Occurrence rates of terrestrial planets orbiting mid-to-late M dwarfs from TESS Sectors 1-42

We analyze a volume-complete sample of 365 mid-to-late M dwarfs within 15 pc with masses between 0.1 and 0.3 M_Sun observed by TESS within Sectors 1 to 42. The median mass of the stars in this sample is 0.17 M_Sun. We search the TESS 2-minute cadence light curves for transiting planets with orbital periods below 7 days using a modified Box-Least Squares algorithm and recover all 6 known planets as well as a likely planet candidate orbiting LHS 475. We further perform a transit injection and recovery analysis to characterize the sensitivity as a function of planet radius, insolation, and orbital period. We find a median sensitivity above 70% for transiting planets with orbital periods below 1 day and radii above 0.6 R_Earth; we also find a median sensitivity near unity for any planet with a radius of at least 1 R_Earth up to an orbital period of 7 days. We estimate an occurrence rate of 0.61 [0.42, 0.85] planets per M dwarf for periods below 7 days. We find that in contrast to heavier stars, the close-in planet population around the smallest M dwarfs is heavily lopsided towards terrestrial planets, which outnumber sub-Neptunes at a ratio of 14 to 1. This discrepancy persists even when accounting for the total incident flux the planets receive from the host star.