 AB 2 and 10 suggested that these stars evolved from an initial mass of about 30 M⊙, while the corresponding track never turns into a WR star.
In the above comparison remains unclear whether the adopted metallicities are causing the different results, or whether other details of the model calculations are the cause. We also compared the HRD positions of our program stars with the non-rotating stellar evolution models from Eldridge & Vink (2006, see Fig. 20, which are calculated for an initial metallicity of 0.28 Z⊙. The mass-loss rates which they adopted for their non-rotating models in the pre-WR phases is comparable to the one used by Meynet & Maeder (2005) for their rotating models. During the WR phase, the models described in Eldridge & Vink (2006) account for a metallicity scaling of the mass-loss rate, while such a dependency was not considered in the older generation of the Geneva models (Meynet & Maeder 2005). Taking into account that the total WR lifetime is nearly independent from the metallicity scaling of the mass-loss rate during the WR phase (Eldridge & Vink 2006), the comparison of these tracks with the ones shown in Figs. 18 and 19 might give some indication of the impact of the metallicity.
For the stars in our sample with a luminosity of log (L/L⊙) ≥ 5.8, there is a good agreement with respect to the tracks from Eldridge & Vink (2006), whereas the two faintest objects (SMC AB 2 and 10) cannot be reproduced at all. Although the tracks from Eldridge & Vink (2006), compared to the Geneva tracks, coincide better with our results, these models also require a minimum initial mass of 45 M⊙ to reach the WR phase and therefore do not reach the WN phase for luminosities as low as those of SMC AB 2 and 10.
The higher the metallicity of the stellar evolution models, the higher the degree of agreement that can be achieved with the HRD positions of the WN stars in the SMC. Our sample is best reproduced with tracks for Z = 0.56 Z⊙ from Meynet & Maeder (2005), which account for the implications of rotation. The model atmospheres used in our analysis have a metallicity of Z = 0.13 Z⊙. Our relatively young WN stars might have been born with a slightly higher metallicity than this average value for the SMC. However, we do not see evidence for a considerably higher iron abundance than the value given in Table 1. An exception is SMC AB 4, which might be reproduced with stellar atmosphere models of higher metallicities as well. The enhanced nitrogen abundance observed (see Table A.3) can be well understood in terms of self-enrichment with products from central helium burning. In conclusion, we suggest that it is not the metallicity itself, but some other effect which is not properly accounted for in the evolution models that are causing the difference between the tracks and the empirical HRD positions.
Same as Fig. 18, but with non-rotating evolution tracks for Z = 0.28 Z⊙ calculated by Eldridge & Vink (2006).
Apart from the discrepancies described above, another disagreement between our analysis and the stellar evolution models is the surface hydrogen abundances. When the evolution tracks cross the empirical HRD positions of our SMC WN stars, they predict a considerably lower hydrogen abundance at the surface than observed. This coincides with the fact that the mass-loss rates derived in our analysis (see Sect. 5.3) are on average lower than the values given by the mass-loss relation from Nugis & Lamers (2000), which is often applied in stellar evolution models4. Thus, the discrepancy in the hydrogen abundance might be caused by too high WR mass-loss rates in the evolution models, which remove too much of the hydrogen-rich envelope. Therefore, higher mass-loss rates in the WR phase would not bring the stellar evolution tracks into accordance with the empirical HRD positions of the SMC WN stars. We conclude that either the mass-loss in a pre-WR stage is significantly higher (via either continous mass-loss or episodic bursts), as suggested by e.g., Sander et al. (2012) to explain the disagreement between WC stars and evolution models at Galactic metallicity (see also Vanbeveren et al. 1998, 2007; Georgy 2012), or that standard models for single star evolution still miss essential physical ingredients.
Such a missing ingredient could be very fast rotation, which lead to full internal mixing and quasi-homogeneous evolution. This type of evolution proceeds roughly speaking directly from the hydrogen zero age main sequence to the helium main sequence (e.g., Maeder 1987; Langer 1992; Yoon & Langer 2005; Woosley & Heger 2006). Homogeneous evolution is expected to be more common at low metallicities, since rotational mixing is more efficient (Brott et al. 2011) and angular momentum loss is lower because of the reduced wind mass-loss (see Sect. 5.3.2). Thus, rapid initial rotation will be conserved for a longer period, facilitating the evolution toward the blue part of the HRD even at relatively low initial masses.
