1. Planetesimal dynamics in self-gravitating discs Giuseppe Lodato IoA - Cambridge

2. Summary Introduction and motivations Numerical models of gravitational instabilities (Lodato & Rice 2004, 2005) Planetesimals in self-gravitating discs (Rice, Lodato et al 2004) Planetesimal formation via gravitational instability (Rice, Lodato et al. 2006) Planetary cores dynamics in massive discs (Lodato, Britsch, Clarke 2006)

3. Why planetesimals in massive discs? Massive discs? –Testi et al. (2001, 2003): In some Herbig objects, large grains: larger disc masses than previously thought (Hartmann et al 2006) –Eisner et al (2005): Massive discs in Class I objects in Taurus (M disc  0.1 - 1 M sun ) –Eisner & Carpenter (2005): Massive discs in Orion (M disc  0.1 - 0.39 M sun in 2% of source) –Clarke (2006): photoevaporation models of the ONC predicts that initially discs have to be self- gravitating

4. Why planetesimals in massive discs? Why planetesimals dynamics? –Easy growth of dust up to meter sizes –Growth beyond m-sizes difficult: Sticking efficiency? (Supulver et al 1997) Migration due to gas drag (Weidenshilling 1977) –Gas rotates at sub-Keplerian speed (pressure) –To first approx., dust is Keplerian Migration time  10 3 yrs for m-size

5. Evolution of massive discs Fast cooling (t cool <3  -1 ): fragmentation (Gammie 2001) Slow cooling: spiral structure, ang. mom. transport (Lodato & Rice 2004, 2005) Fundamental threshold on max. sustainable stress:  0.06 (Rice, Lodato & Armitage 2005)

6. SPH simulations of planetesimals-disc interaction Intermediate-high resolution: 250,000 gas particles Heating via pdV, artificial viscosity Cooling with t cool  =7.5 Disc mass: 0.25M * “ Solid ” component: 125,000 particles Interact through gravitational and drag force (single size assumed) No solid self-gravity

7. Planetesimal dynamics in massive discs Gas 1000cm50cm

8. Planetesimal dynamics in massive discs Collision rate highly enhanced Velocity dispersion decreases within the spiral 50 cm 1000 cm

9. Rice, Lodato et al (2006) Adding the solid self-gravity Same as before, but now consider the solid self-gravity Sizes considered: 150 cm and 1500 cm Solid-to-gas ratio: 1/100 and 1/1000 Particles size: 150 cm Solid/gas ratio = 1/100 Particles size: 150 cm Solid/gas ratio = 1/1000 Particles size: 1500 cm Solid/gas ratio = 1/100

10. Gravitational collapse of the solids If solid/gas ratio high enough: grav. collapse and planetesimal/core formation Typical timescale:  100 yrs (  one dyn. timescale) This is NOT the grav. inst. model for giant planet formation (a la Boss) This is NOT the Goldreich-Ward instability –No need for extremely low velocity dispersion –We find v disp  0.1c s (stirring up due to “ turbulence ” ) –Relatively large fragment mass  0.1 M Earth

11. What happens next? Embryos/cores interact with the spiral structure No efficient drag for this sizes Orbital evolution of cores/embryos (Lodato, Britsch & Clarke 2006) Analogous to Nelson (2005) “ massless ” planetesimals dynamics in MRI turbulence Sizes:  100 meters (no drag) Mass:  1M Earth : no (mass dependent) Type I migration

12. Orbital evolution Cores undergo “ random walk ” (cf. Nelson 2005): 10% variation of semi-major axis over the course of the run (  100 orbits) Significant eccentricity evolution –average e  0.17 at the end of the run –Peak eccentricity: e  0.3 –cf. Nelson (2005): average e  0.05, peak e  0.1 Random walk: helps growth, prevents isolation Eccentricity growth: reduces gravitational focusing, bad for growth Possible solutions: –Coherent structure, not clear increase in vel. disp. –Direct formation of large cores (see before)

13. Conclusions Solid evolution in early phases (Class I) Gas drag + structured discs: significant growth of m-sized boulders –Similar behaviour with other sources of structure in the disc (MRI - Fromang & Nelson 2005, vortices - Johansen, Klahr, Henning 2006 ) Planetesimal/core formation via fragmentation of solid sub-disc (possible growth well beyond km-sizes) Cores orbital evolution in GI (cf. Nelson 2005): –“ Random walk ” –Eccentricity growth (up to e  0.3) –Possible problem for core growth?