Overstability of the 2:1 mean motion resonance: Exploring disc parameters with hydrodynamic simulations
Astronomy & Astrophysics(2024)
摘要
Resonant planetary migration in protoplanetary discs can lead to an interplay
between the resonant interaction of planets and their disc torques called
overstability. While theoretical predictions and N-body simulations hinted at
its existence, there was no conclusive evidence until hydrodynamical
simulations were performed.
Our primary purpose is to find a hydrodynamic setup that induces
overstability in a planetary system with two moderate-mass planets in a
first-order 2:1 mean motion resonance. We also aim to analyse the impact of key
disc parameters, namely the viscosity, surface density, and aspect ratio, on
the occurrence of overstability in this planetary system when the masses of the
planets are kept constant.
We performed 2D locally isothermal hydrodynamical simulations of two planets,
with masses of 5 and 10 M_⊕, in a 2:1 resonance. Upon identifying the
fiducial model in which the system exhibits overstability, we performed
simulations with different disc parameters to explore the effects of the disc
on the overstability of the system.
We observe an overstable planetary system in our hydrodynamic simulations. In
the parameter study, we note that overstability occurs in discs characterised
by low surface density and low viscosity. Increasing the surface density
reduces the probability of overstability within the system. A limit cycle was
observed in a specific viscous model with α_ν = 10^-3. In almost
all our models, planets create partial gaps in the disc, which affects both the
migration timescale and structure of the planetary system.
We demonstrate the existence of overstability using hydrodynamic simulations
but find deviations from the analytic approximation and show that the main
contribution to this deviation can be attributed to dynamic gap opening.
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