**6. Physical Parameters**

As is characteristic of stars approaching the Eddington Limit, a WR's spectrum is heavily influenced by strong stellar winds and high mass-loss rates [140]. Keeping the model's luminosity near, but below, the Eddington limit can make modeling WRs quite a challenge. Additionally, the stars' high surface temperatures mean that the assumption of local thermodynamic equilibrium (LTE) is no longer valid. Instead, the high degree of ionization (and correspondingly decreased opacity) causes the radiation field to decouple from the local thermal field. Furthermore, WR atmospheres are significantly extended when compared to their radius. Thus, plane-parallel geometry cannot be used, and instead spherical geometry must be included. The emission lines that characterize WR spectra are produced in the outflowing winds, with mass-loss rates of order <sup>10</sup>−5*M* yr<sup>−</sup>1. Finally, WR models must be fully blanketed and include the effects of thousands of overlapping metal lines, which occur at the (unobservable) short wavelengths ( <1000 Å) where most of the flux of the star is produced. Two codes are currently capable of including these complexities: the Potsdam Wolf–Rayet Models, or PoWR [141], and the CoMoving Frame GENeral spectrum analysis code, CMFGEN [142]. For a much more detailed description of the physics and complexities involved in modeling a WR, see, e.g., [143–145].

There have been few modeling campaigns of complete samples of WRs in galaxies other than the Magellanic Clouds. In M31, for example, 17 late-type WNs were modeled using PoWR in an attempt to learn more about the wind laws of such stars in different metallicity environments [146]. One limitation of this study was the lack of UV spectroscopy. Nevertheless, they were able to place luminosity constraints on the modeled WRs for values between 10<sup>5</sup> and <sup>10</sup>6*L* and sugges<sup>t</sup> that WRs in M31 form from initial mass ranges between 20 and 60 *M*. This is similar to that found in both the Galaxy and Magellanic Clouds. However, no modeling has taken place for the WC stars in a high metallicity environment like M31.

Conversely, much modeling has been done of WRs in the Magellanic Clouds. Over the past few years, surveys of single and binary WNs in both the SMC and LMC, and the WN3/O3 stars in the LMC have all been performed. In 2014, Hainich et al. determined physical parameters of over 100 WNs in the LMC using grids of PoWR [147] models. They concluded that the bulk ( ∼88%) of the WRs analyzed had progressed through the RSG before becoming WRs, thus implying that they evolved from 20–40 *M* progenitors. They also found that these results were well aligned with studies of Galactic WRs suggesting that there is no metallicity dependence on the range of main sequence masses that evolve into WRs. This research in the LMC was extended to the WR binaries by Shenar et al. in 2019 [148], who looked at the 44 binary candidates and found that 28 of them have composite spectra and five of them show periodically moving WR primaries. They conclude that while 45 ± 30% of the WNs in the LMC have most likely interacted with a companion via mass-transfer, many of these WRs would have evolved to become WRs through single star evolution.

Both the binary and single WNs in the SMC have also been modeled using the PoWR code [149,150]. As discussed earlier, many of the WNs in the SMC have absorption lines that, if not due to a companion, could simply be photospheric lines that are inherent to the stars because of their weak stellar winds. Thus, studying them for photometric and radial velocity variability is necessary to determine their binarity. Based on modeling with the PoWR code, it was concluded again that, while some of these stars are binaries now, they still would have become WRs through single-star evolution given their high initial main-sequence masses.

As discussed above, there has been additional modeling of the LMC WN3/O3s using CMFGEN. All ten of these stars show strong absorption and emission lines as is shown in Figure 9 for one of the newly discovered stars. CMFGEN spectral line fitting was used to determine the physical parameters of these ten stars. Table 2 shows the range of values for the 10 WN3/O3s compared to typical values for an O3V and WN3 star in the LMC (WN3 parameters from [147]. O3V parameters from [151].). While the temperature is a bit on the high side for what we would expect for a LMC WN, the majority of the parameters are within the expected ranges. The one exception is the mass-loss rate which is more similar to that of an O3V than of a normal LMC WN.


**Table 2.** Physical parameters of WN3/O3s, WNs, and O3Vs in the LMC.

Although other WN stars with intrinsic absorption lines are known, the WN3/O3s appear to be unique [93,148], and their place in the evolution of massive stars still unknown. Neugent's study [93] considered the possibility that these stars were the products of homogenous evolution, a situation that can occur if the star is rotating so rapidly that mixing keeps the composition nearly uniform within the star (see, e.g., [152]). However, they ruled this out based upon the stars' low rotational velocities combined with low mass-loss rates, as the latter implies that the high angular momentum could not have been carried off by stellar winds. Based on their absolute magnitudes they are not WN + O3V binaries, though they could be hiding a less-massive companion. It is additionally possible that binarity influenced their previous evolution. However, it is currently thought that instead these stars represent an intermediate stage between O stars an WNs. More research is ongoing in an attempt to answer this question.
