Abstract
ABSTRACT Recent observational missions have uncovered a significant number of compact multi-exoplanet systems. The tight orbital spacing of these systems has led to much effort being applied to the understanding of their stability; however, a key limitation of the majority of these studies is the termination of simulations as soon as the orbits of two planets cross. In this work we explore the stability of compact, three-planet systems, and continue our simulations all the way to the first collision of planets to yield a better understanding of the lifetime of these systems. We perform over 25 000 integrations of a Sun-like star orbited by three Earth-like secondaries for up to a billion orbits to explore a wide parameter space of initial conditions in both the co-planar and inclined cases, with a focus on the initial orbital spacing. We calculate the probability of collision over time and determine the probability of collision between specific pairs of planets. We find systems that persist for over 108 orbits after an orbital crossing and show how the post-instability survival time of systems depends upon the initial orbital separation, mutual inclination, planetary radius, and the closest encounter experienced. Additionally, we examine the effects of very small changes in the initial positions of the planets upon the time to collision and show the effect that the choice of integrator can have upon simulation results. We generalize our results throughout to show both the behaviour of systems with an inner planet initially located at 1 and 0.25 AU.
Highlights
The retired NASA Kepler Space Telescope is responsible for observations leading to the confirmation of hundreds of multi-planet systems (Lissauer et al 2014; Rowe et al 2014)
In the co-planar case we have seen that the distribution of post-crossing survival times are centered at approximately 102.5 orbits and it is known that if the inclination is below the critical threshold i = rH the number of collisions occurring within a factor of three of the orbital crossing increases (Rice et al 2018)
We chose to focus our attention on the effects of orbital spacing and distributed system configurations across a wide range of initial values evenly spaced in β
Summary
The retired NASA Kepler Space Telescope is responsible for observations leading to the confirmation of hundreds of multi-planet systems (Lissauer et al 2014; Rowe et al 2014). The majority of studies performed take a subset of the possible input parameter space for a compact, near-circular, near co-planar system of a given number of planets and evolve this system forward in time checking for either the first close approach, typically specified as one Hill radius, rH , or waiting for an orbital crossing to occur: this is termed the instability event. Our study builds upon the work done by Rice et al (2018) and Lissauer & Gavino (2021) by considering the post-instability evolution of compact, Earth-analogue, three-planet systems across a large range of initial orbital separations spaced in units of mutual Hill radii.
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