2024MNRAS.527.4752C

We analyse the role of the general relativity (GR) on the nodal librations of test particles located at the Habitable Zone (HZ) around a solar-mass star, which evolve under the influence of an eccentric planetary-mass perturber with a semimajor axis of 0.1 au. Based on a secular Hamiltonian up to quadrupole level, we derive analytical criteria that define the nodal libration region of an HZ particle as a function of its eccentricity e₂ and inclination i₂, and the mass m₁ and the eccentricity e₁ of the perturber. We show that an HZ particle can experience nodal librations with orbital flips or purely retrograde orbits for any m₁ and e₁ by adopting a suitable combination of e₂ and i₂. For m₁ < 0.84 M_Jup, the greater the m₁ value, the smaller the e₂ value above which nodal librations are possible for a given e₁. For m₁ > 0.84 M_Jup, an HZ test particle can undergo nodal librations for any e₂ and appropriate values of e₁ and i₂. The same correlation between m₁ and e₂ is obtained for nodal librations with orbital flips, but a mass limit for m₁ of 1.68 M_Jup is required in this case. Moreover, the more massive the inner perturber, the greater the nodal libration region associated with orbital flips in the (e₁, i₂) plane for a given value of e₂. Finally, we find good agreements between the analytical criteria and results from N-body simulations for values of m₁ ranging from Saturn-like planets to super-Jupiters.