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

TL;DR

This work addresses whether the Yarkovsky effect can explain semimajor-axis drifts in super-fast rotating asteroids, where analytical models may break down due to extreme rotation. It introduces a full 3-D numerical Yarkovsky model that resolves heat conduction and photon recoil, benchmarked against THERMOBS and analytic solutions, and applies it to fast rotators including 2011 PT and 2016 GE1. The results show that analytical diurnal drifts remain accurate within about 10% down to spin periods of tens of seconds, while for 2016 GE1 the observed drift is explained primarily by the diurnal component with very low thermal inertia ($Γ$ on the order of 20–100 J m$^{-2}$ K$^{-1}$ s$^{-1/2}$) and large surface temperature swings (~100 K) in a very thin surface layer (~0.1 mm). Overall, the numerical framework validates Yarkovsky-driven drifts in super-fast rotators, provides insight into regolith generation via rapid thermal cycling, and offers an open-source tool for broader application in asteroid dynamics.

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 $1$ $\mathrm{Wm^{-1}K^{-1}}$ 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 $Γ\lesssim20$ $\mathrm{Jm^{-2}K^{-1}s^{-1/2}}$, a value that implies $\sim100$ 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.

Figures (12)

• Figure 1: Schematic representation of the asteroid model used for the numerical calculation of the Yarkovsky effect, showing the adopted reference frames and the key elements relevant for the computation.
• Figure 2: Comparison between TPM delbo-etal_2015 and our model applied to a spherical test asteroid with parameters: $D = 100$ m, $P = 5$ h, $\rho = 2000$ kg/m$^3$, $C_p = 800$ J/kg K, albedo = 0.1, $\epsilon = 0.95$, $a = 1$ au, $e = 0$, and $\gamma = 0^\circ$
• Figure 3: Comparison between the analytical and numerical solutions for varying vertical grid resolutions (as indicated in the plot), applied to a test asteroid with parameters listed in Table \ref{['tab:params_validation']}.
• Figure 4: Comparison between analytical solutions (solid lines) and numerical results (dots) for different rotation periods, using a grid resolution of 32 layers and a surface layer thickness of $0.05\cdot l_d$. The model is applied to the test asteroid with parameters given in Table \ref{['tab:params_validation']}, but using $\gamma = 30^\circ$
• Figure 5: The seasonal Yarkovsky drift for the test asteroid determined from the analytical (black line) and numerical (red dots) model.