Eccentricity Evolution for Planets in Gaseous Disks

By Peter Goldreich, R. Sari. 2002

289 citations recorded by the source corpus.

At least several percent of solar-type stars possess giant planets. Surprisingly, most move on orbits of substantial eccentricity. We investigate the hypothesis that interactions between a giant planet and the disk from which it forms promote eccentricity growth. These interactions are concentrated at discrete Lindblad and corotation resonances. Interactions at principal Lindblad resonances cause the planet's orbit to migrate and open a gap in the disk if the planet is sufficiently massive. Those at first-order Lindblad and corotation resonances change the planet's orbital eccentricity. Eccentricity is excited by interactions at external Lindblad resonances that are located on the opposite side of corotation from the planet, and damped by co-orbital Lindblad resonances that overlap the planet's orbit. If the planet clears a gap in the disk, the rate of eccentricity damping by co-orbital Lindblad resonances is reduced. Density gradients associated with the gap activate eccentricity damping by corotation resonances at a rate that initially marginally exceeds that of eccentricity excitation by external Lindblad resonances. But the corotation torque may be reduced as the result of the trapping of fluid in libration around potential maxima. This nonlinear saturation can tip the balance in favor of eccentricity excitation. A minimal initial eccentricity of the order of 1% is required to overcome viscous diffusion, which acts to unsaturate corotation resonances by reestablishing the large-scale density gradient. Thus, eccentricity growth is a finite-amplitude instability. Formally, the apsidal resonance, which is a special kind of co-orbital Lindblad resonance that exists in pressure-dominated disks, appears to damp eccentricity faster than external Lindblad resonances can excite it. However, the wavelength of the apsidal wave in a pressure-dominated disk is so long that it does not propagate. A self-gravity-dominated disk does not have an apsidal resonance. Nevertheless, apsidal waves are excited at gap edges. Although these propagate, their long wavelengths suggest that they are likely to be reflected at disk edges to form standing waves. Viscous damping of standing waves results in eccentricity damping, but at level far below that which traveling waves would produce. Although the level of eccentricity damping due to apsidal waves is reduced to a modest level in both pressure- and self-gravity-dominated disks, whether it drops well below that of Lindblad resonances depends sensitively on the disk's thickness and planet's mass. However, our analysis shows that with reasonable parameters, planet-disk interactions can promote eccentricity growth.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/fe0fcb73897f676ee6f70be30d4a9ec858d8f70b

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Citations in the corpus

FRIENDS OF HOT JUPITERS. I. A RADIAL VELOCITY SEARCH FOR MASSIVE, LONG-PERIOD COMPANIONS TO CLOSE-IN GAS GIANT PLANETS (2013, background): “…an eccentric, short-period Jupiter in the young Hyades cluster also appears to be consistent with high-eccentricity migration mechanisms (Quinn et al. 2013), although uneven irradiation of disk gaps might excite the eccentricities of Jovian mass planets (Goldreich & Sari 2003; Tsang et al. 2013).”
BREEDING SUPER-EARTHS AND BIRTHING SUPER-PUFFS IN TRANSITIONAL DISKS (2015, background): “…emerge with a GCR 6 This argument is subject to the possibility that gas might actually excite eccentricities, either resonantly by Lindblad torques (Goldreich & Sari 2003; Duffell & Chiang 2015) or stochastically by turbulent density fluctuations (e.g., Ogihara et al. 2007, and references…”
Planet formation by coagulation: A focus on Uranus and Neptune (2004, methodology): “The analysis of Goldreich & Sari (2003), when applied to the cold planetesimal disks, suggests that the apsidal torque will be the most potent one, albeit with lower magnitude than Ward & Hahn (1998, 2003) had calculated.”
Five New Extrasolar Planets (2005, background): “Compelling models include those that invoke perturbations by the protoplanetary disk to pump eccentricities (Goldreich & Sari 2003), as no other planet is required.”
Origins of Eccentric Extrasolar Planets: Testing the Planet-Planet Scattering Model (2007, background): “This is in sharp contrast to current hydrodynamic simulations of migration that suggest K ≃ 1 and theories that predict K < 0 (e.g., Goldreich & Sari 2003; Ogilvie & Lubow 2003).”
Final Stages of Planet Formation (2004, background): “But the main excitation of these waves may occur off resonance at gap edges, and their long wavelengths suggest that they may have more of a standing than a propagating wave character (Goldreich & Sari 2003).”
On the Corotation Torque in a Radiatively Inefficient Disk (2007, background): “This has been studied for an isolated resonance by Goldreich & Sari (2003) and Ogilvie & Lubow (2003), and by Balmforth & Korycansky (2001) and Masset (2001) for a planetary co-orbital region.”
Planet Migration and Binary Companions: The Case of HD 80606b (2003, background): “Under certain circumstances planet-disk interactions may also excite the orbital eccentricity of the planet (see, e.g., Goldreich & Sari 2003).”
Dynamical Outcomes of Planet-Planet Scattering (2007, background): “Since we do not take account of the saturation of corotation resonances, which could lead to the eccentricity excitation by Lindblad resonances (Goldreich & Sari 2003; Moorhead & Adams 2008), the eccentricity damping considered here is an upper limit.”
Five New Multicomponent Planetary Systems (2005, background): “Models of disk pumping of eccentricities (Goldreich & Sari 2003) require more attention (Schäfer et al. 2004).”
Disk eccentricity and embedded planets (2005, background): “…Artymowicz (1992) it was suggested that for sufficiently wide gaps, eccentricity growth can be induced by interaction at the 1:3 resonance in the outer disk, However, for smaller planet masses this is damped by other resonances which are listed in Goldreich & Sari (2003); Sari & Goldreich (2004).”
Starbursts near supermassive black holes: young stars in the Galactic Centre, and gravitational waves in LISA band (2006, background): “It is an open question whether the inspiraling hole can acquire high eccentricity by interacting with the disc or with other orbiting masses (Goldreich and Sari 2003, Chiang et. al.”
Titan's internal structure inferred from a coupled thermal-orbital model (2005, background): “Goldreich and Sari (2003) recently show that Lindblad resonances would be able to overcome the damping interaction processes and significantly excite the orbital eccentricity if the planetary body opens a gap within the gas disk.”
Extrasolar planet population synthesis - II. Statistical comparison with observations (2009, background): “Even though planet-disk interactions can pump eccentricity under certain circumstances too (Goldreich & Sari 2003), the high eccentricities have been interpreted as mainly the result of gravitational interactions between (proto-)planets in initially more crowded systems (e.g. Rasio & Ford 1996;…”
STATISTICAL STUDY OF THE EARLY SOLAR SYSTEM'S INSTABILITY WITH FOUR, FIVE, AND SIX GIANT PLANETS (2012, background): “Changing the damping strength may not be strictly justified, because the semimajor axis migration and eccentricity damping are expected to be coupled (Goldreich & Sari 2003).”