YORP torques with 1D thermal model

Abstract

A numerical model of the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect for objects defined in terms of a triangular mesh is described. The algorithm requires that each surface triangle can be handled independently, which implies the use of a 1D thermal model. Insolation of each triangle is determined by an optimized ray-triangle intersection search. Surface temperature is modeled with a spectral approach; imposing a quasi-periodic solution we replace heat conduction equation by the Helmholtz equation. Nonlinear boundary conditions are handled by an iterative, FFT based solver. The results resolve the question of the YORP effect in rotation rate independence on conductivity within the nonlinear 1D thermal model regardless of the accuracy issues and homogeneity assumptions. A seasonal YORP effect in attitude is revealed for objects moving on elliptic orbits when a nonlinear thermal model is used.Comment: 15 pages, 10 figures, accepted to MNRAS, before language editin

Yarkovsky-O'Keefe-Radzievskii-Paddack effect with anisotropic radiation

“…When the heat conduction is included, the nominal rotation model enters much earlier than in the final averaging: the surface temperature oscillations are lagged with respect to the insolation, and hence we cannot find Q, required by the torque formula, without knowledge of the rotation history. Choosing the simplest principal axis rotation mode (known as the gyroscopic approximation), we can easily add non-Lambertian corrections to the algorithm of Breiter et al (2010) based on a non-linear one-dimensional thermal model.…”

“…Its discrete Fourier transform (DFT) serves to compute the DFT spectrum of Q by an iterative process. Once the spectrum of Q is known, we are able to compute the torque M. Until this step, no essential modifications of the algorithm are required; all we have to do is to replace the constant albedo A (understood as the Bond albedo A B ) in the boundary conditions of Breiter et al (2010) by the hemispheric albedo function A h (μ ). Apart from this point, the heat diffusion solver remains practically unchanged; however, computing the mean torque demands further revision.…”

“…where e x , e y and e z form the body-fixed frame basis, and is the rotation phase measured from the asteroid's equinox (Breiter et al 2010;N.B.the prime is added to avoid confusion with the solid angle of the present paper). Then we add the mean values resulting from the DFT spectrum of Q, obtaining the final averaged torque projections M i = M · e i .…”

“…The main objective of the present work is to include non-Lambertian scattering and radiation into the recent YORP model of Breiter, Bartczak & Czekaj (2010) and to judge the significance of this improvement. Roughly speaking, a departure from the Lambertian model is essentially caused by inter-reflections and occlusions.…”

Yarkovsky-O’Keefe-Radzievskii-Paddack effect on tumbling objects

“…It is noteworthy that the general form () is not restricted to convex objects or isotropic reflection and radiation models. Vector coefficients v n , m may be computed from the values of the torque sampled on a grid of Sun directions in the body frame using a shadowing algorithm for non‐convex objects and more elaborate reflection and emission laws (Statler 2009; Breiter, Bartczak & Czekaj 2010; Breiter & Vokrouhlický 2011). Even for the purpose of numerical integration, the series () may have some advantage, because they are smooth, whereas usual polyhedral models provide the torques that are only continuous.…”