Planetary migration in precessing discs for S-type wide binaries

Abstract

The discovery of numerous circumprimary planets in the last few years has brought to the fore the question of planet formation in binary systems. The significant dynamical influence, during the protoplanetary disk phase, of a binary companion on a giant planet has previously been highlighted for wide binary stars. In particular, highly inclined binary companion can induce perturbations on the disk and the planets, through the Lidov-Kozai resonance, which could inhibit the formation process. In this work, we aim to study how the disk gravitational potential acting on the planet and the nodal precession induced by the wide binary companion with separation of 1000 AU on the disk act to suppress the Lidov-Kozai perturbations on a migrating giant planet. We derive new approximate formulas for the evolution of the disk’s inclination and longitude of the ascending node, in the case of a rigidly precessing disk with a decreasing mass and perturbed by a wide binary companion, which are suitable for N-body simulations. We carry out 3200 simulations with several eccentricity and inclination values for the binary companion. The gravitational and damping forces exerted by the disk on the planet tend to keep the latter in the midplane of the former, and suppress the effect of the binary companion by preventing the planet from getting locked in the Lidov-Kozai resonance during the disk phase. We also confirm that because of nodal precession induced by the binary, a primordial spin-orbit misalignment could be generated for circumprimary planets with an inclined binary companion.

The Lidov-Kozai resonance at different scales

“…Using a symplectic N-body integrator designed for binary star systems, in which the dissipation for the planet due to the disc is implemented following the formulas of Bitsch et al (2013), Roisin and Libert (2021) noted that accumulations of the pericenter arguments around 90 • and 270 • are clearly visible at the dispersal of the disc (left panel of Fig. 7).…”

“…This reflects the significant dynamical influence of a wide binary 60 A.-S. Libert companion (here at 1000 AU) on the evolution of a giant planet during its migration in the protoplanetary disc. However, when considering additional effects related to the disc, such as the disc gravitational potential acting on the planet (e.g., Terquem and Ajmia 2010;Teyssandier et al 2013) and the nodal precession induced by the binary companion on the disc (e.g., Batygin et al 2011;Zanazzi and Lai 2018), Roisin et al (2021) showed that accumulations disappear (right panel of Fig. 7).…”

“…A capture of the planet in the LK resonance is far from being automatic, since only 30% of the systems with an inclined binary companion (inclination above 40 • ) are found in a LK-resonant state in the long term (red color). The non-resonant evolutions which also present high eccentricity and inclination variations are associated with circulation around the LK stability regions and the long-term stability of these systems is not assured (see Roisin and Libert 2021, for more details).…”