1. Asteroid Rotations and Binaries
Petr Pravec1 and Alan W. Harris2
1Astronomical Institute AS CR, Czech Republic
2Space Science Institute
VII Workshop on Catastrophic Disruptions in the Solar System
2007 June 29

2. Three major asteroid size ranges
Asteroid population splits according to properties related to
their rotations into three major ranges at D~60 km and 0.2 km:
Large asteroids, D > 60 km
Small asteroids, D = 0.2 – 60 km
Very small asteroids, D < 0.2 km
Large asteroids – rotations collisionally evolved
Small asteroids – rotations driven by YORP
Spin barrier at sizes D=0.2 to 10 km – suggesting cohesionless structure from 0.2 up to 3 km
Superfast rotators below D=0.2 km – cohesion implied
Binary population among asteroids with D= km – related to critical spins near the spin barrier

3. Large asteroids – collisionally evolved rotations
Variation of <f> with D reduced for: Normalized spin rate = f/<f>
Minimum of <f> at D about 100 km perhaps due to an effect called “angular momentum drain/splash” (Dobrovolskis and Burns 1984; Cellino et al. 1990).
Spin frequency distribution is Maxwellian (Pravec and Harris 2000, Pravec et al. 2002)
Asteroids larger than ~60 km have spin rates with the distribution predicted for a collisionally evolved system.

4. Small asteroids - rotations driven by YORP
YORP detected in 2000 PH5 and Apollo (Lowry et al., Taylor et al., Kaasalainen et al. 2007)
Period change caused by YORP in 2000 PH5:
Acceleration of 2000 PH5 rotation by YORP:
(Lowry et al. 2007)
(Taylor et al. 2007)

5. Small asteroids - rotations driven by YORP
YORP detected in 2000 PH5 and Apollo (Lowry et al., Taylor et al., Kaasalainen et al. 2007)
Excess of both slow and fast rotators among small asteroids (e.g., Pravec and Harris 2000)

6. Small asteroids - rotations driven by YORP
YORP detected in 2000 PH5 and Apollo (Lowry et al., Taylor et al., Kaasalainen et al. 2007)
Excess of both slow and fast rotators among small asteroids (e.g., Pravec and Harris 2000)
Alignment of spin axes of members of the Koronis family (Slivan et al., Vokrouhlický et al.’03)

7. Small asteroids - rotations driven by YORP
YORP detected in 2000 PH5 and Apollo (Lowry et al., Taylor et al., Kaasalainen et al. 2007)
Excess of both slow and fast rotators among small asteroids (e.g., Pravec and Harris 2000)
Alignment of spin axes of members of the Koronis family (Slivan et al., Vokrouhlický et al. ‘03)
Close binary systems among small asteroids with a total angular momentum
near critical (Pravec and Harris 2007)

8. Spin barrier

9. Spin barrier in 2nd dimension
Limiting curves for bulk densities 1, 2, 3, 4, 5 g/cm3 for cohesionless elastic-plastic solid bodies. (Holsapple 2001, 2004)
>99% of measured asteroids larger than 200 m rotate slower than the limit for bulk density of 3 g/cm3 (Harris 1996; Pravec and Harris 2000).
Most NEAs smaller than 200 m rotate too fast to be held together by self-gravitation, some cohesion implied.

10. Scaled tensile strength
Above D=3 km, an upper limit on the tensile strength given by the spin barrier is higher than a scaled tensile strength of cracked but coherent rocks, so the existence of the spin barrier does not constrain whether asteroids in the size range 3-10 km are strengthless objects or just cracked but coherent bodies.
Below D=3 km, the maximum possible tensile strength allowed by the spin barrier for a majority of asteroids in the size range is too low for them to be cracked but coherent bodies (Holsapple 2007); this implies that a cohesionless structure is predominant among asteroids with D=0.2 to 3 km.
The area above the spin barrier is
unpopulated at sizes D>0.2 km
(except the single point 2001 OE84
at D=0.7 km, P=29 min).

11. Binary systems among small asteroids
NEA binaries since 1997 by photometry, since 2000 by radar
Small MBA binaries (D ≤ 10 km) since 2004 – binary Vestoid
3782 Celle (Ryan et al. 2004), many more since then (see Pravec et al. 2006,
Warner et al. 2005, Pravec and Harris 2007)
We are sampling small binaries from NEAs to the inner main belt mostly, but
occassionally sampling the central main belt too.
Binaries have been found numerous among small asteroids (D ≤ 10 km)
everywhere we looked thoroughly enough.

