&=&\mathbb{A}\langle\langle\cdot\rangle\rangle_{\alpha_{1}}\langle\underline{j_{2}}_{E}\rangle_{\alpha_{2}}..\langle\underline{j_{n}}_{E}\rangle_{\alpha_{n}}&=&C^{s}_{\mid\langle\cdot\rangle\mid\underline{j_{2}}_{E},..,\underline{j_{n}}_{E}}.\end{array}$

Where
$C^{s}_{\mid\langle\cdot\rangle\mid\underline{j_{2}}_{E},..,\underline{j_{n}}_{E}}$
is the notation defined in the statement of Proposition 6. Note that
$\underline{j_{2}}_{E},\ldots\underline{j_{n}}_{E}$ are terms, as they are
defined as the decoding of MAM states, which are always terms. Therefore, we
can apply Proposition 6, obtaining that
$C^{s}_{\mid\langle\cdot\rangle\mid\underline{j_{2}}_{E},..,\underline{j_{n}}_{E}}$
is a non-applying leftmost context.∎

prop:leftmost-beta-proj

###### Proof

The proof is exactly the same as the one for $\beta$-projection of the EXAM
(Theorem 7.1) except that the use of the external context read-back lemma
(Lemma 5) is replaced by the leftmost context read-back lemma above (Lemma
6).∎

coro:lexam-correctness

###### Proof

Simply apply the theorem about sufficient conditions for implementations
(Theorem 3.1) using overhead transparency (Proposition 4), which holds for any
pool template, and leftmost $\beta$-projection above (Proposition 7).∎

##  Appendix 0.F Evaluations to Runs

prop:overhead-termination

###### Proof

Note that if $s$ is $\leadsto_{\mathtt{o}}$-normal then all the jobs in (the
support of) its pool (if any) have shape $(\lambda x.t,u:S)_{\\_}$, so that
$|s|_{\mathtt{o}}=0$. Moreover, by definition $|s|_{\mathtt{o}}\geq 0$, and
$|s|_{\mathtt{o}}$ is finite because by the local scope invariant (Lemma 3)
the environment is acyclic. Then, the statement follows from the fact that
$|s|_{\mathtt{o}}$ decreases of exactly 1 for every $\leadsto_{\mathtt{o}}$
transition, as we now prove. Cases:

  1. 1.

_Application search ( $\leadsto_{\mathtt{sea}_{@}}$)._

$\begin{array}[]{rcl}|\llbracket{\mathbb{A}}\hskip 2.0pt|\hskip
2.0pt{(t\,u,S)_{\alpha}\overset{\mathtt{sel}}{\leftharpoondown}P}\hskip
2.0pt|\hskip
2.0pt{E}\rrbracket|_{\mathtt{o}}&=&|(t\,u,S)_{\alpha},E|_{\mathtt{o}}+|\llbracket{\mathbb{A}}\hskip
2.0pt|\hskip 2.0pt{P}\hskip 2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}\\\
&=&1+|(t,u:S)_{\alpha},E|_{\mathtt{o}}+|\llbracket{\mathbb{A}}\hskip
2.0pt|\hskip 2.0pt{P}\hskip 2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}\\\
&=&1+|\llbracket{\mathbb{A}}\hskip 2.0pt|\hskip
2.0pt{(t,u:S)_{\alpha}\overset{\mathtt{dro}}{\rightharpoondown}P}\hskip
2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}\end{array}$

  2. 2.

_Abstraction search ( $\leadsto_{\mathtt{sea}_{\lambda}}$)._ Let $\beta$ be a
fresh name. Then:

$\begin{array}[]{rcll}|\llbracket{\mathbb{A}}\hskip 2.0pt|\hskip
2.0pt{(\lambda
x.\,t,\epsilon)_{\alpha}\overset{\mathtt{sel}}{\leftharpoondown}P}\hskip
2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}&=&|(\lambda
x.t,\epsilon)_{\alpha},E|_{\mathtt{o}}+|\llbracket{\mathbb{A}}\hskip
2.0pt|\hskip 2.0pt{P}\hskip 2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}\\\
&=&1+|(t,\epsilon)_{\alpha},E|_{\mathtt{o}}+|\llbracket{\mathbb{A}}\hskip
2.0pt|\hskip 2.0pt{P}\hskip 2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}\\\
&=&1+|(t,\epsilon)_{\alpha},E|_{\mathtt{o}}+|\llbracket{\mathbb{A}\langle\lambda
x.\,\langle\cdot\rangle_{\alpha}\rangle_{\alpha}}\hskip 2.0pt|\hskip
2.0pt{P}\hskip 2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}\\\
&=&1+|\llbracket{\mathbb{A}\langle\lambda
x.\,\langle\cdot\rangle_{\alpha}\rangle_{\alpha}}\hskip 2.0pt|\hskip
2.0pt{(t,\epsilon)_{\alpha}\overset{\mathtt{dro}}{\rightharpoondown}P}\hskip
2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}\end{array}$

  3. 3.

_Substitution ( $\leadsto_{\mathtt{sub}}$)._ If
$x\in\operatorname{\mathtt{dom}}E$ then:

$\begin{array}[]{rcll}|\llbracket{\mathbb{A}}\hskip 2.0pt|\hskip
2.0pt{(x,S)_{\alpha}\overset{\mathtt{sel}}{\leftharpoondown}P}\hskip
2.0pt|\hskip
2.0pt{E}\rrbracket|_{\mathtt{o}}\par&=&|(x,S)_{\alpha},E|_{\mathtt{o}}+|\llbracket{\mathbb{A}}\hskip
2.0pt|\hskip 2.0pt{P}\hskip 2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}\\\
&=&1+|(E(x)^{\mathtt{R}},S)_{\alpha},E|_{\mathtt{o}}+|\llbracket{\mathbb{A}}\hskip
2.0pt|\hskip 2.0pt{P}\hskip 2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}\\\
&=&1+|\llbracket{\mathbb{A}}\hskip 2.0pt|\hskip
2.0pt{(E(x)^{\mathtt{R}},S)_{\alpha}\overset{\mathtt{dro}}{\rightharpoondown}P}\hskip
2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}\end{array}$

  4. 4.

_Variable search ( $\leadsto_{\mathtt{sea}_{\mathcal{V}}}$)._ Let
$x\notin\operatorname{\mathtt{dom}}E$ and $\beta_{1},..,\beta_{n}$ are fresh
names. Then:

$\begin{array}[]{rcll}&&|\llbracket{\mathbb{A}}\hskip 2.0pt|\hskip
2.0pt{(x,t_{1}:..:t_{n})_{\alpha}\overset{\mathtt{sel}}{\leftharpoondown}P}\hskip
2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}\\\
&=&|(x,t_{1}:..:t_{n})_{\alpha},E|_{\mathtt{o}}+|\llbracket{\mathbb{A}}\hskip
2.0pt|\hskip 2.0pt{P}\hskip 2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}\\\
&=&1+\sum_{i=1}^{n}|(t_{i},\epsilon)_{\beta_{1}},E|_{\mathtt{o}}+|\llbracket{\mathbb{A}}\hskip
2.0pt|\hskip 2.0pt{P}\hskip 2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}\\\
&=&1+\sum_{i=1}^{n}|(t_{i},\epsilon)_{\beta_{1}},E|_{\mathtt{o}}+|\llbracket{\mathbb{A}\langle
x\,\langle\cdot\rangle_{\beta_{1}}..\langle\cdot\rangle_{\beta_{n}}\rangle_{\alpha}}\hskip
2.0pt|\hskip 2.0pt{P}\hskip 2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}\\\
&=&1+|\llbracket{\mathbb{A}\langle
x\,\langle\cdot\rangle_{\beta_{1}}..\langle\cdot\rangle_{\beta_{n}}\rangle_{\alpha}}\hskip
2.0pt|\hskip
2.0pt{(t_{1},\epsilon)_{\beta_{1}}:..:(t_{n},\epsilon)_{\beta_{n}}\overset{\mathtt{add}}{\rightharpoondown}P}\hskip
2.0pt|\hskip 2.0pt{E}\rrbracket|_{\mathtt{o}}\end{array}$

