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A Measurement of the Kuiper Belt's Mean Plane From Objects Classified By Machine Learning

Ian C. Matheson, Renu Malhotra

TL;DR

The study addresses the Kuiper Belt mean-plane problem by measuring the mean plane from a substantially larger set of non-resonant KBOs identified with a machine-learning classifier on well-determined orbits. It employs the sky-plane velocity method to estimate the mean plane while correcting for observational biases, and uses extensive Monte Carlo simulations to quantify uncertainties. The results show that the overall and classical Kuiper Belt mean planes are within roughly 0.7 degrees of the invariable plane and statistically distinct from it at >99.7% confidence, with most bin ranges aligning with the Laplace surface except near resonances where theory may fail, and no support for a warp beyond 50 au. The work strengthens constraints on dynamical models, demonstrates robust handling of biases with a doubled sample, and highlights regions near resonances where refined theory may be required.

Abstract

Mean plane measurements of the Kuiper Belt from observational data are of interest for their potential to test dynamical models of the solar system. Recent measurements have yielded inconsistent results. Here we report a measurement of the Kuiper Belt's mean plane with a sample size more than twice as large as in previous measurements. The sample of interest is the non-resonant Kuiper belt objects, which we identify by using machine learning on the observed Kuiper Belt population whose orbits are well-determined. We estimate the measurement error with a Monte Carlo procedure. We find that the overall mean plane of the non-resonant Kuiper Belt (semimajor axis range 35-150 au) and also that of the classical Kuiper Belt (semimajor axis range 42-48 au) are both close to (within about 0.7 degrees) but distinguishable from the invariable plane of the solar system to greater than 99.7% confidence. When binning the sample into smaller semimajor axis bins, we find the measured mean plane mostly consistent with both the invariable plane and the theoretically expected Laplace surface forced by the known planets. Statistically significant discrepancies are found only in the semimajor axis ranges 40.3-42 au and 45-50 au; these ranges are in proximity to a secular resonance and Neptune's 2:1 mean motion resonance where the theory for the Laplace surface is likely to be inaccurate. These results do not support a previously reported anomalous warp at semimajor axes above 50 au.

A Measurement of the Kuiper Belt's Mean Plane From Objects Classified By Machine Learning

TL;DR

The study addresses the Kuiper Belt mean-plane problem by measuring the mean plane from a substantially larger set of non-resonant KBOs identified with a machine-learning classifier on well-determined orbits. It employs the sky-plane velocity method to estimate the mean plane while correcting for observational biases, and uses extensive Monte Carlo simulations to quantify uncertainties. The results show that the overall and classical Kuiper Belt mean planes are within roughly 0.7 degrees of the invariable plane and statistically distinct from it at >99.7% confidence, with most bin ranges aligning with the Laplace surface except near resonances where theory may fail, and no support for a warp beyond 50 au. The work strengthens constraints on dynamical models, demonstrates robust handling of biases with a doubled sample, and highlights regions near resonances where refined theory may be required.

Abstract

Mean plane measurements of the Kuiper Belt from observational data are of interest for their potential to test dynamical models of the solar system. Recent measurements have yielded inconsistent results. Here we report a measurement of the Kuiper Belt's mean plane with a sample size more than twice as large as in previous measurements. The sample of interest is the non-resonant Kuiper belt objects, which we identify by using machine learning on the observed Kuiper Belt population whose orbits are well-determined. We estimate the measurement error with a Monte Carlo procedure. We find that the overall mean plane of the non-resonant Kuiper Belt (semimajor axis range 35-150 au) and also that of the classical Kuiper Belt (semimajor axis range 42-48 au) are both close to (within about 0.7 degrees) but distinguishable from the invariable plane of the solar system to greater than 99.7% confidence. When binning the sample into smaller semimajor axis bins, we find the measured mean plane mostly consistent with both the invariable plane and the theoretically expected Laplace surface forced by the known planets. Statistically significant discrepancies are found only in the semimajor axis ranges 40.3-42 au and 45-50 au; these ranges are in proximity to a secular resonance and Neptune's 2:1 mean motion resonance where the theory for the Laplace surface is likely to be inaccurate. These results do not support a previously reported anomalous warp at semimajor axes above 50 au.
Paper Structure (5 sections, 9 equations, 1 figure)

This paper contains 5 sections, 9 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Laplace surface
  3. Mean Plane Measurement
  4. Mean Plane Measurement Uncertainty
  5. Sample Selection

Figures (1)

  • Figure 1: Semimajor axis, inclination, and eccentricity of the 931 non-Resonant KBOs with well-determined orbits on $35<a<150$ au from vm17 (red +), and the sample of 1812 non-Resonant KBOs with well-determined orbits on $35<a<150$ au, $q>30.34$ au, in this study (blue $\circ$). Orbital elements for the 1812 non-Resonant KBOs are from jpl_sbdb_api as explained in Section \ref{['sec:sample_selection']}.