12. Binary fraction among small asteroids
NEAs:
15  4 % of NEAs are binary
(Pravec et al. 2006)
Inner MB asteroids:
Debiasing their distribution more sensitive to assumptions on orbit pole distribution; awaiting more data to constrain it. Rough numbers similar to the NEA binary fraction.

13. Binary population among small asteroids
Data on periods
-rotation and orbital-
plus limited shape
information for 51 small binary systems,
major part of them from photometric measurements.
Data published in
Pravec and Harris, 2007,
Icarus, in press.
Available on-line
on URL given in the paper.

14. Binary primaries – spin rates
NEAs:
MBAs:
NEA primaries concentrate in the pile up at f
around 9-10 d-1 (P of 2-3 h) in front of the spin barrier.
MBA primaries have a considerably broader distribution of spin rates, with a lower concentration at fast spin rates and a more pronounced tail (correlated with D).
MBA binaries may be more evolved than NEA binaries, if all have formed near the spin barrier.

15. Binary primaries – shapes
Model of the primary of 1999 KW4 (Ostro et al. 2006)
Primaries of asynchronous binaries,
both among NEAs and MBAs, have
shapes with low equatorial elongation.
The model of 1999 KW4 shows an
equatorial belt that appears like it was
paved by some process.

16. Angular momentum content
αL = Ltot/Lcritsph
where Ltot is a total angular momentum of the system, Lcritsph is angular momentum of an equivalent (i.e., the same total mass and volume), critically spinning sphere.
Binaries with D1 ≤ 10 km have αL between 0.9 and 1.3, as expected for systems originating from critically spinning rubble piles, if no angular momentum was added or removed since formation of the system.
(Pravec and Harris 2007)

17. Size ratio vs primary size

18. Proposed binary formation theories
Ejecta from large asteroidal impacts (e.g., Durda et al. 2004) – may work for small satellites of large asteroids or for wide binary systems among small asteroids, but it does not predict a relation to critical spin for small close binary systems.
Tidal disruptions during close encounters with terrestrial planets (Bottke et al. 1996; Richardson and Walsh) – does not work in the main belt, so, it cannot be a formation mechanism for MB binaries, but it may contribute to and shape the population of NEA binaries.
Fission of critically spinning parent bodies spun up by YORP (e.g., Bottke et al. 2006) – seems to be a primary formation mechanism for small close binaries.
(Walsh and Richardson 2006)

19. Fission of critically spinning parent bodies spun up by YORP
The critical content of angular momentum in small close binaries may be consistent with this mechanism.
YORP may be slowed down after formation of the binary if the primary’s figure is shaped to a more symmetric shape; the total angular momentum is not changed significantly from the critical amount.
Further evolution after YORP is slowed down may be driven by a mechanism transferring angular moment from the primary’s rotation to the orbital motion – resulting in a slow down of primary’s rotation and moving the orbit outward (longer periods). Longer periods of MB binaries are consistent with them being more evolved (being older, or more rapidly evolving) than smaller NEA binaries.

20. Time scales for small binaries
Lifetimes of asteroids:
NEA: ~10 Myr (Gladman et al. 2000)
MBA: ~300 Myr (1-km asteroid)
YORP spin up time scale:
NEA: ~1*D2 [*Myr/km2] -> ~1 Myr (1-km asteroid)
MBA: ~3*D2 [*Myr/km2] -> ~30 Myr (3-km asteroid)
Lifetime of NEA binary: 1-2 Myr (limited by disruptions during close approaches to Earth and Venus; Walsh and Richardson 2006)
Lifetime of MB binary: ~300 Myr (= lifetime of an MBA of size of the secondary, if it is controlled by asteroidal collisions in the main belt).
The estimated short lifetime of NEA binaries suggests that few MB binaries survived since transfer to NEA
orbits; most NEA binaries may have formed after transfer to near-Earth space. It may explain
the observation that NEA binaries concentrate at sizes <2 km (Pravec et al. 2006); larger NEAs
may not have enough time to form binaries.
The strong dependence of lifetime of NEA binaries on relative separation of components
may be an explanation (alternative to that NEA binaries may be less evolved by a “tidal
mechanism”) for the observation that they have a narrower distribution of periods, concentrating
at faster spin rates in front of the spin barrier.

21. Conclusions
Rotations bring important (though sometimes only circumstantial) information on processes in the asteroid population.
Collisions in the main belt – most important effect for large asteroids with D>60 km.
YORP and internal structure (strength) – controlling spins
(and shapes, binaries) of smaller asteroids.

22. ¡Fin! ¡Gracias!

23. (Additional slides for possible discussion follow)

24. Primary rotation vs size

25. Photometric detection of Asynchronous Binary