The fate of particles in the dynamical environment around Kuiper-Belt object (486958) Arrokoth

Abstract

The contact binary Kuiper-Belt object (486958) Arrokoth, targeted by the New Horizons mission, has a unique slope pattern, which is a result of its irregular bilobate surface shape and high spin period. Thus, some peculiar topographic regions on its surface are predisposed to lose or accumulate material, as a long circular depression feature, an impact crater called Maryland, on its small lobe. The equilibrium points of Arrokoth are also directly related to the structure of the environment near these surface features. In this work, we performed numerical simulations around Arrokoth to explore the fate of particles close to equilibrium points and their dynamical connection with its surface features. Our results suggest that most of these particles in a ring inside Arrokoth’s rotational Roche lobe fall near the equatorial region of the Maryland impact crater or close to the Bright spots area on the large lobe. Also, particles in a spherical cloud orbiting Arrokoth accumulate preferentially near low–midlatitude regions close to the longitudes of the Maryland crater and the Bright spots area. In contrast, a few particles will fall in regions diametrically opposite to them, as in the LL_Term boundary on the large lobe. High latitudes are those more empty of impacts, as in polar sites. In addition, particles larger than a couple of micrometers are not significantly perturbed by solar radiation pressure in the environment around Arrokoth.

Appendix:  collisional and escape criteria

The inertia tensor of the Arrokoth contact binary can be used to measure the dimensions of an ‘equivalent’ triaxial ellipsoid around Arrokoth’s surface (Dobrovolskis 1996). This ellipsoid has the following dimensions with principal semiaxes $a$, $b$, and $c$ computed by:

$$\begin{aligned} a=\sqrt{\frac{5(I_{{yy}}+I_{{zz}}-I_{{xx}})}{2M}}, \\ b=\sqrt{\frac{5(I_{{xx}}+I_{{zz}}-I_{{yy}})}{2M}}, \\ c=\sqrt{\frac{5(I_{{xx}}+I_{{yy}}-I_{{zz}})}{2M}}. \end{aligned}$$

(8)

The most recent shape model of the Arrokoth contact binary from Spencer et al. (2020) applied in Eqs. (8) leads us to consider this peculiar minor body with principal semiaxes of $\sim21 \times9 \times5$ km. Our collisional code is implemented considering that the particle hits the surface of Arrokoth when it passes through its polyhedric triangular mesh. The algorithm starts to verify if the particle impacted Arrokoth’s surface when its trajectory is inside the equivalent ellipsoid. This process is performed to reduce the computational time effort during the integration. In addition, the code uses the ray-casting method (Roth 1982) to find the approximate site across all triangular faces that have been impacted by the particle. The signals of the determinants from fives tetrahedra are used for this purpose:

$$\begin{aligned} &\left| \textstyle\begin{array}{c@{\quad}c@{\quad}c@{\quad}c} x_{0} & y_{0} & z_{0} & 1 \\ x_{1} & y_{1} & z_{1} & 1 \\ x_{2} & y_{2} & z_{2} & 1 \\ x_{3} & y_{3} & z_{3} & 1 \end{array}\displaystyle \right|, \left| \textstyle\begin{array}{c@{\quad}c@{\quad}c@{\quad}c} x & y & z & 1 \\ x_{1} & y_{1} & z_{1} & 1 \\ x_{2} & y_{2} & z_{2} & 1 \\ x_{3} & y_{3} & z_{3} & 1 \end{array}\displaystyle \right|, \left| \textstyle\begin{array}{c@{\quad}c@{\quad}c@{\quad}c} x_{0} & y_{0} & z_{0} & 1 \\ x & y & z & 1 \\ x_{2} & y_{2} & z_{2} & 1 \\ x_{3} & y_{3} & z_{3} & 1 \end{array}\displaystyle \right|, \\ &\left| \textstyle\begin{array}{c@{\quad}c@{\quad}c@{\quad}c} x_{0} & y_{0} & z_{0} & 1 \\ x_{1} & y_{1} & z_{1} & 1 \\ x & y & z & 1 \\ x_{3} & y_{3} & z_{3} & 1 \end{array}\displaystyle \right|, \left| \textstyle\begin{array}{c@{\quad}c@{\quad}c@{\quad}c} x_{0} & y_{0} & z_{0} & 1 \\ x_{1} & y_{1} & z_{1} & 1 \\ x_{2} & y_{2} & z_{2} & 1 \\ x & y & z & 1 \end{array}\displaystyle \right|, \end{aligned}$$

where $(x, y, z)$ are the particle coordinates. $(x_{0}, y_{0}, z_{0})$ (polyhedron’s barycenter), $(x_{1}, y_{1}, z_{1})$, $(x_{2}, y_{2}, z_{2})$, and $(x_{3}, y_{3}, z_{3})$ are the tetrahedra vertices. Therefore, the particle impact the surface of the Arrokoth contact binary if the previous five determinants have the same sign.

Additionally, our code also uses escape criteria as a periodic effect. The particle is removed from the numerical simulation if its orbital radius is outside a sphere, with a 100-km radius, far from the dynamical environment around Arrokoth. Both criteria are implemented in the Minor-Mercury package⁸ (Amarante et al. 2021), an N-body integrator from the original Mercury code (Chambers 1999) to handle an irregular-shaped minor body.