Spins and Satellites: Probes of Asteroid Interiors Alan W. Harris and Petr Pravec Sixth Catastrophic Disruption Workshop Cannes, 9-11 June 2003

Probes to Asteroid Interiors Fast rotation barrier - rubble piles Small super-fast rotators - monoliths Tumbling rotation - damping time scale Shapes - required internal strength Binaries - implications for internal structure Very slow rotation - escaped binaries?

Asteroid Rotation Rates vs. Diameter

Fast rotation barrier

Small super-fast rotators – “monoliths”

Main monoliths-rubble piles transition

Slow rotators excess

Running Box Mean Spin vs. Size

Spin Rate Distribution of Large Asteroids

Collisional equilibrium, Gravitational and Material Strength Regimes

Rubble Pile Speed Limit  Centrifugal force = Gravity

Rubble Pile Speed Limit (spherical)

Rotation Rate Limit vs. Shape

Non- principal Axis Rotation The damping time scale to principal-axis rotation is: where  is mechanical rigidity, Q is the energy dissipation factor,  is density, K 3 2 is a shape factor with a possible range from 0.01 (near spherical) to 0.1 (highly elongate). r and  are asteroid radius and rotation rate, respectively. For values of , Q, , and K 3 2 appropriate for “rubble piles”, rotation period P in hours, and diameter D in km, the damping time scale in billions of years is:

Observed Tumbling Asteroids

Strength Implied from Shapes Average slope is 11.5 , maximum is 49 . Thus shape could be maintained by loose regolith. The asteroid shape hugs the Roche lobe within ~1 km average, coming as close as 0.09 km. Similar profiles probably apply to Ida, and even Kleopatra. Figure from Miller, et al., Icarus 155, 3-17 (2002)

Binary Asteroids

Binary primaries – Spin vs. Size

Binary primaries – Amplitude vs. Spin

NEA vs. MB binaries Fast rotation of primaries (relatively to similarly sized single asteroids) in both groups (except for 90 Antiope which is a synchronous double asteroid) Lower amplitudes (i.e., elongations) of primaries of NEA binaries than those of MB binaries – related to size, primary spin rate, size ratio, or orbital class ??

Some points for discussion Greater abundance of NEA binaries may be the result of tidal disruptions. Argues for rubble pile structure. MB/Trojan binaries are likely collision products. Near equal- mass binaries may be nature’s only way to solve an angular momentum excess of a gravitationally bound blob of matter. Time scale of tidal evolution sets constraints on internal properties of primary and secondary, and time of formation. Near-unstable shape/spin configurations of some asteroids (Ida, Eros) suggest very easy formation of satellites from ejecta.

Very Slow Rotation

Slow Rotation by Satellite Escape Characteristics of an initially contact binary that would leave the primary with no spin upon escape of the secondary: r a b

Well, maybe not... The distribution of despun primaries should be uniform in residual rotational energy. Since rotational energy is proportional to f 2, one would expect the resulting distribution of spins to be N(<f )  f 2 instead of the observed N(<f )  f. Stay tuned….

Concluding Remarks The main transition between “rubble piles” and “monoliths” is around D=0.15 km. Fraction of monoliths among asteroids with D=0.2-1 km is on the order of a few percent. (Are there rubble piles below D=0.15 km?) Tumblers suggest that “monoliths” may be a few ten times more rigid (longer damping time scales) than “rubble piles”. NEA binary primaries’ rotations/amplitudes are consistent with rubble pile structure.

The Cruelty of Nature If MB binaries had the average characteristics of TNO binaries the first would probably have been discovered in the 1800’s, by visual observation. If MB binaries had the average characteristics of NEA binaries, they would likely have been found by lightcurves decades ago. Of all the ways to find a binary, the only method that has yet to yield a confirmed discovery is by stellar occultation.