Rotation acceleration of asteroids (10115) 1992 SK, (1685) Toro, and (1620) Geographos due to the YORP effect

Abstract

The rotation state of small asteroids is affected by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect, which is a net torque caused by solar radiation directly reflected and thermally reemitted from the surface. Due to this effect, the rotation period slowly changes, which can be most easily measured in light curves because the shift in the rotation phase accumulates over time quadratically. We collected archived light curves and carried out new photometric observations for asteroids (10115) 1992 SK, (1620) Geographos, and (1685) Toro. We applied the method of light curve inversion to fit observations with a convex shape model. The YORP effect was modeled as a linear change of the rotation frequency $\upsilon \equiv \mathrm{d}\omega / \mathrm{d}t$ and optimized together with other spin and shape parameters. We detected the acceleration $\upsilon = (8.3 \pm 0.6) \times 10^{-8}\,\mathrm{rad}\,\mathrm{d}^{-2}$ of the rotation for asteroid (10115) 1992 SK. This observed value agrees well with the theoretical value of YORP-induced spin-up computed for our shape and spin model. For (1685) Toro, we obtained $\upsilon = (3.3 \pm 0.3) \times 10^{-9}\,\mathrm{rad}\,\mathrm{d}^{-2}$, which confirms an earlier tentative YORP detection. For (1620) Geographos, we confirmed the previously detected YORP acceleration and derived an updated value of $\upsilon$ with a smaller uncertainty. We also included the effect of solar precession into our inversion algorithm, and we show that there are hints of this effect in Geographos' data. The detected change of the spin rate of (10115) 1992 SK has increased the total number of asteroids with YORP detection to ten. In all ten cases, the $\mathrm{d}\omega / \mathrm{d}t$ value is positive, so the rotation of these asteroids is accelerated. It is unlikely to be just a statistical fluke, but it is probably a real feature that needs to be explained.