The interaction of giant planets with a disc with MHD turbulence – IV. Migration rates of embedded protoplanets

By R. Nelson, J. Papaloizou. 2003

218 citations recorded by the source corpus.

We present the results of global cylindrical disc simulations and local shearing box simulations of protoplanets interacting with a disc undergoing magnetohydrodynamic (MHD) turbulence. The specific emphasis of this paper is to examine and quantify the magnitude of the torque exerted by the disc on the embedded protoplanets as a function of the protoplanet mass, and thus to make a first study of the induced orbital migration of protoplanets resulting from their interaction with magnetic, turbulent discs. This issue is of crucial importance in understanding the formation of gas giant planets through the so-called core instability model, and the subsequent orbital evolution post-formation prior to the dispersal of the protostellar disc. Current estimates of the migration time of protoplanetary cores in the 3–30 Earth mass range in standard disc models are τmig≃ 104–105 yr, which is much shorter than the estimated gas accretion time-scale of Jupiter-type planets. The global simulations were carried out for a disc with constant aspect ratio H/r= 0.07 and protoplanet masses of Mp= 3, 10, 30 Earth masses, and 3 Jupiter masses. The local shearing box simulations were carried out for values of the dimensionless parameter (Mp/M*)/(H/R)3= 0.1, 0.3, 1.0 and 2.0, with M*, R and H being the central mass, the orbital radius and the local disc semithickness, respectively. These allow both embedded and gap-forming protoplanets for which the disc response is non-linear to be investigated. In all cases the instantaneous net torque experienced by a protoplanet showed strong fluctuations on an orbital time-scale, and in the low-mass embedded cases oscillated between negative and positive values. Consequently, in contrast to the laminar disc type I migration scenario, orbital migration would occur as a random walk. Running time averages for embedded protoplanets over typical run times of 20–25 orbital periods indicated that the averaged torques from the inner and outer disc took on values characteristic of type I migration. However, large fluctuations occurring on longer than orbital time-scales remained, preventing convergence of the average torque to well-defined values or even to a well-defined sign for these lower mass cases. Fluctuations became relatively smaller for larger masses indicating better convergence properties, to the extent that in the 30-M⊕ simulation consistently inward, albeit noisy, migration was indicated. Both the global and local simulations showed this trend with increasing protoplanet mass, which is due to its perturbation on the disc increasing to become comparable to and then dominate the turbulence in its neighbourhood. The turbulence then becomes unable to produce very large long-term fluctuations in the torques acting on the protoplanet. Eventually gap formation occurs and there is a transition to the usual type II migration at a rate determined by the angular momentum transport in the distant parts of the disc. The existence of significant fluctuations occurring in the turbulent discs on long time-scales is an important unexplored issue for the lower mass embedded protoplanets, which are unable to modify the turbulence in their neighbourhood, and which have been studied here. If significant fluctuations occur on the longest disc evolutionary time-scales, convergence of torque running averages for practical purposes will not occur and the migration behaviour of low-mass protoplanets considered as an ensemble will be very different from predictions of type I migration theory for laminar discs. The fact that noise levels were relatively smaller in the local simulations may indicate the presence of long-term global fluctuations, but the issue remains an important one for future investigation.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/1312ac97624cde55882bd03e084c2633a0cf7e7b

