Abstract 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.

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