Spin Evolution Mechanisms of Asteroids
Polishook – Tel-
What controls asteroid's spin? Can it be changed? Following is a list of scenarios that might effect and determine asteroid rotation period:
The main belt is dens enough to make all asteroids collide with each other throughout the history of the solar system. Collisions have a wide range of effects on the asteroid rotation period. Total destruction of the main body creates a bunch of asteroids that keep their parent-body orbital elements around the Sun and therefore defined as a new Hirayama family. According laboratory experiments large fragments tend to rotate slowly compared to fast spins of small fragments. Part of the angular momentum of the parent-body is distributed to invisible debris which is formed close to the impact point, thus the angular momentum is not "conserved" from observational point of view. The fraction of the original angular momentum that is gained by these macroscopic particles is still an unknown value and has a key role in any theoretical model of collisions. If the debris has low ejection velocities a huge cloud is kept on the surroundings of the big fragments, making a higher probability for the creation of binaries by processes of partial reaccumulation. This model will end with bound pairs having very unequal masses like in the Ida and Dactyl case. However, if the fragments have high ejection velocities, they will rotate faster, pass the 2.2 hours boundary and disrupt to binaries as well. Therefore, collisions can end with two types of binaries.
When a small body (impactor) crash into much bigger asteroid (target) it transfers part of its angular momentum from its orbital and rotational motion to the spin of the target. In the general case, the target will gain a new spin around a new axis, which is not aligned with the old axis that spins around the asteroid's shortest principal axis c. Having more than one axis, the asteroid tumbles or wobbles and has a complex rotation. The spin behavior of these "Tumblers" is described below.
Asteroids that not rotate about one of their principal axis (Non-Principal Axis – NPA) are referred to as tumblers. This spin can be seen as a composition of two (or more) rotational periods, and described mathematically by a two dimensional Fourier series (Pravec et al. 2005) and not by a simple sum of two Fourier series, as done for binary asteroids. Tumbling motion is a non-efficient rotation that put the asteroid in a high or excited energy state. This results in a stress-strain cycling within the body, which in turn induces friction and heat. The excess energy is dissipated in the asteroid's interior and the spin state damps to a lower energy state, by rotating solely around the principal axis c of the maximum moment of inertia. An approximation for the time scale of the damping (τ) was estimated by Harris (1994) as:
where P is the rotation period (hours), D is the mean diameter of the asteroid (kilometers), and K is a constant of about 17±2.5, for τ in billions (109) of years. The constant K was empirically derived and is proportional to the rigidity of the asteroid's material and its anelasticity (or quality) factor, and is inversely proportional to it's density and a dimensionless factor relating to it's shape (or roundness). From Eq. 9 Harris found that most of the asteroids have damping time scales shorter then their presumed age but small and slow rotating asteroids might show tumbling motion. Indeed, observations show that tumbler asteroids rotate slowly (except several unique cases) at a rate of tens and hundreds of hours per one rotation (Fig. 3). However, it is important to emphasize that tumbling does not make an asteroid rotates slowly, but rather slow rotating asteroids manage to keep their tumbling motion. According Eq. 9, one should assume, that for very small asteroids (D<0.15 km) tumbling motion is a common phenomena, because their time scale of damping is high (4.5e9 years) even for fast spins (8 hours). However, observations show (Pravec et al. 2005) that only 2 out of 40 small asteroids (with D<0.15 km) are tumblers, supporting their presumed monolithic structure (as density rise, the time scale decrease).
As mentioned above, collisions cause tumbling rotation, but Tidal forces following an encounter with a planet can also deliver a substantial torque to a new spin axis of the asteroid, thus making it tumble. Radiation forces such as YORP, or mass ejection may also results in an NPA rotation as described below.
When facing close encounter with a planet, the asteroid will be affected by tidal forces from the planet that can bring to the asteroid's disruption after crossing the Roche limit Δ:
Δ = 2.45 ∙ ()1/3 ∙ RP
when and RP are the density and radius of the planet and is the density of asteroid. Recent analytic and numerical studies (Sridhar and Tremaine 1992, Richardson et al. 1998, Davidsson 1999) have modify the Roche limit, and showed that except density and size, disruption is also a function of the asteroid's rubble pile structure, orbital velocity, periapsis point (regarding the planet), elongation of shape, rotation period and spin axis orientation. Generally speaking, elongated asteroids that pass as close to the planet with slow orbital velocity and a rapid prograde spin, will have higher probability to disrupt than spherical asteroids with high periapsis point, high orbital velocity and rapid retrograde spin. Richardson et al. (1998) estimate that 25% of asteroids that encounter a planet will actually disrupt. The major remnant of the disrupted asteroid will change its rotation period according the torque it gets from the planet. This mechanism for spin change is mainly relevant for NEAs that cross Earth and Venus orbits. According Richardson et al. (1998) asteroids-planets encounters occur near Earth and Venus every tens and hundreds of thousands of years (depends on the catastrophe dimensions) thus making it an important mechanism to model and understand.
The YORP effect (named after Yarkovsky–O’Keefe–Radzievskii–Paddack) is a gained torque on a rotating irregular body due to the absorption and subsequent re-emission of sunlight. The reemitted heat is radiated in different directions due to asymmetry of the surface, thus accelerating or decelerating the asteroid's spin. In addition, the orientation of the spin axis is changed toward 00 or 1800. Rubincam (2000) and Vokrouhlický and Čapek (2002) showed that YORP is an efficient mechanism for change of the spin. The timescale of YORP is inversely proportional to the square of the asteroid diameter (D) and the mean distance from the Sun (a):
Thus, for ~1 km size asteroids the spin may significantly changed in tens or hundreds of Myr which is comparable and even shorter than the collisions timescale. YORP can be very efficient for small decameter-sized meteorides. Therefore YORP may be especially relevant to NEAs that have short heliocentric distances and small sizes. YORP might cause slow rotations, tumbling movements or spin ups, which can end with disruption of asteroids after passing their critical spin, resulting with binaries creation. Spin orientation change can affect other physical phenomena such as the Yarkovsky effect (orbit migration due to thermal reemission). It is important to emphasize that YORP is only partially modeled, and the influence of the surface's material of the asteroid on this effect is not yet known.