Empirical Delay Time Distributions of Type Ia Supernovae From The Extended GOODS/HST Supernova Survey

Using the Hubble Space Telescope ACS imaging of the GOODS North and South fields during Cycles 11, 12, and 13, we derive empirical constraints on the delay-time distribution function for type Ia supernovae. We extend our previous analysis to the three-year sample of 56 SNe Ia over the range 0.2<z<1.8, using a Markov chain Monte Carlo to determine the best-fit unimodal delay-time distribution function. The test, which ultimately compares the star formation rate density history to the unbinned volumetric SN Ia rate history from the GOODS/HST-SN survey, reveals a SN Ia delay-time distribution that is tightly confined to 3-4 Gyrs (to >95% confidence). This result is difficult to resolve with any intrinsic delay-time distribution function (bimodal or otherwise), in which a substantial fraction (e.g., >10%) of events are ``prompt'', requiring less than approximately 1 Gyr to develop from formation to explosion. The result is, however, strongly motivated by the decline in the number of SNe Ia at z>1.2. Sub-samples of the HST-SN data confined to lower redshifts (z<1) show plausible delay-time distributions that are dominated by prompt events, which is more consistent with results from low-redshift supernova samples and supernova host galaxy properties. Scenarios in which a substantial fraction of z>1.2 supernovae are extraordinarily obscured by dust may partly explain the differences in low-z and high-z results. Other possible resolutions may include environmental dependencies (such as gas-phase metallicity) that affect the progenitor mechanism efficiency, especially in the early universe.