Can the stellar dynamical tide destabilize the resonant chains of planets formed in the disk?
Creators: name: Kwok, Leon Ka-Wang
name: Bolmont, Emeline
name: Revol, Alexandre
name: Mathis, Stéphane
name: Astoul, Aurélie
name: Charbonnel, Corinne
name: Raymond, Sean
Publisher: name: Zenodo
Year: 2023
Subjects: Stellar Tides
Tidal Interactions
Planetary Dynamics
Orbital Resonances
Resonant Chains
N-body

description: Resonance chains of planets are a common outcome of planetary formation and evolution in the protoplanetary disks. However, from observations, resonant chains are rare (a famous example would be the TRAPPIST-1 system). This implies that most of these chains are destabilized after the end of the disk phase (Izidoro et al. 2017). In stellar convective regions, tidal dissipation consists of two components, first one is the equilibrium tide, a large-scale circulation to recover the hydrostatic equilibrium due to the presence of the companion (Zahn, 1966). The second one is the dynamical tide, which is the inertial waves driven by the Coriolis acceleration (Ogilvie &amp; Lin, 2007). Stellar tide, particularly the dynamical tide, could contribute to the destabilization of the resonance chains. Due to the resonant nature of the dynamical tide, the tidal excitation frequency could correspond to a resonant frequency of the star, implying that the inner planet could experience a migration boost, disrupting the resonant chains' fragile stability. However, some previous studies suggest that one of the famous tidal models, the constant angular lag model, is mathematically contradictory (Efroimsky &amp; Makarov 2013) and that the constant time lag model predicts the pseudo-synchronization for terrestrial objects (Makarov &amp; Efroimsky 2013) which is not observed. Furthermore, these models assume a specific &amp; simple frequency dependence, hence they can not account for the complex multiple frequencies dependence. This is particularly important for eccentric objects, as the multiple frequencies dependence can not be ignored. This suggests that we need a better tidal model for better descriptions. We present the results of our investigation on the influence of the stellar dynamical tide on the stability of the resonant chains using the Kaula model (Kaula, 1961) which accounts for the more complex dependency of the dynamical tide. We use the N-body code Posidonius (Blanco-Cuaresma &amp; Bolmont, 2017) where we have implemented the Kaula model and the dynamical tide. The love number spectra are computed with the code used in Astoul &amp; Barker (2021). We performed simulations of the evolution of the resonant chains and studied their stability with initial conditions for multi-planet systems (multi-super-Earth) from Izidoro et al. (2021). We consider both a population of resonant chains and non-resonant chains which are the outcome of their formation models. We tested these initial conditions without tidal effect first to reproduce the dynamics of the resonant chains. We then applied the tidal forces to see whether the dynamical tide would be able to destabilize the resonant chains. We also applied our model to hypothetical systems of massive planet(s). Our work provides insight into whether the dynamical tide is the corresponding physical mechanism to destabilize the resonant chains, and provides the exoplanet community an N-body code with the dynamical tide &amp; Kaula model for further studies in tidal effects for close-in planets/ binary systems.