Most massive stars, the progenitors of core-collapse supernovae, are in close binary systems and may interact with their companion through mass transfer or merging. We undertake a population synthesis study to compute the delay-time distribution of core-collapse supernovae, that is, the supernova rate versus time following a starburst, taking into account binary interactions. We test the systematic robustness of our results by running various simulations to account for the uncertainties in our standard assumptions. We find that a significant fraction, $15^{+9}_{-8}$%, of core-collapse supernovae are `late, that is, they occur 50-200 Myrs after birth, when all massive single stars have already exploded. These late events originate predominantly from binary systems with at least one, or, in most cases, with both stars initially being of intermediate mass ($4-8M_{odot}$). The main evolutionary channels that contribute often involve either the merging of the initially more massive primary star with its companion or the engulfment of the remaining core of the primary by the expanding secondary that has accreted mass at an earlier evolutionary stage. Also, the total number of core-collapse supernovae increases by $14^{+15}_{-14}$% because of binarity for the same initial stellar mass. The high rate implies that we should have already observed such late core-collapse supernovae, but have not recognized them as such. We argue that $phi$ Persei is a likely progenitor and that eccentric neutron star - white dwarf systems are likely descendants. Late events can help explain the discrepancy in the delay-time distributions derived from supernova remnants in the Magellanic Clouds and extragalactic type Ia events, lowering the contribution of prompt Ia events. We discuss ways to test these predictions and speculate on the implications for supernova feedback in simulations of galaxy evolution.
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