HRD of the single WN stars compared to the evolution tracks that account for very rapid initial rotation (vrot> 500 km s-1, Brott et al. 2011). These evolution models assume an initial metallicity of 0.14 Z⊙ and were calculated roughly until the central hydrogen exhaustion. The labels close to the tracks refer to the initial mass. The color coding in the same as in Figs. 18 and 19 (see also the inlet).
For SMC AB 1 and 2, this scenario was already proposed by Martins et al. (2009), mainly because of the high hydrogen abundance and the location of these two objects in the HRD. As evident from Fig. 21, stellar evolution tracks (Brott et al. 2011), when accounting for vary rapid initial rotation (vrot> 500 km s-1) and a metallicity of 0.14 Z⊙, can at first glance explain the HRD positions of most SMC WN stars. Taking a closer look at the evolution of chemically homogeneous stars, however, reveals that the hydrogen abundance of these models in the corresponding parameter range is considerably lower than derived from the spectral analysis. The 50 M⊙ track close to the position of SMC AB 1, e.g., predicts a hydrogen mass-fraction below 9%, while our analysis (in agreement with the findings of Martins et al. 2009) results in a value of XH = 50%. For comparison, the 80 M⊙ track from Eldridge & Vink (2006) exhibit a hydrogen abundance of about 15% close to the position of SMC AB 1. The disagreement between our results and the evolution tracks published by Brott et al. (2011) is confirmed by the BONNSAI5 Bayesian tool (Schneider et al. 2014), which allows us to qualitatively match the Bonn stellar evolution models (Brott et al. 2011; Köhler et al. 2015) to the results obtained from our stellar atmosphere analyses, accurately accounting for observational uncertainties. With the exception of SMC AB 4, the parameters derived in our analysis could not be consistently reproduced by this tool. Thus, the discrepancy between the hydrogen abundance predicted by the evolution models and the values derived by means of the spectral analysis does not support the scenario of homogeneous evolution.
Evolution of the equatorial rotational velocity as a function of time for the stellar evolution models calculated by Brott et al. (2011, solid lines) and a 60 M⊙ track (dashed line) published by Meynet & Maeder (2005). Both studies account for very rapid rotation (vrot,ini> 500 km s-1) and an initial metallicity of 0.14 Z⊙. The labels close to the tracks refer to the initial mass. The color coding is the same as in Figs. 18 and 19 (see also the inlet).
From homogeneous models, it is expected that the rotational velocity is substantial (vrot> 100 km s-1) during a considerable part of the stellar evolution. For the quasi-homogeneous models shown in Fig. 21 (Brott et al. 2011, vrot,ini> 500 km s-1), the evolution of the equatorial velocity as a function of time is illustrated in Fig. 22. The rotational velocity in these models never falls below 100 km s-1. For comparison we include in this figure a 60 M⊙ track published by Meynet & Maeder (2005) that also accounts for fast rotation (vrot,ini = 500 km s-1) and quasi homogeneous evolution. In contrast to the tracks calculated by Brott et al. (2011), the Geneva track exhibits considerably lower rotational velocities during the WR phase. As discussed in Sect. 5.5, rotational velocities as high as 200 km s-1 at the stellar photosphere could not be excluded for the analyzed WN 3 stars, as long as the winds do not co-rotate with the photosphere. Thus, homogeneous evolution remains a promising possibility to explain the origin of the WN stars in the SMC.
The influence of binary evolution on the rotational velocities of massive stars was recently studied by de Mink et al. (2013) by means of a rapid binary evolution code. Assuming a uniform initial distribution of the rotational velocity with vrot< 200 km s-1, these authors show that the rapid rotators observed in populations of main-sequence stars might consist exclusively of stars that already underwent Roche-lobe overflow. Hence, initially fast rotation could be very rare among