bright stars. Instead, many of these stars might be embedded in their birth clouds, although observational evidence for this is weak. We discuss implications for cosmic reionization and the top end of the initial mass function.

Topics: Initial mass function (64%), Stars (63%), Star formation (61%), Metallicity (59%), Small Magellanic Cloud (58%)

Summary (6 min read)

2. Methods

  • To achieve their goal of providing a more complete picture of luminous SMC stars, the authors employ three data sets in this study.
  • The authors then cross-correlate it with the GAIA DR2 catalog.
  • The second data set is retrieved from GAIA DR2 alone .
  • Therefore the authors can use this data set to estimate the completeness of the B10 catalog.
  • The authors aim is to also calculate temperatures and luminosities for stars in the B10 data set, which contains many more stars than the VSS sample.

2.1. Deriving effective temperature and luminosity

  • The authors used the existing studies from the VSS sample of SMC stars , which provide spectral types as well as temperatures, to derive empirical relations of spectral types and effective temperatures (Teff).
  • For stars of A-type and later, the authors used the SMC spectral type - temperature relations of Evans & Howarth (2003) and Tabernero et al. (2018).
  • The authors applied the spectral type - Teff relations to infer effective temperatures for the remaining 5155 sources.
  • The authors find that the predicted and observed colors match best for a reddening of 1 http://www.pas.rochester.edu/˜emamajek/EEM_dwarf_.
  • To test this method, the authors show the luminosities of the sources brighter than log(L/L ) = 4.5 in Fig. 2 for the sources that are included in the VSS sample and in the B10 data set.

2.2. Investigating the completeness with GAIA photometry

  • It still does not contain all of the brightest stars in the SMC.
  • The trends in this second test are very similar to those described in this section.
  • Both of their completeness tests imply a higher completeness than the completeness quoted for O stars in B10 itself (∼4%).
  • There the authors discuss the luminosity distribution of stars in the B10 sample and compare it with theoretical predictions.

3. General population properties

  • Fig. 5 shows the distribution of the B10 sources in the HRD.
  • In Fig. B.5 the authors compare the HRD positions of stars in Fig. 5 to their HRD positions according to the VSS sample (if they are in the VSS sample).
  • The shape of the population also remains almost intact when different spectral type - temperature relations are used, as the authors show in Fig. B.7.
  • The same is true when the authors take a different input catalog (Fig. B.8, where they use Simbad instead of B10).
  • This demonstrates that the results the authors present later on are robust against the choice of assumptions described in Sect.

3.1. Extinction

  • In order to do so, the authors employed the effective temperature and resulting expected intrinsic color (GBP −GRP)int, which they obtained as described in Sect. 2.1. We then obtained the reddening as E(GBP−GRP) = (GBP−GRP)obs− (GBP−GRP)int, where (GBP−GRP)obs is the observed GAIA color.the authors.
  • The brightest stars also tend to have a slightly higher extinction, although only modestly so.

3.2. Ionizing radiation and its escape fraction

  • Potsdam Wolf-Rayet (POWR) stellar atmosphere models (Hamann et al. 2015; Hainich et al. 2019) provide predictions for the ionizing photon production rate (Q) of bright SMC stars.
  • This is under the rough assumption that all the H I ionizing photons are absorbed by neutral hydrogen.
  • This number would decrease when the extinction continued to decrease with λ below 116 nm.
  • Combining the above, it seems most probable that fesc in the SMC is far lower than their upper limit of 0.28.

3.3. Star formation rate

  • Using a Kroupa (2001) IMF to extrapolate toward lower mass stars, the authors calculated the SFR of the SMC.
  • To do this, the authors counted the number of stars above the 18 M track , assuming constant star formation (CSF).
  • In the best-fitting scenario (where the present-day SFR is relatively low), the SFR 7− 10 Myr ago was about three times higher than for the CSF scenario.
  • Because their method is based on counting massive stars, a steeper IMF would result in a higher inferred SFR.

4.1. Blue supergiants

  • Interestingly, about 200 stars in Fig. 5 reside in the region between the main sequence (MS) and the RSG branch.
  • Emission features make it likely that these are late-MS stars that evolved toward critical velocity in isolation (Ekström et al.
  • The reason is that very high overshooting values of αov = 0.55 are necessary for the TAMS to extend that far (Schootemeijer et al. 2019).
  • It therefore appears to be unavoidable to invoke either internal mixing (Langer 1991; Stothers & Chin 1992; Schootemeijer et al. 2019) or binary interaction (Braun & Langer 1995; Justham et al. 2014) to explain their presence.

4.2. Numbers of helium-burning stars and their progenitors

  • The authors counted the helium-burning stars and compared the corresponding expected number of hydrogen-burning stars (based on stellar models) with the observed number of hydrogen-burning stars.
  • Corrected for a completeness of about half (Table 1), this adds up to ∼450 progenitor stars.
  • This poses a modest discrepancy with the expected 650.
  • The fractional core helium-burning lifetime of such stars is about 7% (Schootemeijer et al. 2019).

