The Effects of Binary Evolution on the Dynamics of Core Collapse and Neutron-Star Kicks

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. 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. Stars with initial masses larger than \sim 11\Ms that experiece core collapse will generally have smaller iron cores at the time of the explosion if they lost their envelopes due to a previous binary interaction. Stars below \sim 11\Ms, 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 which reduces the helium core mass dramatically in single stars does not occur once the hydrogen envelope is lost. We find that the initially more massive stars in binary systems with masses in the range 8 - 11\Ms are likely to undergo an electron-capture supernova, while single stars in the same mass range would end as ONeMg white dwarfs. 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 explosion rather than a delayed neutrino-driven explosion and that this naturally produces neutron stars with low-velocity kicks. 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 illustrate the consequences of such a dichotomous kick scenario using binary population synthesis simulations and discuss its implications. This scenario has also important consequences for the minimum initial mass of a massive star that becomes a neutron star. (Abbreviated.)