6. GROWTH OF PLNETS: AN OVERVIEW 6.1. Observational Constraints a. The planets’ masses and radii and the age of the Solar System M E R E Neptune Uranus Earth R E M E Formed within the age of the Solar System : Gyr ± a few Myr (CAI age)

6. GROWTH OF PLNETS: AN OVERVIEW b. a few Earth masses of hydrogen and helium (Guillot 1999) Mass M Equatorial radius a Gravitational moments J2, J4, and J6 (Laplace series expansion of gravitational moment) Pioneer and Voyager about 25% rock, 60 to 70% ice 5 to 15% H and He Uranus and Neptune were formed prior to gas-disk dissipation.

Solar-type stars suggest that circumstellar disks dissipate over a timescale of several million years [Brice˜no, Vivas & Calvet 2001; Haisch, Lada & Lada 2001; Hillenbrand 2004; Lagrange, Backman & rtymowicz 2000; Strom, Edwards & Skrutskie 1993] 6. GROWTH OF PLNETS: AN OVERVIEW Uranus and Neptune were formed within ~ 0.1Gyrs

6. GROWTH OF PLNETS: AN OVERVIEW Why Uranus and Neptune? Easy to make within 0.1 Gyrs : core accretion (0.1Gyr) or streaming instability (0.1 Myr) Hard to stay there (no migrations of giants) Pure gravitational instability : less than ~Myrs (severe depends on disk model) Streaming instability triggers GI: less than ~0.1Myrs Core accretion : need longer than solar system age Not much H and He : Probably formed at the end of gas-disk dissipation Enough time to form planetesimals

6. GROWTH OF PLNETS: AN OVERVIEW 6.2. Minimum Mass Solar Nebula The Minimum Mass Solar Nebula (MMSN) [Hayashi 1981]: A protoplanetary disk that contains the minimum amount of solids necessary to build the planets of the solar system Size of Uranus and Neptune, core size for Jupiter and Saturn: Default model in this study : MMSN But, possibly higher (ejected mass: Oort cloud 1 – 30 M E )

6. GROWTH OF PLNETS: AN OVERVIEW 6.3. Need for Gravitational Focusing From equation 41, mass accretion time is,,

6. GROWTH OF PLNETS: AN OVERVIEW Uranus : Neptune : About hundred times longer than age of the solar system There must be a mechanism to shorten formation time scale. Gravitational focusing Alternative: Uranus and Neptune are formed between Jupiter and Saturn

6. GROWTH OF PLNETS: AN OVERVIEW 6.4. Cooling is Necessary, so Accreted Bodies were Small Initial random velocity : Collision cross section is smaller than viscous stirring cross section. No gravitational focusing Viscous stirring dominates. Planetesimals heats upto Embryo eat up most of planetesimals in entire region Takes too long time to grow Only some of planetesimals within Hill radius collide with embryo. Need to keep random velocity slow to shorten formation time Confirmed by N-body simulation : Levison & Stewart 2001

6. GROWTH OF PLNETS: AN OVERVIEW How small should be the planetesimals? assuming To form Neptune within age of the solar system, Size of planetesimals : a few kilometers

6. GROWTH OF PLNETS: AN OVERVIEW Formation of Earth without gravitational focusing

6. GROWTH OF PLNETS: AN OVERVIEW 6.5. Completion: When Small Bodies Have been Consumed Complete with 20 Gyr for Neptune At this speed, small bodies will frequently collide each others fragmentation Kinetic energy loss :

6. GROWTH OF PLNETS: AN OVERVIEW Completion with Planet can be easily formed within 10 Myr. But, accrete only small body within annulus of 5 R Hill Not enough mass : about factor 5 small, Possible modifications Migration of embryo Migration of small bodies More massive disk