4.3. Age and relative age distribution

  • The gray dot-dashed line in Fig. 5 denotes the location of stars that are halfway through their MS lifetime.
  • Instead of ∼50% of the stars being in the first half of their MS lifetime, this number is only 7% for the B10 sample.
  • More likely, the explanation for the relatively larger fraction of young stars in the VSS sample could be that this sample is biased towards hot stars simply because of a greater interest in them, and young massive stars tend to be hot.
  • The authors investigate in Fig. 9 whether a decreasing SFR can explain this heavily lopsided distribution of relative ages.
  • From the model population, the authors drew 106 stars with random ages between 0 and 10 Myr, and random masses between 18 and 100 M .

4.4. Luminosity distribution

  • The left panel in Fig. 11 shows the luminosity distribution of the stars shown in their HRD (referred to as ‘observational’; Fig. 5).
  • The authors show the observed luminosity distributions corrected for completeness in the right panel of Fig. 11.
  • Then, the theoretical SFH3 distribution matches the observed distribution best.
  • The uncorrected luminosity distribution is fit best for Γ ≈ −1.9.
  • This means that in principle, the authors can resolve the lack of bright stars by assuming a steeper IMF.

5. Number comparisons

  • In this section the authors discuss the number of massive SMC stars obtained by previous studies.
  • The authors first discuss the studies of the SMC massive star population that have been performed before (Humphreys & McElroy 1984; Blaha & Humphreys 1989; Massey et al. 1995).
  • When stars in WR systems are excluded and completeness is not corrected for, Fig. 5 contains 22 of such massive stars (Sect. 4.2).
  • This is in line with the 0.5 dex difference between the uncorrected theoretical CSF luminosity distribution and the observed distribution without WR stars above log(L/L ) = 5.5 in the left panel of Fig. 11.
  • The number of helium-burning star progenitors is also significantly lower than the authors would expect a priori.

6.1.1. Steeper initial mass function

  • In principle, a steeper IMF could help to explain the lack of bright stars.
  • A steeper universal IMF would have dramatic implications for the early universe because it is commonly thought that toward lower metallicity, massive stars become more common (Larson & Starrfield 1971; Schneider et al. 2018b).
  • This is currently an unsatisfying explanation because it cannot resolve the apparent lack of young stars.
  • An explanation that would have to be ruled out is a bias against young stars (Sect. 6.1.6): because very massive stars (which live only for a short time) tend to be young, such a bias would make the IMF appear steeper than it really is.
  • Moreover, the SFR in the SMC could be low enough for stochasticity to play a role (see da Silva et al. 2012).

6.1.2. Model uncertainties

  • In principle, the stellar models of Schootemeijer et al. (2019) that the authors used could overpredict stellar temperatures and therefore the inferred stellar ages.
  • This is significantly larger than the shift of 0.05 dex for stars at critical rotation (Paxton et al. 2019).
  • The authors conclude that rotation and envelope inflation are unlikely to affect their conclusions about the dearth of young stars.
  • This is meant to explain why the distribution of their sample stars in the HRD avoids cool temperatures above the 32 M track (cf. their fig.
  • The reason is that they show a significant amount of hydrogen at their surfaces, which means that if they were chemically homogeneous, they would burn hydrogen in their cores.

6.1.3. Star formation history

  • The authors have shown that it can explain both the lack of young and the lack of bright stars.
  • If the SFH is the explanation for the inferred lack of young stars, the SFR accordingly needs to have been quenched throughout the entire SMC at the same time.
  • A dearth of young massive stars has been seen in different environments.
  • It is even more unlikely that something similar happened in the two other local, but separated, star-forming environments: the LMC and the Milky Way.

6.1.4. Observational biases

  • Related to the ‘embedding’ scenario described below in Sect. 6.1.6, observational biases might be at play.
  • B.1 that the B10 sample is complete enough for biases not to affect their conclusions about the dearth of young and bright stars.
  • Next, the authors visually inspected UV images from Cornett et al. (1997), taken with the Ultraviolet Imaging Telescope (their fig.
  • Therefore the authors deem the unresolved cluster explanation to be highly unlikely, as long as the bright young stars are not embedded (Sect. 6.1.6 and 6.2).

6.1.5. Binary companions

  • Because luminosity scales strongly with mass, the error will be significantly smaller for unequal-mass binaries.
  • To what extent this can change the apparent spectral types is not easy to gauge from first principles.
  • It is unlikely that unresolved binary companions could systematically shift the apparent spectral types of the population by that much.
  • An explanation of the factor-of-a-few underabundance of WR star progenitors (Sect.4.2) and of stars with log(L/L ) > 5.5 in the luminosity distribution (Sect.4.4) would still require an extreme increase in multiplicity of stars towards the high-mass end.

