Effects of general relativity on habitable zone particles under the presence of an inner perturber around solar-mass stars.

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 e 2 and inclination i 2, and the mass m 1 and the eccentricity e 1 of the perturber. We show that an HZ particle can experience nodal librations with orbital flips or purely retrograde orbits for any m 1 and e 1 by adopting a suitable combination of e 2 and i 2. For m 1 < 0.84 MJup, the greater the m 1 value, the smaller the e 2 value above which nodal librations are possible for a given e 1. For m 1 > 0.84 MJup, an HZ test particle can undergo nodal librations for any e 2 and appropriate values of e 1 and i 2. The same correlation between m 1 and e 2 is obtained for nodal librations with orbital flips, but a mass limit for m 1 of 1.68 MJup is required in this case. Moreover, the more massive the inner perturber, the greater the nodal libration region associated with orbital flips in the (e 1, i 2) plane for a given value of e 2. Finally, we find good agreements between the analytical criteria and results from N -body simulations for values of m 1 ranging from Saturn-like planets to super-Jupiters. [ABSTRACT FROM AUTHOR]