Non-Gravitational Forces and Spin Evolution of Comets

Abstract

Motion of many comets is affected by non-gravitational forces caused by outgassing from their surfaces. Outgassing also produces reactive torques resulting in cometary spin evolution. We propose that the two processes are correlated and show that the change of cometary spin rate over its heliocentric orbit scales linearly with the amplitude of its non-gravitational acceleration. The proportionality constant depends on the comet size and orbital elements (semi-major axis and eccentricity) and on the (dimensionless) lever arm parameter $\zeta$ that relates the outgassing-induced torque and acceleration. We determine $\zeta$ for 7 comets for which both non-gravitational acceleration and change of spin period $\Delta P$ were measured and verify this relation. This sample spanning almost 4 decades in $\Delta P$ yields $\log\zeta=-2.21\pm 0.54$, surprisingly small value and spread. We then apply our framework to 209 comets with measured non-gravitational accelerations and determine the objects most likely to exhibit large spin period changes, $\Delta P\gtrsim 20$ min per orbit assuming rotation period of 10 hr and $\zeta$ comparable to our control sample. These objects should be primary targets for future studies of cometary spin variability, further constraining distribution of $\zeta$. Lack of comets with very high expected spin rate changes (which is not equivalent to having the highest non-gravitational acceleration) suggests that (1) cometary fission due to outgassing-driven spin-up must be an important process and (2) the distribution of $\zeta$ has a lower limit $\sim 10^{-3}$.