6.1.6. Embedding in birth clouds

  • Another possible explanation for the lack of young and bright stars could be that young stars are still embedded in the clouds from which they are born.
  • Naively, the authors might expect young stars in lowmetallicity environments to be less obscured because there is less dust.
  • The duration of the embedding may be more relevant than the duration of the accretion phase to explain the lack of young massive stars.

6.2. Implications of the embedding scenario

  • A decrease in SFR and a prolonged embedding phase appear to be the most likely to simultaneously explain the dearth of young and bright stars.
  • The authors discuss the plausibility and implications of the embedding scenario below.
  • If massive stars are embedded in their birth cloud for a relatively long part of their life, there must be a large number of such objects in the SMC.
  • Several dozen to several hundreds of both massive YSOs and compact H II regions are indeed observed.
  • The authors tested this prediction by examining observational studies in different wavelength regimes.

6.2.1. Infrared observations

  • It contains 984 ’intermediate- to high-mass’ YSO candidates.
  • The authors present physical parameters of 452 of these, which they can fit well to YSO models.
  • For 3 of these, their temperatures above 32 kK fall in the O-star range (Table A.1) while also luminosities above log(L/L ) = 4.5 are derived.
  • From the analysis of the Sewiło et al. (2013) catalog, the authors conclude that the current observations fail to agree directly with the embedding scenario.
  • This scenario would only be plausible if many other embedded hot massive stars were not in this catalog.

6.2.2. Radio observations of (ultra-)compact H II regions

  • It is not known how complete this catalog is, therefore the true number could be higher.
  • Moreover, compact H II regions could theoretically harbor more than one young bright star.
  • Conversely, it is not evident that every compact H II region in the Wong et al. (2012) catalog contains a star that matches the criteria of their missing hot and bright stars.
  • The authors conclude that observations of (ultra-)compact H II regions neither rule out nor confirm the presence of several hundred deeply embedded young and bright stars.

6.2.3. Submillimeter observations

  • Star-forming regions harboring proto- and young stellar objects can also be identified by their submillimeter dust emission.
  • The APEX Telescope Large Area Survey of the Galaxy has provided a map of 870 µm emission in the Galactic disk using the Atacama Pathfinder 12 m submm telescope (APEX, Schuller et al. 2009).
  • This claim is supported by the fact that in the Milky way, deeply embedded O-type stars have been confirmed (e.g., Messineo et al. 2018).
  • A survey of 1100 µm dust emission in the SMC with the ASTE 10- meter telescope was sensitive to condensations with molecular gas masses in excess of 104 M (Takekoshi et al. 2017), which is on the same order as the mass limit estimated from ATLASGAL.
  • Regardless of the exact assumptions, APEX or any other singledish submm telescope could detect only rather large star-forming associations in the SMC.

6.2.4. Theoretical expectations

  • The authors also briefly considered the embedding scenario from the theoretical side.
  • With such high extinction, they would most likely not pass the selection criteria for studies at optical wavelengths aimed at massive stars on the MS; if they would, their method would underestimate their luminosity by at least two orders of magnitude, so that they would not show up in their Fig.
  • The authors adopted the approximation that the stars in the first half of their MS lifetime are deeply embedded in their birth cloud (cf. Fig. 9).
  • The result would be that H I ionizing photons are emitted by MS stars at a rate that is four times lower than if embedding does not play a role (half of the stars are obscured, the average unobscured star has half the H I ionizing photon emission rate; see Fig.7).
  • This in turn would cause the SFR inferred from Hα emission to be underestimated.

7. Conclusions

  • The authors have used literature data to obtain a nearly complete overview of the brightest stars in the SMC.
  • This means that the embedding scenario is challenged as well unless more of such objects are found.
  • The authors suggest to further investigate the currently unsolved issue of the dearth of young and bright stars.
  • Comprehending the dearth of young and bright stars in the SMC is crucial because the SMC is at this point their main stepping stone toward a better understanding of massive star evolution in the early universe.
  • The authors thank the referee Tomer Shenar for a very constructive referee report, which was highly valuable for improving the discussions in the paper.

