  The time delay between the formation of a population of stars and the onset
of type Ia supernovae (SNe Ia) sets important limits on the masses and nature
of SN Ia progenitors. Here we use a new observational technique to measure this
time delay by comparing the spatial distributions of SNe Ia to their local
environments. Previous work attempted such analyses encompassing the entire
host of each SN Ia, yielding inconclusive results. Our approach confines the
analysis only to the relevant portions of the hosts, allowing us to show that
even so-called "prompt" SNe Ia that trace star-formation on cosmic timescales
exhibit a significant delay time of 200-500 million years. This implies that
either the majority of Ia companion stars have main-sequence masses less than 3
solar masses, or that most SNe Ia arise from double-white dwarf binaries. Our
results are also consistent with a SNe Ia rate that traces the white dwarf
formation rate, scaled by a fixed efficiency factor.
