On the Migration of Protogiant Solid Cores

By F. Masset, G. D’Angelo, W. Kley. 2006

155 citations recorded by the source corpus.

The increase of computational resources has recently allowed high-resolution, three-dimensional calculations of planets embedded in gaseous protoplanetary disks. They provide estimates of the planet migration timescale that can be compared to analytical predictions. While these predictions can result in extremely short migration timescales for cores of a few Earth masses, recent numerical calculations have given an unexpected outcome: the torque acting on planets with masses between 5 and 20 M⊕ is considerably smaller than the analytic, linear estimate. These findings motivated the present work, which investigates existence and origin of this discrepancy or "offset," as we shall call it, by means of two- and three-dimensional numerical calculations. We show that the offset is indeed physical and arises from the co-orbital corotation torque, since (1) it scales with the disk vortensity gradient, (2) its asymptotic value depends on the disk viscosity, (3) it is associated to an excess of the horseshoe zone width. We show that the offset corresponds to the onset of nonlinearities of the flow around the planet, which alter the streamline topology as the planet mass increases: at low mass the flow nonlinearities are confined to the planet's Bondi sphere, whereas at larger mass the streamlines display a classical picture reminiscent of the restricted three-body problem, with a prograde circumplanetary disk inside a "Roche lobe." This behavior is of particular importance for the subcritical solid cores (M ≲ 15 M⊕) in thin (H/r ≲ 0.06) protoplanetary disks. Their migration could be significantly slowed down, or reversed, in disks with shallow surface density profiles.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/b210f064fe495da837ccfb34e2f971cdb32eaf98

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In Astronomy and Astrophysics

1. C. Mordasini
2. W. Kley
3. R. Nelson
4. Th. Henning
5. A. Morbidelli
6. D. Lin
7. Y. Alibert
8. Shigeru Ida

In Instrumentation

1. R. Nelson
2. W. Kley
3. C. Baruteau
4. C. Mordasini
5. A. Crida
6. Sheng Jin
7. G. Kennedy
8. R. van Boekel

Citations in the corpus

• Planet Formation around Stars of Various Masses: The Snow Line and the Frequency of Giant Planets (2007, background): “Recent studies indicate that for cores less massive than ∼10M⊕ the timescale is longer (Masset et al. 2006), and may be reduced to a random walk due to magnetohydrodynamic turbulence (Nelson & Papaloizou 2004).”
• Planet-Disk Interaction and Orbital Evolution (2012, background): “…migration include: strong corotation torques operating in regions where there are steep positive surface density gradients (socalled ‘planet traps’) (Masset et al., 2006); reductions in the differential Lindblad torque in regions of sharp opacity transition (Menou & Goodman, 2004); magnetic…”
• CHARACTERIZING THE COOL KOIs. IV. KEPLER-32 AS A PROTOTYPE FOR THE FORMATION OF COMPACT PLANETARY SYSTEMS THROUGHOUT THE GALAXY (2012, unknown): “…quantities, and Γtot is the total torque on the planet from Linblad, corotation, and horseshoe torques Γtot = [−1.36 + 0.62γ + 0.43βT + 1.36(3/2− γ)] Γ0 (5) (also see Masset et al. 2006), and Γ0 = ( mp M⋆ )2 ( H ap )−2 Σpa 4 pΩ 2 p. (6) As a baseline model we use a disk surface density…”
• A torque formula for non-isothermal Type I planetary migration – II. Effects of diffusion (2010, background): “The entropy-related horseshoe drag seems to play an important role in three-dimensional discs as well (Kley et al. 2009), and it has been shown that, in an isothermal set-up, the effect of the horseshoe drag is stronger in three dimensions (Masset et al. 2006).”
• Toward a Deterministic Model of Planetary Formation. IV. Effects of Type I Migration (2008, background): “…variation in the surface density and temperature gradient (Masset et al. 2006b), intrinsic turbulence in the disk (Laughlin et al. 2004; Nelson & Papaloizou 2004), self-induced unstable flow (Koller & Li 2004; Li et al. 2005), and nonlinear radiative and hydrodynamic feedback (Masset et al. 2006a).”
• On the Corotation Torque in a Radiatively Inefficient Disk (2007, background): “Masset et al. (2006) have given an estimate of xs in the isothermal case, that reads xs ≈ 1.16rp √ q/h(rp).”
• Radial Migration of Gap-opening Planets in Protoplanetary Disks. I. The Case of a Single Planet (2018, background): “This boost of the positive torque could be explained by the nonlinear effects of the corotation torque discussed by Masset et al. (2006) and Duffell (2015).”
• A torque formula for non-isothermal type I planetary migration – I. Unsaturated horseshoe drag (2009, background): “…ow nloaded from https://academ ic.oup.com /m nras/article-abstract/401/3/1950/1097210 by guest on 02 N ovem ber 2019 out that the results of Masset et al. (2006) and Paardekooper & Papaloizou (2009b) could be used to derive approximate functional forms for the mass dependence of C and d.”
• PLANETARY POPULATION SYNTHESIS COUPLED WITH ATMOSPHERIC ESCAPE: A STATISTICAL VIEW OF EVAPORATION (2014, background): “Recent studies have shown that, depending on the temperature profile of the disc, type I migration can also induce outward migration (e.g., Masset et al. 2006; Paardekooper & Mellema 2008; Kley et al. 2009; Uribe et al. 2011).”
• Rapid inward migration of planets formed by gravitational instability (2011, unknown): “The 5 Jupiter-mass planet (q/h3 ∼ 5 ≫ 1) is, however, more prone to non-linear effects (e.g., Masset et al. 2006).”