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Astronomy & Astrophysics manuscript no. main © ESO 2020
December 14, 2020
A dearth of young and bright massive stars in the Small Magellanic
Cloud
A. Schootemeijer
1
, N. Langer
1,2
, D. Lennon
3,4
, C. J. Evans
5
, P. A. Crowther
6
, S. Geen
7
, I. Howarth
8
, A. de Koter
7
, K.
M. Menten
2
, and J. S. Vink
9
1
Argelander-Institut f
¨
ur Astronomie, Universit
¨
at Bonn, Auf dem H
¨
ugel 71, 53121 Bonn, Germany
e-mail: aschoot@astro.uni-bonn.de
2
Max-Planck-Institut f
¨
ur Radioastronomie, Auf dem H
¨
ugel 69, 53121 Bonn, Germany
3
Instituto de Astrof
´
ısica de Canarias, E-38200 La Laguna, Tenerife, Spain
4
Departamento de Astrof
´
ısica, Universidad de La Laguna, E-38205 La Laguna, Tenerife, Spain
5
UK Astronomy Technology Centre, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
6
Department of Physics and Astronomy, University of Sheeld, Sheeld, S3 7RH, UK
7
Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
8
University College London, Gower Street, London WC1E 6BT, UK
9
Armagh Observatory, College Hill, Armagh BT61 9DG, UK
Received September ; accepted
ABSTRACT
Context. Massive star evolution at low metallicity is closely connected to many fields in high-redshift astrophysics, but is poorly
understood so far. Because of its metallicity of 0.2 Z
, its proximity, and because it is currently forming stars, the Small Magellanic
Cloud (SMC) is a unique laboratory in which to study metal-poor massive stars.
Aims. We seek to improve the understanding of this topic using available SMC data and a comparison to stellar evolution predictions.
Methods. We used a recent catalog of spectral types in combination with GAIA magnitudes to calculate temperatures and luminosities
of bright SMC stars. By comparing these with literature studies, we tested the validity of our method, and using GAIA data, we
estimated the completeness of stars in the catalog as a function of luminosity. This allowed us to obtain a nearly complete view of
the most luminous stars in the SMC. We also calculated the extinction distribution, the ionizing photon production rate, and the star
formation rate.
Results. Our results imply that the SMS hosts only 30 very luminous main-sequence stars (M 40 M
; L & 3 · 10
5
L
), which
are far fewer than expected from the number of stars in the luminosity range 3 · 10
4
< L/L
< 3 · 10
5
and from the typically
quoted star formation rate in the SMC. Even more striking, we find that for masses above M & 20 M
, stars in the first half of their
hydrogen-burning phase are almost absent. This mirrors a qualitatively similar peculiarity that is known for the Milky Way and Large
Magellanic Cloud. This amounts to a lack of hydrogen-burning counterparts of helium-burning stars, which is more pronounced for
higher luminosities. We derived the H I ionizing photon production rate of the current massive star population. It agrees with the H α
luminosity of the SMC.
Conclusions. We argue that a declining star formation rate or a steep initial mass function are unlikely to be the sole explanations for
the dearth of young bright stars. Instead, many of these stars might be embedded in their birth clouds, although observational evidence
for this is weak. We discuss implications for the role that massive stars played in cosmic reionization, and for the top end of the initial
mass function.
Key words. Stars: massive Stars: early-type Stars: evolution Galaxies: star formation Galaxies: stellar content
1. Introduction
Massive stars in low-metallicity environments are linked to
spectacular astrophysical phenomena, such as mergers of two
black holes (Abbott et al. 2016), long-duration gamma-ray
bursts (Graham & Fruchter 2017), and superluminous super-
novae (Chen et al. 2017). Moreover, massive stars are thought
to have played a crucial role in providing ionizing radiation and
mechanical feedback in galaxies in the early universe (Hopkins
et al. 2014).
Massive star evolution at low metallicity therefore is of
great importance, but it is also poorly understood. For exam-
ple, some theoretical predictions suggest that very massive stars
are more more likely to form in low-metallicity environments
(e.g., Larson & Starrfield 1971; Abel et al. 2002), although the
arguments for this are debated (Keto & Wood 2006; Krumholz
et al. 2009; Bate 2009; Kuiper & Hosokawa 2018). This in turn
would have important consequences for the extent to which these
astrophysical phenomena take place. While studies of individ-
ual stars in the early universe are currently not feasible, a re-
cent analysis of the starburst region 30 Doradus in the nearby
Large Magellanic Cloud (half the solar metallicity) did indeed
find an overabundance of very massive stars (Schneider et al.
2018b). This overabundance would be in line with the predic-
tions mentioned above, but it is currently unknown if metallicity
eects and/or environmental eects cause this excess of massive
stars. Neither do we know whether this trend continues toward
lower metallicity. Because it has only about one-fifth of the solar
metallicity (Hill et al. 1995; Korn et al. 2000; Davies et al. 2015),
a better understanding of the Small Magellanic Cloud (SMC) is
a crucial stepping stone. Earlier studies have been unable to find
indications of an overabundance of massive stars in the SMC,
1
arXiv:2012.05913v1 [astro-ph.GA] 10 Dec 2020

