On the Corotation Torque in a Radiatively Inefficient Disk

By C. Baruteau, F. Masset. 2007

183 citations recorded by the source corpus.

We consider the angular momentum exchange at the corotation resonance between a two-dimensional gaseous disk and a uniformly rotating external potential, assuming that the disk flow is adiabatic. We first consider the linear case for an isolated resonance, for which we give an expression of the corotation torque that involves the pressure perturbation and which reduces to the usual dependence on the vortensity gradient in the limit of a cold disk. Although this expression requires the solution of the hydrodynamic equations, it provides some insight into the dynamics of the corotation region. In the general case, we find an additional dependence on the entropy gradient at corotation. This dependence is associated with the advection of entropy perturbations. These are not associated with pressure perturbations. They remain confined to the corotation region, where they yield a singular contribution to the corotation torque. In a second part, we check our torque expression by means of customized two-dimensional hydrodynamical simulations. In a third part, we contemplate the case of a planet embedded in a Keplerian disk, assumed to be adiabatic. We find an excess of corotation torque that scales with the entropy gradient, and we check that the contribution of the entropy perturbation to the torque is in agreement with the expression obtained from the linear analysis. We finally discuss some implications of the corotation torque expression for the migration of low-mass planets in the regions of protoplanetary disks where the flow is radiatively inefficient on the timescale of the horseshoe U-turns.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/49bb47443e39f618049edb31e9d6affd704f08dd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

Citations in the corpus

Characterization of exoplanets from their formation - II. The planetary mass-radius relationship (2012, result): “Based on the results of Paardekooper & Mellema (2006), Baruteau & Masset (2008), Kley & Crida (2008), Kley et al. (2009) and Paardekooper et al. (2010), we now distinguish several sub-types of type I migration which lead to different migration directions and rates.”
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).”
A torque formula for non-isothermal type I planetary migration – I. Unsaturated horseshoe drag (2009, methodology): “This was confirmed numerically by Baruteau & Masset (2008b), who also showed that the impact of self-gravity on the corotation torque is small.”
A torque formula for non-isothermal Type I planetary migration – II. Effects of diffusion (2010, methodology): “8 of Baruteau & Masset (2008b).”
Pebble-isolation mass: Scaling law and implications for the formation of super-Earths and gas giants (2018, background): “Planets embedded in protoplanetary discs interact gravitationally with the disc and move through the disc (Paardekooper & Mellema 2006; Baruteau & Masset 2008; Kley et al. 2009; Paardekooper et al. 2011).”
Breaking the chains: hot super-Earth systems from migration and disruption of compact resonant chains (2017, background): “Planets may either migrate inward or outward depending on the combination of different torques from the disc (Paardekooper & Mellema 2006, 2008; Baruteau & Masset 2008; Paardekooper & Papaloizou 2008; Kley, Bitsch & Klahr 2009).”
Extrasolar planet population synthesis - II. Statistical comparison with observations (2009, background): “Paardekooper & Mellema (2006) and Baruteau & Masset (2008) have also shown that depending on specific local thermodynamic disk properties, the net torque can also be positive, i.e. causing outward migration.”
The Disk Substructures at High Angular Resolution Project (DSHARP). VII. The Planet–Disk Interactions Interpretation (2018, methodology): “We carry out 2D hydrodynamical planet–disk simulations using the modified version of the grid-based code FARGO (Masset 2000) called Dusty FARGO-ADSG (Baruteau & Masset 2008a, 2008b; Baruteau & Zhu 2016).”
Dynamics of pebbles in the vicinity of a growing planetary embryo: hydro-dynamical simulations (2012, result): “Recent results on migration in radiatively cooling disks (Paardekooper & Mallema 2006; Baruteau & Masset 2008; Kley & Crida 2008; Paardekooper et al. 2010; Masset & Casoli 2010; Bitsch & Kley 2011) show that the embryos migrate from all directions toward an orbital radius where migration is…”
Planet-Disk Interaction and Orbital Evolution (2012, methodology): “We comment briefly that the influence of disk self–gravity on type I migration of low-mass embedded planets has been considered by Pierens & Huré (2005) and Baruteau & Masset (2008b).”
The structure of protoplanetary discs around evolving young stars (2014, background): “However, the migration of cores cores depends on the thermodynamics in the disc, and even outward migration of planetary cores is possible (Paardekooper & Mellema 2006; Kley & Crida 2008; Baruteau & Masset 2008; Kley et al. 2009).”