Analytic Theory for the Yarkovsky–o’keefe–radzievski–paddack Effect on Obliquity

The Yarkovsky–O’Keefe–Radzievski–Paddack (YORP) effect is a thermal radiation torque that causes small objects to speed up or slow down their rotation and modify their spin vector orientation. This effect has important implications for spin dynamics of diameter D 50 km asteroids. In our previous work we developed an analytic theory for the component of the YORP torque that affects the spin rate. Here we extend these calculations to determine the effect of the YORP torque on obliquity. Our theory is limited to objects with near-spherical shapes. Two limiting cases are studied: (1) immediate emission of the thermal energy that occurs for surface thermal conductivity K = 0; (2) the effects of K = 0 in the limit of small temporal variations of the surface temperature. We use the linearized heat transport equation to model (2). The results include explicit scaling of the YORP torque on obliquity with physical and dynamical parameters such as the thermal conductivity and spin rate. The dependence of torques on the obliquity is given as series of the Legendre polynomials. Comparisons show excellent agreement of the analytic results with the numerically calculated YORP torques for objects such as asteroids 1998 KY26 and (66391) 1999 KW4. We suggest that an important fraction of main belt asteroids may have specific obliquity values (generalized Slivan states) arising from the roots of the Legendre polynomials.