The Population Synthesis of Wolf–Rayet Stars Involving Binary Merger Channels

Wolf–Rayet (W-R) stars are very important massive stars. However, their origin and the observed binary fraction within the entire W-R population are still debated. We investigate some possible merger channels for the formation of W-R stars, including main sequence (MS)/Hertzsprung gap (HG) + MS, He + HG/giant branch (GB). We find that many products produced via binary merger can evolve into W-R stars, the MS/HG + MS merger channel can explain W-R stars with luminosities higher than ∼10 ^5.4 L _⊙ , while the He + HG/GB merger channel can explain low-luminosity W-R stars in the range of 10 ^4.7 L _⊙ ∼ 10 ^5.5 L _⊙ . In the population synthesis analysis of W-R stars, we assume an initial binary fraction ( f _ini,bin ) of 50% and 100% for massive stars. We also assume that MS/HG + MS merger products are nonrotating or rapidly rotating ( ω / ω _crit = 0.8). In different cases, the calculated single fractions of W-R stars range from 22.2%–60.6% in the Milky Way (MW) and from 8.3%–70.9% in the Large Magellanic Cloud (LMC). The current observations fall within the range of our calculations. When the merger product of MS/HG + MS rotates rapidly, we estimate that there are approximately 1015–1396 W-R stars in the MW and 128–204 W-R stars in the LMC. Our model also roughly reproduces the observed single-peak luminosity distribution of W-R stars in the MW. However, the weak bimodal luminosity distribution observed in the LMC is not reproduced in our model. We assess that this may be due to the model underestimating the mass-loss rate in the LMC. In conclusion, we consider that the binary merger is a significant formation channel for W-R formation, and can explain the observed high fraction of the single W-R stars in the total population.