An Increase in Small-planet Occurrence with Metallicity for Late-type Dwarf Stars in the Kepler Field and Its Implications for Planet Formation

Planet formation through planetesimal accretion is believed to be slow by relatively efficient at turning a disk’s complement of metals into planetary embryos. On the other hand, planet formation via pebble accretion is thought to be fast but relatively inefficient due to its reliance on the rapid radial migration of solid material. We show that for late-type dwarf stars in the Kepler field (1) planet occurrence increases with metallicity for all planet radii R_p down to at least R_p = 2 R_Earth and (2) that in the range 2 R_Earth < R_p < 5 R_Earth planet occurrence scales linearly with metallicity Z. We establish that the expected solid mass in planets around late-type dwarfs in the Kepler field is comparable to the total amount of planet-making solids in their protoplanetary disks. We argue that this high efficiency of planet formation favors planetesimal accretion over pebble accretion as the origin of the small planets observed by Kepler around late-type dwarf stars. Extrapolating our results, we predict that short-period planets with R_p < 2 R_Earth should be rare around early-M dwarf stars with [M/H] < -0.5 or late-M dwarf stars with [M/H] < +0.0. This dependence of planet occurrence on metallicity observed in the Kepler field emphasizes the need to control for metallicity in estimates of planet occurrence for late-type dwarf stars like those targeted by Kepler’s K2 extension and the Transiting Exoplanet Survey Satellite.