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
12/3/2018
From Stars to Planets

2. 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

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
12/3/2018
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 
12/3/2018
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.
12/3/2018
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).
12/3/2018
From Stars to Planets

7. Recent observations VLA image of class 0 object IRAS 16293-2422B.
Mstar = 0.8 M
Mdisk = M
Rout = ~ 25 au
(Rodriguez et al., ApJ, 621, L133,2005)
12/3/2018
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
12/3/2018
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).
12/3/2018
From Stars to Planets

10. 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
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11. 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

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!
12/3/2018
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.
12/3/2018
From Stars to Planets