Numerical Validation of the Yarkovsky Effect in Super-Fast Rotating Asteroids

Abstract

Recent discoveries show that asteroids spinning in less than a few minutes undergo sizeable semi-major-axis drifts, possibly driven by the Yarkovsky effect. Analytical formulas can match these drifts only if very low thermal inertia is assumed, implying a dust-fine regolith or a highly porous interior that is difficult to retain under such extreme centrifugal forces. With analytical theories of the Yarkovsky effect resting on a set of assumptions, their applicability to cases of super-fast rotation should be verified. We aim to evaluate the validity of the analytical models in such scenarios and to determine whether the Yarkovsky effect can explain the observed drift in rapidly rotating asteroids. We have developed a numerical model of the Yarkovsky effect tailored to super-fast rotators. The code resolves micrometre-scale thermal waves on millisecond time steps, capturing the steep gradients that arise when surface thermal inertia is extremely low. A new 3-D heat-conduction and photon-recoil solver is benchmarked against the THERMOBS thermophysical code and the analytical solution of the Yarkovsky effect, over a range of rotation periods and thermal conductivities. The analytical Yarkovsky drift agrees well with the numerical solver. For thermal conductivities from $0.0001$ to $1$ $\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ and spin periods as short as 10 s, the two solutions differ by no more than $15\%$. Applied to the 34-s rapid rotator 2016 GE1, the best match of the measured drift is obtained with $\Gamma \lesssim 20$ $\mathrm{J}{\mathrm{m}}^{-2}{\mathrm{K}}^{-1}{\mathrm{s}}^{-1/2}$, a value that implies $\sim 100$ K temperature swings each spin cycle. This confirms that the observed semi-major axis drifts for super-fast rotators can be explained by the Yarkovsky effect and very low thermal inertia, which might point to rapid thermal fatigue as a regolith-generation mechanism.

9 Pages, 12 figures

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