The Kozai Mechanism and the Stability of Planetary Orbits in Binary Star Systems

Innanen, K. A.; Zheng, J. Q.; Mikkola, Seppo; Valtonen, Mauri

doi:10.1086/118405

Cited by 327 publications

(331 citation statements)

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“…"Short-period" companions alter planetary orbits independent of each other, while "long-period" companions cause the entire system only to precess as a unit. Innanen et al (1997) have performed billion-year integrations of the orbits of the outer giant planets and found them to be stable against the perturbative effects of a 0.05 M , companion on a 400 AU circular orbit, for all inclination angles. This result, scaled by preserving the tidal field M/a 3 , indicates that similar stability would occur for a 1 M , companion on a ∼1000 AU orbit.…”

Section: Duplicitymentioning

confidence: 99%

Nearby Young Solar Analogs. I. Catalog and Stellar Characteristics

Gaidos

1998

PUBL ASTRON SOC PAC

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ABSTRACT. We present a catalog of 38 young solar analogs within 25 pc, stars that are uniquely well suited for observations of their circumstellar environments to improve our understanding of conditions within the solar system during the Hadean/early Archean eons (prior to 3.8 Gyr ago). These G and early K stars were selected from the Hipparcos astrometric catalog based on lack of known stellar companions within 800 AU, bolometric luminosities close to that of the zero-age Sun and consistent with the zero-age main sequence, and ROSAT X-ray luminosities commensurate with the higher rotation rate and level of dynamo-driven activity in solar-mass stars less than 0.8 Gyr old. While many of these objects have been previously identified, this sample is novel in two respects: The selection criteria specifically consider the planetary environment, and the selection is uniform and all-sky. The X-ray emission from these young analogs is spectrally soft and consistent with a coronal origin. Calcium H and K emission, rotation periods, lithium abundances, and kinematics support an age range of 0.2-0.8 Gyr for most of these stars. Three stars have exceptionally high space motions with respect to the local standard of rest and may be old disk or halo stars that are anomalously X-ray luminous.

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Section: Duplicitymentioning

confidence: 99%

Nearby Young Solar Analogs. I. Catalog and Stellar Characteristics

Gaidos

1998

PUBL ASTRON SOC PAC

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“…have recently reinvigorated the research into this problem (see, e.g., Innanen et al 1997;Mazeh et al 1997;Holman et al 1997). Unlike the nearly circular and coplanar planetary orbits in the Solar System, some exoplanets are found on eccentric and/or inclined orbits (see review by Winn & Fabrycky 2014 and references therein).…”

mentioning

confidence: 99%

Double-averaging can fail to characterize the long-term evolution of Lidov–Kozai Cycles and derivation of an analytical correction

Luo

Katz

Dong

2016

Mon. Not. R. Astron. Soc.

131

153

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The double-averaging (DA) approximation is widely employed as the standard technique in studying the secular evolution of the hierarchical three-body system. We show that effects stemmed from the short-timescale oscillations ignored by DA can accumulate over long timescales and lead to significant errors in the long-term evolution of the Lidov-Kozai cycles. In particular, the conditions for having an orbital flip, where the inner orbit switches between prograde and retrograde with respect to the outer orbit and the associated extremely high eccentricities during the switch, can be modified significantly. The failure of DA can arise for a relatively strong perturber where the mass of the tertiary is considerable compared to the total mass of the inner binary. This issue can be relevant for astrophysical systems such as stellar triples, planets in stellar binaries, stellar-mass binaries orbiting massive black holes and moons of the planets perturbed by the Sun. We derive analytical equations for the short-term oscillations of the inner orbit to the leading order for all inclinations, eccentricities and mass ratios. Under the test particle approximation, we derive the "corrected double-averaging" (CDA) equations by incorporating the effects of short-term oscillations into the DA. By comparing to N-body integrations, we show that the CDA equations successfully correct most of the errors of the long-term evolution under the DA approximation for a large range of initial conditions. We provide an implementation of CDA that can be directly added to codes employing DA equations.

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“…There is potentially also an additional precession due to the presence of a distant M dwarf companion, a 0.26M⊙ M dwarf located at 1260 AU (Mugrauer et al 2006). However, this is too small to affect the dynamics of the planetary configuration on small scales, although it can generate precession of the system as a unit (Innanen et al 1997;Kaib et al 2011;Boue' & Fabrycky 2014). In order to better match the observations, we furthermore assume that the planetary system invariable plane is inclined at 37 • to the line of sight, except for the transitting 55 Canc e. This increases all the masses by a factor of 1.25 from that inferred in the radial velocity solution.…”

Section: Secular Architecturementioning

confidence: 99%

“…The presence of an M-dwarf companion at > 1000 AU can, in principle, induce precession of the planetary system (Innanen et al 1997;Kaib et al 2011;Boue' & Fabrycky 2014) if the orbit is sufficiently eccentric and inclined. However, the precession timescales are long compared to the time it takes 55 Canc e to cross the resonance, and so the orbit tilting discussed here is insensitive to the influence of the external companion.…”

Section: Effect Of the Companionmentioning

confidence: 99%

“…It has also been suggested (Kaib, Raymond & Duncan 2011) that the presence of a distant M-dwarf companion (Mugrauer et al 2006) can induce a coherent precession of the entire planetary system (Innanen et al 1997), potentially leading to a substantial obliquity offset between the stellar spin and the orbital plane of the planetary system. However, for the 55 Cancri system, spin-orbit coupling between the star and the planets likely quenches such an offset unless the companion is in a highly eccentric (e ∼ 0.95) orbit (Boue' & Fabrycky 2014).…”

Section: Introductionmentioning

confidence: 99%

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On the potentially dramatic history of the super-Earth ρ 55 Cancri e

Hansen

Zink

2015

Monthly Notices of the Royal Astronomical Society

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We demonstrate that tidal evolution of the inner planet ('e') of the system orbiting the star ρ 55 Cancri could have led to passage through two secular resonances with other planets in the system. The consequence of this evolution is excitation of both the planetary eccentricity and inclination relative to the original orbital plane. The large mass ratio between the innermost planet and the others means that these excitations can be of substantial amplitude and can have dramatic consequences for the system organisation. Such evolution can potentially explain the large observed mutual inclination between the innermost and outermost planets in the system, and implies that tidal heating could have substantially modified the structure of planet e, and possibly reduced its mass by Roche lobe overflow. Similar inner secular resonances may be found in many multiple planet systems and suggest that many of the innermost planets in these systems could have suffered similar evolutions.

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The Kozai Mechanism and the Stability of Planetary Orbits in Binary Star Systems

Cited by 327 publications

References 0 publications

Nearby Young Solar Analogs. I. Catalog and Stellar Characteristics

Nearby Young Solar Analogs. I. Catalog and Stellar Characteristics

Double-averaging can fail to characterize the long-term evolution of Lidov–Kozai Cycles and derivation of an analytical correction

On the potentially dramatic history of the super-Earth ρ 55 Cancri e

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