Damping of Terrestrial‐Planet Eccentricities by Density‐Wave Interactions with a Remnant Gas Disk

Agnor, C. B.; Ward, William R.

doi:10.1086/338415

Cited by 52 publications

(48 citation statements)

References 28 publications

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“…It is also interesting that both planets damp at the same rate, even though their individual torques and angular momenta are unequal. Again, this is due to communication between the planetary pair via their mutual torque (e.g., Agnor & Ward 2002). Using the same semimajor axes as before, g( 1 3 ) = 0.51, (sin I s ) À1 dI s /dt % 0.097l d 2 , and damp $ 140l À1 d yr. For this example, the external resonance lies at a distance r r $ (a 2 /a 1 ) 3/7 a 2 /f f = 1.6a 2 = 24 AU, in pretty good agreement with the $25 AU value of Figure 2. …”

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confidence: 91%

Spiral Bending Waves Launched at a Vertical Secular Resonance

Ward

Hahn

2003

Astron J

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The excitation of spiral bending waves at a secular vertical resonance in a particle disk is examined. These waves are one-armed spirals of very long wavelength that are launched at sites where a secondary's nodal regression rate matches that of the disk. Nodal bending waves usually propagate radially outward as leading waves from a secular resonance exterior to the perturber, and inward as trailing waves from a secular resonance that lies interior. Their pattern speed is negative, so the spiral pattern rotates in a retrograde sense. The waves carry negative angular momentum but very little energy, and their excitation can damp the inclination of the secondary. Here we apply this theory to the case of two mutually precessing planets orbiting in a particle disk and compare their damping rate with the more familiar inclination excitation due to mean motion vertical resonances. We suggest that under certain circumstances, nodal wave damping may be an important element in maintaining planetary and/or embryo orbits in a nearly coplanar state.

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confidence: 91%

Spiral Bending Waves Launched at a Vertical Secular Resonance

Ward

Hahn

2003

Astron J

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“…If the timescale is long, the velocity dispersion of planetesimals is suppressed by the gas drag. Hence, the gravitational focusing effect of protoplanets is enhanced, resulting in a fast cleanup of remnant planetesimals and a lower eccentricity distribution of the final planets (Agnor & Ward 2002;Kominami & Ida 2002, 2004Nagasawa et al 2005;Ogihara et al 2007). On the other hand, if the timescale of gas dissipation is short, planetesimals remain unaccreted by protoplanets for a longer period of time.…”

Section: Introductionmentioning

confidence: 99%

Formation and Accretion History of Terrestrial Planets from Runaway Growth through to Late Time: Implications for Orbital Eccentricity

Morishima

Schmidt

Stadel

et al. 2008

Astrophysical Journal

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Remnant planetesimals might have played an important role in reducing the orbital eccentricities of the terrestrial planets after their formation via giant impacts. However, the population and the size distribution of remnant planetesimals during and after the giant impact stage are unknown, because simulations of planetary accretion in the runaway growth and giant impact stages have been conducted independently. Here we report results of direct N-body simulations of the formation of terrestrial planets beginning with a compact planetesimal disk. The initial planetesimal disk has a total mass and angular momentum as observed for the terrestrial planets, and we vary the width (0.3 and 0.5 AU ) and the number of planetesimals (1000Y5000). This initial configuration generally gives rise to three final planets of similar size, and sometimes a fourth small planet forms near the location of Mars. Since a sufficient number of planetesimals remains, even after the giant impact phase, the final orbital eccentricities are as small as those of the Earth and Venus.

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“…Kominami & Ida (2002 performed N-body simulations, taking into account the eccentricity damping caused by tidal interaction with a remnant gas disk and found that final eccentricities can be small enough to be consistent with those of Earth and Venus. The remnant disk with Σ g = 10 −4 -10 −3 Σ g,MMSN allows orbit crossing, but it is still enough to damp eccentricities of Earth-mass planets to 0.01 within disk depletion timescale ∼ 10 6 -10 7 years (Kominami & Ida 2002;Agnor & Ward 2002). …”

Section: Introductionmentioning

confidence: 99%

Accretion of terrestrial planets from oligarchs in a turbulent disk

Ogihara

Ida

Morbidelli

2007

Icarus

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We have investigated the final accretion stage of terrestrial planets from Mars-mass protoplanets that formed through oligarchic growth in a disk comparable to the minimum mass solar nebula (MMSN), through N-body simulation including random torques exerted by disk turbulence due to Magneto-Rotational-Instability. For the torques, we used the semi-analytical formula developed by Laughlin et al. (2004). The damping of orbital eccentricities (in all runs) and type-I migration (in some runs) due to the tidal interactions with disk gas are also included. Without any effect of disk gas, Earth-mass planets are formed in terrestrial planet regions in a disk comparable to MMSN but with too large orbital eccentricities to be consistent with the present eccentricities of Earth and Venus in our Solar system. With the eccentricity damping caused by the tidal interaction with a remnant gas disk, Earth-mass planets with eccentricities consistent with those of Earth and Venus are formed in a limited range of disk gas surface density (∼ 10 −4 times MMSN). However, in this case, on average, too many ( 6) planets remain in terrestrial planet regions, because the damping leads to isolation between the planets. We have carried out a series of N-body simulations including the random torques with different disk surface density and strength of turbulence. We found that the orbital eccentricities pumped up by the turbulent torques and associated random walks in semimajor axes tend to delay isolation of planets, resulting in more coagulation of planets. The eccentricities are still damped after planets become isolated. As a result, the number of final planets decreases with increase in strength of the turbulence, while Earth-mass planets with small eccentricities are still formed. In the case of relatively strong turbulence, the number of final planets are 4-5 at 0.5-2AU, which is more consistent with Solar system, for relatively wide range of disk surface density (∼ 10 −4 -10 −2 times MMSN).keywords: planetary formation, planet-disk interactions, terrestrial planets -2 -

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Damping of Terrestrial‐Planet Eccentricities by Density‐Wave Interactions with a Remnant Gas Disk

Cited by 52 publications

References 28 publications

Spiral Bending Waves Launched at a Vertical Secular Resonance

Spiral Bending Waves Launched at a Vertical Secular Resonance

Formation and Accretion History of Terrestrial Planets from Runaway Growth through to Late Time: Implications for Orbital Eccentricity

Accretion of terrestrial planets from oligarchs in a turbulent disk

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