Eccentricity Evolution of Extrasolar Multiple Planetary Systems Due to the Depletion of Nascent Protostellar Disks

Nagasawa, Makiko; Lin, D. N. C.; Ida, Shigeru

doi:10.1086/367884

Cited by 49 publications

(49 citation statements)

References 48 publications

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“…1a by using a sampling interval of 50 yr, which is long compared to the orbital timescales). Plots of the variations in the orbital elements of the HD 168443 planets in Marcy et al (2001), Nagasawa, Lin, & Ida (2003), and Udry, Mayor, & Queloz (2003, from calculations by W. Benz) show similar behaviors and are probably due to the use of astrocentric coordinates. In contrast, in Jacobi coordinates (Fig.…”

Section: Introductionmentioning

confidence: 86%

Secular Evolution of Hierarchical Planetary Systems

Lee

Peale

2003

ApJ

161

196

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(Abridged) We investigate the dynamical evolution of coplanar hierarchical two-planet systems where the ratio of the orbital semimajor axes alpha=a_1/a_2 is small. The orbital parameters obtained from a multiple Kepler fit to the radial velocity variations of a star are best interpreted as Jacobi coordinates and Jacobi coordinates should be used in any analyses of hierarchical planetary systems. An approximate theory that can be applied to coplanar hierarchical two-planet systems with a wide range of masses m_j and orbital eccentricities e_j is the octupole-level secular perturbation theory (OSPT). The OSPT shows that if the ratio of the maximum orbital angular momenta, lambda \approx (m_1/m_2) alpha^{1/2}, for given a_j is approximately equal to a critical value lambda_{crit}, then libration of the difference in the longitudes of periapse, w_1-w_2, about either 0 or 180 deg. is almost certain, with possibly large amplitude variations of both e_j. We establish that the OSPT is highly accurate for systems with alpha<0.1 and reasonably accurate even for systems with alpha as large as 1/3, provided that alpha is not too close to a significant mean-motion commensurability or above the stability boundary. The HD 168443 system is not in a secular resonance and its w_1-w_2 circulates. The HD 12661 system is the first extrasolar planetary system found to have w_1-w_2 librating about 180 deg. The libration of w_1-w_2 and the large-amplitude variations of both e_j in the HD 12661 system are consistent with the analytic results on systems with lambda \approx lambda_{crit}. The HD 12661 system with the best- fit orbital parameters and sin i = 1 is affected by the close proximity to the 11:2 commensurability, but small changes in the outer orbital period can result in configurations that are not affected by mean-motion commensurabilities.Comment: 32 pages, including 8 figures; uses AASTeX v5.0; accepted for publication in Ap

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Section: Introductionmentioning

confidence: 86%

Secular Evolution of Hierarchical Planetary Systems

Lee

Peale

2003

ApJ

161

196

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“…One concern is that we find that spacings of more than 20 Hill radii are typically sufficient to produce stable systems (at least on timescales of 100 Myr, the expected formation timescale). Preliminary simulations suggest that the introduction of Jupiter and Saturn stirs the system enough to produce embryo interaction, and resonance sweeping involving the removal of the disk potential (here neglected; see Nagasawa et al 2003) is another possibility. We will return to this issue in a subsequent paper.…”

Section: Evolution Of Interembryo Spacingmentioning

confidence: 99%

Effects of Type I Migration on Terrestrial Planet Formation

2005

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Planetary embryos embedded in a gas disc suffer a decay in semimajor axis -- type I migration -- due to the asymmetric torques produced by the interior and exterior wakes raised by the body (Goldreich & Tremaine 1980; Ward 1986). This presents a challenge for standard oligarchic approaches to forming the terrestrial planets (Kokubo & Ida 1998) as the timescale to grow the progenitor objects near 1 AU is longer than that for them to decay into the Sun. In this paper we investigate the middle and late stages of oligarchic growth using both semi-analytic methods (based upon Thommes et al. 2003) and N-body integrations, and vary gas properties such as dissipation timescale in different models of the protoplanetary disc. We conclude that even for near-nominal migration efficiencies and gas dissipation timescales of ~1 Myr it is possible to maintain sufficient mass in the terrestrial region to form Earth and Venus if the disc mass is enhanced by factors of ~2-4 over the minimum mass model. The resulting configurations differ in several ways from the initial conditions used in previous simulations of the final stages of terrestrial accretion (e.g. Chambers 2001), chiefly in (1) larger inter-embryo spacings, (2) larger embryo masses, and (3) up to ~0.4 Earth masses of material left in the form of planetesimals when the gas vanishes. The systems we produce are reasonably stable for ~100 Myr and therefore require an external source to stir up the embryos sufficiently to produce final systems resembling the terrestrial planets.Comment: 49 pages, 22 figures; accepted in AJ, expected Dec '0

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“…Other scenarios have been suggested ( Rasio & Ford 1996;Nagasawa et al 2003;Murray et al 1998), all of which involve significant excitation of orbital eccentricity. Once a planet is in the vicinity of the star, however, tidal forces will tend to circularize the orbit as well as synchronize the planetary spin .…”

Section: Orbit Evolution Due To Tidal Dampingmentioning

confidence: 99%

On the Survival of Short‐Period Terrestrial Planets

Mardling

Lin²

2004

ApJ

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The currently feasible method of detecting Earth-mass planets is transit photometry, with detection probability decreasing with a planet's distance from the star. The existence or otherwise of short-period terrestrial planets will tell us much about the planet-formation process, and such planets are likely to be detected first, if they exist. Tidal forces are intense for short-period planets and result in decay of the orbit on a timescale that depends on properties of the star as long as the orbit is circular. However, if an eccentric companion planet exists, orbital eccentricity (e i , where i is the inner orbit) is induced, and the decay timescale depends on properties of the shortperiod planet, reduced by a factor of the order of 10 5 e 2 i if it is terrestrial. Here we examine the influence companion planets have on the tidal and dynamical evolution of short-period planets with terrestrial structure, and we show that the relativistic potential of the star is fundamental to their survival.

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Eccentricity Evolution of Extrasolar Multiple Planetary Systems Due to the Depletion of Nascent Protostellar Disks

Cited by 49 publications

References 48 publications

Secular Evolution of Hierarchical Planetary Systems

Secular Evolution of Hierarchical Planetary Systems

Effects of Type I Migration on Terrestrial Planet Formation

On the Survival of Short‐Period Terrestrial Planets

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