Prevalence of chaos in planetary systems formed through embryo accretion

Abstract

The formation of the solar system's terrestrial planets has been numerically modeled in various works, and many other studies have been devoted to characterizing our modern planets' chaotic dynamical state. However, it is still not known whether our planets fragile chaotic state is an expected outcome of terrestrial planet accretion. We use a suite of numerical simulations to present a detailed analysis and characterization of the dynamical chaos in 145 different systems produced via terrestrial planet formation in Kaib & Cowan (2015). These systems were created in the presence of a fully formed Jupiter and Saturn, using a variety of different initial conditions. They are not meant to provide a detailed replication of the actual present solar system, but rather serve as a sample of similar systems for comparison and analysis. We find that dynamical chaos is prevalent in roughly half of the systems we form. We show that this chaos disappears in the majority of such systems when Jupiter is removed, implying that the largest source of chaos is perturbations from Jupiter. Chaos is most prevalent in systems that form 4 or 5 terrestrial planets. Additionally, an eccentric Jupiter and Saturn is shown to enhance the prevalence of chaos in systems. Furthermore, systems in our sample with a center of mass highly concentrated between ∼0.8-1.2 AU generally prove to be less chaotic than systems with more exotic mass distributions. Through the process of evolving systems to the current epoch, we show that late instabilities are quite common in our systems. Of greatest interest, many of the sources of chaos observed in our own solar system (such as the secularly driven chaos between Mercury and Jupiter) are shown to be common outcomes of terrestrial planetary formation. Thus, consistent with previous studies such as Laskar (1996), the solar system's marginally stable, chaotic state may naturally arise from the process of terrestrial planet formation.

Stability of Neptune's distant resonances in the presence of Planet Nine

“…For each particle in our simulations, we compute the various possible resonant angles over 1 Gyr from simulation outputs every 10,000 years, and calculate the circular standard deviation (Mardia 1972) for each time window of interest. We confirmed via visual inspection of sample distributions that objects with a resonant angle standard deviation 2.0 exhibit significant libration for at least 20% of the given epoch (see also : Clement & Kaib 2017). Figure 1 depicts five different example evolutionary sequences that are characterized by our classification system as resonant.…”

Mars’ growth stunted by an early giant planet instability

“…Figure 1 shows an example of this evolution for a simulation in the n1 batch. To verify that the planets are in a MMR, libration about a series of resonant angles is checked for using the method described in Clement & Kaib (2017).…”

The early instability scenario: Terrestrial planet formation during the giant planet instability, and the effect of collisional fragmentation

“…Since the parameter space of possible primordial orbits for the outer planets is exhaustive, we use the most successful 5 and 6 planet configurations from Nesvorný & Morbidelli (2012) (denoted n1 and n2 in Paper 1, henceforward 5GP and 6GP for simplicity; table 1). The giant planets are migrated into the appropriate configuration using an additional force designed to approximate gas disk interactions by modifying the equations of motion with forced migration ( ȧ) and eccentricity damping ( ė) terms (Lee & Peale 2002;Clement & Kaib 2017). The resonant chains are then integrated with a 20 day time-step in the presence of 1000 equal-mass primordial Kuiper Belt objects (see Paper 1) up until the point when two giant planets first pass within 3 mutual Hill Radii.…”