A. Schootemeijer et al.: A dearth of young and bright massive stars in the Small Magellanic Cloud
however (Blaha & Humphreys 1989; Massey et al. 1995). For
field stars in the SMC, Lamb et al. (2013) derived an exponent
of Γ = 2.3 for the initial mass function (IMF), which is much
steeper than the canonical Salpeter exponent of Γ = 1.35 (with
dN M
Γ
d log M, where N is the number of stars that are born,
and M is the stellar mass).
In addition to the IMF, there is much to gain from a more
complete picture of the massive star content of the SMC. A
prevalence of blue supergiants can constrain internal mixing
(Schootemeijer et al. 2019; Higgins & Vink 2020) and bi-
nary interaction (Justham et al. 2014). Moreover, models of
gravitational wave progenitors (e.g., de Mink & Mandel 2016;
Marchant et al. 2016; Belczynski et al. 2016; Kruckow et al.
2018), of which the physical assumptions are extrapolated to-
ward low metallicity, can be put to the test. Furthermore, we can
investigate the amount of ionizing radiation that is emitted by
massive stars at low metallicity.
A main tool that is used to test stellar evolution predictions is
the Hertzsprung-Russell diagram (HRD). This has been applied
for the SMC massive star population in dedicated studies pub-
lished about two to three decades ago. They used two dierent
approaches: photometry, and spectroscopy. Massey (2002) and
Zaritsky et al. (2002) took the first approach and mapped U BV
magnitudes of SMC sources, which are indications for the lo-
cation of these sources in the HRD. While these studies can be
expected to be highly complete, they lack accuracy in predict-
ing the eective temperatures and luminosities of hot stars (e.g.,
Massey 2003). Eective temperatures can be predicted more ac-
curately from spectral types, which then also reduces the uncer-
tainty in luminosity. Blaha & Humphreys (1989) and Massey
et al. (1995) have used this method to compile HRDs of bright
SMC stars. Inevitably, the completeness of their input catalogs is
lower than for the photometry catalogs. The main focus of these
studies was the IMF, which they found to be consistent with the
IMF in the Milky Way (see the discussion above).
Since then, various developments in the field of observa-
tional astronomy have taken place that allow a major leap for-
ward. First, spectral types of many more SMC stars have be-
come available, which have been compiled in the catalog of
Bonanos et al. (2010), hereafter referred to as B10. Second, the
second data release (DR2) of the all-sky GAIA survey (Gaia
Collaboration et al. 2018) provides a spatially complete catalog
of SMC sources with information on their magnitudes and mo-
tions, thereby yielding information about which sources are in
the foreground. Third, detailed atmosphere analyses on subsets
of massive SMC stars (Trundle et al. 2004; Trundle & Lennon
2005; Mokiem et al. 2006; Hunter et al. 2008b; Bouret et al.
2013; Dufton et al. 2019; Ramachandran et al. 2019) can im-
prove our understanding of how eective temperature correlates
with spectral type. They also enable a systematic verification of
the reliability of the HRD positions based on spectral types. In
summary, new observations allow a large improvement in terms
of sample size, accuracy, completeness assessment, and identifi-
cation of foreground sources.
Our goal is to fully exploit these new observations. We use
them to provide an extinction distribution, ionizing photon emis-
sion rates, and the relations of spectral type and temperature for
massive SMC stars, and most importantly, also the improved
HRD. This paper is organized in the following way. In Sect. 2 we
describe our methods and the catalogs we used. Then, in Sect. 3,
we present the general properties of the stars in our sample. In
Sect. 4 we perform an in-depth analysis of features of the mas-
sive star population in the SMC. We find that it contains only
a few bright stars and young stars. This is the main result of
this paper. We further discuss our main result in Sect. 5, where
we compare numbers. In Sect. 6 we consider possible explana-
tions for our main result: a steeper IMF, model uncertainties, star
formation history, observational biases, unresolved binaries, and
embedding in birth clouds. Finally, we present our conclusions
in Sect. 7.
2. Methods
To achieve our goal of providing a more complete picture of lu-
minous SMC stars, we employ three data sets in this study. We
describe them in detail in Appendix A. The first and most essen-
tial data set is retrieved from the B10 spectral type catalog (their
table 1). We then cross-correlate it with the GAIA DR2 catalog.
Out of the 5324 B10 sources, we find a match in 5304 cases. All
of these have listed G magnitudes in GAIA DR2. We note that
only 3000 sources have a V magnitude listed in the B10 cata-
log. As a result, the use of G magnitudes improves the number of
sources for which we can calculate a luminosity. Out of the 5304
matched sources, 5269 pass our foreground test (Appendix A).
We discuss potential biases in the B10 catalog in Sect. 6.1.4.
The second data set is retrieved from GAIA DR2 alone
(again, see Appendix A for details). The completeness of GAIA
DR2 (see Gaia Collaboration et al. 2018; Arenou et al. 2018) is
essentially 100% in the magnitude range of our sources of inter-
est, which extends to G 16. Therefore we can use this data set
to estimate the completeness of the B10 catalog.
The third data set is a compilation of literature data in which
atmosphere analyses have been performed on a sample of bright
SMC stars. This data set is referred to as the various spectro-
scopic studies (VSS) sample, and is extracted from the studies of
Trundle et al. (2004), Trundle & Lennon (2005), Mokiem et al.
(2006), Hunter et al. (2008b), Bouret et al. (2013), Dufton et al.
(2019), and Ramachandran et al. (2019). The VSS data set con-
tains temperatures and luminosities, while the other two do not.
It consists of 545 sources. Of these, 160 fall in the luminosity
range of our main HRD (log(L/L
) > 4.5; Fig. 5).
Our aim is to also calculate temperatures and luminosities for
stars in the B10 data set, which contains many more stars than
the VSS sample. We use relations of spectral type and temper-
ature to calculate eective temperatures of the stars in the B10
data set. For OB-type stars, we derive our own relations based on
data from the VSS sample. For A-types and later, we use exist-
ing relations. Then, we use their GAIA G magnitudes to obtain
a luminosity and place the B10 sources in an HRD. We describe
these procedures in more detail in Sect. 2.1, and we explain our
estimation of the B10 completeness with the GAIA data set in
Sect. 2.2.
2.1. Deriving effective temperature and luminosity
We used the existing studies from the VSS sample of SMC stars
(last paragraph of Appendix A), which provide spectral types as
well as temperatures, to derive empirical relations of spectral
types and eective temperatures (T
e
). For each spectral type,
we took the average derived temperature. We did this separately
for stars with luminosity class (LC) V+IV, LC III+II, and LC
I. When only one star of a certain spectral type was available,
the temperature that we adopted was the average of its derived
temperature and the temperatures we found for the two neigh-
boring types. As an example: for spectral type B0, a neighbor-
ing type is O9.7, and a neighbor of a neighbor would be O9.5.
Next, for all spectral types that have neighbors and neighbors-of-
neighbors at either side, we smoothed the relations of spectral
2

