Adventures in the Kozai-Lidov Mechanism

Institution: | The Ohio State University |
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Department: | |

Year: | 2016 |

Keywords: | Astronomy; Astrophysics; Physics; stellar dynamics; binary stars; triple stars; compact objects; gravitational waves; n-body problem; gravitational scattering; exoplanets; stellar collisions; supermassive black holes |

Posted: | 02/05/2017 |

Record ID: | 2071579 |

Full text PDF: | http://rave.ohiolink.edu/etdc/view?acc_num=osu1450697815 |

Hierarchical triple systems are ubiquitous in our Galaxy. The population ofSun-like stars in triple systems is ~10% and this fraction rises forhigh mass stars. The most powerful dynamical phenomenon exhibited byhierarchical triples is the Kozai-Lidov (KL) mechanism. If the orbit of thetertiary is at high inclination relative to the orbit of the inner binary,it can drive the inner binary to high eccentricity over timescales longcompared to the orbital periods. In principle a tertiary at some criticalinclination (close to, though not generally exactly equal to 90 degrees)can drive the inner binary to arbitrarily high eccentricity.The equations of motion of the KL mechanism can be derived by taking amultipole expansion of the gravitational potential of the triple system andemploying the von Zeipel transformation to average over each binary orbit.From the equations of motion I derive the period of KL oscillations exactlyusing the quadrupole term and in the test particle limit. I then explorethe variation of the period of KL oscillations over the parameter space ofall possible triples in the test particle limit. The KL period does notvary by more than a factor of a few except for a narrow band around theseparatrix between circulation and libration where the KL period diverges.When the next term of the multipole expansion, the octupole term, isconsidered, the maximum inclination achieved by the triple system variesfrom one KL oscillation to the next (the ``eccentric KL mechanism'' or EKM).If the EKM causes the inclination of the triple to pass through 90 degrees(a 'flip'), the individual KL oscillations can be extremely strong, oftenpushing the inner binary to eccentricities of e ~ 0.99999. I derivethe period of oscillations induced by the octupole term by averaging theequations of motion over individual KL oscillations. I demonstrate thatwhen constants of motion are held fixed, the period of EKM oscillationsvaries as epsilon_oct^-1/2.I demonstrate using N-body integrations that the orbital motion of thetertiary induces fluctuations in the angular momentum of the inner binary,violating the double orbit averaged approximation. I also derive theequations of motion of a hierarchical by averaging only over the innerbinary of the triple and find excellent agreement between the N-body andsemi-secular calculations. I show that these fluctuations are of constantmagnitude, and so when the inner binary has an angular momentum less thanthe magnitude of the fluctuations (as during the maximum of a KLoscillation), they can lead to large changes in the eccentricity. Thesefluctuations can then push the inner binary to much higher eccentricitiesthan predicted in secular theory. I show that for mergers of supermassiveblack holes in triples these fluctuations can lead the binary to merge withsubstantial eccentricity (e > 0.8), even when relativisticcorrections are included.Scattering events involving triples are common, particularly in clusterenvironments, and are a potential mechanism to form multiple systems. Icalculate the cross section… Advisors/Committee Members: Thompson, Todd (Advisor).