The Yarkovsky seasonal effect on asteroidal fragments: A nonlinearized theory for the plane-parallel case

The "seasonal" Yarkovsky force is due to radiation pressure recoil, which acts on anisotropically emitting rotating bodies, heated by sunlight to different temperatures at different latitudes on their surfaces. This force gives rise to a significant draglike effect on rapidly spinning asteroid fragments approximate to 1-100 m in size. Here we present a new treatment of this effect, based on the numerical solution of the heat transfer equation with no linearization in the ratio between the peak temperature difference and the average temperature on the body's surface. Our treatment is restricted to the large-body (plane-parallel) case, valid for radii larger than the penetration depth of the seasonal thermal wave (approximate to 1-20 m depending on the conductivity of the surface layer). Also, we solve numerically the Gaussian perturbation equations for the evolution of the orbital eccentricity, as well of the semimajor axis under the seasonal Yarkovsky force. We find the results to be in broad agreement with the linearized model of D. P. Rubincam, with two main discrepancies: (i) for the same thermal and optical parameters and near-circular orbits, the semimajor axis decay rate predicted by the improved, nonlinearized theory is some 15% lower, and (ii) for some directions of the spin axis relative to the perihelion direction, the Yarkovsky force can cause a secular growth of the eccentricity. When gravitationally induced perihelion precession, spin axis precession, and collisional reorientations are accounted for, however, the eccentricity on average is found to decrease. We also show that the theory can be easily generalized to bodies of spheroidal shapes, with typical discrepancies of a factor of 2 in the semimajor axis decay rate with respect to the spherical case.