For single stars the critical mass may be as high as 10-12 M solar, while for close binaries it may be as low as 6-8 M solar.
This scenario has also important consequences for the minimum initial mass of a massive star that becomes a neutron star. We illustrate the consequences of such a dichotomous kick scenario using binary population synthesis simulations and discuss its implications. This leads to a dichotomous distribution of neutron star kicks, as inferred previously, where neutron stars in relatively close binaries attain low kick velocities. We suggest that the core collapse in an electron-capture supernova (and possibly in the case of relatively small iron cores) leads to a prompt or fast explosion rather than a very slow, delayed neutrino-driven explosion and that this naturally produces neutron stars with low-velocity kicks. We find that the initially more massive stars in binary systems with masses in the range 8-11 M solar are likely to undergo an electron-capture supernova, while single stars in the same mass range would end as ONeMg white dwarfs. Stars below ~11 M solar, on the other hand, can end up with larger helium and metal cores if they have a close companion, since the second dredge-up phase that reduces the helium core mass dramatically in single stars does not occur once the hydrogen envelope is lost. Stars with initial masses larger than ~11 M solar that experience core collapse will generally have smaller iron cores at the point of explosion if they lost their envelopes through a binary interaction during or soon after core hydrogen burning. Interactions with a companion star may change the final rate of rotation, the size of the helium core, the strength of carbon burning, and the final iron core mass. We systematically examine how the presence in a binary affects the final core structure of a massive star and its consequences for the subsequent supernova explosion.
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