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 12/3/2018 From Stars to Planets

Overview Self-gravitating disc evolution and stability. Solid particle evolution in self-gravitating discs. Implications for planetesimal formation. Conclusions. 12/3/2018 From Stars to Planets

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 12/3/2018 From Stars to Planets

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  12/3/2018 From Stars to Planets

“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. 12/3/2018 From Stars to Planets

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). 12/3/2018 From Stars to Planets

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) 12/3/2018 From Stars to Planets

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 12/3/2018 From Stars to Planets

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). 12/3/2018 From Stars to Planets

Dust evolution 1000 cm 50 cm gas 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 12/3/2018 From Stars to Planets

Grain growth 1000 cm 50 cm 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. 12/3/2018 From Stars to Planets

Direct planetesimal growth 150 cm particles Mdust/Mgas == 1/100 Mdust/Mgas == 1/1000 Consistent with the metal-rich nature of planet host stars! 12/3/2018 From Stars to Planets

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. 12/3/2018 From Stars to Planets