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Adventures in the Kozai-Lidov Mechanism

Antognini, Joseph M
http://orcid.org/0000-0002-5976-5396
http://rave.ohiolink.edu/etdc/view?acc_num=osu1450697815

Abstract Details

2016, Doctor of Philosophy, Ohio State University, Astronomy.
Hierarchical triple systems are ubiquitous in our Galaxy. The population of Sun-like stars in triple systems is ~10% and this fraction rises for high mass stars. The most powerful dynamical phenomenon exhibited by hierarchical triples is the Kozai-Lidov (KL) mechanism. If the orbit of the tertiary is at high inclination relative to the orbit of the inner binary, it can drive the inner binary to high eccentricity over timescales long compared to the orbital periods. In principle a tertiary at some critical inclination (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 a multipole expansion of the gravitational potential of the triple system and employing the von Zeipel transformation to average over each binary orbit. From the equations of motion I derive the period of KL oscillations exactly using the quadrupole term and in the test particle limit. I then explore the variation of the period of KL oscillations over the parameter space of all possible triples in the test particle limit. The KL period does not vary by more than a factor of a few except for a narrow band around the separatrix between circulation and libration where the KL period diverges. When the next term of the multipole expansion, the octupole term, is considered, the maximum inclination achieved by the triple system varies from 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, often pushing the inner binary to eccentricities of e ~ 0.99999. I derive the period of oscillations induced by the octupole term by averaging the equations of motion over individual KL oscillations. I demonstrate that when constants of motion are held fixed, the period of EKM oscillations varies as epsilon_oct^-1/2. I demonstrate using N-body integrations that the orbital motion of the tertiary induces fluctuations in the angular momentum of the inner binary, violating the double orbit averaged approximation. I also derive the equations of motion of a hierarchical by averaging only over the inner binary of the triple and find excellent agreement between the N-body and semi-secular calculations. I show that these fluctuations are of constant magnitude, and so when the inner binary has an angular momentum less than the magnitude of the fluctuations (as during the maximum of a KL oscillation), they can lead to large changes in the eccentricity. These fluctuations can then push the inner binary to much higher eccentricities than predicted in secular theory. I show that for mergers of supermassive black holes in triples these fluctuations can lead the binary to merge with substantial eccentricity (e > 0.8), even when relativistic corrections are included. Scattering events involving triples are common, particularly in cluster environments, and are a potential mechanism to form multiple systems. I calculate the cross section of various outcomes from binary-binary, triple-single, and triple-binary scattering events using a suite of N-body integrations. I explore the dependence of the cross sections on the semi-major axis ratio, mass ratio, eccentricities, and incoming velocity. I derive the velocity dependence of the cross section for new triple formation from triple-single scattering and show that it is shallower at high velocities than the cross section for triple formation from binary-binary scattering. I derive the cumulative cross section for changes to the orbital parameters from flybys and show that the cross section for large changes to the orbital parameters is similar to the cross section for ionization. I apply these results to the Type Ia supernova progenitor problem. While the KL-accelerated WD-WD merger model has a number of attractive features, it has the difficulty that KL oscillations would drive the stars to strong tidal interaction on the main sequence, thereby quenching future KL oscillations. Scattering can push triple systems from low inclination to high inclination after the stars have evolved into WDs. However, I derive the rate of new triple formation in the field to be many orders of magnitude smaller than the SN Ia rate. In open clusters the new triple formation rate is smaller by a factor of ~10, but the uncertainties in the estimate are too large to rule out scattering in open clusters. In globular clusters the new triple formation rate is comparable to the Galactic SN Ia rate scaled by mass, but it is unclear if the specific SN Ia rate is enhanced in globular clusters. I estimate the rate of scattering-induced stellar mergers and find it to be lower than the observed rate of 0.5/yr by an order of magnitude. I calculate the cross section for planets to be ejected due to scattering with an interloping system and show that most free floating planets are not ejected in this way. Finally, I show that in all environments the timescale of KL oscillations is short compared to the timescale for disruption due to scattering.
Todd Thompson (Advisor)
Christopher Kochanek (Committee Member)
Marc Pinsonneault (Committee Member)
190 p.
Astronomy; Astrophysics; Physics
stellar dynamics; binary stars; triple stars; compact objects; gravitational waves; n-body problem; gravitational scattering; exoplanets; stellar collisions; supermassive black holes

Recommended Citations

Citations

  • Antognini, J. M. (2016). Adventures in the Kozai-Lidov Mechanism [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1450697815

    APA Style (7th edition)

  • Antognini, Joseph. Adventures in the Kozai-Lidov Mechanism. 2016. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1450697815.

    MLA Style (8th edition)

  • Antognini, Joseph. "Adventures in the Kozai-Lidov Mechanism." Doctoral dissertation, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1450697815

    Chicago Manual of Style (17th edition)

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This open access ETD is published by The Ohio State University and OhioLINK.