**7. Comparisons to Evolutionary Models**

As discussed in the Introduction, comparing the observed WC/WN ratio with evolutionary model predictions is one of the most important reasons to search for WRs. Currently, we have complete samples of the WR populations for the Magellanic Clouds, M31, and M33. The galaxy's metallicities and WC/WN ratios are shown in Table 3. We have included the Milky Way, although here the data are far less certain that the statistical uncertainties would indicate. As is expected, the WC/WN ratio increases with increasing metallicity due to the strength of the stellar winds. We can now compare these observational results to those of the evolutionary models.


**Table 3.** WC/WN ratio vs. metallicity for the Local Group Galaxies.

There are two primary sets of evolutionary models currently used in the massive star community. The first is the Geneva Evolutionary Models [1] that model the evolution of single stars. The other is the Binary Population and Spectral Synthesis (BPASS) models that focus on binary evolution [153,154]. Besides the obvious difference between the two of modeling single vs. binary stars, the models also have some important differences. In the case of the Geneva models, there are only results for a few metallicities, as is shown in the figure below. This makes comparisons between the observations and the models quite difficult because there are only a few points. However, these models have been created with different initial rotation rates as it plays quite a large effect on the resulting physics. Conversely, the BPASS models have results spanning a wide range of metallicities, but these models do not include rotation. Thus, due to these differences, it is difficult to compare the observations directly to either set of models. However, in time, the models will continue to improve.

In Figure 11, we show the agreemen<sup>t</sup> between the WC/WN ratios and the evolutionary models. We have not included NGC 6822 or IC 1613 in this diagram, as they each have too few WRs for meaningful statistics (4 and 1, respectively). We also have not included IC 10, as we feel the current value is, at best, an upper limit. We have included the value for the MW determined as described above, although we suspect that this too is an upper limit. As for the predictions: The solid line is from the older Geneva evolutionary models, the first to include rotation [1]. The green dashed line is an updated version of the predictions from BPASS2 [5], and these 2.2.1 predictions were kindly provided by Eldridge (2019, private communication). The models assume continuous star formation, a Salpeter IMF slope, and an upper mass limit of 300 *M*. The BPASS models also include the effects of binary evolution. Finally, the two ×'s denote results from the latest single-star evolutionary models. The higher metallicity value comes from [155], while the lower metallicity point was computed by Cyril Georgy from preliminary Geneva z = 0.006 models, and used in [77]. There is good agreemen<sup>t</sup> between the newer Geneva single-star models and the binary evolution models; this may simply be that the BPASS models do not ye<sup>t</sup> include the effects of rotation. Including rotation can reduce the expected ratio of WC/WN stars; see Figure 10 in [77]. Although the observational data at all metallicities are now in relatively good shape, improvements are still pending in the evolutionary models. Still, we can conclude that the large issue at high metallicity with the oldest models has largely gone away.

**Figure 11.** WC/WN ratio vs. metallicity compared to both BPASS2.2.1 and Geneva Evolutionary models. Notice the improved results between the observed WC/WN ratio and the Geneva Evolutionary models, but the lack of models at a variety of metallicities. In addition, notice the good agreemen<sup>t</sup> between the BPASS2.2.1 models and both the observed results. The error bars come from √ *N* statistics; see [73,77].

### **8. Conclusions and the Future of WRs**

WRs are the bare stellar cores of massive stars, and the last stage in a massive star's lifetime before they turn into supernovae. Observing a complete set of both the nitrogen and carbon rich WRs within a galaxy allows for important comparisons between the observed WC/WN ratio and that predicted by the evolutionary models. Because the evolution of WRs is highly dependent on the metallicity of the surrounding environment, it is important to do these comparisons across a wide range of galaxies with different metallicities, such as the galaxies in the Local Group.

Finding WRs observationally is done using a combination of interference filters and photometric techniques before the identified candidates are confirmed spectroscopically. This method has been used with grea<sup>t</sup> success over the past few decades and led to the discovery of hundreds of WRs in both our galaxy and even those far enough away that we can only observe the integrated light coming from clusters of WRs. While this method has led to the discovery of mostly complete samples of WRs within the Local Group, there is still much progress to be made in more distant galaxies.

The binary fraction of WRs is still highly contested with current observations putting it somewhere between 30–40% for the close binary frequency. However, as the distance between binaries expands, and the effect of binarity on the evolution of WRs in the past is considered, it is difficult to fully understand what role binaries play in the evolution of WRs. Modeling the spectra of the currently known WRs using sophisticated modeling codes such as PoWR and CMFGEN allow us to ge<sup>t</sup> a better handle on the physical properties of both the binaries and single stars and compare them across a wide range of metallicities.

As discussed in Section 2, while much progress has been made in the field of WR research, there is still much to be done. With *Gaia*, it is now possible to determine distances to nearby WRs within our own Galaxy leading to better observations of their reddenings and better modeling of their physical properties. We are additionally learning more about the content of other types of massive stars (such as O/B stars, RSGs, etc.) that allow us to compare the ratio of those stars vs. WRs to the evolutionary model predictions placing further constraints on the models. Finally, we are continuing to push the observational boundaries to further and further galaxies in an attempt to observe complete samples of WRs in both the galaxies of the Local Group and beyond!

**Author Contributions:** K.N. wrote the majority of the paper with P.M. contributing primarily to Sections 2 and 4.

**Funding:** This research was partially funded by the National Science Foundation, most recently through AST-1612874, as well as through Lowell Observatory.

**Acknowledgments:** The authors acknowledge all of their dear friends, family, and collaborators who have supported them though many years of Wolf–Rayet research. They additionally thank J.J. Eldridge for her help with better understanding WR binary evolution, Paul Crowther for useful information on Galactic WR surveys, as well as an anonymous referee whose suggestions improved the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
