[Paper Review] Non-Gravitational Forces and Spin Evolution of Comets

Roman R. Rafikov|arXiv (Cornell University)|Sep 13, 2018

Astro and Planetary Science2 references5 citations

TL;DR

This paper proposes a linear correlation between cometary non-gravitational acceleration and spin period changes, linking them via a dimensionless lever arm parameter ζ. Using 7 comets with measured spin period variations and non-gravitational accelerations, it finds log ζ = −2.21 ± 0.54, and applies this to 209 comets, identifying those most likely to undergo large spin-up, suggesting rotational fission is a key destruction mechanism with ζ ≥ 10⁻³.

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 $ζ$ that relates the outgassing-induced torque and acceleration. We determine $ζ$ for 7 comets for which both non-gravitational acceleration and change of spin period $ΔP$ were measured and verify this relation. This sample spanning almost 4 decades in $ΔP$ yields $\logζ=-2.21\pm 0.54$, 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, $ΔP\gtrsim 20$ min per orbit assuming rotation period of 10 hr and $ζ$ comparable to our control sample. These objects should be primary targets for future studies of cometary spin variability, further constraining distribution of $ζ$. 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 $ζ$ has a lower limit $\sim 10^{-3}$.

Motivation & Objective

• To establish a direct physical link between non-gravitational acceleration and spin evolution in comets.
• To determine the lever arm parameter ζ that connects non-gravitational torque to acceleration.
• To identify comets most susceptible to large spin period changes for future observational targeting.
• To constrain the distribution of ζ using observed spin variability and assess implications for cometary fission.

Proposed method

• Derive a heuristic linear relation between spin period change and non-gravitational acceleration, parameterized by ζ.
• Use observed spin period changes and non-gravitational accelerations for 7 comets to calibrate ζ.
• Apply the calibrated ζ relation to a sample of 209 comets with measured non-gravitational accelerations.
• Define ΔΩ₁ as the spin rate change per orbit assuming ζ = 1 to assess potential spin-up for target selection.
• Use rotational fission criteria (P_crit = 1 hr) to infer lower bounds on ζ from lack of observed high-spin-up comets.
• Assess survival bias: absence of comets with high ΔΩ₁ suggests ζ ≥ 10⁻³ to avoid fission.

Experimental results

Research questions

• RQ1 Is there a measurable correlation between non-gravitational acceleration and spin period changes in comets?
• RQ2 What is the value and distribution of the lever arm parameter ζ that links torque and acceleration?
• RQ3 Which comets are most likely to exhibit large spin period changes per orbit?
• RQ4 Why are no comets observed with extremely high spin-up rates despite high non-gravitational accelerations?
• RQ5 What constraints does the absence of such comets place on the minimum value of ζ?

Key findings

• The linear relation between spin period change and non-gravitational acceleration is validated using 7 comets, with log ζ = −2.21 ± 0.54.
• The inferred ζ value is surprisingly small, with a broad spread, indicating low effective lever arms.
• Among 209 comets, several dozen are predicted to exhibit spin period changes of order an hour per orbit.
• A handful of comets are at risk of rotational fission due to rapid spin-up, indicating this is a major destruction pathway.
• The lack of comets with high spin-up rates (ΔΩ₁ > 1 s⁻¹) implies a lower limit on ζ of ∼10⁻³.
• Survival bias from rotational fission likely suppresses the detection of objects with very low ζ, explaining the small observed ζ values.