Formation via Disk Instability

Abstract

In the disk instability model, giant planets form from direct collapse of the gas in the protoplanetary disk. The disk fragments into gravitationally bound clumps with sizes comparable to giant planets as a result of gravitational instability [1]. The idea that planets in the solar system could condense directly out of the nebula is one of the oldest in astrophysics since it dates back to Laplace in the eighteenth century. The concept was revived by Kuiper [2] and Cameron [3] in the context of the solar system. Since the discovery of extrasolar planets, the interest in disk instability has grown because fragmentation, when feasible, occurs quickly, naturally producing multiple giant planets [1, 4, 5] on a timescale comparable to the orbital time in the protoplanetary disk, that is, <100 years. A short formation timescale is attractive because the presence of protoplanetary disks becomes increasingly rare around stars older than a few million years [6], suggesting fairly short disk dissipation timescales.Gravitational instability requires high mass densities and low temperatures as it demands that the self-gravity of the gas, which drives the collapse, prevails over the stabilizing effect of thermal pressure. This translates into the requirement that, at some stage, the protoplanetary disk had to be very cold and massive. Furthermore, a protoplanetary disk revolving around its host star is in differential rotation. This causes shear, which also opposes the tendency toward collapse promoted by gravity. The competing effects of self-gravity, thermal pressure, and shear in the disk are nicely encapsulated in the Toomre Q parameter [7]:In Eq. (4.1), the gas surface density measures the importance of self-gravity, the sound speed c s is related to thermal pressure, and κ, the epicyclic frequency, determines the strength of the shear. The Toomre parameter can be derived via a local perturbative stability analysis of infinitesimally thin differentially rotating disks [8]. If Q < 1 then the gas is unstable to gravitational collapse, while if Q > 1 Formation and Evolution of Exoplanets. Edited by Rory Barnes

14 Her: a likely case of planet-planet scattering

“…Whether resulting from core accretion or gravitational instability, planets are expected to form in disks, causing multi-planet systems to be coplanar as a consequence (Hubickyj 2010;Mayer 2010). Multi-planet systems tend to have lower eccentricities than single-planet systems (Wright et al 2009), possibly because low eccentricites are energetically favorable for long-term stability.…”