Planetesimal formation in self-gravitating accretion discs

1. Planetesimal formation in self-gravitating accretion discs Ken Rice Institute for Astronomy University of Edinburgh Collaborators : Phil Armitage - University of Colorado Giuseppe Lodato – University of Leicester Jim Pringle - University of Cambridge Ian Bonnell, Kenny Wood - University of St Andrews Matthew Bate - University of Exeter From Stars to Planets

2. Overview • Self-gravitating disc evolution and stability. • Solid particle evolution in self-gravitating discs. • Implications for planetesimal formation. • Conclusions. From Stars to Planets

3. Self-gravitating protoplanetary discs • An accretion disc is gravitationally unstable if (Toomre 1964) • The stability of a self-gravitating disc is determined by the balance between the heating rate (through the growth of the instability) and the cooling rate (Gammie 2001; Rice et al. 2003) . • If unstable a disc may either stably transport angular momentum, or it may fragment into bound objects - protoplanets in protoplanetary discs (Boss 1998), stars in AGN discs (Goodman & Tan 2003). Q ~ 1 in young protostellar discs From Stars to Planets

4. Cooling rates • Assume we have an ‘adiabatic’ disk that has a radially dependent cooling time • Justification i.e. with alpha disc(Shakura & Sunyaev 1973) Thermal equilibrium  From Stars to Planets

5. “Long” cooling times Mdisk = 0.5 Mstar, tcool = 7.5 -1 • Initial transient phase? • Ultimately reaches a quasi-steady, long-lived state - Q ~ 1. • Stable angular momentum transport. From Stars to Planets

6. Angular momentum transport • Effective viscosity related to the cooling time. • Mass transfer - dM/dt = 3. • Viscous timescale - t = R2/. with but expected actual Disk evolves on the viscous timescale  self-gravitating phase may be long-lived (Lodato & Rice 2004, 2005). From Stars to Planets

7. Recent observations VLA image of class 0 object IRAS 16293-2422B. Mstar = 0.8 M Mdisk = 0.3 - 0.4 M Rout = ~ 25 au (Rodriguez et al., ApJ, 621, L133,2005) From Stars to Planets

8. Gas drag • The disc gas and small planetesimals/dust grains are coupled via a drag force (e.g., Weidenschilling 1977) • For standard disc geometries, the drag force causes dust grains to lose angular momentum and spiral in towards the central star with a radial velocity that depends on the grain size. relative velocity dust density particle size From Stars to Planets

9. Self-gravitating discs • Pressure gradient changes sign across spiral structures. • Dust grains/small planetesimals can drift both inwards and outwards. • Net effect - grains concentrate in the center of the spiral structures (Haghighipour & Boss 2003; Rice et al. 2004). Vortices? (Barge & Sommeria 1995; Godon & Livio 2000; Klahr & Bodenheimer 2003) . MRI turbulence (Johansen et al. 2006). From Stars to Planets

10. Dust evolution • Intermediate size particles • gas drag causes significant drift. • concentrate in the center of the spiral arms. • Large particles • decoupled from gas. • Structure largely matches that of the disc gas. 1000 cm 50 cm gas From Stars to Planets

11. 1000 cm 50 cm Grain growth no drag 1000 cm 50 cm • The densities achieved may be sufficient for the dust itself to be self-gravitating (Goldreich & Ward 1973; Youdin & Shu 2002). • Concentrating grains in the spiral arms can increase the collision rate by 2 orders of magnitude. From Stars to Planets

12. Direct planetesimal growth 150 cm particles Mdust/Mgas == 1/100 Mdust/Mgas == 1/1000 • Consistent with the metal-rich nature of planet host stars! From Stars to Planets

13. Conclusions • Quasi-steady self-gravitating discs evolve on viscous timescales and may persist for many dynamical timescales. • Solid-particles in a self-gravitating disc may become highly concentrated at the centre of the spiral density waves. • The amount of concentration depends on the particle size. • If the density of solid particles in the spiral arms becomes sufficiently high, planetesimal formation may occur via direct gravitational. • Depends on the total mass of solid particles of the appropriate size. From Stars to Planets