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

Abstract

Context. 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., the number of planets) of the systems they inhabit. Aims. 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. Methods. In order to examine the correlation between multiplicity and orbital eccentricity, for every multiplicity case considered (2 ≤ M ≤ 6), 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), which is a diagnostic parameter successfully used in the study of the solar system and recently applied to exosystems as well. Results. 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 the data and the fits. Specifically, our best fit reproduces well the behaviour of the average eccentricities for all systems with M > 1, including the additional cases of TRAPPIST-1 (M = 7) and of the 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.

Predicting multiple planet stability and habitable zone companions in the TESS era

“…• Mass ratio (µ = M pl /M ) and orbital eccentricity are very influential in determining a system's overall dynamical stability. In particular, we find that even moderate orbital eccentricities can prove to be destabilising, a finding that re-enforces the results of several studies that highlight the inverse relationship between multiplicity and eccentricity (Carrera et al 2016;Agnew et al 2017;Zinzi & Turrini 2017).…”

“…Even more impressive is the range of destabilisation in semi-major axis in Figure 5c, reaching out in both directions to the locations of the 3 : 1 inner resonance and the 1 : 4 outer resonance with the planet's orbit in the highest eccentricity case we examined (e pl = 0.3). In contrast, the unstable regions in the circular case only reached to the 5 : 3 inner, and just beyond the 1 : 2 outer respectively, re-enforcing the significance of even moderate orbital eccentricities on multiple system stability (Zinzi & Turrini 2017).…”

“…We only explore between e = 0 and e = 0.3, given that existing literature shows that multiple planet systems (especially where one is a potentially habitable terrestrial planet) are uncommon for high eccentricity orbits (e > 0.4). This has been explained as being most likely attributable to planet-planet scattering during planetary formation and evolution (Matsumura et al 2016;Carrera et al 2016;Agnew et al 2017;Zinzi & Turrini 2017).…”

The contribution of the ARIEL space mission to the study of planetary formation

“…The first statistical studies of their orbital properties revealed the existence of an anti-correlation between the number of planets in planetary systems (i.e. a parameter also indicated as multiplicity) and their average eccentricities (Limbach & Turner 2015;Zinzi & Turrini 2017). Planets inhabiting systems with low multiplicity on average possess higher orbital eccentricities than planets in systems with high multiplicity, a trend holding from systems with multiplicity of two to the multiplicity of eight of the Solar System (Zinzi & Turrini 2017).…”

“…a parameter also indicated as multiplicity) and their average eccentricities (Limbach & Turner 2015;Zinzi & Turrini 2017). Planets inhabiting systems with low multiplicity on average possess higher orbital eccentricities than planets in systems with high multiplicity, a trend holding from systems with multiplicity of two to the multiplicity of eight of the Solar System (Zinzi & Turrini 2017). This trend suggests that processes of chaotic exchange are widespread among multi-planet systems (Zinzi & Turrini 2017), supporting the idea that migration by planetplanet scattering plays an important role in shaping the structure of planetary systems.…”