The detection efficiency of Type Ia supernovae from the Zwicky Transient Facility: limits on the intrinsic rate of early flux excesses

Samples of young Type Ia supernovae have shown 'early excess' emission in a few cases. Similar excesses are predicted by some explosion and progenitor scenarios and hence can provide important clues regarding the origin of thermonuclear supernovae. They are, however, only predicted to last up to the first few days following explosion. It is therefore unclear whether such scenarios are intrinsically rare or whether the relatively small sample size simply reflects the difficulty in obtaining sufficiently early detections. To that end, we perform toy simulations covering a range of survey depths and cadences, and investigate the efficiency with which young Type Ia supernovae are recovered. As input for our simulations, we use models that broadly cover the range of predicted luminosities. Based on our simulations, we find that in a typical 3 d cadence survey, only ~10 per cent of Type Ia supernovae would be detected early enough to rule out the presence of an excess. A 2 d cadence, however, should see this increase to ~15 per cent. We find comparable results from more detailed simulations of the Zwicky Transient Facility surveys. Using the recovery efficiencies from these detailed simulations, we investigate the number of young Type Ia supernovae expected to be discovered assuming some fraction of the population comes from scenarios producing an excess at early times. Comparing the results of our simulations to observations, we find that the intrinsic fraction of Type Ia supernovae with early flux excesses is $\sim 28^{+13}_{-11}{{\ \rm per\ cent}}$.