A torque formula for non-isothermal Type I planetary migration – II. Effects of diffusion

By S. Paardekooper, C. Baruteau, W. Kley. 2010

370 citations recorded by the source corpus.

We study the effects of diffusion on the non-linear corotation torque, or horseshoe drag, in the two-dimensional limit, focusing on low-mass planets for which the width of the horseshoe region is much smaller than the scaleheight of the disc. In the absence of diffusion, the non-linear corotation torque saturates, leaving only the Lindblad torque. Diffusion of heat and momentum can act to sustain the corotation torque. In the limit of very strong diffusion, the linear corotation torque is recovered. For the case of thermal diffusion, this limit corresponds to having a locally isothermal equation of state. We present some simple models that are able to capture the dependence of the torque on diffusive processes to within 20 per cent of the numerical simulations.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/9059d21d365162838cd205a7e660de5db8e99866

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Citations in the corpus

GLOBAL SIMULATIONS OF PROTOPLANETARY DISKS WITH OHMIC RESISTIVITY AND AMBIPOLAR DIFFUSION (2015, background): “…by the level of turbulence (Gressel et al. 2011, 2012), and the migration of low mass planets is also highly sensitive to the presence or otherwise of turbulence, with significant stress levels being required to unsaturate corotation torques (Paardekooper et al. 2011; Baruteau et al. 2011).”
TRANSITIONAL DISKS AS SIGNPOSTS OF YOUNG, MULTIPLANET SYSTEMS (2011, background): “…of planet migration in viscous disks with nonzero thermal diffusivity demonstrates that the corotation torque may halt inward migration or even drive outward migration (Paardekooper & Mellema 2006, Kley & Crida 2008, Kley et al. 2009, Paardekooper et al. 2010, Paardekooper et al. 2011).”
The structure of protoplanetary discs around evolving young stars (2014, background): “Instead, one can calculate the torque acting on an embedded planet from the disc structure (Paardekooper et al. 2010, 2011).”
Fossilized condensation lines in the Solar System protoplanetary disk (2015, background): “A second possibility is offered by the subtle action of the entropy-driven corotation torque (Paardekooper and Mellema, 2006b; Paardekooper et al., 2010, 2011; Masset and Casoli, 2009, 2010).”
The habitability of Proxima Centauri b. I. Irradiation, rotation and volatile inventory from formation to the present (2016, background): “Bodies more massive than ∼0.1–1 M⊕ are subject to migration from tidal interactions with the protoplanetary disk (Goldreich & Tremaine 1980; Paardekooper et al. 2011).”
The great dichotomy of the Solar System: Small terrestrial embryos and massive giant planet cores (2015, background): “But at this stage, the thermal structure of the disk becomes relevant, as it can excite an entropy-driven corotation torque on the core (Paardekooper and Mellema, 2006; Paardekooper et al., 2010, 2011; Masset and Casoli, 2009, 2010).”
Forming the cores of giant planets from the radial pebble flux in protoplanetary discs (2014, background): “Kretke & Lin (2012) give an overview of the migration rates in power-law discs (Tanaka et al. 2002; Paardekooper et al. 2010, 2011).”
Breaking the chains: hot super-Earth systems from migration and disruption of compact resonant chains (2017, background): “(5) Following Paardekooper et al. (2010, 2011) and assuming a gravitational smoothing length for the planet potential of b = 0.4h, the total torque from the gas experienced by a type-I migrating planet can be expressed by tot = L L + C C, (6) where L is the Lindblad torque and C is the corotation…”
Pebble-isolation mass: Scaling law and implications for the formation of super-Earths and gas giants (2018, background): “However, the corotation torque is prone to saturation, which depends on the local viscosity of the protoplanetary discs (Paardekooper et al. 2011), where a lower viscosity allows an easier torque saturation, preventing outward migration.”
Rapid inward migration of planets formed by gravitational instability (2011, methodology): “Despite the large value of α in our disc model, the horseshoe drag is found to be fully unsaturated, as the diffusion timescale across the planet’s horseshoe region remains larger than the U-turn timescale (Baruteau & Masset 2008a; Masset & Casoli 2010; Paardekooper et al. 2011).”
Origin of water in the inner Solar System: Planetesimals scattered inward during Jupiter and Saturn's rapid gas accretion (2017, background): “Orbital migration of planets embedded in gaseous protoplanetary disks is unavoidable (Goldreich and Tremaine, 1980; Lin and Papaloizou, 1986; Ward, 1997; Armitage, 2007; Paardekooper et al., 2011).”