The Orbital Evolution of Planet-Disk Solar Systems.

Abstract

The extrasolar planets discovered to date possess larger eccentricities and smaller semi-major axes than similar planets in our solar system. It is not thought possible for these planets to form in situ; we propose they result from a combination of disk torques, planet-planet scattering, and magnetohydrodynamical turbulence. The torques exerted on planets during Type II migration in circumstellar disks readily decrease the semi-major axes a, whereas scattering between planets increases the orbital eccentricities e. Disk turbulence induces a random walk in the planets' orbital elements. We present a parametric exploration of the possible parameter space for this migration scenario using a range of timescales for eccentricity damping (due to the disk) and the overall magnitude of the MHD turbulence. Many realizations of the simulations are performed in order to determine the distributions of the resulting orbital elements of the surviving planets, roughly 10000 in all. The action of disk torques and planet-planet scattering results in a distribution of final orbital elements that fills the ae plane, in rough agreement with the orbital elements of observed extrasolar planets.

We pair this parametric study with a more in-depth analysis of the disk's effect on orbital eccentricity. Several recent analytic calculations suggest that disk-planet interactions excite eccentricity, while numerical studies generally produce eccentricity damping. We address this controversy using a quasi-analytic approach, removing several approximations from the traditional calculation of disk torques. We encounter neither uniform damping nor uniform excitation of orbital eccentricity, but rather a function de/dt that varies in both sign and magnitude depending on initial solar system properties. Most significantly, we find that for every combination of disk and planet properties investigated herein, corotation torques produce negative values of de/dt for some range in e within the interval [0.1, 0.5]. If corotation torques are saturated, this region of eccentricity damping disappears, and excitation occurs on a short timescale of less than 0.08 Myr. Thus, our study does not produce eccentricity excitation on a timescale of a few Myr -- we obtain either eccentricity excitation on a short time scale, or eccentricity damping on a longer time scale.