A 3D thermophysical model for binary asteroid systems: Application to the BYORP effect on (175706) 1996 FG3

Abstract

Binary asteroids originate from a wide range of evolutionary pathways, and are the targets of several previous and upcoming spacecraft missions. Differential heating and radiation on asymmetric asteroids can cause measurable changes in their rotation rates and spin axes, collectively known as the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect. In binary systems, such radiation-driven torques can cause changes to the mutual asteroid orbits, termed the binary YORP or BYORP effect. To study how binary asteroid shapes and thermophysical properties affect surface temperatures and BYORP, we developed a new 3D thermophysical model. This model can be applied to binary asteroid systems, solitary asteroids, and other airless bodies with complex topography. The model balances direct insolation, 1D conduction, visible light reflection, and mutual heating through scattered infrared radiation. Using 3D ray tracing, we include eclipses, shadowing from horizons and topography, as well as the mutual radiation exchange between the primary and secondary asteroids. Using this model, we perform global temperature modeling of the binary asteroid (175706) 1996 FG3, a target of the Janus mission. At perihelion, we find that the 1996 FG3 system experiences temperatures between $\sim$100 and 475 K. We also find that eclipses and thermal inertia can alter surface temperatures on the secondary by up to 14%, with a mean difference due to radiation from the primary of just over 1%. These radiative effects decrease with higher thermal inertia. We also present a model for calculating the BYORP effect using the results of the binary thermophysical model. This model compares well to analytical approximations of the BYORP coefficient $B$, and suggests that thermal effects such as eclipses and thermal inertia can reduce torque in the 1996 FG3 system and alter the BYORP coefficient $B$ by up to several percent. Though small, these second-order effects may produce significant dynamical changes. For 1996 FG3, eclipses alter $B$ by approximately 7%, resulting in a lower torque on the secondary. In the absence of tidal effects, this change would reduce the contraction of the semimajor axis by about 20 meters over 10,000 years. Mutual radiation from the primary also causes a small nonzero change to $B$, although of an order of magnitude smaller. Our findings suggest that thermal effects can alter temperatures and BYORP calculations sufficiently that they should be included when modeling binaries, and the relative importance of each effect is predicted to vary with the properties of the system being studied.