Overstability of the 2:1 mean motion resonance: Exploring disc parameters with hydrodynamic simulations

¹ Department of Physics, Faculty of Sciences, Ferdowsi University of Mashhad, Mashhad 91775-1436, Iran
e-mail: zahra.afkanpour@mail.um.ac.ir; sarehataiee@um.ac.ir
² Institut für Astronomie und Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
³ Astronomy Unit, School of Physical and Chemical Sciences, Queen Mary University of London, London E1 4NS, UK
⁴ Astrophysics Group, Department of Physics, Imperial College London, Prince Consort Rd, London SW7 2AZ, UK
⁵ Grupo de Dinâmica Orbital e Planetologia, São Paulo State University, UNESP, Guaratinguetá, CEP 12516-410 São Paulo, Brazil
⁶ Department of Earth, Planetary, and Space Sciences, The University of California, Los Angeles, 595 Charles E. Young Drive East, Los Angeles, CA 90095, USA

Received: 3 December 2023
Accepted: 21 March 2024

Abstract

Context. 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.

Aims. 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.

Methods. 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.

Results. 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_v = 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.

Conclusions. 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.