A. Schootemeijer et al.: A dearth of young and bright massive stars in the Small Magellanic Cloud
O2 O4 O7 B0 B5 B9
Spectral type
10
15
20
25
30
35
40
45
50
T
eff
[kK]
P13
LC V&IV
LC III&II
LC I
Fig. 1. Derived relations of spectral types and eective tempera-
tures (crosses) for dierent luminosity classes (LCs). The solid
gray line shows the relation for Galactic dwarf stars (P13; Pecaut
& Mamajek 2013).
type and temperature. Illustrated for type B0, the applied for-
mula is as follows: T
e,B0,smooth
= (0.25T
e,O9.5
+ 0.5T
e,O9.7
+
T
e,B0
+ 0.5T
e,B0.2
+ 0.25T
e,B0.5
)/2.5.
The resulting spectral type - T
e
relations are shown in Fig. 1
and Table A.1. For stars of A-type and later, we used the SMC
spectral type - temperature relations of Evans & Howarth (2003)
and Tabernero et al. (2018). We compared our results with rela-
tions for Galactic dwarf (LC V) stars (from Pecaut & Mamajek
2013, their extended table 5)
1
. The evolved LC I stars are cooler
than dwarf stars that have the same spectral type. Moreover,
early-type dwarfs at low metallicity are hotter than their Galactic
counterparts with the same spectral type. These two trends are in
line with the trends shown in Trundle et al. (2007). The trend for
types earlier than O7 is not in line with these trends; the line for
LC III and II stars lies above the values for LC V and IV stars.
However, the LC III and II line there has only one data point as
a consequence of how rare such stars are, so that some scatter
can be expected. The typical dierences between the Pecaut &
Mamajek (2013) spectral type - T
e
relations and ours do not
exceed 1 2 kK.
We were unable to convert the spectral type of 114 sources
in the B10 data set into a temperature (e.g., ‘Be? + XRB’). We
applied the spectral type - T
e
relations to infer eective tem-
peratures for the remaining 5155 sources. When the temperature
was known, the bolometric correction (BC) in the G band was
taken from the MIST (Dotter 2016; Choi et al. 2016) website
2
.
Because the surface gravity of most of the sources in the B10
data set is unknown, we used the BCs for log g = 3. At higher
and lower log g, these BCs match temperature values that are
typically well within 1 kK. In the B10 data set, 116 sources have
the label ‘binary’. We used the spectral type that is mentioned
first for them and further treated them as single stars. We high-
light them in Fig. B.10.
For stars in the VSS sample, we compared the GAIA col-
ors that are predicted for their eective temperatures to their
observed GAIA colors. The predicted colors are calculated
as BC(G
BP
) BC(G
RP
) as given by MIST. We find that the
predicted and observed colors match best for a reddening of
1
http://www.pas.rochester.edu/
˜
emamajek/EEM_dwarf_
UBVIJHK_colors_Teff.txt
2
http://.waps.cfa.harvard.edu/MIST/model_grids.html,
where we take those with the label ‘DR2Rev’
4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2
log(
L
B10
/
L
)
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
log(
L
VSS
/
L
) log(
L
B10
/
L
)
Fig. 2. Dierence between the logarithm of the luminosities re-
ported in the various spectroscopic studies (VSS) sample and
those derived by our method using spectral types of B10 as
a function of log(L
B10
/L
). Each dot represents an individual
source. The dotted line shows where L
B10
= L
VSS
; the solid line
is a linear fit to the scatter points.
E(G
BP
G
RP
) = 0.14. This value corresponds to an extinction of
A
G
= 0.28 in the G band and A
V
= 0.35 in the V band (table 3
from Wang & Chen 2019, see also Gordon et al. 2003). We use
these extinction values throughout the paper.
Furthermore, we adopted a distance modulus (DM) of the
SMC of 18.91 (Hilditch et al. 2005). Then we calculated the
absolute bolometric magnitude of a source using
M
bol
= m
G
+ BC DM A
G
, (1)
which is translated into luminosity using log(L/L
) =
0.4(M
bol
M
bol,
). Here, we adopt a solar value of M
bol,
=
4.74.
To test this method, we show the luminosities of the sources
brighter than log(L/L
) = 4.5 in Fig. 2 for the sources that are
included in the VSS sample and in the B10 data set. On the y-
axis we show the dierence between the luminosity reported in
the VSS sample and the luminosity we obtained with our method
based on the B10 data set. The black line, showing a linear fit,
indicates that there is no systematic oset between the luminosi-
ties derived by our B10 method and the VSS literature values.
The values of log(L
VSS
/L
) log(L
B10
/L
) have a standard de-
viation of σ = 0.13 dex.
2.2. Investigating the completeness with GAIA photometry
Although the B10 catalog contains more stars than the VSS
sample, it still does not contain all of the brightest stars in the
SMC. We can expect the GAIA data to be much more complete.
This is supported by the fact that we found a GAIA counter-
part for 99.6% of the B10 sources; see also a discussion of this
in Appendix B.1. Unfortunately, however, GAIA colors are less
accurate in determining eective temperatures (and therefore lu-
minosities) than spectral types, and the results strongly depend
on extinction. This is especially true for the hotter stars.
Using GAIA colors and magnitudes, we therefore cannot in-
dividually derive reliable luminosities for our sources. However,
the colors and magnitudes can be used to estimate the complete-
ness of an ensemble of stars, in this case, the B10 catalog. With
‘completeness’ we mean the completeness fraction of hot, bright
stars that can be identified as such by the relevant observational
approaches, that is, spectroscopy, and/or photometry in the opti-
cal.
3

