On the detectability of transiting planets orbiting white dwarfs using LSST

White dwarfs are one of the few types of stellar objects for which we know almost nothing about the possible existence of companion planets. Recent evidence for metal contaminated atmospheres, circumstellar debris disks and transiting planetary debris all indicate that planets may be likely. However, white dwarf transit surveys are challenging due to the intrinsic faintness of such objects, the short timescale of the transits and the low transit probabilities due to their compact radii. The Large Synoptic Survey Telescope (LSST) offers a remedy to these problems as a deep, half-sky survey with fast exposures encompassing approximately 10 million white dwarfs with $r<24.5$ apparent magnitude. We simulate LSST photometric observations of 3.5 million white dwarfs over a ten-year period and calculate the detectability of companion planets with $P<10$ d via transits. We find typical detection rates in the range of $5 \times 10^{-6}$ to $4 \times 10^{-4}$ for Ceres-sized bodies to Earth-sized worlds, yielding $\sim 50$ to $4\,000$ detections for a 100% occurrence rate of each. For terrestrial planets in the continuously habitable zone, we find detection rates of $\sim 10^{-3}$ indicating that LSST would reveal hundreds of such worlds for occurrence rates in the range of 1% to 10%.