Using the stellar evolution code-Modules for Experiments in Stellar Astrophysics (MESA), we investigate the evolution of massive stars with different rotational velocities and metallicities towards Wolf-Rayet stars. In our simulations, the initial rotating velocities are taken as 0, 250, 500 and 650 km s −1 , and the metallicities equal to 0.02, 0.014, 0.008, 0.006, 0.004 and 0.002. We show our rapid rotation models in the HR diagram compared with the observations. We find that the rotational mixing is less efficient at high metallicity, and these stars become Wolf-Rayet (WR) stars when the helium in their center is ignited. However, rapid rotating massive stars at low metallicity can easily evolve into WR stars due to the rotation resulted in chemically homogeneous evolution. This can explain the origin of single WR stars in galaxy at low metallicity. In our models, the observed SMC WR stars are consistent with the single-star evolution models. However at higher metallicities our single-star evolution models can only explain the luminous, hydrogen-rich WN stars and O stars (which are classified as WR stars previously).

The white dwarf (WD) + helium (He) star binary channel plays an important role in the single degenerate scenario for the progenitors of type Ia supernovae (SNe Ia). Previous studies on the WD + main sequence star evolution have shown that the magnetic fields of WDs may significantly influence their accretion and nuclear burning processes. In this work we focus on the evolution of magnetized WD + He star binaries with detailed stellar evolution and binary population synthesis (BPS) calculations. In the case of magnetized WDs, the magnetic fields may disrupt the inner regions of the accretion disk, funnel the accretion flow onto the polar caps and even confine helium burning within the caps. We find that, for WDs with sufficiently strong magnetic fields, the parameter space of the potential SN Ia progenitor systems shrinks toward shorter orbital periods and lower donor masses compared with that in the non-magnetized WD case. The reason is that the magnetic confinement usually works with relatively high mass transfer rates, which can trigger strong wind mass loss from the WD, thus limiting the He-rich mass accumulation efficiency. The surviving companion stars are likely of low-mass at the moment of the SN explosions, which can be regarded as a possible explanation for the non-detection of surviving companions after the SNe or inside the SN remnants. However, the corresponding birthrate of Galactic SNe Ia in our high-magnetic models is estimated to be ∼(0.08–0.13) × 10−3 yr−1 ( ∼0.17–0.28 × 10−3 yr−1 for the non-magnetic models), significantly lower than the observed Galactic SN Ia birthrate.

Magnetars form a special population of neutron stars with strong magnetic fields and long spin periods. About 30 magnetars and magnetar candidates known currently are probably isolated, but the possibility that magnetars are in binaries has not been excluded. In this work, we perform spin evolution of neutron stars with different magnetic fields in wind-fed high-mass X-ray binaries and compare the spin period distribution with observations, aiming to find magnetars in binaries. Our simulation shows that some of the neutron stars, which have long spin periods or are in widely-separated systems, need strong magnetic fields to explain their spin evolution. This implies that there are probably magnetars in high-mass X-ray binaries. Moreover, this can further provide a theoretical basis for some unclear astronomical phenomena, such as the possible origin of periodic fast radio bursts from magnetars in binary systems.