The supernova rate and delay time distribution in the Magellanic Clouds

We use the supernova remnants (SNRs) in the two Magellanic Clouds (MCs) as a supernova (SN) survey, 'conducted' over tens of kyr, from which we derive the current SN rate, and the SN delay time distribution (DTD), i.e. the SN rate versus time that would follow a hypothetical brief burst of a star formation. In a companion paper we have compiled a list of 77 SNRs in the MCs, and argued that it is a fairly complete record of the SNRs that are now in the Sedov phase of their expansions. We recover the SN DTD by comparing the numbers of SNRs observed in small individual 'cells' in these galaxies to the star formation histories of each cell, as calculated from resolved stellar populations by Harris & Zaritsky. We identify the visibility times of SNRs in each cell with the Sedov-phase lifetimes, which depend on the local ambient densities. The local densities are estimated from 21-cm emission, from an inverse Schmidt-Kennicutt law based on either Hα emission or the star formation rate from the resolved stellar populations, and from combinations of these tracers. This is the first SN DTD that is based on resolved stellar populations. We detect a population of 'prompt' Type Ia SNe (that explode within 330 Myr of star formation) at >99 per cent confidence level (CL). The best fit for the number of prompt Type Ia SNe per stellar mass formed is 2.7 -11.0 × 10^-3 M^-1_⊙, depending on the density tracer used. The 95 per cent CL range for a 'delayed' (from 330 Myr to a Hubble time) Type Ia component is <1.6 × 10^-13 SN yr^-1 M^-1_⊙, consistent with rate measurements in old populations. The current total (core-collapse+Ia) SN rate in the MCs is 2.5-4.6 SNe per millennium (68 per cent CL+systematics), or 1.7-3.1 SNuM [SNe (100 yr 10¹⁰ M_⊙) ^-1], in agreement with the historical record and with rates measured in other dwarf irregulars. Conversely, assuming the SNRs are in free expansion, rather than in their Sedov phase, would impose on the SNRs a maximum age of 6 kyr, and would imply an MC SN rate per unit mass that is five times higher than in any type of galaxy, and a low-mass limit for core-collapse progenitors in conflict with stellar evolution theory.