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

A Measurement of the Kuiper Belt's Mean Plane From Objects Classified By Machine Learning Submitted to AJ 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 0.7 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 the ν These results do not support a previously reported anomalous warp at semimajor axes above 50 au. INTRODUCTION Chiang & Choi (2008) posed the question:"If we could map, at fixed time, the instantaneous locations in threedimensional space of all Kuiper Belt objects [KBOs], on what two-dimensional surface would the density of KBOs be greatest?" The authors demonstrated that this surface, also known as the Laplace surface, is given by the Laplace-Lagrange linear secular theory (Murray & Dermott 1999). This theory is based on the time-variable forcing arising from the planets' secular variations; consequently, the local normal on the Laplace surface varies only slowly with time; secular timescales for KBOs are much longer than 10 The Laplace surface for particles within the Kuiper Belt is not a flat plane because it has warps owing to secular resonances in certain localized regions of semimajor axes within the belt where the rate of orbit pole precession coincides with one of the inclination secular mode frequencies of the planets; at large semimajor axes the Laplace surface converges to the solar system's invariable plane.