Three-dimensional calculations of high- and low-mass planets embedded in protoplanetary discs

By Matthew R. Bate, S. Lubow, Gordon I. Ogilvie, K. A. Miller. 2003

226 citations recorded by the source corpus.

We analyse the non-linear, three-dimensional response of a gaseous, viscous protoplanetary disc to the presence of a planet of mass ranging from 1 Earth mass (1 M⊕) to 1 Jupiter mass (1 MJ) by using the ZEUS hydrodynamics code. We determine the gas f ow pattern, and the accretion and migration rates of the planet. The planet is assumed to be in a f xed circular orbit about the central star. It is also assumed to be able to accrete gas without expansion on the scale of its Roche radius. Only planets with masses Mp 0.1 MJ produce significan perturbations in the surface density of the disc. The fl w within the Roche lobe of the planet is fullythree-dimensional.GasstreamsgenerallyentertheRochelobeclosetothediscmid-plane, but produce much weaker shocks than the streams in two-dimensional models. The streams supply material to a circumplanetary disc that rotates in the same sense as the orbit of the planet. Much of the mass supply to the circumplanetary disc comes from non-coplanar fl w. The accretion rate peaks with a planet mass of approximately 0.1 MJ and is highly efficient occurring at the local viscous rate. The migration time-scales for planets of mass less than 0.1 MJ, based on torques from disc material outside the Roche lobes of the planets, are in excellent agreement with the linear theory of type I (non-gap) migration for three-dimensional discs.ThetransitionfromtypeItotypeII(gap)migrationissmooth,withchangesinmigration times of about a factor of 2. Starting with a core which can undergo runaway growth, a planet can gain up to a few MJ with little migration. Planets with fina masses of the order of 10 MJ would undergo large migration, which makes formation and survival difficult

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/e9bf163351a678da479909653c8e98e8e9f3876d

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In Astronomy and Astrophysics

1. Philip Armitage
2. C. Mordasini
3. A. Morbidelli
4. Y. Alibert
5. Anders Johansen
6. R. Nelson
7. W. Kley
8. Th. Henning

Citations in the corpus

• Irregular Satellites of the Planets: Products of Capture in the Early Solar System (2007, background): “In a recent paper, by considering an accretion disk (Lubow et al. 1999; d’Angelo et al. 2002; Bate et al. 2003) instead of an extended atmosphere, Cuk & Burns (2004) have argued that gas-drag retardation can indeed account for the capture of the prograde (Himalia) cluster of Jovian irregular…”
• THREE-DIMENSIONAL MAGNETOHYDRODYNAMIC SIMULATIONS OF CIRCUMBINARY ACCRETION DISKS: DISK STRUCTURES AND ANGULAR MOMENTUM TRANSPORT (2011, methodology): “There has been extensive theoretical study of this situation, using both analytic and numerical methods (e.g., Goldreich & Tremaine 1980; Lin & Papaloizou 1986, 1993; Bryden et al. 1999; Ivanov et al. 1999; Bate et al. 2003; Nelson & Papaloizou 2003; Winters et al. 2003).”
• Gas Flow across Gaps in Protoplanetary Disks (2005, methodology): “Current migration models in the planet mass range considered here (0.05MJ–1MJ) suggest that migration occurs on about the local viscous timescale (e.g., Bate et al. 2003).”
• On the width and shape of gaps in protoplanetary disks (2005, methodology): “Thus, this is usually considered as a second independent criterion for gap opening, in addition to (3) (Bate et al., 2003).”
• Disk eccentricity and embedded planets (2005, unknown): “Bryden et al. 1999; Kley 1999; Kley et al. 2001; D’Angelo et al. 2002; Bate et al. 2003).”
• Standing on the shoulders of giants : Trojan Earths and vortex trapping in low mass self-gravitating protoplanetary disks of gas and solids (2008, methodology): “We performed a 3D simulation of planet-disk interaction in spherical coordinates, similar to those of Bate et al. (2003), Kley et al. (2005) and Edgar & Quillen (2008), but inviscid instead of viscous.”
• Origins of Eccentric Extrasolar Planets: Testing the Planet-Planet Scattering Model (2007, background): “For example, 3-d simulations have suggested that the gaps induced by giant planets might not be as well cleared as assumed in many 2-d disk models (Bate et al. 2003; D’Angelo et al. 2003).”
• Demographics of Transition Objects (2007, background): “…disc (within Rinner), are expected to allow continued accretion on to both planet and star, the latter through the replenishment of an inner disc (Lubow, Seibert & Artymowicz 1999; see also Kley 1999; Bryden et al. 1999; D’Angelo, Henning, & Kley 2002; Bate et al. 2003; Lubow & D’Angelo 2006).”
• Radial Migration of Gap-opening Planets in Protoplanetary Disks. I. The Case of a Single Planet (2018, methodology): “The transition between the different types of migrations has been studied in terms of the analytical model (Ward 1997) and hydrodynamic simulations (e.g., Bate et al. 2003; Masset & Papaloizou 2003).”
• Models of giant planet formation with migration and disc evolution (2004, background): “Contrary to laminar discs (as considered by Tanaka et al. 2002 and Bate et al. 2003) the migration proceeds as a random walk, and the mean value of the migration velocity seems to be highly reduced, compared to the laminar case.”
• The Evolution of Gravitationally Unstable Protoplanetary Disks: Fragmentation and Possible Giant Planet Formation (2003, background): “Therefore, the disk might be dissipated well before a planet can grow up to the many Jupiter masses of some of the extrasolar planets (Bate et al. 2003).”
• A torque formula for non-isothermal type I planetary migration – I. Unsaturated horseshoe drag (2009, methodology): “This formula has been confirmed by fully nonlinear, isothermal, hydrodynamical calculations (Bate et al. 2003; D’Angelo, Kley & Henning 2003a).”
• Evolution of protoplanetary disks: Constraints from DM Tauri and GM Aurigae (2005, background): “…the presence of a Jupiter-mass planet would lower the accretion rate onto the star, because part of the material from the outer disk would be accreted by the planet (e.g. D’Angelo et al. 2002, Bate et al. 2003), and part of the disk’s gravitational energy would be used to push the planet inward.”
• Planet formation and migration (2005, unknown): “The results of full numerical simulations in general confirm the linear analysis (e.g., D’Angelo et al 2003, Bate et al 2003).”
• Supermassive Stars in Quasar Disks (2003, background): “We are not aware of any calculations for disks supported largely by radiation pressure, but Bate et al. (2003) and Lufkin et al. (2003) have recently simulated threedimensional accretion from a protostellar disk onto embedded planets ranging in mass from that of earth (M⊕) to that of Jupiter (MJ).”
• Dust filtration at gap edges: Implications for the spectral energy distributions of discs with embedded planets (2006, background): “The presence of a planet can significantly influence the velocity structure of the gas in the vicinity of the planet (Kley 1999; Bate et al. 2003).”
• Spiral Structure in the Circumstellar Disk around AB Aurigae (2004, background): “Theoretical calculations show that a forming planet located in a disk opens a gap (Takeuchi, Miyama, & Lin 1996) that is often associated with a spiral structure extending inward and outward into the disk from the planet (e.g., Bate et al. 2003).”
• The interaction of giant planets with a disc with MHD turbulence – IV. Migration rates of embedded protoplanets (2003, result): “This disc model is equivalent to that described in Bate et al. (2003), and figure 1 is directly comparable with their figure 10.”