∎

l:addresses-unfolding

###### Proof

Simply note that the definition of $\underline{s}$ is an extension of
$\mathbb{A}$ by plugging terms in its holes, so all constructors of
$\mathbb{A}$ but holes are in $\underline{s}$ at the same address.∎

prop:beta-reflection

###### Proof

Let $s=\llbracket{\mathbb{A}}\hskip 2.0pt|\hskip 2.0pt{P}\hskip 2.0pt|\hskip
2.0pt{E}\rrbracket$. In a $\leadsto_{\mathtt{o}}$-normal reachable state all
jobs in $P$ have shape $(\lambda x.t,u:S)_{\alpha}$ for some $\alpha$, $t$,
$u$, and $S$ specific to the job. Note that $P$ cannot be empty, otherwise the
state is final and by the halt property (Proposition 5) $\underline{s}$ would
be normal, against hypothesis. If $\underline{s}\rightarrow_{\mathtt{x}}u$
then there is an external context $E$ such that
$\underline{s}=E\langle(\lambda x.t)t^{\prime}\rangle$, $u=E\langle
t\\{x{\leftarrow}t^{\prime}\\}\rangle$. Let $\mathbbm{a}$ be the address of
the abstraction $\lambda x.t$ taking part to the $\beta$-redex in
$\underline{s}$. Note that $\mathbbm{a}$ cannot be a defined address in
$\mathbb{A}$, because by Lemma 7 all addresses in $\mathbb{A}$ are addresses
in $\underline{s}$ locating the same constructor, but definition of
approximant there are no applied abstractions in $\mathbb{A}$. Then,
$\mathbbm{a}$ extends the address of a hole $\langle\cdot\rangle_{\alpha}$ in
$\mathbb{A}$. Let $\mathbbm{a}=\mathbbm{a}_{\alpha}\cdot\mathbbm{a}^{\prime}$
where $\mathbbm{a}_{\alpha}$ is the address of $\langle\cdot\rangle_{\alpha}$
in $\mathbb{A}$. By the bijection invariant (Lemma 3.3), there is a job
$(\lambda y.r,q:S)_{\alpha}$ of name $\alpha$ in $P$. The suffix address
$\mathbbm{a}^{\prime}$ then is an address in the read-back of such a job, that
is, in $\underline{(\lambda
y.\underline{r}_{E})}_{\underline{q}_{E}:\underline{S}_{E}}$. It is easily
seen that $\mathbbm{a}^{\prime}$ is exactly the address of $\lambda
y.\underline{r}_{E}$ in $\underline{(\lambda
y.\underline{r}_{E})}_{\underline{q}_{E}:\underline{S}_{E}}$, that is, that
$x=y$, $t=\underline{r}_{E}$ and $t^{\prime}=\underline{q}_{E}$, because
otherwise if $\mathbbm{a}^{\prime}$ is the address of a sub-term in
$\underline{r}_{E}$ or in the read-back stack then the surrounding context
(both in $\underline{(\lambda
y.\underline{r}_{E})}_{\underline{q}_{E}:\underline{S}_{E}}$, and in s) is not
external, against the hypothesis. Then we have:

$\llbracket{\mathbb{A}}\hskip 2.0pt|\hskip 2.0pt{(\lambda
x.r,q:S)_{\alpha}\overset{\mathtt{sel}}{\leftharpoondown}P}\hskip 2.0pt|\hskip
2.0pt{E}\rrbracket\ \ \leadsto_{\beta}\ \ \llbracket{\mathbb{A}}\hskip
2.0pt|\hskip
2.0pt{(r,S)_{\alpha}\overset{\mathtt{dro}}{\rightharpoondown}P}\hskip
2.0pt|\hskip 2.0pt{[x{\leftarrow}q]:E}\rrbracket$

and one shows that the read-back of the target state is the reduct term by
reasoning as for the $\beta$-projection property.∎

coro:exam-completeness

###### Proof

Simply apply the theorem about sufficient conditions for implementations
(Theorem 3.1) using overhead termination (Proposition 8) and
$\beta$-reflection above (Proposition 9).∎


###### Abstract

A review of the properties of the Tarantula Nebula (30 Doradus) in the Large
Magellanic Cloud is presented, primarily from the perspective of its massive
star content. The proximity of the Tarantula and its accessibility to X-ray
through radio observations permit it to serve as a Rosetta Stone amongst
extragalactic supergiant HII regions since one can consider both its
integrated characteristics and the individual properties of individual massive
stars. Recent surveys of its high mass stellar content, notably the VLT FLAMES
Tarantula Survey (VFTS), are reviewed, together with VLT/MUSE observations of
the central ionizing region NGC 2070 and HST/STIS spectroscopy of the young
dense cluster R136, provide a near complete Hertzsprung-Russell diagram of the
region, and cumulative ionizing output. Several high mass binaries are
highlighted, some of which have been identified from a recent X-ray survey.
Brief comparisons with the stellar content of giant HII regions in the Milky
Way (NGC 3372) and Small Magellanic Cloud (NGC 346) are also made, together
with Green Pea galaxies and star forming knots in high$-z$ galaxies. Finally,
the prospect of studying massive stars in metal poor galaxies is evaluated.

###### keywords:

galaxies: star formation – galaxies: star clusters: general – open clusters
and associations: individual: 30 Doradus – stars: massive – stars: early-type

xx 1 1 Academic Editor: Roberta Humphreys Received: date; Accepted: date;
Published: date Massive stars in the Tarantula Nebula: A Rosetta Stone for
Extragalactic Supergiant HII Regions Paul A Crowther* Paul A Crowther
Correspondence<EMAIL_ADDRESS>
##  1 Introduction

The Tarantula Nebula (alias 30 Doradus) in the Large Magellanic Cloud (LMC) is
the brightest supergiant HII region in the Local Group of galaxies, and serves
as a local analogue to metal-poor starburst knots in high redshift galaxies
Kennicutt (1998). Its proximity (50 kpc), and high galactic latitude (and
hence low extinction) have permitted a myriad of ground-based and space-based
surveys across the electromagnetic spectrum, revealing an exceptional
population of massive stars ($\geq 8M_{\odot}$), including the dense, young
star cluster R136 that is home to some of the most massive stars known. The
advent of modern highly multiplexed spectrographs coupled with large ground-
based telescopes, has permitted multi-epoch optical spectroscopic surveys of
the massive star population of the Tarantula Nebula for the first time. The
VLT FLAMES Tarantula Survey, hereafter VFTS Evans et al. (2011), has provided
the multiplicity, rotational velocities and initial mass function of massive
stars. In distant starburst regions it is not possible to resolve individual
stars, such that studies rely on techniques based on their integrated
properties, which themselves involve assumptions of binarity, stellar rotation
and mass function.

Figure 1: (left) Optical image of the Tarantula Nebula from the MPG/ESO 2.2m
WFI, with NGC 2060 and SN1987A indicated; (centre) Optical VLT/FORS2 image
centred on NGC 2070, with Hodge 301 to the upper right; (right) an infrared
VLT/MAD image of the central R136 region, with the massive colliding wind
binary Mk 34 indicated. Credit: ESO/P. Crowther/C.J. Evans

The Tarantula Nebula is not the sole example of a supergiant H ii region
within the Local Group. However, studies of the richest Milky Way star-forming
regions are limited by dust extinction (e.g. Westerlund 1, NGC 3603).
Counterparts in other Local Group galaxies suffer from a number of
limitations, including a relatively modest stellar content (NGC 346 in the
Small Magellanic Cloud, SMC) or much greater distance (NGC 604 in M 33), such
that the Tarantula – whose metallicity is approximately half-solar Tsamis and
Péquignot (2005) – serves as the only credible Rosetta Stone for rich
extragalactic star-forming regions. This review will provide a brief overview
of the structural properties of the Tarantula Nebula, but will largely focus
on its massive star content, drawn from results from VFTS and other optical
spectroscopic surveys, supplemented by the recent deep Chandra X-ray survey
‘Tarantula - Revealed by X-rays’ (T-ReX). Finally, comparisons with local and
high-redshift star-forming regions will be provided to put the properties of
the Tarantula into a broader context. Indeed, the nebular properties of the
central NGC 2070 region of the Tarantula are strikingly similar to Green Pea
galaxies, exhibiting intense [O iii] $\lambda$4959, 5007 emission, and its
star-formation rate is comparable to intense star-forming clumps at high
redshift.

