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Formation of Planets by Tidal Downsizing of Giant Planet Embryos

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Formation of Planets by Tidal Downsizing of Giant Planet Embryos Mon. Not. R. Astron. Soc. 000, 1–5 (2008) Printed 29 May 2018 (MN LATEX style file v2.2) Formation of planets by tidal downsizing of giant planet embryos Sergei Nayakshin Department of Physics & Astronomy, University of Leicester, Leicester, LE1 7RH, UK E-mail: [email protected] Received ABSTRACT We hypothesise that planets are made by tidal downsizing of migrating giant planet embryos. The proposed scheme for planet formation consists of these steps: (i) a mas- sive young protoplanetary disc fragments at R ∼ several tens to hundreds of AU on gaseous clumps with masses of a few Jupiter masses; (ii) the clumps cool and contract, and simultaneously migrate closer in to the parent star; (iii) as earlier suggested by Boss (1998), dust sediments inside the gas clumps to form terrestrial mass solid cores; (iv) if the solid core becomes more massive than ∼ 10 M⊕, a massive gas atmosphere collapses onto the solid core; (v) when the gas clumps reach the inner few AU from the star, tidal shear and evaporation due to stellar irradiation peel off the outer metal- poor envelope of the clump. If tidal disruption occurs quickly, while the system is still in stage (iii), a terrestrial planet core is left. If it happens later, in stage (iv), a metal rich gas giant planet with a solid core emerges from the envelope. 1 INTRODUCTION dust sedimentation is too slow a process to yield observed solid cores in giant embryos of mass < Jupiter’s mass; (c) There are currently two competing theories for planet for- OB stars are too rare to explain the abundance∼ of Jupiter- mation in which the planet making action starts from oppo- like planets observed in extrasolar planetary systems, and site ends. The core accretion (CA) model (e.g., see Safronov (d) there seems to be no way to form terrestrial planets like (1969); Pollack et al. (1996); Ida & Lin (2008), and chap- the Earth. ters 4-6 in Armitage (2010)) stipulates that planets form in The goal of our Letter is to show that this criticism a bottom-up scenario. First, microscopic dust in the pro- has long outlived itself. All of the points raised above can toplanetary disc grows into grains. There is then a poorly be addressed if one upgrades the 1990-ies version of the understood but necessary step (e.g., Wetherill 1990) of GI model with more modern ideas – formation of Giant grains joining up somehow (see Youdin & Goodman 2005; planet Embryos (GE hereafter) far from the parent star Johansen et al. 2007) to make km-sized objects (planetesi- where the process is allowed (Rafikov 2005), and then let- mals), which then collide and stick to form ever larger solids arXiv:1007.4159v1 [astro-ph.EP] 23 Jul 2010 ting them migrate radially inwards, as massive planets do up to terrestrial planet masses. When the solid core reaches (Goldreich & Tremaine 1980). a critical mass of about 10 Earth masses, a massive gas en- We have recently revisited (paper I, Nayakshin 2010a, velope builds up by accretion of gas from the disc. to appear in MNRAS) the suggestions of Boss (1998); In contrast, the Gravitational Instability (GI) model Boss et al. (2002) on dust sedimentation in GEs assuming suggests that giant planets form “big”, e.g., directly by con- that they are formed at Rp 100 AU. Such GEs are cooler ∼ traction of gaseous condensations born in a massive self- by an order of magnitude than those studied by Helled gravitating disc (e.g., Bodenheimer 1974; Boss 1997). Gi- and co-authors. GEs with masses below about 10-20 Jupiter ant planets in the Solar System contain massive solid cores masses (MJ ) are found (paper II, Nayakshin 2010b, submit- (Fortney & Nettelmann 2009), as predicted by the core ac- ted to MNRAS) to be excellent sites of solid core formation. cretion model. In the context of GI, Boss (1998) suggested Thus addressing point (a) addresses point (b) automatically. that such cores could result from dust sedimentation inside Below we estimate the migration time of the embryos gaseous proto-planets. Boss et al. (2002) showed that re- in a realistic young massive protoplanetary disc. We note moval of the gas envelope by photoionisation due to a nearby that as embryos migrate closer to the parent star, their Hill OB star could make the ice giants of the Solar System. radius decreases faster than they can shrink due to internal Of these two models, the GI is the one that received cooling. When these two are equal, we assume that the GE the lion’s