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

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.