Dynamics and Collisional Evolution of Closely Packed Planetary Systems

Jason Hwang

doi:https://doi.org/10.21985/N2N17D

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Dynamics and Collisional Evolution of Closely Packed Planetary Systems

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Of the thousands of planetary candidates discovered by the Kepler mission, roughly a third are in known multiple transiting-planet systems. High-multiplicity Kepler systems (referred to as Kepler Multis) are often tightly packed and may be on the verge of instability. Many systems of this type could have experienced past instabilities, where the compact orbits and often low densities make physical collisions likely outcomes. Since the structure of many of these planets is such that the mass is dominated by a rocky core, but the volume is dominated by a tenuous gas-envelope, the sticky-sphere approximation used in dynamical integrators may be a poor approximation. These planet-planet collisions are important in shaping both the orbits and planet structures in these systems, and we perform several studies examining the characteristics of typical collisions in Kepler Multis, and modeling the outcomes of these collisions in detail. We use numerical simulations to study the dynamical instabilities and planet-planet interactions in a synthetically generated sample of a representative closely-packed, high-multiplicity system. We focus specifically on systems resembling Kepler-11, a Kepler Multi with six planets that may be on the verge of instability, and run a suite of dynamical integrations, sampling the initial orbital parameters around the nominal values reported in Lissauer et al. (2011a), finding that most of the realizations are unstable, resulting in orbit crossings and, eventually, collisions and mergers. We study in detail the dependence of stability on the orbital parameters of the planets and planet-pair characteristics to identify possible precursors to instability, compare the systems that emerge from dynamical instabilities to the observed Kepler sample (after applying observational corrections), and propose possible observable signatures of these instabilities. We examine the characteristics of each planet-planet collision, categorizing collisions by the degree of contact and collision energy, and find that grazing collisions are more common than direct impacts. Finally, we rerun a subset of our dynamical calculations using instead a modified prescription replacing the sticky-spheres approximation to handle collisions, finding, in general, higher multiplicity remnant systems. The prevalence of instabilites in systems very similar to Kepler-11 suggest that dynamical instabilities may have been common and play an important role in sculpting both the orbits and planet structures observed in the Kepler sample. To better understand these collisions, we develop a pipeline of numerical tools to perform realistic simulations. Specifically, we use an N-body code to generate a population of collisions from initially non-crossing orbits, a stellar evolution code to generate realistic gas-envelopes, equations of state from geophysics to model differentiated planet-cores, and a Smoothed-Particle-Hydrodynamics (SPH) code to resolve the collision in detail. Because the structure of these planets is such that the gas-envelope and rocky-core both have significant mass and volume fractions, we develop additional algorithms to resolve both components while handling the large density-gradient and abrupt change in equation of state at the interfaces. Finally, after each collision, we use a prescription to estimate the densities of the remnant planets and an N-body code to study the stability of the final orbits. We present two representative calculations of collisions found in our simulations of Kepler-11 analogs and find that the collisions differ greatly from the sticky-sphere approximation used in N-body codes. We perform five sets of hydrodynamic calculations simulating typical planet-planet collisions between sub-Neptunes, sampling various mass-ratios and core-mass fractions. In our primary set of calculations, we use Kepler-36 as a nominal remnant-system, as the two planets have a small dynamical separation and an extreme density ratio. The orbits and planet-properties may be indicative of a previous planet-planet collision, where the more massive planet was able to retain a majority of the disrupted gas, while the smaller planet lost much of its gas envelope. In addition, we perform four additional sets of calculations combining planets of mass-ratio, q = 1 and q = 1/3, and core-mass fractions, m c /M = 0.85 and m c /M = 0.95. We find several distinct outcomes including scatterings, mergers, and even a potentially long-lived planet-planet binary. We find that collisions resulting in two surviving planets are more stable and affect the gas-mass fractions, where the amount of gas retained is very sensitive to the core-mass. Finally, we aggregate the data to provide prescriptions for predicting the outcomes and modeling the changes in mass and orbits during planet-planet collisions in post-disk planetary systems for general use in dynamical integrators.

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