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Citations in the corpus

Planet formation and migration (2005, methodology): “…due to isolation, competition with other cores, gap formation (Thommes et al 2002) and how mobile the cores are under a modified type I migration which may be stochastic in the presence of turbulence (Nelson & Papaloizou 2004) or be reversed by large scale toroidal magnetic fields (Terquem 2003).”
Migration and the Formation of Systems of Hot Super-Earths and Neptunes (2006, background): “Note that type I migration has been shown to follow a random walk in a turbulent disk (Nelson & Papaloizou 2004).”
A torque formula for non-isothermal type I planetary migration – I. Unsaturated horseshoe drag (2009, background): “It has been shown that including magnetic fields, either regular (Terquem 2003) or turbulent (Nelson & Papaloizou 2004), may slow down or even stop type I migration.”
Models of giant planet formation with migration and disc evolution (2004, background): “On the other hand, suggestions of increased type I migration timescales can be found in Nelson & Papaloizou (2004).”
EMPIRICAL CONSTRAINTS ON TURBULENCE IN PROTOPLANETARY ACCRETION DISKS (2010, background): “One series of papers (Papaloizou & Nelson 2003; Papaloizou et al. 2004; Nelson & Papaloizou 2003, 2004) explores in detail the effects of turbulence on planet-forming disks.”
Three-dimensional simulations of multiple protoplanets embedded in a protostellar disc (2008, background): “Solving the type I problem remains an active area of research, and recently suggested remedies include: stochastic migration in a turbulent disc (Nelson & Papaloizou 2004; Nelson 2005); corotation torques operating in a region of positive gradient in disc surface density (Masset et al. 2006);…”
The excitation of spiral density waves through turbulent fluctuations in accretion discs – II. Numerical simulations with MRI-driven turbulence (2008, background): “The density perturbations associated with these may play an important role in driving protoplanetary migration (e.g. Nelson & Papaloizou 2004; Nelson 2005) and may play a role in exciting quasi-periodic oscillations in discs around close binary stars.”
On the ionisation fraction in protoplanetary disks. I. Comparing different reaction networks (2005, background): “Simulations of planets in disks indicate that turbulence may have a significant influence on planet migration and gap formation, as well as the velocity dispersion of planetesimals (Nelson & Papaloizou 2003, 2004; Winters, Balbus & Hawley 2003; Nelson 2005).”
Toward a Deterministic Model of Planetary Formation. IV. Effects of Type I Migration (2008, background): “…include 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…”
On the Migration of Protogiant Solid Cores (2006, background): “In such disks, however, the torque exerted by the gas on an embedded protoplanet displays large temporal fluctuations that tend to yield a random walk of the planet semi-major axis, rather than a steady drift of the latter (Nelson & Papaloizou 2004; Nelson 2005).”
Toward a Deterministic Model of Planetary Formation. II. The Formation and Retention of Gas Giant Planets around Stars with a Range of Metallicities (2004, methodology): “We also carry out the calculations with 3 times larger/smaller dMc=dt. Note that we do not consider the change in a of the cores due to the radial migration because the migration can be a random walk (Nelson & Papaloizou 2004).”
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).”
Post-oligarchic Evolution of Protoplanetary Embryos and the Stability of Planetary Systems (2007, background): “But the efficiency of this process may be suppressed by turbulence and nonlinear response in the disks (Koller et al. 2003; Laughlin et al. 2004; Nelson & Papaloizou 2004).”
On the evolution of multiple protoplanets embedded in a protostellar disc (2006, result): “…to adjust migration rates in 2D models, and an appropriately chosen value of will give migration rates that are consistent with those obtained for 3D disc models, where the vertical structure provides a natural softening of the disc potential (e.g. Tanaka et al. 2002; Nelson & Papaloizou 2004).”
Gravoturbulent Formation of Planetesimals (2005, background): “In simulations of the interaction between a planet and a magnetorotationally turbulent disc, Nelson & Papaloizou (2004) find that the average migration velocity of the planets is not changed by the presence of MRI turbulence (whereas the spread in drift velocity causes some planets to even drift…”
Planet-Disk Interaction and Orbital Evolution (2012, methodology): “For example, good agreement is found for the migration timescales of giant planets in turbulent disks, these being approximately equal to the viscous timescale of the disks at the planet locations ' 105 yr (Nelson & Papaloizou, 2003, 2004; Uribe et al., 2011).”
Extrasolar planet population synthesis I: Method, formation tracks and mass-distance distribution (2009, background): “The prevalence of extrasolar planets have led to suspect that the actual type I migration rate is probably significantly lower than currently estimated (Menou & Goodman 2003; Nelson & Papaloizou 2004).”
Accelerated planetesimal growth in self-gravitating protoplanetary discs (2004, background): “However, this long formation time-scale problem might be solved in light of the results of recent numerical simulations of the evolution of planetary cores embedded in turbulent accretion discs (Nelson & Papaloizou 2004).”