Issue number 25 : 20/05/2004
A scientific publication by SGF and NEODyS

The mysteries of the asteroid rotation day
by Alessandro Rossi - ISTI

Why there are no asteroids with diameter larger than about 100 m rotating faster than about 11 revolutions per day (corresponding to a period of about 2.2 hours)? Why do we observe so many binaries among Near Earth Asteroids? How is a binary asteroid created? Why is 253 Mathilde rotating so slowly? Why the rotation of most of the NEAs, with known pole orientation, appears to be retrograde? Is it true that NEAs are rotating faster than Main belt asteroids (see dictionary: Asteroid) and why is it so? Is it more efficientto kick a stone or to gently push it? These are some of the questions we tried to answer during the 'Asteroid Rotation Day' held at the ISTI-CNR in Pisa, on April 26, 2004 (http://apollo.isti.cnr.it/rot_day/rot_day.html).

Studies of asteroid rotation rates and lightcurve properties (see dictionary: lightcurve) provide important data to understand the asteroids structure and their physical processes. About 1400 reliable asteroids rotation periods are currently recorded (e.g. http://cfa-www.harvard.edu/iau/lists/LightcurveDat.html).Many interesting conclusions can be immediately drawn by the sample of objects in this large, and ever increasing, database.

In a system of particles dominated by collisions (such as a perfect gas in a given volume) the distribution of particle velocities is well fitted by a Maxwellian function. Therefore it does not come as a surprise that the distribution of spin rates of the asteroids larger than 40 km is very well approximated by a 3D Maxwellian function. On the other hand, it is now clear, as more data on small asteroids become available, that the distribution of the spins of bodies with diameters between 0.15 and 10 km is definitely not Maxwellian, and even nearly flat. So some physical processes other than collisions must be responsible for the evolution of the spin rate.
If we plot the spin rate of the bodies versus their diameter, a striking feature is immediately apparent. There is a barrier. No body larger than a few hundred meters is rotating faster than approximately 2 hours. If we put a particle on the surface of a rotating body, the particle stays there until the gravity force acting on it is stronger than the centrifugal force. If the body rotates too fast, the particle finally flies away from the surface. If the asteroid is not a coherent piece of rock (a monolith), but is instead an aggregate of rocks held together by the mutual gravitational attraction (a so-called rubble-pile), then it is subject to this same phenomenon and cannot rotate too fast. Therefore this limit is the rotational breakup limit for aggregates with no tensile strength. Objects rotating faster than a few hours must be monoliths otherwise they are torn apart by the centrifugal force.
And we indeed observe objects rotating as fast as 0.0222 h of period (2000 WH10). At the other end of the distribution, an excess (with respect to the number expected by statistical arguments) of slow rotating asteroids is clearly observed. Where do these extreme behaviors come from? What is responsible for these altered spin states?
As it is often the case, it is most probably a sum of effects. For NEAs, it has been shown by D.J. Scheeres et al. (Icarus, in press) that close encounters with the terrestrial planets (namely Venus and Earth) can be responsible for a significant alteration of the spin rate and state of the objects. In particular, the time evolution of a population of NEAs, with initial spin rate distribution matching that of MBAs, has been simulated. After repeated close encounters with the Earth and Venus, during 4.5 billion years, the final spin distribution is broadened, with a considerable spin up of the population and a tail of slow rotators, with periods larger than 100 hours, down to about 1000 hours. Moreover, if these bodies are supposed to be rubble piles, about a few percent of them are pushed over the rotational disruption limit and are therefore broken. These broken objects can either escape each other or, in same cases, can become a binary, thus incrementing the large population of observed binary NEAs (presently there are 22 know binary NEAs). And, considering that this is written in 'Tumbling Stone', it must be noticed that about 0.5 % of the asteroids are observed to enter a tumbling state after the close encounters.

Therefore, some of the observed rotational properties of NEAs can be explained by tidal planetary encounters. But extremely rapid rotators (with period less than 1 hour) and the full excess of slow rotators cannot be explained just by the tidal effects. And, moreover, what happens to MBAs, where close encounters cannot be responsible? Is there something missing? Yes, and again Dr. Yarkovsky steps in (see dictionary: Yarkovski effect). Some years ago it has been shown that the Yarkovsky effect allows the injection of a steady state flux of small and intermediate sized asteroids into the major dynamical resonances (see dictionary: resonance). Now La Spina et al. (Nature, 2004) have shown that a signature of the Yarkovsky effect is visible in the NEAs pole distribution. This signature is the abundance of retrograde NEAs. The orbital semi-major axis of a main belt asteroid is decreased by Yarkovsky if the rotation of the asteroid is retrograde, and the opposite is true for prograde spin. Therefore, retrograde bodies can enter a resonance 'backward' (i.e., coming from a semimajor axis larger than the resonant one) and prograde bodies can enter a resonance 'forward', (i.e., coming from smaller semimajor axis). So, only retrograde bodies can enter the nu6 secular resonance which is close to the inner border of the main belt and is the dominant source of NEAs.

But a variant of the Yarkovsky effect acts also on the spin of a body. The so-called YORP (Yarkovsky-O'Keefe-Radzievskii-Paddack) effect is a torque on a rotating irregular body due to the absorption and subsequent re-emission of sunlight. YORP evolution can be a secular deceleration of the rotation rate or a permanent acceleration of the body's rotation, possibly resulting in rotational fission. With an order of magnitude calculation, according to A.W. Harris, it can be shown that the spin-up or down due to YORP is proportional to the inverse square of the object's diameter and semi-major axis. By applying this simple relation to some of the observed asteroids, Harris concludes that the spins of asteroids as large as about 60 km in diameter appear to be substantially affected by YORP evolution and, in particular, asteroids smaller than about 10 km diameter are profoundly altered by YORP. The time scale of spin alteration of km-sized asteroids is about 10 cycles/day in one million year, enough to lead to rotational fissioning of km-size asteroids in about 10 m.y. YORP is also sufficient to spin up monolithic asteroids with a diameter of about 100 m to the observed ultra-fast rotation periods of about 1-minute in only about one million years. Also very slow rotators such as 253 Mathilde could be explained by the action of YORP. Some caveats could be added to these estimates, in particular since for very fast rotating objects the YORP thermal effect may be less efficient due to an averaging of the thermal properties of the body, but there is no doubt now that YORP is a key component, perhaps the missing key, of the asteroids rotation scenario. The despinning of a body due to YORP has been also probably already observed in the case of 25143 Itokawa a small (0.35 km) asteroid with an evolved slow rotation period (12.132 hours). The comparison of its recent lightcurves with the predictions based on the lighcurves of the previous years shows a marked spin-down effect, than can tentatively (until further investigations will confirm the results) attributed to YORP.

So now there are a few ways to spin-up and break an asteroid. As noted above these broken objects can possibly form a binary. And if YORP can form binaries as well, there should be a large number of them also in the main belt. The detection of binaries among small main belt asteroids is a difficult observational task. But it is an extremely important one, since an excess of binaries among NEAs would speak in favour of a predominant tidal splitting driven formation with respect to YORP spin-up.

But not all the broken objects end up forming a stable binary and the fragments may mutually escape after only several orbits, separating into non interacting asteroids. Interestingly, D.J. Scheeres showed that analytic constraints and bounds can be placed on the final rotation rates of the separated asteroids. Due to the energy balance of the complex dynamical system arising after an asteroid fission, a population of such 'divorced binaries' would show a strong bias toward slow rotators, indicating that slow rotators can arise also as end products of asteroid fission.
And finally an answer to the last question. Well, I wouldn't like to kick a stone. It hurts!