2018ApJ...867...75D

We run a suite of dissipative N-body simulations to determine which regions of phase space for smooth disk migration are consistent with the GJ876 system, an M-dwarf hosting three planets orbiting in a chaotic 4:2:1 Laplace resonance. We adopt adaptive mesh refinement (AMR) methods that are commonly used in hydrodynamical simulations to efficiently explore the parameter space defined by the semimajor axis and eccentricity damping timescales. We find that there is a large region of phase space that produces systems in the chaotic Laplace resonance and a smaller region consistent with the observed eccentricities and libration amplitudes for the resonant angles. Under the assumptions of Type I migration for the outer planet, we translate these damping timescales into constraints on the protoplanetary disk surface density and thickness. When we strongly (weakly) damp the eccentricities of the inner two Laplace planets, these timescales correspond to disk surface densities around ten thousand (a few hundred) grams per square centimeter and disk aspect ratios between 1% and 10%. Additionally, smooth migration produces systems with a range of chaotic timescales, from decades and centuries to upward of thousands of years. In agreement with previous studies, the less chaotic regions of phase space coincide with the system being in a low-energy double apsidal corotation resonance. Our detailed modeling of multiplanetary systems coupled with our AMR exploration method enhances our ability to map out the parameter space of planet formation models and is well suited to study other resonant chain systems such as Trappist-1, Kepler-60, and others.