Close binary evolution based on Gaia DR2 The origin of late WC-type Wolf-Rayet stars with low luminosity

Context. The observed late-type WC Wolf-Rayet stars (WC7-9) with low luminosity below log L/L-circle dot  < 5.4 in the HR diagram cannot be reproduced satisfactorily by the evolutionary track of single stars. The mass transfer due to Roche lobe overflow drastically modifies the internal structure and surface compositions of two components. Therefore, binaries provide a very promising evolutionary channel to produce these WC stars. Aims. The Gaia satellite provides accurate distances to WC stars and confirms the luminosities of WC stars. Based on a small grid containing single stars and binaries, we aim to investigate the extent to which the evolution of a single or a close binary can reproduce the properties of these stars. Methods. We considered single-star models with masses between 20 and 40 M-circle dot. We calculated the evolution for three binaries with a 30 M-circle dot primary star with a 27 M-circle dot companion star with initial orbital periods of 6.0, 20.0, 500.0, and 1000.0 days. Results. The rotating single star can evolve into a late-type WC star but with high luminosity (i.e., log L/L-circle dot  > 5.4). Enhanced wind mass loss rates during RSG and WR stages, as proposed in the literature, can cause the star to approach the observational range of low-luminosity WC stars and favor the formation of low-luminosity WO stars. In a wide binary system with initial P-orb  = 1000 days, the primary star can evolve into a late-type WC star and be compatible with the observed properties of the low-luminosity WC stars. The result is almost insensitive to the adopted accretion efficiency 1 - beta. Conclusions. Compared with single stars, the low brightness is due to a smaller temperature gradient inside the star after the Case C Roche lobe overflow, while the low effective temperature is due to envelope expansion. There are four physical reasons for the formation of the expanding envelope. Firstly, less helium envelope can be transferred to the companion star in this system. Heavy helium envelopes can be heated by the helium burning shell and this creates the necessary conditions for the envelope expansion. Secondly, the expansion of the helium envelope can also be boosted by the sharp shrinkage of the larger carbon-oxygen core through the mirror effect. Thirdly, a more massive WC star can attain a higher Eddington factor because of its higher L/M ratio. The increase in L/M with mass is the primary cause for the extended envelopes in WC stars. Finally, the iron opacity bump at T  similar to  10(5.25) K may also trigger envelope inflation because it can lead to a larger Eddington factor.