Quantitative Criteria for Defining Planets

Abstract: The current IAU definition of "planet" is problematic because it is vague and excludes exoplanets. Here, we describe aspects of quantitative planetary taxonomy and examine the results of unsupervised clustering of Solar System bodies to guide the development of possible classification frameworks. Two unsurprising conclusions emerged from the clustering analysis: (1) satellites are distinct from planets and (2) dynamical dominance is a natural organizing principle for planetary taxonomy. To generalize an existing dynamical dominance criterion, we adopt a universal clearing timescale applicable to all central bodies (brown dwarfs, stars, and stellar remnants). Then, we propose two quantitative, unified frameworks to define both planets and exoplanets. The first framework is aligned with both the IAU definition of planet in the Solar System and the IAU working definition of an exoplanet. The second framework is a simpler mass-based framework that avoids some of the difficulties ingrained in current IAU recommendations.

• The paper proposes a new quantitative framework for defining planets, addressing limitations of the IAU's qualitative definition and applicable to both Solar System bodies and exoplanets.
• The framework is based on the distinction between satellites and planets and the concept of dynamical dominance, introducing a planetary discriminant (Π) to quantify a body's ability to clear its orbit.
• Two classification frameworks are presented: a quantified version of the IAU definition incorporating dynamical and hydrostatic criteria, and a simplified mass-based taxonomy, both intended to improve consistency in astronomical surveys.

An Examination of Quantitative Criteria for Planetary Definition

The paper Quantitative Criteria for Defining Planets by Margot et al. proposes a revised framework for planetary classification, addressing longstanding issues with the International Astronomical Union (IAU) definition of a planet. The IAU's existing definition is criticized for its lack of quantification and exclusion of exoplanets. Margot et al. strive to remedy these deficiencies through a comprehensive quantitative taxonomy applicable to both Solar System entities and exoplanets.

Foundations of the Proposed Framework

The authors base their redefinition attempts on two universally observed characteristics from a clustering analysis of Solar System bodies: the separation between satellites and planets, and the concept of dynamical dominance. Satellites are distinctly categorized as bodies orbiting planets, clearly demarcating them from planets. This foundational differentiation underscores the need for significant gravitational interaction with a central stellar object to qualify as a planet, enforcing a natural dichotomy between planets and satellites.

Dynamical dominance serves as another pivotal organizing principle. This parameter quantifies a body's capability to clear its orbital zone—an attribute the authors deem integral to planetary categorization. The paper introduces a new metric, the planetary discriminant $\Pi$, computed from a body’s mass and its semimajor axis, which gauges a body's ability to clear its orbital path in a specified time frame. Notably, Solar System planets naturally group together into an $\Pi$ value cluster that sharply contrasts with other minor celestial bodies, implying a robust classification marker.

The Proposed Taxonomies

Margot et al. develop two distinctive frameworks. The first aligns with IAU Resolution B5 yet enhances it with quantification, borrowing from the IAU's working definition for exoplanets. It stipulates:

1. A planet must orbit a star, brown dwarf, or stellar remnant.
2. It must exhibit dynamical dominance within the prescribed timescale, quantified by $m > 0.0012\, m_{\rm central}^{5/8}\, a^{9/8}$.
3. It should possess sufficient mass for hydrostatic equilibrium, proposed at a threshold of $10^{21}$ kg.
4. Its mass must remain below the fusion limit of deuterium, approximately 13 Jupiter masses.
5. The planet-to-central body mass ratio should remain under the Lagrangian instability limit.

The second, simplified mass-based framework proposes merely:

• The mass bounds for classification, devoid of dynamical or hydrostatic constraints, setting these limits at $10^{23}$ kg and 13 Jupiter masses.

Implications and Future Prospects

The methodological approach and datasets used in this research offer notable contributions to astronomical nomenclature and classification standards. The proposed frameworks aim to make planetary taxonomy both quantitative and applicable across known exoplanets and undiscovered bodies, enabling consistent classification irrespective of new discoveries.

Theoretically, these proposals not only establish clearer demarcations within the heterogeneous spectrum of celestial bodies but also promote the dynamic revisability of astronomical definitions as empirical data accumulate. Practically speaking, the clarity and simplicity embedded in these definitions could transform the efficiency of classification in burgeoning astronomical surveys and research on exoplanet missions, such as those conducted by TESS and Kepler.

Potential critiques, particularly regarding the dependency of a body's planetary status on its semimajor axis, highlight areas for further discourse and refinement. These concerns, alongside decisions about integrating or dismissing physical attributes like hydrostatic equilibrium within broader definitions, will likely guide future developments triggered by this work.

The paper’s provision of a well-defined classification system promises to spark broader discussions in the astronomical community, influencing the adoption of uniform criteria possibly across IAU's domain. Overall, Margot et al. have constructed a rigorously quantified approach to planetary classification, providing a robust scaffold from which the scope of celestial taxonomy can further evolve.