Searching for exoplanets with HEPS: I. detection probability of Earth-like planets in multiple systems

The astrometry method has great advantages in searching for exoplanets in the habitable zone around solar-like stars. However, the presence of multiple planets may cause a problem with degeneracy when trying to compute accurate planet parameters from observation data and reduce detectability. The degeneracy problem is extremely critical, especially in a space mission which has limited observation tune and cadence. In this series of papers, we study the delectability of habitable Earth-mass planets in different types of multi-planet systems, aiming to find the most favorable targets for the potential space mission- Habitable ExoPlanet Survey (HEPS). In the first paper, we present an algorithm to find planets in the habitable zone around solar-like stars using astrometry. We find the detectability can be well described by planets' signal-to-noise ratio (SNR) and a defined parameter S = M-2/(T-1-T-2)(2), where M-2 and T-2 are the mass and period of the second planet, respectively. T-1 is the period of the planet in the habitable zone. The parameter S represents the influence of planetary architectures. We fit the detectability as a function of both the SNR of the planet in the habitable zone and the parameter S. An Earth-like planet in a habitable zone is harder to detect (with detectability P-HP < 80%) in a system with a hot Jupiter or warm Jupiter (within 2 AU), in which the parameter S is large. These results can be used in target selections and to determine the priority of target stars for HEPS, especially when we select and rank nearby planet hosts with a single planet.