Table 1: Physical scales within the Tarantula Nebula, adapted from Walborn Walborn (1991). Ionizing outputs, N(LyC) are obtained from the present work. Region | Angular | Physical | N(LyC) | Content | Reference
---|---|---|---|---|---
| radius (′′) | radius (pc) | ($10^{51}$ ph s-1) |  |
R136a | 0.8 | 0.2 | 2 | R136a1 (WN5h), R136a2 (WN5h) | Crowther et al. (2010)
R136 | 4 | 1.0 | 4 | R136b (O4 If/WN8), R136c (WN5h+) | Crowther et al. (2016)
NGC 2070 | 80 | 20. | 9 | R140a (WC4+WN6+), Mk34 (WN5h+WN5h) | Castro et al. (2018, in prep.)
Tarantula | 600 | 150. | 12 | Hodge 301, PSR J0537-6910 (pulsar), N157B (SNR) | Doran et al. (2013)

##  2 Tarantula Nebula

The Tarantula Nebula is the most striking star-forming region in the LMC,
whether viewed in the far ultraviolet (hot, luminous stars), H$\alpha$
(ionized gas) or mid-IR (warm dust), extending over several hundred parsec,
owing to a massive stellar content producing an ionizing output which is a
thousand-fold higher than the Orion Nebula Baldwin et al. (1991).

NGC 2070 is the dominant ionized region within the Tarantula Nebula, powered
by a large number of hot luminous stars from R136 at its heart plus many more
within its vicinity. NGC 2060, located 6 arcmin (90 pc) to the southwest, is
host to a more modest population of OB stars plus an X-ray pulsar PSR
J0537-6910 and its supernova remnant (SNR) N157B. Hodge 301 is located 3
arcmin (45 pc) to the north west of R136, but does not possess significant
nebulosity since previous supernovae are likely to have cleared this region of
gas, and its stellar population (B-type stars and red supergiants) does not
possess a significant Lyman continuum output. NGC 2070 is often referred to as
a cluster in the literature but it extends over tens of parsecs whereas
genuine star clusters are an order of magnitude smaller, such that the only
rich star clusters within the Tarantula are R136, with an age of 1–2 Myr
Crowther et al. (2016) and Hodge 301 with an age of 20–30 Myr Britavskiy et
al. (2019) with a few additional lower mass young, compact clusters (e.g.
TLD1, SL 639). Table 1 compares various regions within the Tarantula Nebula,
adapted from a previous review by Walborn Walborn (1991). Although the focus
of the present review is on spectroscopic results for massive stars, Sabbi et
al. Sabbi et al. (2013) have undertaken a deep Hubble Space Telescope (HST)
multi-colour photometric survey, known as the Hubble Tarantula Treasury
Project (HTTP) which permits lower mass stars in the Tarantula Nebula to be
studied.

A number of complementary studies of the star formation history of the
Tarantula Nebula have been carried out, exploiting pre-main sequence low mass
stars De Marchi et al. (2011); Sabbi et al. (2016) and massive stars Schneider
et al. (2018). Significant star formation commenced $\sim$25 Myr ago, as
witnessed by Hodge 301, and reached a peak several Myr ago, with the young
massive star cluster R136 at its heart no more than 2 Myr old. It is apparent
that star formation within the Tarantula Nebula has not been limited to
specific parsec-scale star clusters, such as Hodge 301 or R136, but has been
distributed across the entire region, akin to a super OB association. Wright
et al. Wright et al. (2016) have established from proper motion observations
that star formation in the far smaller Milky Way Cygnus OB2 region did not
originate in a star cluster, but involved individual sub-regions in virial
equilibrium. Indeed, median ages of massive stars show little radial
dependence on their projected distance from R136, with very massive stars
($\geq 100M_{\odot}$) identified throughout the region Schneider et al.
(2018). Infrared and radio observations of the Tarantula reveal ongoing
regions of massive star formation, to which the reader is referred to the
review by Walborn Walborn (2002) and a more recent study of the brightest
embedded sources based on Spitzer/IRAC imaging Walborn et al. (2013). Atacama
Large Millimetre Array (ALMA) has obtained high resolution observations of
parsec-scale clumps within the Tarantula Indebetouw et al. (2013), with the
rate of star formation in the Tarantula anticipated to decline in the future.

Table 2: Integrated nebular properties of nearby giant HII regions, adapted from Kennicutt Kennicutt (1984) for an assumed O7V Lyman continuum output of 1049 ph s-1. Region (galaxy) | Diameter | L(H$\alpha$) | N(O7V)
---|---|---|---
| pc | 1039 erg s-1 |
NGC 3372 (Milky Way) | 200: | 0.8 |  0045
NGC 346 (SMC) | 220 | 0.8 |  0045
NGC 3603 (Milky Way) | 100 | 1.5 |  0110
NGC 604 (M33) | 400 | 4.5 |  0320
Tarantula (LMC) | 370 | 15.0 | 1100

##  3 Massive star content

The integrated nebular properties of the Tarantula Nebula and other selected
giant H ii regions in the Local Group is presented in Table 2. The ionizing
output of the Tarantula Nebula corresponds to the equivalent of over a
thousand O7V stars, each with 1049 ph s-1. In reality, the Tarantula hosts
somewhat fewer O-type stars since the most extreme examples – early O stars
and luminous Wolf-Rayet (WR) stars – each produce an order of magnitude more
Lyman continuum photons. Nevertheless, this population represents an order of
magnitude more O and WR stars than any Milky Way or SMC giant HII regions, and
is not likely to be improved upon until extremely large telescopes are capable
of resolving the massive stellar content of more extreme giant HII regions,
such as NGC 5461, 5462 and 5471 in M 101 Kennicutt (1998).

Historically, there have been several photometric and spectroscopic surveys of
early-type stars in the Tarantula Nebula, each of which have employed
contemporary (Galactic) temperature calibrations to produce Hertzsprung-
Russell diagrams. Parker Parker (1993); Parker and Garmany (1993) obtained the
first extensive study of the entire region. Subsequently, Massey & Hunter
Massey and Hunter (1998) obtained high-spatial resolution HST spectroscopy of
early-type stars in the central, crowded R136 region, revealing an exceptional
population of very early O stars, whilst Melnick and colleagues Bosch et al.
(1999); Selman et al. (1999) obtained spectroscopy for a large number of
early-type stars in the NGC 2070 region. The advent of efficient multi-object
spectrographs on 8-10m telescopes, has permitted the most comprehensive
optical spectroscopic survey of massive stars in the Tarantula Nebula to date
through the VLT FLAMES Tarantula Survey (VFTS) Evans et al. (2011). Multi-
object, multi-epoch spectroscopy of $\sim$800 massive stars across the entire
region, for which detailed spectroscopic analyses have been undertaken for
over 500 O and early B stars, such that temperature calibrations are no longer
necessary. Although this represents the most extensive of early-type stars in
a single star-forming region to date, this survey is incomplete owing the
fibre-placement limitations, sampling $\sim$70% of massive stars exterior to
the dense R136 cluster from comparison with photometric surveys Doran et al.
(2013).

Table 3: Summary of stellar content of the Tarantula Nebula from recent spectroscopic surveys (excluding sources in common, although including individual components within SB2 binaries). Telescope/inst | Target | N(O-type) | N(B-type) | N(WR) | N(Of/WN) | N(A+) | Reference
---|---|---|---|---|---|---|---
VLT/FLAMES | 30 Dor | 369 | 436 | 9 | 6 | 35 | Evans et al. (2011)
HST/STIS | R136 | 57 | .. | 3 | 2 | .. | Crowther et al. (2016)
VLT/MUSE | NGC 2070 | 115 | 79 | .. | .. | 1 | Castro et al. (2018)
Other | 30 Dor | 29 | 8 | 16 | .. | 5 | Parker and Garmany (1993); Massey and Hunter (1998); Bosch et al. (1999); Breysacher et al. (1999)
Total | 30 Dor | 570 | 523 | 28 | 8 | 41 |

Two additional surveys have recently provided complete optical spectroscopic
observations of all bright sources within the central crowded region of the
Tarantula: (a) the central 4 arcsec (1 pc) of the R136 cluster exploiting the
high spatial resolution of HST/STIS Crowther et al. (2016); (b) the central
2$\times$2 arcmin (30$\times$30 pc) region of NGC 2070 using the VLT/MUSE
integral field spectrograph Castro et al. (2018). Although these lack the
multi-epoch capabilities of VFTS, they are complementary since the richest
stellar populations of the Tarantula are found within NGC 2070/R136, and
provide extended wavelength coverage (yellow and red for MUSE, ultraviolet for
STIS), albeit at reduced spectral resolution. A summary of these three
contemporary surveys is provided in Table 3, together with literature results.
In total, approximately 1100 early-type massive stars have been
spectroscopically observed. Our discussion of the massive star content of the
Tarantula will largely draw upon results from VFTS, but include others where
appropriate. It should be noted that analyses based on spectroscopic fibre-fed
observations of early-type stars in regions of strong, highly variable
nebulosity, is inherently problematic owing to the lack of local sky
subtraction. Such issues do no affect long-slit STIS or integral field MUSE
observations.

