Abstract: Reliable detections of Earth-sized planets in the habitable zone remain elusive in the Kepler sample, even for M dwarfs. The Kepler sample was once thought to contain a considerable number of M-dwarf stars ( T-eff < 4000 K), which hosted enough Earth-sized ([0.5, 1.5] R-circle plus) planets to estimate their occurrence rate (eta(circle plus)) in the habitable zone. However, updated stellar properties from Gaia have shifted many Kepler stars to earlier spectral type classifications, with most stars (and their planets) now measured to be larger and hotter than previously believed. Today, only one partially reliable Earth-sized candidate remains in the optimistic habitable zone, and zero in the conservative zone. Here we performed a new investigation of Kepler's Earth-sized planets orbiting M-dwarf stars, using occurrence rate models with considerations of updated parameters and candidate reliability. Extrapolating our models to low instellations, we found an occurrence rate of eta(circle plus) = 8.58( – 8.22 )(+ 17.94) % for the conservative habitable zone (and 14.22 (- 12.71) (+ 24.96 )% for the optimistic one), consistent with previous works when considering the large uncertainties. Comparing these estimates to those from similarly comprehensive studies of Sun-like stars, we found that the current Kepler sample does not offer evidence to support an increase in eta(circle plus) from FGK to M stars. While the Kepler sample is too sparse to resolve an occurrence trend between early and mid-to-late M dwarfs for Earth-sized planets, studies including larger planets and/or data from the K2 and TESS missions are well suited to this task.

Abstract: Planet formation imprints signatures on the physical structures of disks. In this paper, we present high-resolution (similar to 50 mas, 8 au) Atacama Large Millimeter/submillimeter Array observations of 1.3 mm dust continuum and CO line emission toward the disk around the M3.5 star 2MASSJ04124068+2438157. The dust disk consists of only two narrow rings at radial distances of 0 47 and 0 78 (similar to 70 and 116 au), with Gaussian sigma widths of 5.6 and 8.5 au, respectively. The width of the outer ring is smaller than the estimated pressure scale height by similar to 25%, suggesting dust trapping in a radial pressure bump. The dust disk size, set by the location of the outermost ring, is significantly larger (by 3 sigma) than other disks with similar millimeter luminosity, which can be explained by an early formation of local pressure bump to stop radial drift of millimeter dust grains. After considering the disk's physical structure and accretion properties, we prefer planet-disk interaction over dead zone or photoevaporation models to explain the observed dust disk morphology. We carry out high-contrast imaging at the L' band using Keck/NIRC2 to search for potential young planets, but do not identify any source above 5 sigma. Within the dust gap between the two rings, we reach a contrast level of similar to 7 mag, constraining the possible planet below similar to 2-4M(Jup). Analyses of the gap/ring properties suggest that an approximately Saturn-mass planet at similar to 90 au is likely responsible for the formation of the outer ring, which can potentially be revealed with JWST.