F. S. Masset et al. 2006 ApJ 652 730 doi:10.1086/507515
F. S. Masset1,4,5, G. D'Angelo2,6 and W. Kley3
Show affiliationsThe 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.
accretion, accretion disks; hydrodynamics; methods: numerical; planetary systems: formation; planetary systems: protoplanetary disks
Issue 1 (2006 November 20)
Received 2006 May 22, accepted for publication 2006 July 7
F. S. Masset et al. 2006 ApJ 652 730
Gleb Arutyunov et al 2007 J. Phys. A: Math. Theor. 40 3583
S E Derkachov et al 1990 J. Phys. A: Math. Gen. 23 5563
A T Blumenau et al 2002 J. Phys.: Condens. Matter 14 12741
Seung Ki Baek et al 2009 J. Phys. A: Math. Theor. 42 478001
A P F Atman et al 2005 J. Phys.: Condens. Matter 17 S2391
Alessandro Arcovito et al 2009 J. Phys.: Conf. Ser. 190 012195
Sergey V Meleshko 2002 J. Phys. A: Math. Gen. 35 3515
S L A de Queiroz 1995 J. Phys. A: Math. Gen. 28 6315
M Patra et al 2009 J. Phys.: Condens. Matter 21 486003