Spin-up and down with planetary tidal forces

Tidal disruption also changes the spin rates of rubble piles. This can be done by applying a torque to the non-spherical mass distribution of the object, redistributing the object's mass (and thereby altering its moment of inertia), removing mass (and angular momentum) from the system, or some combination of the three. Fig. 3 shows the spin periods of the remnant rubble piles ($P_{\rm rem}$) for the 195 disruption cases described above. Recall that the range of starting P values was 4, 6, 8, 10, and 12 h for prograde rotation, P = 6 and 12 h for retrograde rotation, and the no-spin case $P= \infty$.

The mean spin period for 79 S-class outcomes is $5.6 \pm 2.2$ hours, while the comparable value for the 40 B-class and 76 M-class events is $5.2 \pm 1.1$ and $4.9 \pm 1.1$ hours, respectively. Note that these last two values are close to the real spin period of Geographos (5.22 h). These similar values indicate that mass shedding only occurs when the km-sized bodies are stretched and spun-up to rotational break-up values. The final rotation rate of the rubble pile is then determined by the extent of the mass loss; in general, more mass shedding (S-class events) means a loss of more rotational angular momentum, which in turn translates into a slower final spin rate. Though the points of Fig. 3 do show some scatter, the 195 disruption events together have a mean $P_{\rm rem}$ value of $5.2 \pm 1.7$ hours, a good match with Geographos once again.

fig3