A. Schootemeijer et al.: A dearth of young and bright massive stars in the Small Magellanic Cloud
3.63.84.04.24.44.64.85.0
log(
T
eff, phot
/
K
)
4.6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
6.2
log(
L
phot
/
L
)
15 19
27 35
88 131
130 231
236 563
284 732
N
B10
N
GAIA
A
V
= 0.35
GAIA
B10
Fig. 3. Hertzsprung-Russell diagram of bright SMC sources con-
structed with GAIA photometry. Black markers indicate sources
from the GAIA sample. The smaller red markers are sources in
the B10 sample. Therefore, red points with black edges (all but
one of the red points, see Appendix A) are sources that are listed
in both samples. We count the number of sources that are hotter
than 10
3.8
K for both samples in dierent luminosity intervals.
The numbers are displayed on the left side of the plot. The lu-
minosity intervals are indicated by dashed blue lines. For com-
pleteness, we also show the cool sources with crosses.
Table 1. Number of stars with T
e
& 10
3.8
K counted in dierent
luminosity intervals.
log(L
B10
/L
) N
B10
N
GAIA, phot
N
B10
/N
GAIA, phot
5.75+ 15 19 0.79
5.50-5.75 27 35 0.77
5.25-5.50 88 131 0.67
5.00-5.25 130 231 0.56
4.75-5.00 236 563 0.42
4.50-4.75 284 732 0.39
Total 780 1640 0.47
We used GAIA photometry, and again MIST BCs, to calcu-
late the photometric temperature and luminosity of the B10 and
GAIA sources
3
: T
e, phot
and L
phot
. We then plotted them in an
HRD that we refer to as the ‘photometric HRD’ (Fig. 3). Next,
we used this HRD to estimate the completeness of the B10 cat-
alog as a function of luminosity. For this estimate we also used
an HRD for which we used B10 spectral types instead of GAIA
colors (Fig. 5), as we explain below. We only considered temper-
atures above T
e
= 10
3.8
K because for cooler temperatures we
rely on the results of Davies et al. (2018) on cool, bright SMC
stars. The way we operate is described below.
1. We counted the number of sources in Fig. 5 in dierent lu-
minosity intervals. The numbers are listed under N
B10
in
Table 1. For example, in Fig. 5 we count 15 stars above
log(L
B10
/L
) = 5.75.
3
The observed GAIA color is used to infer a temperature. Apart from
this, the procedure is the same as described in Sect. 2.1.
4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2
log(
L
phot
/
L
)
4.50
4.75
5.00
5.25
5.50
5.75
6.00
6.25
log(
L
/
L
)
VSS
B10
Fig. 4. Correlation between the luminosity of sources as calcu-
lated using their GAIA color and magnitude (L
phot
) and the lu-
minosity of the same source derived in various spectroscopic
studies (VSS) or its luminosity based on the temperature derived
from the spectral type listed in B10.
2. Then we examined the photometric HRD (Fig. 3), from high
to low luminosity. In this example we considered the 15
brightest stars in B10, which represent the log(L
B10
/L
) >
5.75 bin.
3. We counted the number of GAIA sources until we found 15
sources that were also in the B10 catalog. We took this ap-
proach to have the same number of B10 sources in each lumi-
nosity bin. This counting in Fig. 3 took place in the intervals
that are separated by dashed blue lines. They do not by def-
inition coincide exactly with the luminosity intervals listed
in the left column of Table 1. In this example at the bright
end, we count N
GAIA, phot
= 19. For the log(L
B10
/L
) > 5.75
bin, we thus estimate that it has a completeness fraction of
15/19 = 0.79.
4. We repeated this for each luminosity interval (i.e., also for
5.50 < log(L
B10
/L
) < 5.75 with the 16th to 42nd bright-
est star from the B10 catalog method, etc.) listed in Table 1
to calculate the completeness fraction of the B10 catalog:
N
B10
/N
GAIA, phot
.
Fig. 3 and Table 1 show that the completeness level of the
B10 catalog is 70% to 80% for the brightest sources. The com-
pleteness drops below 40% around log(L/L
) = 4.5.
For this estimate to be reliable, the values of L
B10
and L
phot
need to be similar for most of the stars. We note that if L
phot
had no predictive power, we would expect to measure the same
completeness in all luminosity bins. We investigate this further
in Fig. 4, where we compare L
phot
of the sources to their VSS lu-
minosity and the luminosity calculated using their B10 spectral
type. This figure shows that while the scatter is large, the lumi-
nosities obtained with GAIA photometry on average give a good
indication in which luminosity segment most sources belong.
In Appendix B.1 we provide another (simpler) test in which
we count blue sources in the B10 and GAIA DR2 catalogs. The
trends in this second test are very similar to those described in
this section.
Both of our completeness tests imply a higher completeness
than the completeness quoted for O stars in B10 itself (4%).
However, their number is based on an estimate of 2800 O stars of
M > 20 M
from the conference proceedings of Massey (2010).
This number is in turn based on U BV photometry from Massey
(2002). In their table 8b, all 70 blue stars that are known to have
O types have a photometry-derived temperature in the O-star
regime. Because of the uncertainties in determining the tem-
4

