The next stage is called oligarchic accretion. It is characterized by the dominance of several hundred of the largest bodies—oligarchs, which continue to slowly accrete planetesimals. No body other than the oligarchs can grow. At this stage the rate of accretion is proportional to R2, which is derived from the geometrical cross-section of an oligarch. The specific accretion rate is proportional to ; and it declines with the mass of the body. This allows smaller oligarchs to catch up to larger ones. The oligarchs are kept at the distance of about (= is the Hill radius, where a is the semimajor axis, e is the orbital eccentricity, and Ms is the mass of the central star) from each other by the influence of the remaining planetesimals. Their orbital eccentricities and inclinations remain small. The oligarchs continue to accrete until planetesimals are exhausted in the disk around them. Sometimes nearby oligarchs merge. The final mass of an oligarch depends on the distance from the star and surface density of planetesimals and is called the isolation mass. For the rocky planets it is up to , or one Mars mass. The final result of the oligarchic stage is the formation of about 100 Moon- to Mars-sized planetary embryos uniformly spaced at about . They are thought to reside inside gaps in the disk and to be separated by rings of remaining planetesimals. This stage is thought to last a few hundred thousand years.
