Finite Element Method approach 3-dimensional thermophysical model for YORP torque computation

Abstract

We present a new thermophysical model suitable for simulating the thermal conditions of small celestial bodies, such as asteroids and comet nuclei, as well as local topographic features like rocks, boulders, and craters. The model employs a Finite Element Method (FEM) approach to solve the 3-dimensional heat conduction problem, explicitly accounting for heat conduction between neighboring FEM elements. This sets it apart from other thermophysical models that typically neglect lateral heat conduction. The model takes into account scattering sunlight, self-heating due to thermal radiation, and both horizon and cast shadows. We validated our model against an analytical solution for the transient temperature distribution of a sphere under convective boundary conditions. Additionally, we compared our results with earlier thermophysical modeling works and observational data of asteroid (101955) Bennu. Using the shape models of Bennu as well as scaled versions of (162173) Ryugu, (25143) Itokawa, and (6489) Golevka to match Bennu’s surface area, we investigated the effects of shape and lateral heat conduction on the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) torque. Results indicate that contact binary and non-classified/irregular objects experience a stronger YORP torque compared to spheroidal objects. The lateral heat conduction can enhance or dampen the YORP torque. Further analysis is important to obtain more robust statistical conclusions.