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The Yarkovsky--O'Keefe--Radzievskii--Paddack (YORP) effect governs the spinevolution of small asteroids. The axial component of YORP, which alters therotation rate of the asteroid, is mostly independent of its thermal inertia,while the obliquity component is very sensitive to the thermal model of theasteroid.  Here we develop a semi-analytic theory for the obliquity component of YORP.We integrate an approximate thermal model over the surface of an asteroid, andfind an analytic expression for the obliquity component in terms of two YORPcoefficients.  This approach allows us to investigate the overall evolution of asteroidrotation state, and to generalize the results previously obtained in the caseof zero thermal inertia.  The proposed theory also explains how a non-zero obliquity component of YORPoriginates even for a symmetric asteroid due to its finite thermal inertia. Inmany cases, this causes equatorial planes of asteroids to align with theirorbital planes.  The studied non-trivial behavior of YORP as a function of thermal modelallows for a new kind of rotational equilibria, which can have importantevolutionary consequences for asteroids.

Limiting behavior of asteroid obliquity and spin using a semi-analytic thermal model of the YORP effect