Hydrodynamical simulations predict that a large amount of hydrogen (>0.1 solar masses) is removed from a hydrogen-rich companion star by the SN explosion in the single-degenerate scenario of Type Ia supernovae (SNe Ia). However, non-detection of hydrogen-rich material in the late-time spectra of SNe Ia suggests that the hydrogen mass stripped from the progenitor system is <0.001-0.058 solar masses. In this letter we include thermohaline mixing into self-consistent binary evolution calculations for the helium-enriched main-sequence (HEMS) donor channel of SNe Ia for the first time. We find that the swept-up hydrogen masses expected in this channel are around 0.10-0.17 solar masses, which is higher than the observational limits, although the companion star is strongly helium-enriched when the SN explodes. This presents a serious challenge to the HEMS donor channel.
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