A new metric to quantify the similarity between planetary systems - application to dimensionality reduction using T-SNE

Abstract

Planet formation models are now often considering the formation of planetary systems, with more than one planet per system. This raises the question of how to represent planetary systems in a convenient way, (e.g. for visualisation purpose) and how to define the similarity between two planetary systems, for example to compare models and observations. We define a new metric to infer the similarity between two planetary systems, based on the properties of planets that belong to these systems. We then compare the similarity of planetary systems with the similarity of protoplanetary discs in which they form. We first define a new metric based on mixture of gaussians, and then use this metric to apply a dimensionality reduction technique, in order to represent planetary systems (which should be represented in a high dimension space) in a 2 dimension space. This allows us study the structure of a population of planetary systems and its relation with the characteristics of protoplanetary discs in which planetary systems form. We show that the new metric can help finding the underlying structure of populations of planetary systems. In addition, the similarity between planetary systems as we define in this paper is correlated with the similarity between the protoplanetary discs in which these systems form. We finally compare the distribution of inter-system distances for a set of observed exoplanets, with the distributions obtained from two models: a population synthesis model, and a model where planetary systems are constructed by randomly picking synthetic planets. The observed distribution is shown to be closer to the one derived from the population synthesis model than from the random systems.

Accepted in A&A. Movies available at http://nccr-planets.ch/research/phase2/domain2/project5/machine-learning-and-advanced-statistical-analysis/

References in corpus (16)

• Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1
• A low mass for Mars from Jupiter's early gas-driven migration
• Models of Giant Planet formation with migration and disc evolution
• The formation and retention of gas giant planets around stars with a range of metallicities
• Extrasolar planet population synthesis I: Method, formation tracks and mass-distance distribution
• Protoplanetary Disk Structures in Ophiuchus II: Extension to Fainter Sources
• The nature of the TRAPPIST-1 exoplanets
• Characterization of exoplanets from their formation I: Models of combined planet formation and evolution
• Characterization of exoplanets from their formation II: The planetary mass-radius relationship
• Toward a Deterministic Model of Planetary Formation VI: Dynamical Interaction and Coagulation of Multiple Rocky Embryos and Super-Earth Systems around Solar Type Stars
• Theoretical models of planetary system formation: mass vs semi-major axis
• Planet formation models: the interplay with the planetesimal disc
• Critical core mass for enriched envelopes: the role of H2O condensation
• The formation of mini-Neptunes
• Interior characterization in multiplanetary systems: TRAPPIST-1
• Theoretical models of planetary system formation. II. Post-formation evolution

Cited by in corpus (13)

• The New Generation Planetary Population Synthesis (NGPPS). IV. Planetary systems around low-mass stars
• StarHorse results for spectroscopic surveys + Gaia DR3: Chrono-chemical populations in the solar vicinity, the genuine thick disk, and young-alpha rich stars
• CHEOPS observations of the HD 108236 planetary system: A fifth planet, improved ephemerides, and planetary radii
• Pebble-driven planet formation for TRAPPIST-1 and other compact systems
• Pebbles versus Planetesimals: The case of Trappist-1
• An information theoretic framework for classifying exoplanetary system architectures
• The New Generation Planetary Population Synthesis (NGPPS). VI. Introducing KOBE: Kepler Observes Bern Exoplanets. Theoretical perspectives on the architecture of planetary systems: Peas in a pod
• A framework for the architecture of exoplanetary systems. I. Four classes of planetary system architecture
• An N-body population synthesis framework for the formation of moons around Jupiter-like planets
• Using Deep Neural Networks to compute the mass of forming planets
• A framework for the architecture of exoplanetary systems. II. Nature versus nurture: Emergent formation pathways of architecture classes
• Quantifying the Similarity of Planetary System Architectures
• Earth-like planets hosting systems: Architecture and properties