Habitable zones for Earth-mass planets in multiple planetary systems

We perform numerical simulations to study the Habitable zones (HZs) and dynamical structure for Earth-mass planets in multiple planetary systems. For example, in the HD 69830 system, we extensively explore the planetary configuration of three Neptune-mass companions with one massive terrestrial planet residing in 0.07 AU ≤ a ≤ 1.20 AU, to examine the asteroid structure in this system. We underline that there are stable zones of at least 10⁵ yr for low-mass terrestrial planets locating between 0.3 and 0.5 AU, and 0.8 and 1.2 AU with final eccentricities of e < 0.20. Moreover, we also find that the accumulation or depletion of the asteroid belt are also shaped by orbital resonances of the outer planets, for example, the asteroidal gaps at 2:1 and 3:2 mean motion resonances (MMRs) with Planet C, and 5:2 and 1:2 MMRs with Planet D. In a dynamical sense, the proper candidate regions for the existence of the potential terrestrial planets or HZs are 0.35 AU < a < 0.50 AU, and 0.80 AU < a < 1.00 AU for relatively low eccentricities, which makes sense to have the possible asteroidal structure in this system.