share of the criticism. The most notable prob- can be disrupted by the tidal field of the star, which nor- lems of the model are: (a) protoplanetary discs cannot mally occurs at a few AU distance. However, we find that form giant planet embryos at the location of Jupiter (e.g., grain sedimentation time is shorter than the migration time Rafikov 2005) contrary to earlier results by Boss (1997); (b) for plausible parameter values. Thus, by the time the em- Helled & Schubert (2008); Helled et al. (2008) found that bryos are due to be disrupted, they may already contain c 2008 RAS 2 S. Nayakshin 4 1/2 massive solid cores. Depending on the properties of the GE 1/2 10 yrs Remb (t) = 0.8 AU κ∗ . (4) at disruption, removal of the outer metal poor gas shell re- t veals either a terrestrial planet or a metal-rich giant planet. We therefore argue that such a “tidal downsizing” scheme may explain planets of all types without recourse to plan- 2.2 Dust growth and sedimentation etesimals (Safronov 1969; Wetherill 1990). We echo the approach of Boss (1998) here; the resulting Our hypothesis is a hybrid scenario: giant planet forma- grain growth time scale in a constant density embryo, for a tion starts with dust sedimentation inside a self-gravitating grain with initial size a0 to reach the final size a is gas clump (Boss 1998), as in the GI model, but continues as in the CA model with accretion of a massive metal-rich gas 3cs a tgr,0 = ln , (5) envelope from within the GE. Additionally, solid cores left πfgρ0GR0 a0 by the GE disruption in the protoplanetary disc may grow 3 where ρ0 = 3Memb/4πR , cs and fg 0.01 are the initial further like in the CA model – by accreting smaller solid emb ≈ embryo mean density, the sound speed, and the grain frac- debris from the disc. Giant planets may accrete more gas tion by mass, respectively. In paper I we improved on this and also migrate radially, as in the “standard theory”. model by allowing the embryo to contract, in which case the growth time is a geometric combination of the cooling and 3/7 4/7 the initial grain growth time, tgr = t0 tgr,0: 2 GIANT PLANET EMBRYO MODEL 4/7 3 −2/7 −4/7 9/21 ln(a/a0) tgr = 3 10 yr m1 f−2 k∗ , (6) 2.1 Birth and contraction × 20 Massive young gas discs are gravitationally unstable and where f−2 = fg/0.01. The vaporisation time, tvap, is the fragment on clumps when the disc cooling time is no longer time it takes for the embryo to heat up to the vaporisation than a few times the local dynamical time, 1/Ω (e.g., temperature of Tvap 1400 K. This is trivially obtained 3 1/2 ≈ Gammie 2001), where Ω = (GM∗/Rp) is the Keple- by solving the equation T (tvap) = Tvap (using eq. 1), and a rian angular frequency at radius Rp from the star of mass good approximation is > M∗. This limits the fragmentation region to Rp 30 100 2 − 4 Tvap −2 AU (e.g., Rafikov 2005; Stamatellos & Whitworth∼ 2008; tvap = 1.5 10 years m1 κ∗ , (7) × 1400 K Meru & Bate 2010). At the point of marginal gravitational stability the density in the disc midplane is about the tidal Grains sediment to the centre of the core when tgr < tvap, 3 and vaporise before they could sediment if tgr >tvap. density at that point, ρt = M∗/(2πRp). Thus, when the disc just fragments, the disc cooling time is about the free-fall The mass of refractory material (e.g., silicates) that can timescale for the material in the disc, tff 1/√Gρ. As the be used to build a massive core is expected to be about 1/3 ∼ ∼ clumps contract further, their cooling time becomes longer of the total heavy elements mass, or about 20 Earth masses than their free-fall times. The initial state of a GE is thus for Memb = 10MJ (Boss et al. 2002). However, due to en- that of a polytropic clump (Cameron et al. 1982), similar ergy release associated with the solid core accretion, strong to the “first cores” studied in the context of star formation convective motions near the core may develop. The grains (Larson 1969; Masunaga & Inutsuka 2000). For simplicity also melt at too high core accretion rates. Thus the final we assume that GEs evolve at constant mass after their for- mass of the core is usually much smaller than the maximum mation. condensible mass (paper II). Introducing dust opacity as a power-law in temperature and assuming that the embryo is optically thick, we obtained 2.3 Radial migration of embryos an approximate analytic solution for the radiative cooling of the giant embryo in paper I1. For example, for κ(T ) = Gravitational torques between the disc and massive κ0(T/10K), we have planets are significant (e.g., Goldreich & Tremaine 1980; 1/2 1/2 Tanaka et al.
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