VFTS and other surveys have revealed that the Tarantula hosts extreme examples
of stellar exotica, including the most massive stars known Crowther et al.
(2010), a Luminous Blue Variable, R143 Walborn et al. (2017), a very massive
runaway Lennon et al. (2018), the fastest rotating stars Dufton et al. (2011),
a massive overcontact binary Almeida et al. (2015), and a supernova remnant
N157B Chen et al. (2006), with SN 1987A located $\sim$300 pc to the south west
(Fig 1).

Figure 2: (left) Chandra ACIS X-ray logarithmic intensity image of the core of
NGC 2070 from T-ReX, centred on R136c, adapted from Pollock et al. (2018),
showing the relative brightness of the colliding wind binary Melnick 34
(WNh5+WN5h) Tehrani et al. (2019) to the R136a star cluster (hosting multiple
WN5h stars) and R136c (WN5h+?); (right) HST WFC3/F555W logarithmic intensity
image of the same 19$\times$19 arcsec region, highlighting the rich stellar
population of R136a with respect to R136c and Melnick 34.

R136a, the central cluster, merits special consideration since it was
considered by some to be a supermassive star as recently as the early 1980s
Savage et al. (1983). Speckle interferometry resolved R136a into multiple
sources Weigelt and Baier (1985), and it was subsequently established as a
compact star cluster Hunter et al. (1995). Massey & Hunter Massey and Hunter
(1998) established that dozens of the brightest sources within the central
parsec were hot, early O stars. Spectroscopic studies of the brightest
components R136a1, a2, a3, with nitrogen-sequence Wolf-Rayet spectral types,
indicated masses of $\sim 100M_{\odot}$ de Koter et al. (1997); Massey and
Hunter (1998). They established that these relatively weak-lined WN stars are
luminous main-sequence stars close to their Eddington limits, rather than
classical Wolf-Rayet stars. Subsequent analyses of the WN stars in R136
indicated significantly higher masses of 150–300 $M_{\odot}$ Crowther et al.
(2010) as a result of increased spectroscopic luminosities, owing to higher
stellar temperatures and IR photometry less affected by dust extinction.
Indirectly inferred masses of massive stars are notoriously imprecise, and if
binarity were established for individual stars their inferred luminosities and
masses would be reduced. To date, faint companions to members of R136a have
been detected with extreme adaptive optics imaging Khorrami et al. (2017).
Melnick 34 is spectroscopically similar to the WN5-stars in R136a, and has
recently been shown to be a colliding wind binary system comprising two WN5
components, with a total mass exceeding 250 $M_{\odot}$ Tehrani et al. (2019).
Fig. 2 shows that Melnick 34 is an order of magnitude brighter than R136a in
X-rays, indicating that there are no colliding wind binaries comparable to
Melnick 34 within R136a Pollock et al. (2018).

Overall, the Tarantula hosts a remarkable number of $\sim$50 early-type stars
with bolometric luminosities exceeding $10^{6}L_{\odot}$. For reference, the
Milky Way’s Carina Nebula (NGC 3372) hosts $\approx$5 massive stars with such
extreme properties Smith (2006). As such, the Tarantula Nebula represents our
best opportunity to study the highest mass stars known, both individually and
collectively. Schneider et al. Schneider et al. (2018) analysed VFTS
spectroscopic results to establish an excess of massive stars with respect to
a standard Salpeter Initial Mass Function (|MF), indicating 1/3 more stars
with $\geq 30M_{\odot}$ in 30 Doradus compared to expectations from a standard
IMF. Finally, although we focus primarily on high mass early-type stars in the
Tarantula Nebula, it also hosts red supergiants (RSG). Since RSG are the
evolved descendants of moderately massive stars, and star formation in the
Tarantula has peaked relatively recently, of order $\sim$10 RSG are known,
most of which are associated with mature star clusters Hodge 301 and SL 639
Britavskiy et al. (2019).

##  4 Physical properties

The determination of physical properties ($T_{\rm eff},\log g$) of individual
early-type stars ideally requires high S/N ($\geq$50) intermediate resolution
spectroscopy of suitable diagnostics, usually He i-ii lines (Si ii-iv) for
temperatures of O-type (B-type) stars, plus Balmer lines for surface
gravities, plus grids of model atmospheres obtained with modern codes, such as
FASTWIND Puls et al. (2005) for O stars and blue supergiants, CMFGEN Hillier
and Miller (1998) or PoWR Gräfener et al. (2002) for emission-line stars, or
TLUSTY Lanz and Hubeny (2007) for low luminosity B stars. Analysis of late-
type supergiants requires model atmosphere codes in which molecular opacities
have been incorporated, such as MARCS Gustafsson et al. (2008). Hot O stars
require alternative temperature diagnostics to helium, with nitrogen commonly
used since the blue visual spectrum of O stars includes lines of N iii-v.
Wolf-Rayet stars are especially problematic since photospheres are masked by
the dense wind, such that gravities cannot be directly measured and
temperatures usually refer to deep layers, with an optical depth of $\tau\sim
10-20$, rather than the effective temperature at $\tau=2/3$. If stellar
distances are uncertain, comparisons with evolutionary models can be made
using the so-called spectroscopic Hertzsprung-Russell (sHR) diagram Langer and
Kudritzki (2014), involving temperature and ${\mathscr{L}}=T_{\rm eff}^{4}/g$,
the inverse of the flux-weighted gravity, where $g$ is the surface gravity.

The determination of stellar luminosities requires comparisons between
synthetic spectral energy distributions and photometry, taking account of
interstellar extinctions and distance moduli, 18.5 mag in the case of the
Large Magellanic Cloud. Visual extinctions of early-type stars in the
Tarantula Nebula are usually modest, although near-IR photometric comparisons
usually lead to more robust luminosities since typical dust extinctions are
0.1–0.2 mag in the K-band, versus 1–2 mag in the V-band, and the lack of
sensitivity of K-band extinctions to any variations in the overall extinction
law. Luminosities of RSG can also be reliably estimated by integrating
observed spectral energy distributions from visual to mid-IR wavelengths
Gordon et al. (2016); Davies et al. (2018). Historically, stellar estimates of
masses and ages from evolutionary models involved by-eye comparisons between
their position on a conventional Hertszprung-Russell (HR) diagram and
theoretical isochrones. However, additional physical information is often
available, such as helium abundance or projected rotational velocities. Tools
now exist which additionally take such information into account for the
calculation of stellar ages and initial masses such as BONNSAI Schneider et
al. (2014). Significant discrepancies exist between current mass estimates
from spectroscopic ($\log g$) and evolutionary approaches for a subset of VFTS
O dwarfs Sabín-Sanjulián et al. (2017).

Figure 3: Hertzsprung-Russell diagram of the Tarantula Nebula, based on
results from VFTS Bestenlehner et al. (2014); McEvoy et al. (2015); Sabín-
Sanjulián et al. (2017); Ramírez-Agudelo et al. (2017); Dufton et al. (2018),
MUSE Castro et al. (in prep.), HST/STIS Bestenlehner et al. ("in prep.") and
other literature results, with typical uncertainties from each survey
indicated. Filled symbols are within NGC 2070, open symbols elsewhere in the
Tarantula. Non-rotating tracks for 10, 15, 25, 40, 60, 100 and 200 $M_{\odot}$
LMC metallicity stars have been included from Brott et al. (2011); Köhler et
al. (2015) which terminate at the onset of He-burning.

