Orbits and Interiors of Planets

Citation

Batygin, Konstantin (2012) Orbits and Interiors of Planets. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KQVW-GF86. https://resolver.caltech.edu/CaltechTHESIS:05202012-233257444

Abstract

The focus of this thesis is a collection of problems of timely interest in orbital dynamics and interior structure of planetary bodies.

The first three chapters are dedicated to understanding the interior structure of close-in, gaseous extrasolar planets (hot Jupiters). In order to resolve a long-standing problem of anomalously large hot Jupiter radii, we proposed a novel magnetohydrodynamic mechanism responsible for inflation. The mechanism relies on the electro-magnetic interactions between fast atmospheric flows and the planetary magnetic field in a thermally ionized atmosphere, to induce electrical currents that flow throughout the planet. The resulting Ohmic dissipation acts to maintain the interior entropies, and by extension the radii of hot Jupiters at an enhanced level. Using self-consistent calculations of thermal evolution of hot Jupiters under Ohmic dissipation, we demonstrated a clear tendency towards inflated radii for effective temperatures that give rise to significant ionization of K and Na in the atmosphere, a trend fully consistent with the observational data. Furthermore, we found that in absence of massive cores, low-mass hot Jupiters can over-flow their Roche-lobes and evaporate on Gyr time-scales, possibly leaving behind small rocky cores. In systems where a transiting hot Jupiter is perturbed by a long-period companion, apsidal precession of the hot Jupiter that results from its tidal bulge plays an important, and often dominant role in determining the nature of the dynamical state onto which the system settles. This precession is in turn a strong function of the planet's degree of central concentration and is characterized by the planetary Love number. Utilizing this connection, we have shown that in tidally relaxed systems, measurement of the hot Jupiter's eccentricity directly yields the planetary Love number, which can then be used to place meaningful constraints on the physical structure of the planet with the aid of thermal evolution calculations.

Chapters four through six focus on the improvement and implications of a model for orbital evolution of the solar system, driven by dynamical instability (termed the ``Nice" model). Hydrodynamical studies of the orbital evolution of planets embedded in protoplanetary disks suggest that giant planets have a tendency to assemble into multi-resonant configurations. Following this argument, we used analytical methods as well as self-consistent numerical N-body simulations to identify fully-resonant primordial states of the outer solar system, whose dynamical evolutions give rise to orbital architectures that resemble the current solar system. We found a total of only eight such initial conditions, providing independent constraints for the solar system's birth environment. Next, we addressed a significant drawback of the original Nice model, namely its inability to create the physically unique, cold classical population of the Kuiper Belt. Specifically, we showed that a locally-formed cold belt can survive the transient instability, and its relatively calm dynamical structure can be reproduced. We developed a simple analytical model for dynamical excitation in the cold classical region and showed that comparatively fast apsidal precession and nodal recession of Neptune, during its eccentric phase, are essential for preservation of an unexcited state. Subsequently, we confirmed our findings with self-consistent N-body simulations, suggesting that the cold classical Kuiper belt's unique physical characteristics are a result of its remote formation site. Finally, we showed that the solar system may have initially hosted an additional ice-giant planet, that was ejected from the system during the transient phase of instability. Namely, we demonstrated that a large array of 5-planet (2 gas giants + 3 ice giants) multi-resonant initial states can lead to an adequate formation of the outer solar system, deeming the construction of a unique model of solar system's early dynamical evolution impossible.

The last four chapters of this thesis address various aspects and consequences of dynamical relaxation of planetary orbits through dissipative effects as well as the formation of planets in binary stellar systems. Using octopole-order secular perturbation theory, we demonstrated that in multi-planet systems, tidal dissipation often drives orbits onto dynamical ``fixed points," characterized by apsidal alignment and lack of periodic variations in eccentricities. We applied this formalism towards investigating the possibility that the large orbital eccentricity of the transiting Neptune-mass planet Gliese 436b is maintained in the face of tidal dissipation by a second planet in the system and computed a locus of possible orbits for the putative perturber. Following up along similar lines, we used various permutations of secular theory to show that when applied specifically to close-in low-mass planetary systems, various terms in the perturbation equations become separable, and the true masses of the planets can be solved for algebraically. In practice, this means that precise knowledge of the system's orbital state can resolve the sin(i) degeneracy inherent to non-transiting planets. Subsequently, we investigated the onset of chaotic motion in dissipative planetary systems. We worked in the context of classical secular perturbation theory, and showed that planetary systems approach chaos via the so-called period-doubling route. Furthermore, we demonstrated that chaotic strange attractors can exist in mildly damped systems, such as photo-evaporating nebulae that host multiple planets. Finally, we considered planetary formation in highly inclined binary systems, where orbital excitation due to the Kozai resonance apparently implies destructive collisions among planetesimals. Through a proper account of gravitational interactions within the protoplanetary disk, we showed that fast apsidal recession induced by disk self-gravity tends to erase the Kozai effect, and ensure that the disk's unwarped, rigid structure is maintained, resolving the difficulty in planet-formation. We also showed that the Kozai effect can continue to be wiped out as a result of apsidal precession, arising from planet-planet interactions in a mature planetary system. However, if such a system undergoes a dynamical instability, its architecture may change in such a way that the Kozai effect becomes operative, giving rise to the near-unity eccentricities, observed in some extrasolar planetary systems.

Thesis Files