Orbital Circularization of a Planet Accreting Disk Gas: Formation of Distant Jupiters in Circular Orbits based on Core Accretion Model

Recently, gas giant planets in nearly circular orbits with large semimajor axes ($a \sim$ 30--1000AU) have been detected by direct imaging. We have investigated orbital evolution in a formation scenario for such planets, based on core accretion model: i) Icy cores accrete from planetesimals at $\lesssim$ 30AU, ii) they are scattered outward by an emerging nearby gas giant to acquire highly eccentric orbits, and iii) their orbits are circularized through accretion of disk gas in outer regions, where they spend most of time. We analytically derived equations to describe the orbital circularization through the gas accretion. Numerical integrations of these equations show that the eccentricity decreases by a factor of more than 5 during the planetary mass increases by a factor of 10. Because runaway gas accretion increases planetary mass by $\sim$ 10--300, the orbits are sufficiently circularized. On the other hand, $a$ is reduced at most only by a factor of 2, leaving the planets in outer regions. If the relative velocity damping by shock is considered, the circularization is slowed down, but still efficient enough. Therefore, this scenario potentially accounts for the formation of observed distant jupiters in nearly circular orbits. If the apocenter distances of the scattered cores are larger than the disk sizes, their $a$ shrink to a quarter of the disk sizes; the $a$-distribution of distant giants could reflect outer edges of the disks in a similar way that those of hot jupiters may reflect inner edges.