Planet Migration and Gap Formation by Tidally Induced Shocks

By R. Rafikov. 2001

143 citations recorded by the source corpus.

Gap formation in a gas disk triggered by disk-planet tidal interaction is considered. Density waves launched by the planet are assumed to be damped as a result of their nonlinear evolution leading to shock formation and its subsequent dissipation. As a consequence, wave angular momentum is transferred to the disk, leading to evolution of its surface density. Planetary migration is an important ingredient of the theory; effects of the planet-induced surface density perturbations on the migration speed are considered. A gap is assumed to form when a stationary solution for the surface density profile is no longer possible in the frame of reference migrating with the planet. An analytical limit on the planetary mass necessary to open a gap in an inviscid disk is derived. The critical mass turns out to be smaller than the mass M1 for which the planetary Hill radius equals the disk scale height by a factor of at least Q5/7 (Q is the Toomre stability parameter), depending on the strength of the migration feedback. In viscous disks the critical planetary mass could vary from ~0.2M1 to M1, depending on the disk viscosity. This implies that a gap could be formed by a planet with mass of 2-15 M⊕, depending on the disk aspect ratio, viscosity, and the planet's location in the nebula.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/c76b943ea419f4fc53d6e2b9bdc928eb5415ce89

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Citations in the corpus

On the width and shape of gaps in protoplanetary disks (2005, methodology): “It is transported away by density waves (Goldreich and Nicholson, 1989 ; Papaloizou and Lin, 1984 ; Rafikov, 2002 ; see Appendix C).”
On planet formation in HL Tau (2015, background): “These waves can freely propagate across the dusty disc without being damped by dissipative phenomena (Rafikov 2002).”
Planet-Disk Interaction and Orbital Evolution (2012, background): “Under this circumstance the opening criterion depends of the disk mass as well (Rafikov, 2002), which has been confirmed by numerical simulations (Li et al., 2009).”
Multiple Disk Gaps and Rings Generated by a Single Super-Earth (2017, background): “Goodman & Rafikov (2001) showed that in an inviscid disk having a two-dimensional (2D) adiabatic index γ, waves launched to either side of the planet’s orbit travel a radial distance lsh ≈ 0.8 ( γ + 1 12/5 Mp Mthermal )−2/5 h (2) before shocking and dissipating (see also Rafikov 2002a).”
Atmospheres of Protoplanetary Cores: Critical Mass for Nucleated Instability (2004, background): “…fashion, as demonstrated by hydrodynamic 6 When condition (19) is violated, a gap can form around the planetary orbit (Lin & Papaloizou 1993; Rafikov 2002), additionally complicating the geometry of the protoplanetary atmosphere. simulations of planet-disk interaction (e.g., D’Angelo et al.…”
THE POPULATION OF VISCOSITY- AND GRAVITATIONAL WAVE-DRIVEN SUPERMASSIVE BLACK HOLE BINARIES AMONG LUMINOUS ACTIVE GALACTIC NUCLEI (2009, background): “The condition for a gap to open is that the mass ratio exceeds the critical value q max{(H0/R0)3, (10α)1/2(H0/R0)5/2} (e.g., Rafikov 2002; note that H0 is evaluated at the position of the secondary R0).”
ON THE ROLE OF DISKS IN THE FORMATION OF STELLAR SYSTEMS: A NUMERICAL PARAMETER STUDY OF RAPID ACCRETION (2009, background): “(33) 10 Here, rH = (Ms/3M∗)1/3 is the Hill radius, Ms, and M∗ are the masses of the secondary and primary, and the numerical factor fH , represents how many Hill radii an object can feed from in the disk – numerical simulations suggest fH ∼ 3.5 (Lissauer 1987; Rafikov 2002).”
Halting type I planet migration in non-isothermal disks (2006, background): “See, however, Rafikov (2002) on gap formation for low-mass planets; 3.”
Radial Migration of Gap-opening Planets in Protoplanetary Disks. I. The Case of a Single Planet (2018, methodology): “A gap formation criterion has been considered by many previous works (e.g., Lin & Papaloizou 1993; Rafikov 2002; Crida et al. 2006; Edgar et al. 2007).”
Pebble-isolation mass: Scaling law and implications for the formation of super-Earths and gas giants (2018, methodology): “In contrast, the original formula from Lambrechts et al. (2014), which is at the base of the new, refined formula proposed here, is similar to the expression of the critical mass for the wake to shock in a disc (Goodman & Rafikov 2001; Rafikov 2002).”
Fragmentation of massive protostellar discs (2006, unknown): “Rafikov (2002) estimates Mgap = 2c3ad 3ΩG α 0.043 = 0.37 α/0.30 Q Mfrag.”
Planet formation and migration (2005, background): “However, note that Rafikov (2002) argues that gap formation may occur for planets of mass as low as 2 M⊕.”
Starbursts near supermassive black holes: young stars in the Galactic Centre, and gravitational waves in LISA band (2006, unknown): “(9), (B4) and (B5) of Rafikov (2002), and Ward (1986).”