**4. Physical Properties**

The determination of physical properties (*T*eff, log *g*) of individual early-type stars ideally requires high S/N (≥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 [41] for O stars and blue supergiants, CMFGEN [42] or PoWR [43] for emission-line stars, or TLUSTY [44] for low luminosity B stars. Analysis of late-type supergiants requires model atmosphere codes in which molecular opacities have been incorporated, such as MARCS [45]. 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 *τ* ∼ 10–20, rather than the effective temperature at *τ* = 2/3. If stellar distances are uncertain, comparisons with evolutionary models can be made using the so-called spectroscopic Hertzsprung-Russell (sHR) diagram [46], involving temperature and L = *<sup>T</sup>*4eff/*<sup>g</sup>*, 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 [47,48]. 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 [49]. Significant discrepancies exist between current mass estimates from spectroscopic (log *g*) and evolutionary approaches for a subset of VFTS O dwarfs [50].

Figure 3 presents the HR diagram of the Tarantula Nebula, comprising single star results from VFTS [50–54], VLT/MUSE [11], HST/STIS [55] and literature results for other stars within 160 parsec of R136, including Wolf-Rayet stars [56]. Results for binary systems have been incorporated, primarily drawn from [57] for VFTS B-type binaries, Tarantula Massive Binary Monitoring (TMBM) for VFTS O-type binaries [58] and recent literature for WR stars [37,59]. Evolutionary tracks for non-rotating, LMC metallicity massive stars up to the onset of He-burning have been included for reference [60,61]. Over 1170 massive stars have been included, revealing a well populated main sequence population up to ∼200 *M*, plus classical Wolf-Rayet stars to the left of the main sequence, and evolved blue supergiants up to log(*L*/*L*) ∼ 6, and cool supergiants, up to log(*L*/*L*) ∼5.3 [48]. 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 [40]. The overwhelming majority of the older massive stellar population—i.e., evolved stars with masses below 30 *M*—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 ± 25 parsec from R136.

**Figure 3.** Hertzsprung-Russell diagram of the Tarantula Nebula, based on results from VLT FLAMES Tarantula Survey (VFTS) [50–54], MUSE [11], Hubble Space Telescope (HST)/STIS [55] 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* LMC metallicity stars have been included from [60,61] which terminate at the onset of He-burning.

### **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" [62]. The high frequency of close binaries amongs<sup>t</sup> O stars in young Galactic clusters obtained from radial velocity monitoring established that only a minority of massive stars follow single stellar evolution [63]. In contrast with the majority of previous spectroscopic surveys of early-type stars, VFTS comprised multiple epochs, such that [64] were able to establish that 53% of O stars in the Tarantula Nebula inhabit a binary system with a period below 1500 days, such that binary interaction will occur. In total, 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 [65].

The inferred rate of envelope stripping and spin-up in the Tarantula is rather lower than [63] obtained for O stars in Milky Way clusters (Figure 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 amongs<sup>t</sup> massive stars in the Tarantula, binary orbits require follow-up surveys, notably the TMBM survey [58,66].

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 [67] 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 [63,64].

Reliable measurements of projected rotation rates, *ve* 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 [68]. The lack of a spectral features originating in the hydrostatic layers of Wolf-Rayet stars prevents a direct determination of their rotational velocities. Figure 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 *ve* sin *i* ∼ 100 km s<sup>−</sup>1, albeit with 10% exceeding 300 km s<sup>−</sup><sup>1</sup> [69], of which some examples are rotating close to their critical rates [29]. This high velocity tail is suspected of being spun-up mass gainers in former close binaries. The lack of fast rotators amongs<sup>t</sup> O stars in VFTS binary systems supports this interpretation [70]. Figure 5 illustrates that rotational velocities of VFTS B-type stars are higher, with *ve* sin *i* ∼ 200 km s<sup>−</sup><sup>1</sup> on average, and 20% exceeding 300 km s<sup>−</sup><sup>1</sup> [71].

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. [55] utilised HST/STIS spectroscopy to reveal 150 km s<sup>−</sup><sup>1</sup> on average for a sample of 55 massive stars within the central parsec of R136, with no examples exceeding 250 km s<sup>−</sup>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. [72] 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. [73] 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. [28] have exploited Gaia DR2 proper motions to conclude that VFTS 16 (O2 III) [74] was likely ejected from R136 during its formation 1–2 Myr ago. Renzo et al. [75] 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 *LX*/*L*Bol ∼ 10−<sup>7</sup> [76]. 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) [77]. 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 [78], including # 38 from [34] comprising an O3 V + O6 V in a circular 3.4 day orbit, with component masses 57 and 23 *M*. 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 [79] with lower limits of ∼66 + 78 *M* for individual component, recently revised downward to 54 + 69 *M* [58]. R139 is amongs<sup>t</sup> the brightest X-ray sources in the Tarantula in T-ReX with *<sup>L</sup>*X,corr ∼ 5 × 10<sup>33</sup> erg s<sup>−</sup><sup>1</sup> and an enhanced *<sup>L</sup>*X,corr/*<sup>L</sup>*Bol ∼ 9 × 10−<sup>7</sup> based on TMBM bolometric luminosities [58].

**Figure 5.** Cumulative distribution of rotational rates for single VFTS O (red) and B stars (blue) [69,71].

The most remarkable X-ray source in the Tarantula is VFTS 399 with *<sup>L</sup>*X,corr ∼ 5 × 10<sup>34</sup> erg s<sup>−</sup><sup>1</sup> despite being associated with a low luminosity O9 giant, implying *<sup>L</sup>*X,corr/*<sup>L</sup>*Bol ∼ 2 × 10−4. Clark et al. [80] 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 (*ve* sin *i* = 324 km s<sup>−</sup>1, according to [53]), 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 *<sup>L</sup>*X,corr = 3.2 × 10<sup>35</sup> erg s<sup>−</sup>1, exceeding *η* Carina at X-ray maximum [38]. 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* for each of the WN5h components [37]. Individual masses of 130–140 *M* are favoured from spectroscopic analysis, such that Melnick 34 is likely to be the most massive binary known to date, with *<sup>L</sup>*X,corr/*<sup>L</sup>*bol = 1.7 × 10−<sup>5</sup> at X-ray maximum. This arises from the collision of dense, fast moving winds at a minimum separation of ∼1.2 AU or 13 stellar radii for an assumed orbital inclination of *i* = 50◦. Almeida et al. [30] identify the overcontact binary VFTS 352 as a prototype of systems which, at low metallicity, are plausible black hole-black hole merger progenitors.
