A new multiple-arc model of the resonant Kuiper belt objects -- Plutinos

TL;DR

This paper introduces a three-arc model for Plutinos in the Kuiper belt to improve gravitational perturbation calculations in planetary ephemerides, showing significant differences from traditional ring models especially at higher eccentricities.

Contribution

The paper presents a novel three-arc modeling approach for Plutinos, capturing their resonant characteristics more accurately than uniform-ring models.

Findings

The three-arc model reduces perturbation estimation errors by up to 170 km.

Perturbation differences between arc and ring models increase with eccentricity.

The model's validity is confirmed through comparisons with observed planetary positions.

Abstract

To incorporate the gravitational influence of Kuiper belt objects (KBOs) in planetary ephemerides, uniform-ring models are commonly employed. In this paper, for representing the KBO population residing in Neptune's 2:3 mean motion resonance (MMR), known as the Plutinos, we introduce a three-arc model by considering their resonant characteristics. Each `arc' refers to a segment of the uniform ring and comprises an appropriate number of point masses. Then the total perturbation of Plutinos is numerically measured by the change in the Sun-Neptune distance ($\Delta d_{SN}$). We conduct a comprehensive investigation to take into account various azimuthal and radial distributions associated with the resonant amplitudes ($A$) and eccentricities ($e$) of Plutinos, respectively. The results show that over a 100-year period: (1) at the smallest $e=0.05$, the Sun-Neptune distance change $\Delta d_{SN}$ caused by Plutinos decreases significantly as $A$ reduces. It can deviate from the value of $\Delta d_{SN}$ obtained in the ring model by approximately 100 km; (2) as $e$ increases in the medium range of 0.1-0.2, the difference in $\Delta d_{SN}$ between the arc and ring models becomes increasingly significant; (3) at the largest $e\gtrsim0.25$, $\Delta d_{SN}$ can approach zero regardless of $A$, and the arc and ring models exhibit a substantial difference in $\Delta d_{SN}$, reaching up to 170 km. Then the applicability of our three-arc model is further verified by comparing it to the perturbations induced by observed Plutinos on the positions of both Neptune and Saturn. Moreover, the concept of the multiple-arc model, designed for Plutinos, can be easily extended to other MMRs densely populated by small bodies.