Gravitationally unstable protoplanetary disks

Formation of the resonant populations in the Kuiper belt: gas-drag-induced resonant capture

“…The gravitational instability can create the protoplanet very rapidly, on dynamical (orbital) time‐scales ∼10 4 yr, provided that the disc‐cooling time is similarly shot (Rice, Lodato & Armitage 2005; Clarke, Harper‐Clark & Lodato 2007: Griv 2007). The instability can give rise to torques that can help to clear cooled discs around stars on time‐scales of ∼10 6 yr (Griv 2006, 2007; Griv, Liverts & Mond 2008), in accord with astronomical requirements (Greaves 2005; Hillenbrand 2008).…”

“…An infinitesimally thin, spatially homogeneous, isothermal and non‐self‐gravitating fluid annulus in equilibrium is considered, whose evolution is described by the momentum and continuity equations. As we only consider the two‐dimensional coplanar orbits, the equations of motion are similar to the ones used in Goldreich & Tremaine (1982), Meyer‐Vernet & Sicardy (1987), Griv (2006, 2007) and Griv et al (2008). The linearized equations of motion read (written with respect to a rotating frame with angular velocity Ω Nep ) where v r , v ϕ and Σ 1 are, respectively, the perturbations of the radial velocity, azimuthal velocity and surface density of the proto‐KBO subsystem, Σ=Σ 0 +Σ 1 ( r , t ), Σ 0 is the equilibrium surface density, |Σ 1 /Σ 0 | ≪ 1, c s is the local speed of sound, ω * = m (Ω−Ω Nep ), Ω( r ) is the angular velocity at a distance r from the Sun and Ω Nep = ( M Sun G / r 3 ) 1/2 .…”

“…An infinitesimally thin, spatially homogeneous, isothermal and non-self-gravitating fluid annulus in equilibrium is considered, whose evolution is described by the momentum and continuity equations. As we only consider the twodimensional coplanar orbits, the equations of motion are similar to the ones used in Goldreich & Tremaine (1982), Meyer-Vernet & Sicardy (1987), Griv (2006Griv ( , 2007 and Griv et al (2008). The linearized equations of motion read (written with respect to a rotating frame with angular velocity Nep )…”

“…As a complementary study, Jiang & Yeh (2004, 2007 investigated the effect of a protostellar gaseous disc analogous to the primordial solar nebula on the resonance capture of solid particles, or 'proto-KBOs', ∼4 Gyr ago when the dynamical structure of the Kuiper belt was presumably established. 3 de la Fuente Marcos & de la Fuente Marcos (2008) further investigated this mechanism.…”

“…It was shown numerically by Jiang & Yeh (2004, 2007 and de la Fuente Marcos & de la Fuente Marcos (2008) that the gaseous drag of a protostellar disc can trap proto-KBOs into resonances rather easily, and the resonant populations are correlated with the gaseous drag strength. Here, we present an analytical study intended to describe Jiang & Yeh's (2004, 2007 and de la Fuente Marcos & de la Fuente Marcos' (2008) drag-induced mechanism of resonant capture for proto-KBOs when gas was still around. considered by us as rather dynamically cold and that the pressure gradient in it is much smaller than both the gravitational and the centrifugal forces.…”