Figure 3 presents the HR diagram of the Tarantula Nebula, comprising single
star results from VFTS Bestenlehner et al. (2014); McEvoy et al. (2015);
Sabín-Sanjulián et al. (2017); Ramírez-Agudelo et al. (2017); Dufton et al.
(2018), VLT/MUSE Castro et al. (in prep.), HST/STIS Bestenlehner et al. ("in
prep.") and literature results for other stars within 160 parsec of R136,
including Wolf-Rayet stars Hainich et al. (2014). Results for binary systems
have been incorporated, primarily involving VFTS B-type binaries Garland et
al. (2017), Tarantula Massive Binary Monitoring (TMBM) O-type binaries Mahy et
al. ("submitted") and recent literature for WR stars Shenar et al. (2019);
Tehrani et al. (2019). Evolutionary tracks for non-rotating, LMC metallicity
massive stars up to the onset of He-burning have been included for reference
Brott et al. (2011); Köhler et al. (2015). Over 1170 massive stars have been
included, revealing a well populated main sequence population up to $\sim
200M_{\odot}$, plus classical Wolf-Rayet stars to the left of the main
sequence, and evolved blue supergiants up to $\log(L/L_{\odot})\sim 6$, and
cool supergiants, up to $\log(L/L_{\odot})\sim$5.3 Davies et al. (2018). The
addition of all luminous early-type stars from R136 and NGC 2070 fills in the
extreme upper main sequence which is somewhat under populated from VFTS alone
Schneider et al. (2018). The overwhelming majority of the older massive
stellar population – i.e. evolved stars with masses below $30M_{\odot}$ – are
spatially exterior to NGC 2070 (open symbols), although NGC 2070 is host to
one luminous M supergiant, Melnick 9. Conversely, beyond NGC 2070, the main-
sequence population at the highest stellar masses is relatively
underpopulated, albeit with several WN5h stars (R146, R147) and early O stars
(VFTS 16, BI 253) located 95$\pm$25 parsec from R136.

##  5 Binaries, rotation and runaways

Until recently, the significance of close binary evolution for massive stars
was not fully recognised, in spite of a few binary “champions" Vanbeveren et
al. (1998). The high frequency of close binaries amongst O stars in young
Galactic clusters obtained from radial velocity monitoring established that
only a minority of massive stars follow single stellar evolution Sana et al.
(2012). In contrast with the majority of previous spectroscopic surveys of
early-type stars, VFTS comprised multiple epochs, such that Sana et al. (2013)
were able to establish that 53% of O stars in the Tarantula Nebula inhabit a
binary system with a period below 1,500 days, such that binary interaction
will occur. 18% of O-type binaries, those with very short periods are
anticipated to merge with a companion, 27% will be stripped of their envelopes
(primaries, mass donors) and 8% are predicted to be spun up (secondaries, mass
gainers), as summarised in Figure 4 together with counterparts in Milky Way
clusters. Broadly similar results have been obtained for VFTS B-type stars
Dunstall et al. (2015).

The inferred rate of envelope stripping and spin-up in the Tarantula is rather
lower than Sana et al. (2012) obtained for O stars in Milky Way clusters (Fig.
4), but it is probable that the true incidence is rather higher since a subset
of the current O star sample is likely to have already undergone binary
evolution. Although VFTS has established the binary frequency amongst massive
stars in the Tarantula, binary orbits require follow-up surveys, notably the
TMBM survey Almeida et al. (2017); Mahy et al. ("submitted").

Consequences of close binary evolution include mass gaining secondaries being
spun-up, and a subset of secondaries possessing high space velocities as a
result of the disruption of the binary following the core-collapse supernova
(ccSN) of the original primary. Other “observables" are more challenging,
including the identification of stripped primaries in close binaries which
will usually be masked at visual wavelengths by mass gaining secondaries
Götberg et al. (2018) which should be more common in older star clusters such
as Hodge 301.

Figure 4: Pie charts, courtesy Hugues Sana and Selma de Mink, illustrating the
fraction of O stars undergoing single stellar evolution versus mergers,
primaries being stripped of their envelopes, and secondaries being spun up,
for Milky Way young clusters (left) and VFTS O stars (right), adapted from
Sana et al. (2012, 2013).

Reliable measurements of projected rotation rates, $v_{e}\sin i$, are often
problematic because strong hydrogen and helium lines are predominantly
affected by pressure broadening, with an additional contribution
from“macroturbulence”. A Fourier Transform approach applied to metallic lines
offers the most robust results, albeit requiring high resolution, high S/N
spectroscopy of suitable diagnostics Simón-Díaz and Herrero (2014). The lack
of a spectral features originating in the hydrostatic layers of Wolf-Rayet
stars prevents a direct determination of their rotational velocities. Fig. 5
compares projected rotational velocities for a large sample of VFTS O and
B-type stars. Typical rotational velocities of single O stars are modest, with
$v_{e}\sin i\sim$ 100 km s-1, albeit with 10% exceeding 300 km s-1 Ramírez-
Agudelo et al. (2013), of which some examples are rotating close to their
critical rates Dufton et al. (2011). This high velocity tail is suspected of
being spun-up mass gainers in former close binaries. The lack of fast rotators
amongst O stars in VFTS binary systems supports this interpretation Ramírez-
Agudelo et al. (2015). Fig. 5 illustrates that rotational velocities of VFTS
B-type stars are higher, with $v_{e}\sin i\sim$ 200 km s-1 on average, and 20%
exceeding 300 km s-1 Dufton et al. (2013).

Of particular interest is the rotational velocity distribution of massive
stars within the young R136 star cluster, whose severe crowding prevented
inclusion in VFTS. Bestenlehner et al. Bestenlehner et al. ("in prep.")
utilised HST/STIS spectroscopy to reveal 150 km s-1 on average for a sample of
55 massive stars within the central parsec of R136, with no examples exceeding
250 km s-1, although the low S/N of these datasets prevented distinguishing
between rotational and macroturbulence, adding to the interpretation that
rapid rotators originate from close binary evolution. Wolff et al. Wolff et
al. (2008) obtained somewhat higher rotational velocities for OB stars in the
periphery of R136, where contamination from the field population is
significant.

The Tarantula hosts a number of candidate early-type runaway stars from their
measured (radial and/or tangential) velocities with respect to the average for
their environment, although radial velocity outliers may be unresolved
binaries. Runaways can originate either from disrupted secondaries following
the core collapse of primaries in close binaries, or following the dynamical
ejection of stars from young star-forming regions. Platais et al. Platais et
al. (2018) have investigated high proper motion stars in the Tarantula from
HST imaging obtained 3 years apart, revealing a number of potential stars
ejected from R136, while Lennon et al. Lennon et al. (2018) have exploited
Gaia DR2 proper motions to conclude that VFTS 16 (O2 III) Evans et al. (2010)
was likely ejected from R136 during its formation 1–2 Myr ago. Renzo et al.
Renzo et al. (2019) discuss the origin of the candidate ‘walkaway’ very
massive star VFTS 682 (WN5h).

The Tarantula hosts several notable massive binary systems, whose physical and
orbital properties have been obtained from spectroscopic monitoring, with
searches for massive binaries also greatly benefitting from the recent Chandra
T-ReX survey (PI Leisa Townsley) which monitored the Tarantula in X-rays for
almost 2 years with a total integration time of 2 Ms. Single hot, luminous
stars tend to produce (thermal) X-rays due to shocks in the winds, but these
are generally soft X-ray emitters with $L_{X}/L_{\rm Bol}\sim 10^{-7}$
Pallavicini et al. (1981). Massive stars in binary systems may lead to excess
X-ray emission arising from wind-wind collisions, usually relatively hard,
providing the separations are not too small (low wind velocities) or too large
(low wind densities) Stevens et al. (1992). A close binary comprising an
early-type star and compact remnant (neutron star or black hole) will be
extremely X-ray bright if the accretion disk of the remnant is being fed by
the wind of the massive star or via Roche Lobe overflow.

