Anti-correlation between multiplicity and orbital properties in exoplanetary systems as a possible record of their dynamical histories

Previous works focused on exoplanets discovered with the radial velocity (RV) method reported an anti-correlation between the orbital eccentricities of the exoplanets and the multiplicity M (i.e., number of planets) of their system. We further investigate this reported anti-correlation here using a dataset comprising exoplanets discovered with both the RV and transit methods, searching for hints of its causes by exploring the connection between the number of planets and the dynamical state of the exosystems. To examine the correlation between multiplicity and orbital eccentricity, for every multiplicity case considered (1<M<7), we computed the weighted average eccentricities instead of the median eccentricities used previously. The average eccentricities were calculated using the inverse of the uncertainty on the eccentricity values as weights. The analysis of the dynamic state of the exosystems was performed by computing their angular momentum deficit (AMD), a diagnostic parameter used in the study of solar system and recently applied to exosystems. Our results confirm the reported multiplicity-eccentricity anti-correlation and show that the use of the uncertainties on the orbital eccentricities in the analysis allows for a better agreement between data and fits. Our best fit reproduces well the behaviour of average eccentricities for all systems with M>1, including the additional cases of TRAPPIST-1 (M=7) and solar system (M=8). The AMD analysis, while not conclusive due to the limited number of exosystems that could be analysed, also suggests the existence of an anti-correlation between the multiplicity and the AMD of exosystems. This second anticorrelation, if confirmed by future studies, raises the possibility that the population of low-multiplicity exosystems is contaminated by former high-multiplicity systems that became dynamically unstable and lost some of their planets.