A. Schootemeijer et al.: A dearth of young and bright massive stars in the Small Magellanic Cloud
3.63.84.04.24.44.64.8
log(
T
eff
/
K
)
4.50
4.75
5.00
5.25
5.50
5.75
6.00
6.25
log(
L
/
L
)
0.5
t
MS
W1
W2
W3
W4
W5
W6(O)
W7(O)
W8(O)
W9
W10
W11
W12
A
V
= 0.35
sc
= 10
ov
= 0.33
16M
20M
25M
32M
40M
50M
80M
Fig. 5. Hertzsprung-Russell diagram of luminous stars in the SMC. Red dots represent sources from the B10 data set. Open dark
red squares are red supergiants from Davies et al. (2018), where the T
e
is obtained using relations from Tabernero et al. (2018).
We show the Wolf-Rayet stars (Hainich et al. 2015; Shenar et al. 2016, 2017) labeled with a ‘W’ and their identifying number. Whe
they have an O-star companion that is brighter in the V-band, we show this instead (indicated by ‘(O)’). We also show evolutionary
tracks of Schootemeijer et al. (2019) with a semiconvection parameter of α
sc
= 10, and an overshooting parameter of α
ov
= 0.33.
Solid lines indicate hydrogen- and helium-core burning phases; dashed lines indicate the in between phase. The dash-dotted gray
line shows the location of these models halfway through their main-sequence (MS) lifetime, t
MS
.
peratures of hot stars with photometry (e.g., Massey 2003), this
means that flagging many B-type stars as O-type stars seems un-
avoidable with this method. This has also been argued by Smith
(2019), and we refer to Appendix B.1 for a quantitative discus-
sion that supports this view. It therefore seems likely that the
O-star completeness fraction quoted in B10 is severely underes-
timated.
In the Simbad catalog
4
, we inspected the four most luminous
sources in Fig. 3 that are not in the B10 catalog. From high to low
luminosity in Fig. 3, these are i) Sk 177 (Sanduleak 1969) with
the unusable spectral type information of ‘OB’; ii) the O5.5 V
star of log(L/L
) 5.3 in Lamb et al. (2013); iii) Sk 183, which
4
http://simbad.u-strasbg.fr
is an O3 V star with log(L/L
) = 5.66 (Evans et al. 2012); and
iv) a source without information on spectral type.
We return to the luminosity-dependent completeness fraction
presented in Table 1 in Sect. 4.4. There we discuss the luminos-
ity distribution of stars in the B10 sample and compare it with
theoretical predictions.
3. General population properties
Fig. 5 shows the distribution of the B10 sources in the HRD. It
contains 780 stars with T
e
> 10
3.8
K that are more luminous
than 10
4.5
L
. Below T
e
= 10
3.8
K, we rely on the red super-
giant (RSG) sample of Davies et al. (2018), which we overplot
on the HRD. To avoid duplicates, the B10 sources in this low-
5

Figures (27)
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