What s s New? Planetary Formation Scenarios Revisited: Core-Accretion versus Disk Instability. Taro Matsuo (Nagoya University)

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1 Planetary Formation Scenarios Revisited: Core-Accretion versus Disk Instability What s s New? Different conditions for as iants formation etallicity of a, Planet ass, Disk ass Taro atsuo (Naoya University) Hiroshi Shibai, Takafumi Ootsubo (Naoya University), and otohide Tamura (NAOJ) Dependence of the metallicity on dust and as surface density & $ fd [ Fe / H ] ' lo0 % f # " f d ( ) :The scalin factor for the dust (as) surface density of the inimum ass Solar Nebulae model ( f d ( ) = )

2 2 Host Star Planetary Formation Scenarios Core-Accretion e.. Safronov 969; Hayashi et al. 985; Pollack et al. 996 Heavy element cores are built by the accretion of planetesimals. 2 Rapid as accretion occurs onto the core and a as iant is formed. 3 Gas dissipates from a. (The as depletion timescale: 0 7 yrs) Terrestrial Planet Gas Giant Disk Instability (e.., Kuiper 95; Cameron 978; Boss 997). If a is sufficiently massive, the instability does occurs. 2. The entire is lobal instable. A local frament forms. 3 Such clumps contract to form iant aseous protoplanets. Gas Giants The Reion Where Gas Giants Are Formed By Core-Accretion (CA-Reion) The Conditions For Gas Giant Formation () The core mass increases over the critical core mass before the as dissipates " c, acc a " a (2) The core isolation mass is larer than the critical core mass: c, iso c, crit a # a max = min = 4." 0 [ Fe/ H ] [ Fe/ H ] a (AU) a min -0. a max CA-Reion [ Fe / H ] =0 = 5 =

3 Upper Limits For Planet ass In Core-Accretion odel p, max ([ Fe / H ] = 0.5, f = ) a min CA-Reion [ Fe / H ] 0.0, = [ Fe / H ] 0.5, = a max a (AU) Gas Giants Formation Scenario *Heavy element cores are built by the accretion of planetesimals. * When core mass is hiher than critical core mass, as accretes rapidly onto the core. * When the ravitational scatterin is equal to pressure radient and viscous diffusion, a ap is formed = 5 =0 = Upper Limits For Planet ass In Core-Accretion odel aximum planet mass Riht after a ap formation 0 yrs after a ap formation CA-Reion [ Fe / H ] Evolution of protoplanet after a ap formation * Durin the protoplanet is embedded in the accretion, as around the ap is accreted onto the protoplanet * The planet mass increases until as dissipates from the (~0yr)

4 4 The Reion Where Gas Giants Are Formed By Core-Accretion (CA-Reion) 00 0 =0 CA-Reion = 5 = Fe / H [ ] & v $ w ' m % r 2 ( # " Planetary Formation By Disk Instability < cr (e.. Kuiper 95; Cameron 978; Lauhlin & Bodenheimer 994; Boss 997 ) When self-ravity of a is stroner than tidal force and as pressure (Q < ), the instability occurs. When a spatial scale of a perturbation equals to the critical wavelenth: Q ~ the frament mass is minimum one. = cr > cr Toomre-Q (Toomre 964) # c $ Q = # crit s ep & 2 % " f T ' G# 2 * *When Q is less than, self-ravity of a is stroner than tidal force and as pressure. *The rane where the instability occurs (DI-Reion) is determined by the temperature and the as surface density

5 5 ) ( J p The Reion Where Gas Giants Are Formed By Disk Instability (DI-Reion) p,min = p (a=a min ) 2 =5 =0 a min a(au ) DI-Reion The dependence of the minimum planet mass formed by instability on the semi-major axis. As the as surface density of the s increases, the DI-Reion widens inwardly. 2. As the as surface density of the s increases, the lower limits for the planet mass decrease. The reason is that, as the reion is nearer the host star, the as pressure is hiher and the ravitation of the host star is stroner Core-Accretion vs. Disk Instability (G-type stars: 60) CA-Reion * Core-Accretion model has the upper limits for planet mass and the lower limits for metallicity of the.

6 6 Core-Accretion vs. Disk Instability (G-type stars: 60) Core-Accretion vs. Disk Instability (G-type stars: 60) =0 =5 DI-Reion * Disk Instability model has the lower limits for planet mass =0 =5 DI-Reion CA-Reion 0 * 90% (54/60) of the planets detected so far occur in the reion where the as iants can be explained by the core-accretion model. * The rest 0% can only explained by the instability model

7 7 Conclusions We derived the conditions for metallicity of the s and planet mass for as iant formation usin the core-accretion model and the instability model. we checked whether the planets detected (6 cases) so far satisfy the above conditions. 90% of the planets detected occur in the rane where as iants can be explained ed by the core accretion model. The rest 0% can only explained by the instability model, not by the core- accretion model,, in case that miration is not considered.