A number of eclipsing binaries in the proximity of R136 have been identified
Massey et al. (2002), including # 38 from Hunter et al. (1995) comprising an
O3 V+O6 V in a circular 3.4 day orbit, with component masses 57 and 23
$M_{\odot}$. This represented the first robust stellar mass determination for
an O3 star in the LMC. VFTS revealed a large number of binaries within the
Tarantula, many of which have been followed-up with TMBM. Most notably R139
has been established as an eccentric system comprising a pair of mid O
supergiants in a 154 day orbit Taylor et al. (2011) with lower limits of $\sim
66+78M_{\odot}$ for individual component, recently revised downward to
$54+69M_{\odot}$ Mahy et al. ("submitted"). R139 is amongst the brightest
X-ray sources in the Tarantula in T-ReX with $L_{\rm X,corr}\sim 5\times
10^{33}$ erg s-1 and an enhanced $L_{\rm X,corr}/L_{\rm Bol}\sim 9\times
10^{-7}$ based on TMBM bolometric luminosities Mahy et al. ("submitted").

Figure 5: Cumulative distribution of rotational rates for single VFTS O (red)
and B stars (blue) Ramírez-Agudelo et al. (2013); Dufton et al. (2013)

The most remarkable X-ray source in the Tarantula is VFTS 399 with $L_{\rm
X,corr}\sim 5\times 10^{34}$ erg s-1 despite being associated with a low
luminosity O9 giant, implying $L_{\rm X,corr}/L_{\rm Bol}\sim 2\times
10^{-4}$. Clark et al. Clark et al. (2015) conclude that VFTS 399 is a high-
mass X-ray binary hosting a neutron star remnant, with the O giant known to be
a rapid rotator ($v_{e}\sin i=324$ km s-1, according to Ramírez-Agudelo et al.
(2017)), as one would expect for a mass gainer in a close binary system.

Two point sources in the Tarantula are even brighter in X-rays than VFTS 399.
Of these, R140a is a compact group of stars including two WR stars, so likely
hosts one or more colliding wind binaries, while X-ray variability for Melnick
34 reveals a 155 day period, peaking at $L_{\rm X,corr}=3.2\times 10^{35}$ erg
s-1, exceeding $\eta$ Carina at X-ray maximum Pollock et al. (2018). Melnick
34 has been confirmed to be a colliding wind binary system in a 155 day
eccentric orbit, with minimum masses of 60–65 $M_{\odot}$ for each of the WN5h
components Tehrani et al. (2019). Individual masses of 130–140 $M_{\odot}$ are
favoured from spectroscopic analysis, such that Melnick 34 is likely to be the
most massive binary known to date, with $L_{\rm X,corr}/L_{\rm bol}=1.7\times
10^{-5}$ at X-ray maximum. This arises from the collision of dense, fast
moving winds at a minimum separation of $\sim$1.2 AU or 13 stellar radii for
an assumed orbital inclination of $i=50^{\circ}$. Almeida et al. Almeida et
al. (2015) identify the overcontact binary VFTS 352 as a prototype of systems
which, at low metallicity, are plausible black hole-black hole merger
progenitors.

Figure 6: Unclumped mass-loss rates of O-type, Of/WN and Wolf-Rayet stars in
the Tarantula Nebula (based on results from VFTS Bestenlehner et al. (2014);
Sabín-Sanjulián et al. (2017); Ramírez-Agudelo et al. (2017), HST/STIS
Bestenlehner et al. ("in prep.") and other surveys Hainich et al. (2014);
Shenar et al. (2019); Tehrani et al. (2019) for WR stars). Filled symbols are
within NGC 2070, open symbols elsewhere in the Tarantula. Theoretical mass-
loss rates for zero age main sequence massive stars at the LMC metallicity
Vink et al. (2001) are included (solid line), based on LMC metallicity
evolutionary models Brott et al. (2011); Köhler et al. (2015)

##  6 Wind properties

The underlying theory responsible for outflows by hot luminous stars has been
known for several decades Castor et al. (1975), with a metallicity dependence
primarily arising from the variation in iron-peak elemental abundances Vink et
al. (2001); Mokiem et al. (2007). Individual wind properties of O stars or
blue supergiants usually rely on spectroscopic fits to H$\alpha$, as
parameterised by the wind strength parameter, $Q$ Puls et al. (2005), from
which the mass-loss rate requires knowledge of the physical radius (from
$T_{\rm eff},\log L$) and measured or adopted wind velocity. Wind velocities
of OB stars cannot be measured from optical spectroscopy, so usually spectral
type calibrations are adopted based on measured velocities from UV P Cygni
profiles of C iv, N v or Si iv Prinja et al. (1990). Until recently, high S/N,
high quality UV spectroscopy of OB stars in the Large Magellanic Cloud has
been in short supply, but the situation has improved via the HST Large Program
METAL (GO 14675, PI Julia Roman-Duval) Roman-Duval et al. (2019) and upcoming
ULLYSES initiative111http://www.stsci.edu/stsci-research/research-topics-and-
programs/ullyses.

Specifically for the Tarantula, low resolution UV spectroscopy of the R136
star cluster has added a significant number of wind measurements for early O
stars Crowther et al. (2016). Wind velocities exceed 3000 km s-1 at the
earliest subtypes (O2–3), reducing to $\sim$1500 km s-1 for late O-types.
Mass-loss rates of emission line stars typically rely on an alternative wind
scaling relation, namely the transformed radius, $R_{t}$ Schmutz et al.
(1989), which also requires knowledge of wind velocities, although these can
be estimated from optical spectroscopy for Wolf-Rayet stars. An added
complication arises because radiatively-driven winds are known to be
inherently unstable, leading to clumped winds. Wolf-Rayet winds have been
known to be clumped for 30 years St.-Louis et al. (1988); Hillier (1991), but
the degree of clumping for O stars via the H$\alpha$ diagnostic remains
unclear, with conflicting results obtained from UV resonance lines Fullerton
et al. (2006) unless the wind comprises a mixture of optically thin and thick
clumps within a much lower density inter-clump medium Sundqvist and Puls
(2018).

Fig 6 presents unclumped mass-loss rates of O, Of/WN and Wolf-Rayet stars in
the Tarantula Nebula, obtained from VFTS Bestenlehner et al. (2014); Sabín-
Sanjulián et al. (2017); Ramírez-Agudelo et al. (2017), HST/STIS Bestenlehner
et al. ("in prep.") and other literature results. Uncertainties have been
included wherever possible. Since the primary wind diagnostic in the majority
of instances presented here is H$\alpha$, it is apparent that uncertainties
are large for those stars with weak stellar winds. In addition, mass-loss
rates for Of/WN and Wolf-Rayet stars are anticipated to be reduced
significantly owing to wind clumping, as indicated with downward arrows. If
volume filling factors are $\sim$10%, mass-loss rates will be reduced by a
factor of $\sqrt{10}$.

Theoretical mass-loss rates Vink et al. (2001) for zero-age main sequence
stars at LMC composition Brott et al. (2011); Köhler et al. (2015) are
included in Fig 6. At face value it would appear that the theoretical mass-
loss rates of LMC O stars are supported by theory. However, the following
should be borne in mind. It is not clear how significantly wind clumping
affects the inferred mass-loss rates of normal O stars, although H$\alpha$
results for supergiants are likely to be sensitive to wind clumping. In
addition, the vast majority of mass-loss rates of VFTS O stars shown here have
been inferred by adopting wind velocities from an assumed scaling relation
involving escape velocities Lamers et al. (1995); Kudritzki and Puls (2000),
which are themselves dependent upon spectroscopic gravities. Exceptions are
HST/STIS results for early-type stars in R136 which are based on measured UV
wind velocities, and span dwarfs, giants, supergiants and main sequence WN
stars. In order to verify predictions for lower luminosity ($\log
L/L_{\odot}<5.5$) O stars, more sensitive diagnostics would need to be
employed, such as UV P Cygni lines, providing complications such as porosity
are accounted for Sundqvist and Puls (2018).

It is clear from Fig. 6 that rates for the highest luminosity main-sequence
Of/WN and WN stars significantly exceed theoretical predictions. This
discrepancy is partially addressed through wind clumping, but very massive
stars close to their Eddington limits are observed to exhibit enhanced mass-
loss rates which are not taken into account in standard theoretical
predictions Gräfener et al. (2011); Bestenlehner ("in prep."). Unsurprisingly,
classical Wolf-Rayet stars with $\log(L/L_{\odot})=5.5-6$ possess the
strongest winds amongst early-type stars in 30 Doradus, with clumping-
corrected wind densities an order of magnitude higher than O stars with
similar luminosities. It is well known that the wind momenta of WR stars,
$\dot{M}v_{\infty}$, exceeds the momentum provided by their radiation field,
$L/c$, owing to multiple photon absorption and re-emission within their
optically thick winds, permitting $\dot{M}v_{\infty}/(L/c)>1$ Puls et al.
(2008).

