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

Differential heating and radiation on asymmetric asteroids can cause measurable changes in their rotation rates and spin axes, known as the YORP effect. In binary systems, such radiation-driven torques can change 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 which balances 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, and mutual radiation exchange between the primary and secondary asteroids. We perform global modeling of the binary asteroid (175706) 1996 FG3, a Janus mission target. At perihelion, we find that the 1996 FG3 system experiences temperatures between 100 and 475 K. We find that eclipses and thermal inertia can alter secondary surface temperatures by up to 14%, with a mean difference due to radiation from the primary of just over 1%. We also present a model for calculating the BYORP effect using binary thermophysical model results. This model compares well to analytical approximations of the BYORP coefficient B, and suggests that thermal effects like eclipses and thermal inertia can reduce torque in the 1996 FG3 system and alter the BYORP coefficient by up to several percent. For 1996 FG3, eclipses alter B by approximately 7%, resulting in a lower torque on the secondary. Though small, in the absence of tidal effects this would reduce the contraction of the semimajor axis by about 20 meters over 10,000 years. Our findings suggest that thermal effects can alter temperatures and BYORP calculations sufficiently that they should be included when modeling binaries. The relative importance of each effect is predicted to vary with the properties of the studied system.