Planetesimal dynamics in self-gravitating discs

Giuseppe LodatoIoA - Cambridge

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)

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 (Mdisc 0.1 - 1 Msun)

– Eisner & Carpenter (2005): Massive discs in Orion (Mdisc 0.1 - 0.39 Msun in 2% of source)

– Clarke (2006): photoevaporation models of the ONC predicts that initially discs have to be self-gravitating

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 103 yrs for m-size

Evolution of massive discs

• Fast cooling (tcool<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)

SPH simulations of planetesimals-disc interaction

• Intermediate-high resolution: 250,000 gas particles

• Heating via pdV, artificial viscosity• Cooling with tcool=7.5• Disc mass: 0.25M*• “Solid” component: 125,000 particles• Interact through gravitational and drag

force (single size assumed) • No solid self-gravity

Planetesimal dynamics in massive discs

Gas

1000cm50cm

Planetesimal dynamics in massive discs

Collision rate highly enhancedVelocity dispersion decreases within the spiral

50 cm1000 cm

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 cmSolid/gas ratio = 1/100

Particles size: 150 cmSolid/gas ratio = 1/1000Particles size: 1500 cmSolid/gas ratio = 1/100

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 vdisp 0.1cs (stirring up due to

“turbulence”)– Relatively large fragment mass 0.1 MEarth

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: 1MEarth: no (mass dependent) Type

I migration

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)

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?