##  7 Fate of massive stars in the Tarantula

The conventional picture of massive star evolution close to solar metallicity
is that those with initial masses of 8 – 25 $M_{\odot}$ will end their lives
as red supergiants (RSG), undergo a H-rich core collapse supernova, leaving
behind a neutron star remnant, while higher mass counterparts will either
circumvent the RSG phase or subsequently proceed to a Wolf-Rayet stage prior
to undergoing core collapse, leading to a H-deficient supernova (neutron star
remnant) or faint/failed supernova (black hole remnant) Langer (2012). If one
considers the global WR vs RSG population in the LMC, the lower boundary to
the luminosity of WR stars is $\log(L/L_{\odot})$ = 5.3, while the upper
luminosity of RSG is $\log(L/L_{\odot})$ = 5.5 Davies et al. (2018),
supporting a transition from RSG to WR for higher mass progenitors at $\sim$25
$M_{\odot}$.

Close binary evolution severely complicates this scenario, since primaries
below 25 $M_{\odot}$ can be stripped of their hydrogen envelope, leading to a
type IIb or Ib/c instead of a H-rich supernova, while secondaries will be
rejuvenated, spun-up, with the potential for a core-collapse supernova for
secondaries whose initial masses fall below 8$M_{\odot}$. To date, there are
no unambiguous cases of pre-supernova close binaries in the Tarantula hosting
stripped (Wolf-Rayet or helium) stars, although it has been suggested that the
WN3 binary BAT99-49 elsewhere in the LMC is the product of close binary
evolution Shenar et al. (2019). Rapid rotation of the bright O giant component
of the high mass X-ray binary VFTS 399 is consistent with this evolutionary
scenario. The absence of low luminosity Wolf-Rayet stars in the Tarantula does
not exclude the binary channel since low-mass stripped stars would be unlikely
to exhibit a Wolf-Rayet spectral appearance Götberg et al. (2018).

Initially very close binaries may merge on the main sequence, prior to
following a relatively conventional evolution, albeit with unusually high
rotation rates, which would lead to increased luminosities and potentially
evolve blueward off the main sequence Brott et al. (2011); Köhler et al.
(2015). Extremely rapid rotation in some VFTS OB stars favours close binary
evolution or stellar mergers. Very massive stars in the Tarantula up to $\sim
300M_{\odot}$ are expected to lead to 30–50 $M_{\odot}$ CO cores and black
hole fates, unlikely to produce any associated supernova Yusof et al. (2013),
such that a subset of binary VMS are plausible progenitors of LIGO black hole
binary mergers, although their exact fate crucially depends on their mass-loss
properties, which remain uncertain.

Figure 7: Comparison between observed He ii $\lambda$1640 emission equivalent
widths in R136 Crowther et al. (2016) versus predicted emission from BPASS
(v.2.2.1, red) and Starburst99 (blue) population synthesis models (absorption
lines are shown as negative values).

##  8 Integrated properties and comparison with star-forming regions, near and
far

The Tarantula Nebula would subtend little more than one arcsec if it were
located at a distance of 50 Mpc, and so provides us with a unique opportunity
to compare the individual spatially-resolved properties of an intensively
star-forming region and its aggregate characteristics. Using integrated
H$\alpha$ observations of the Tarantula Nebula Pellegrini et al. (2010), an
age of $\sim$3.5 Myr would be inferred from a comparison between the inferred
H$\alpha$ equivalent width of 1100Å and population synthesis models for a
coeval population at LMC metallicity Doran et al. (2013). This is in
reasonable agreement with the typical age of massive stars, albeit failing to
reflect the complexity in its star-formation history (recall Fig. 3).

An analysis of the integrated UV spectrum of NGC 2070 supports a young
($\leq$3 Myr) starburst episode Vacca et al. (1995), while the high spatial
resolution of HST/STIS has permitted a comparison between the individual and
integrated UV spectroscopic appearance of the central R136 cluster Crowther et
al. (2016). Very massive stars contributed a significant fraction of its far
UV continuum flux, and completely dominate the strong, broad He ii
$\lambda$1640 emission. The integrated UV spectroscopic appearance of R136
closely resembles some star clusters in star-forming galaxies at Mpc
distances, such as NGC5253-5 Smith et al. (2016), suggesting the presence of
VMS in these other young massive clusters. From comparison with the
predictions of standard population synthesis models, both Starburst99 Levesque
et al. (2012) and BPASS Eldridge et al. (2017) models fail to predict any
significant emission prior to the conventional Wolf-Rayet phase (Fig. 7),
owing to the use of inadequate wind theory for VMS Gräfener et al. (2011);
Bestenlehner ("in prep."). Consequently, neither Starburst99 nor BPASS
accounts for the powerful winds of very massive stars in R136, and the adopted
mass function follows a Salpeter slope, rather than the top heavy IMF
identified by Schneider et al. (2018) for the Tarantula region as a whole.

Table 4: Top ten stellar systems contributing to the Lyman continuum output of the Tarantula Nebula, comprising very massive early O stars and WN5 stars, and classical Wolf-Rayet stars, updated from Doran et al. (2013). Star (alias) | Sp Type | $\log L/L_{\odot}$ |  $\log$ N(LyC) | Reference
---|---|---|---|---
R136a1 (BAT99-108) | . WN5h | 6.8 | 50.6 | Bestenlehner et al. ("in prep.")
Mk 34 (BAT99-116) | WN5h+WN5h | 6.4+6.4 | 50.6 | Tehrani et al. (2019)
R136a2 (BAT99-109) | WN5h | 6.7 | 50.5 | Bestenlehner et al. ("in prep.")
R144 (BAT99-118) | WN5-6+WN6-7 | 6.7 | 50.5 | Sana et al. (2013); Hainich et al. (2014)
R136a3 (BAT99-106) | WN5h | 6.6 | 50.5 | Bestenlehner et al. ("in prep.")
Mk 49 (BAT99-98) | WN6(h) | 6.7 | 50.5 | Hainich et al. (2014)
R145 (BAT99-119) | WN6h+O3.5If/WN7 | 6.3+6.3 | 50.4 | Shenar et al. (2019)
Mk 42 (BAT99-105) | O2 If | 6.6 | 50.4 | Bestenlehner et al. (2014)
VFTS 682 | WN5h | 6.5 | 50.4 | Bestenlehner et al. (2014)
R136c (BAT99-112) | WN5h+? | 6.6 | 50.4 | Bestenlehner et al. (2014)

An estimate of the cumulative ionizing and mechanical feedback from massive
stars within the Tarantula has revealed a major contribution from VMS towards
the collective ionizing output and a dominant role from WR stars to the
mechanical feedback Doran et al. (2013). However this analysis relied on
calibrations and estimates of spectral types for a significant subset of the
massive star content, so we are able to provide updates from recent
spectroscopic observations (e.g. VLT/MUSE, HST/STIS) and analyses. We present
the updated cumulative ionizing output from 1170 massive stars in the
Tarantula Nebula in Figure 8, indicating a total Lyman continuum ionizing
output of 1.2$\times 10^{52}$ ph s-1 within 150 pc of R136a. A quarter of the
total ionizing radiation originates from the R136a cluster, while members of
NGC 2070 produce three quarters of the global feedback. Ten systems alone,
listed in Table 4, collectively contribute a quarter of the ionizing budget of
the Tarantula Nebula, comprising main sequence and classical WR stars, plus
early O supergiants. Indeed, half of the global ionizing output originates
from 40 early O stars, main sequence WN stars and classical WR stars, with
1130 stars contributing the remaining 50%. The collective bolometric
luminosity of these stars is $10^{8.4}L_{\odot}$, of which the 40 UV-bright
stars contribute $10^{8.0}L_{\odot}$.

