Secular Behavior of Exoplanets: Self-Consistency and Comparisons With the Planet-Planet Scattering Hypothesis

Abstract

If mutual gravitational scattering among exoplanets occurs, then it may produce unique orbital properties. For example, two-planet systems that lie near the boundary between circulation and libration of their periapses could result if planet-planet scattering ejected a former third planet quickly, leaving one planet on an eccentric orbit and the other on a circular orbit. We first improve upon previous work that examined the apsidal behavior of known multiplanet systems by doubling the sample size and including observational uncertainties. This analysis recovers previous results that demonstrated that many systems lay on the apsidal boundary between libration and circulation. We then performed over 12,000 three-dimensional N -body simulations of hypothetical three-body systems that are unstable, but stabilize to two-body systems after an ejection. Using these synthetic two-planet systems, we test the planet-planet scattering hypothesis by comparing their apsidal behavior, over a range of viewing angles, to that of the observed systems and find that they are statistically consistent regardless of the multiplicity of the observed systems. Finally, we combine our results with previous studies to show that, from the sampled cases, the most likely planetary mass function prior to planet-planet scattering follows a power law with index -1.1. We find that this pre-scattering mass function predicts a mutual inclination frequency distribution that follows an exponential function with an index between -0.06 and -0.1.

Scattering Outcomes of Close-in Planets: Constraints on Planet Migration

“…Changing β to more extreme values would not change our main conclusion because, even if the number of collisions per ejection decreases, showed that the eccentricity of the surviving planet after the ejection would decrease with decreasing β (for reference Ford & Rasio 2008 find e 0.2 for β = 1/9). Likewise, the final inclinations after ejections are also limited as one decreases β (e.g., Timpe et al 2013). In conclusion, the excitation of eccentricities and inclinations is inefficient even if the mass ratio departs from unity.…”

Long-Lived Chaotic Orbital Evolution of Exoplanets in Mean Motion Resonances With Mutual Inclinations

“…Specifically we focus on the "Mixed2" distribution of Raymond et al (2008) in which the planets' masses follow a power-law distribution with exponent −1.1. This distribution has recently been shown to reproduce many observed dynamical properties of exoplanets (Timpe et al 2013). This suite of simulations consisted of 1000 systems, and we examined 49 that had period ratios with 10% of 2, of which 24 were identified as being in an e-resonance by Raymond et al (2008).…”

Orbital Dynamics of Multi-Planet Systems With Eccentricity Diversity

“…The simulations we used were presented in several previous studies of planet-planet scattering and its consequences (Raymond et al 2008(Raymond et al , 2009(Raymond et al , 2010Timpe et al 2013). We focused on a particular set of simulations referred to as the mixed set in previous papers.…”

“…For multi-planet systems, additional constraints are imposed on eccentricity values due to the requirement that the system remain dynamically sta-ble. Dynamical interactions of multi-planet systems in the context of eccentricity and formation models have been investigated by numerous authors Jurić & Tremaine 2008;Malmberg & Davies 2008;Matsumura et al 2008;Raymond et al 2008Raymond et al , 2010Wang & Ford 2011;Timpe et al 2013). From the known multi-planet systems, there are four in particular which stand out with respect to the diversity of eccentricities present within the system.…”