How Flow Isolation May Set the Mass Scale for Super-Earth Planets

Much recent work on planet formation has focused on the growth of planets by accretion of grains whose aerodynamic properties make them marginally coupled to the nebular gas, a theory commonly referred to as "pebble accretion." While the rapid growth rates of pebble accretion can ameliorate some problems in planet formation theory, they raise new concerns as well. A particular issue is the preponderance of observed planets that end their growth as "super-Earths" or "sub-Neptunes," with masses in the range 2-10M(circle plus). Once planets reach this mass scale, growth by pebble accretion is so rapid that ubiquitously ending growth at super-Earth masses is difficult unless growth rates drop at this mass scale. In this work, we highlight this issue in detail using our previously published model of pebble accretion, and also propose a reason for this change in growth rate: feedback between the growing planet's atmosphere and the gas disk inhibits accretion of smaller particle sizes by forcing them to flow around the growing planet instead of being accreted. For reasonable fiducial disk parameters, this "flow isolation" will inhibit accretion of all available particle sizes once the planet reaches super-Earth masses. We also demonstrate that the characteristics of this "flow isolation mass" agree with previously published trends identified in the Kepler planets.