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

Abstract

We analyze 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 a 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 a 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 MJup, the greater the m1 value, the smaller the e2 value above which nodal librations are possible for a given e1. For m1 > 0.84 MJup, a 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 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 (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.