Spin Evolution
Mechanisms of Asteroids
By David
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):
cycles/day/million years
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.