Charbonneau, DavidMent, Kristo2023-06-0220232023-05-122023-05Ment, Kristo. 2023. Three Terrestrial Planets Transiting Mid-to-Late M Dwarfs and Constraints on the Occurrence of Such Worlds. Doctoral dissertation, Harvard University Graduate School of Arts and Sciences.30492640https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37375876While the planet population around Solar-type stars has been relatively well studied and characterized, the same cannot be said for the least massive stars with masses below 0.3 M$_\odot$. Planet formation and evolution processes are dependent on stellar mass as well as irradiation environment. I aim to constrain the occurrence rate of planets within a volume-complete sample of mid-to-late M dwarfs with masses between 0.1-0.3 M$_\odot$~within 15 pc of the Sun. To this end, I first present the discoveries of three terrestrial planets within that sample, found via the transit method. I then proceed to estimate the incidence rate of such worlds through a thorough investigation of TESS photometric data. I present the discovery of LHS 1140 c, a terrestrial planet with a mass of $1.81 \pm 0.39$ M$_\oplus$~and a radius of $1.28 \pm 0.02$ R$_\oplus$~on a 3.78-day orbit around a nearby M dwarf. This planet was identified from a single transit observation to which the trained neural network assigned a low probability of being caused by atmospheric variations or telescope systematics. I then present the discovery of TOI 540 b, a sub-Earth-sized planet with a radius of $0.90 \pm 0.05$ R$_\oplus$~on a 1.24-day orbit around a magnetically active M dwarf. The star has a high X-ray luminosity and is one of the few known M dwarf planetary systems where the stellar rotation period (17.4 hours) is shorter than the orbital period of the planet. Finally, I announce the discovery of LHS 475 b, another terrestrial planet with a radius of $0.96 \pm 0.02$ R$_\oplus$~on a 2.03-day orbit around an M dwarf 12.5 pc from the Sun. I produce independent estimates of planet detection sensitivity for every mid-to-late M dwarf within the 15 pc sample observed by TESS as a function of orbital period, planet radius, and insolation. The median mass of this sample is 0.17 M$_\odot$. I calculate a cumulative occurrence rate of $0.61^{+0.24}_{-0.19}$ planets with orbital periods less than 7 days and radii above 0.5 R$_\oplus$~per M dwarf. This corresponds to an incidence rate of $0.49^{+0.19}_{-0.15}$ planets per star with insolations above 4 S$_\oplus$. I find that for insolations above 4 S$_\oplus$, rocky planets heavily outnumber non-rocky planets around low-mass M dwarfs at a ratio of 13 to 1, in contrast to the planet population around early M dwarfs (median mass 0.50 M$_\odot$) where rocky and non-rocky planets are equally abundant. I place an upper limit of 0.07 planets with radii above 1.5 R$_\oplus$~per mid-to-late M dwarf, within the orbital period range of 0.5-7 days. The cumulative occurrence rate of planets with insolations above 4 S$_\oplus$~is lower around mid-to-late M dwarfs (0.17 M$_\odot$) than it is around early M dwarfs (0.50 M$_\odot$), in contrast with previous studies that have found an inverse correlation between planet incidence and stellar mass amongst early-M and FGK dwarfs.application/pdfenexoplanetslow-mass starsplanet demographicstransiting planetsAstronomyAstrophysicsThesis or Dissertation2023-06-020000-0001-5847-9147