With the increasing number of observed magnetic white dwarfs (WDs), the role of magnetic field of the WD in both single and binary evolutions should draw more attentions. In this study, we investigate the WD/main-sequence star binary evolution with the Modules for Experiments in Stellar Astrophysics (MESA code), by considering WDs with non-, intermediate and high magnetic field strength. We mainly focus on how the strong magnetic field of the WD (in a polar-like system) affects the binary evolution towards type Ia supernovae (SNe Ia). The accreted matter goes along the magnetic field lines and falls down onto polar caps, and it can be confined by the strong magnetic field of the WD, so that the enhanced isotropic pole-mass transfer rate can let the WD grow in mass even with a low mass donor with the low Roche-lobe overflow mass transfer rate. The results under the magnetic confinement model show that both initial parameter space for SNe Ia and characteristics of the donors after SNe Ia are quite distinguishable from those found in pervious SNe Ia progenitor models. The predicted natures of the donors are compatible with the non-detection of a companion in several SN remnants and nearby SNe.
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