Figure 8: Cumulative ionizing output (1050 ph/s) from spectroscopically
classified early-type stars in the Tarantula, obtained from VFTS Bestenlehner
et al. (2014); Sabín-Sanjulián et al. (2017); Ramírez-Agudelo et al. (2017),
VLT/MUSE Castro et al. (in prep.), HST/STIS Bestenlehner et al. ("in prep.")
and literature results Hainich et al. (2014), updated from Doran et al.
(2013). Specific regions within 30 Dor are indicated from Table 1

Recalling Table 2, the highest mass stars and evolved high mass stars in other
giant H ii regions in the Local Group dominate their radiative and mechanical
feedback, including NGC 3372 (Carina Nebula) in the Milky Way, N206 in the LMC
and NGC 346 in the SMC. By way of example, Smith Smith (2006) established that
only a handful of early O-type stars and H-rich WN stars contribute the
majority of the Lyman continuum flux of the Carina Nebula, while $\eta$ Car,
four Wolf-Rayet stars and two early O supergiants completely dominate the
stellar mechanical luminosity. The central ionizing cluster of the Galactic
NGC 3603 star-forming region is host to a stellar content analogous to R136a,
including a number of early O stars, nitrogen-sequence Wolf-Rayet stars Moffat
et al. (2002); Melena et al. (2008). Weak main-sequence wind properties of
metal-poor massive stars conspire to even fewer massive stars (HD 5980, Sk 80)
dominating the cumulative stellar feedback in NGC 346. Similar conclusions
were reached by Ramachandran et al. Ramachandran et al. (2019) for the
supergiant shell in the wing of the SMC.

Figure 9: Comparison between the integrated star-formation rate versus size of
the Tarantula (filled red square) and star-forming knots from galaxies
spanning a range of redshifts, adapted from Johnson et al. (2017).

Although the Tarantula Nebula is the most extreme giant H ii region in the
Local Group, how does it rank against star-forming regions of galaxies in the
near universe or knots at high redshift? Fig 11 compares the star-formation
rate versus size of regions spanning $z$=0 to 3.4, adapted from Johnson et al.
(2017), indicating that the Tarantula (red square) is forming stars more
vigorously than typical low-redshift counterparts, resembling some star-
forming regions at high redshift. Indeed, 80% of the cumulative ionizing
radiation originates from NGC 2070, such that this region corresponds closely
with typical clumps in the lensed galaxy SDSS J1110+6459 at $z$=2.5 (green
circles).

Figure 10: BPT diagram illustrating the similarity in integrated strengths
between the Tarantula Nebula (red square), Green Pea (green circles), extreme
Green Peas (blue diamonds), Lyman-continuum leaking Green Peak (pink
triangles), updated from Micheva et al. (2017), plus SDSS star-forming
galaxies.

In addition to its unusually high star formation rate, the Tarantula also
possesses high ionization parameter nebular properties with respect to star-
forming galaxies in the local universe. Fig 10 presents a Baldwin, Philipps &
Terlevich (Baldwin et al., 1981, BPT) diagnostic diagram of Sloan Digital Sky
Survey (SDSS) galaxies, in which the Tarantula (red square) has been
indicated, along with Green Pea galaxies from Micheva et al. Micheva et al.
(2017) which are low-metallicity, intensively star-forming galaxies exhibiting
unusually strong [O iii] $\lambda$5007 emission. Steidel et al. Steidel et al.
(2014) showed that $z$=2–3 star forming galaxies share similar extreme nebular
properties, and a subset of Green Pea galaxies have been established as Lyman
continuum leakers Izotov et al. (2016a, b). Focusing again on NGC 2070, this
sits amongst the extreme Green Pea galaxies in the BPT diagram.

Figure 11: Comparison between present-day star formation rates, as measured by
H$\alpha$ luminosity Kennicutt et al. (2008), distance modulus (mag), and
oxygen metal content (squares: $\geq$20% of solar value, triangles: $<$20% of
solar value, for Local Group dwarf galaxies. Metal-poor galaxies possess low
star-formation rates, so host small numbers of OB stars, and these are $\geq$6
magnitudes fainter than Magellanic Cloud counterparts.

##  9 Summary and outlook

Recent comprehensive spectroscopic and imaging surveys have revealed that the
Tarantula Nebula hosts the most exceptional massive star population within the
Local Group of galaxies, including the most massive stars identified to date,
the fastest rotating early-type stars, and the X-ray brightest colliding wind
system. In particular, the VFTS survey has revealed an excess of massive stars
with respect to a Salpeter IMF Schneider et al. (2018) and added support from
previous results for the importance of close binary evolution in the evolution
of massive stars Sana et al. (2013). As such, the Tarantula Nebula is the
closest analogue to the Hubble Deep Field for the community interested in the
evolution of massive stars since its richness provides us with a huge breadth
of extreme stars.

The integrated appearance of R136 resembles young extragalactic star clusters,
while the integrated nebular properties of NGC 2070 is analogous to extreme
Green Pea galaxies at low redshift and star-forming knots in high-redshift
galaxies. Typical metallicities of Green Pea galaxies are lower than the LMC,
as measured from oxygen nebular lines, while the oxygen content of high-$z$
star forming galaxies tends to be similar to those of the Magellanic Clouds.
However, $\alpha$/Fe abundances of high redshift galaxies are likely to be
higher than young populations in the Milky Way, such that winds from OB stars
at high redshift are anticipated to be weaker than in the LMC or SMC Steidel
et al. (2016).

The LMC metallicity is only a factor of two below that of the Solar
neighbourhood Tsamis and Péquignot (2005), so ideally we would like to
supplement the extensive survey of the Tarantula Nebula with counterparts at
significantly lower metallicity. The SMC (1/5 solar) represents our best
opportunity to study the formation and evolution of massive stars at a
metallicity significantly below that of the LMC. Alas, it does not host as
rich a massive star-forming region as the Tarantula, but cumulatively does
host a substantial number of O stars so is key towards our improved
understanding of massive stars at low metallicity, especially as it can be
studied in exquisite detail with current instrumentation.

Figure 12: Comparison between far UV spectroscopy of mid O giants in metal-
rich Walborn et al. (1985) and metal-deficient Garcia et al. (2019)
environments, illustrating the extreme differences in wind features (e.g. N,̇v
$\lambda$1240, Si iv $\lambda$1400, C iv $\lambda$1550) and the iron forest
(Fe iv-v).

Since we need to look beyond the SMC to study metal-poor counterparts to the
Tarantula Nebula, Fig 11 compares the star-formation rate, metallicity, and
distance modulus of Local Group dwarf galaxies. Rates of star formation in
metal-poor ($\leq$20% of solar oxygen content) galaxies are significantly
lower than the Magellanic Clouds, so there are no rich metal-poor massive star
populations elsewhere in the Local Group, and those few that are present are
much more distant. The absence of nearby metal-poor counterparts to the
Tarantula implies that we currently have to rely on the interpretation of
integrated populations in order to understand massive stellar evolution at low
metallicity, notably extremely metal-poor dwarf star-forming galaxies I Zw 18
and SBS-0335.

In order to test predictions of the metallicity dependence of massive star
winds, it is necessary to measure mass-loss properties across a wide range of
metallicities. Although theory has been qualitatively supported from the
observed wind properties of Milky Way, LMC and SMC early-type stars Mokiem et
al. (2007), some issues remain, including weak winds in low luminosity OB
stars. Our only opportunity to study individual massive stars below 1/10th of
the solar oxygen content is to observe O stars in Sextans A and B with 7%
solar van Zee et al. (2006) or the Sagittarius Dwarf Irregular Galaxy (SgrDIR)
with 5% solar Saviane et al. (2002). Stellar winds from early-type stars at
such low metallicities are anticipated to be much weaker than in metal-rich
populations, which has been confirmed by UV spectroscopy. By way of example,
Fig. 12 compares the far UV spectrum of $\xi$ Per (O7.5 iii) with a
counterpart in Sextans A Garcia et al. (2019), revealing negligible wind
signatures in the latter (e.g. C iv $\lambda$1550).

This research received no external funding

###### Acknowledgements.

This review is dedicated to the memory of Nolan Walborn, from whom the author
learnt a great deal about the Tarantula Nebula. Thanks to Leisa Townsley and
Patrick Broos for access to T-ReX point source results prior to publication,
Miriam Garcia for the UV spectrum of Sextans A OB 326, Selma De Mink for the
VFTS pie chart, Heloise Stevance for the BPASS predictions, and Joachim
Bestenlehner for converting $Q$ wind density results into mass-loss rates.
Feedback from Fabian Schneider, Chris Evans, Joachim Bestenlehner, Andy
Pollock, Roberta Humphreys and external referees on an earlier draft is
greatly appreciated. The author declares no conflict of interest. References
yes

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