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The nature of the progenitors of type Ia supernovae (SNe Ia) remains a mystery. Binary systems consisting of a white dwarf (WD) and a main-sequence (MS) donor are potential progenitors of SNe Ia, in which a thermonuclear explosion of the WD may occur when its mass reaches the Chandrasekhar limit during accretion of material from a companion star. In the present work, we address theoretical rates and delay times of a specific MS donor channel to SNe Ia, in which a helium (He) star + MS binary produced from a common envelope event subsequently forms a WD + MS system without the He star undergoing mass transfer by Roche lobe overflow. By combining the results of self-consistent binary evolution calculations with population synthesis models, we find that the contribution of SNe Ia in this channel is around 2.0 × 10−4 yr−1. In addition, we find that delay times of SNe Ia in this channel cover a range of about 1.0–2.6 Gyr, and almost all SNe Ia produced in this way (about 97%) have a delay time of ≳1 Gyr. While the rate of SN Ia in this work is about 10% of the overall SN Ia rate, the channel represents a possible contribution to the old population (1–3 Gyr) of observed SNe Ia. [ABSTRACT FROM AUTHOR]

Context. Type Iax supernovae (SNe Iax) are proposed as one new sub-class of SNe Ia since they present sufficiently distinct observational properties from the bulk of SNe Ia. Observationally, SNe Iax have been estimated to account for ~5%-30% of the total SN Ia rate, and most SNe Iax have been discovered in late-type galaxies. In addition, observations constrain the progenitor systems of some SN Iax progenitors that have ages of <80 Myr. Although the identity of the progenitors of SNe Iax is unclear, the weak deflagration explosions of Chandrasekhar-mass (Ch-mass) carbon/oxygen white dwarfs (C/OWDs) seem to provide a viable physical scenario. Aims. Comparing theoretical predictions from binary population synthesis (BPS) calculations with observations of SNe Iax, we put constraints on the single-degenerate (SD) Ch-mass model as a possible SN Iax progenitor. Methods. Based on the SD Ch-mass model, the SN rates and delay times are predicted by combining binary evolution calculations for the progenitor systems into a BPS model. Moreover, with current X-ray observations of SNe Iax, we constrain the pre-explosion mass-loss rates of stellar progenitor systems by using two analytic models. Results. From our calculations, the long delay times of ≳3Gyr and low SN rates of ~3 × 10-5 yr-1 are found in the red-gaint donor channel, indicating that this channel is unlikely to produce SNe Iax. With our standard models, we predict that the Galactic SN Iax rate from the main-sequence (helium-star) donor scenario is ~1.5 × 10-3 yr-1 (~3 × 10-4 yr-1). The total rate of these two models is consistent with the observed SN Iax rate. The short delay times in the helium-star donor channel (<100 Myr) support the young host environments of SNe Iax. However, the relatively long delay times in the main-sequence donor channel (~250 Myr-1Gyr) are less favourable for the observational constraints on the ages of SN Iax progenitors. Finally, with current X-ray observations for SNe Iax, we set an upper limit on the pre-SN mass-loss rate at Ṁ ≳ a few× 10-4 M⊙ yr-1 (for a wind velocity of vw = 100 km s-1). Conclusions. The delay times in the SD Ch-mass model do not account for a significant number of SNe Iax being located in late-type, star-forming galaxies. However, at least one SN Iax event (SN 2008ge) is hosted by an S0 galaxy with no signs of star formation. Current X-ray observations for SNe Iax cannot rule out the SD Ch-mass model. Taking all these into account and considering the uncertainty of the observed rate for SN Iax events, we suggest that some SNe Iax may be produced from weak deflagrations of Ch-mass C/O WDs in SD progenitor systems, especially in the helium-star donor channel. This is consistent with recent analysis of HST observations, which suggests that the SN Iax SN2012Z had a progenitor system which contained a helium-star companion. However, this SD deflagration model is still unlikely to be the most common progenitor scenario for SNe Iax. [ABSTRACT FROM AUTHOR]