Strongly lensed SNe Ia in the era of LSST: observing cadence for lens discoveries and time-delay measurements

The upcoming Large Synoptic Survey Telescope (LSST) will detect many strongly lensed Type Ia supernovae (LSNe Ia) for time-delay cosmography. This will provide an independent and direct way for measuring the Hubble constant $H_0$, which is necessary to address the current $4.4 \sigma$ tension in $H_0$ between the local distance ladder and the early Universe measurements. We present a detailed analysis of different observing strategies for the LSST, and quantify their impact on time-delay measurement between multiple images of LSNe Ia. For this, we produced microlensed mock-LSST light curves for which we estimated the time delay between different images. We find that using only LSST data for time-delay cosmography is not ideal. Instead, we advocate using LSST as a discovery machine for LSNe Ia, enabling time delay measurements from follow-up observations from other instruments in order to increase the number of systems by a factor of 2 to 16 depending on the observing strategy. Furthermore, we find that LSST observing strategies, which provide a good sampling frequency (the mean inter-night gap is around two days) and high cumulative season length (ten seasons with a season length of around 170 days per season), are favored. Rolling cadences subdivide the survey and focus on different parts in different years; these observing strategies trade the number of seasons for better sampling frequency. In our investigation, this leads to half the number of systems in comparison to the best observing strategy. Therefore rolling cadences are disfavored because the gain from the increased sampling frequency cannot compensate for the shortened cumulative season length. We anticipate that the sample of lensed SNe Ia from our preferred LSST cadence strategies with rapid follow-up observations would yield an independent percent-level constraint on $H_0$.