The vectorial torque efficiency introduced in Eq. (5) can be evaluated for any general cometary body.

It provides a generalization of the scalar torque efficiency in Keller et al. (2015b) and Attree et al. (2019) that controls the rotational period alone.

The signs of all three components of the vectorial torque efficiency lead to the specification of a domain decomposition into a maximum of eight distinct regions on the surface.

In particular, this applies to the bilobed shape as well as to the body shape of comet 67P/C-G.

Geometric symmetry for idealized cases can reduce the number of regions.

The oblate ellipsoid features zero and the near-prolate ellipsoid features four nonempty regions.

The domain decomposition is divided into two subsets containing four regions each.

One subset is linked to the southern hemisphere, ASH, and the other is linked to the northern hemisphere, ANH.

For comet 67P/C-G in the time between 2014 and 2016, uniform activity leads to a mismatch between model and observations for directions of the rotation state.

This mismatch is resolved with a best-fit solution for effective active fractions.

This directional switch by approximately 90◦is illustrated in Fig. 14 for angular velocity and in Fig. 15 for torque.

The fit quality for the data is on the order of 0.1◦for the ω direction and 75 s for the rotation period.

Only one region A1,1,1 is constrained by the data with values at 0.06 ≤fEAF,1,1,1 ≤0.08.

It is located on the southern hemisphere, ASH, which is the hemisphere that has a high solar irradiation (and negative SSL) around the perihelion passage of comet 67P/C-G in 2015.

Thus, torque activity at that time is high for A1,1,1 and according to the construction of
45°
135°
s
0°
89.5 89
bilobed A bilobed 67P A 67P
-45°
s
-90° Fig. 15.

Longitude, λs, and latitude, ϕs, for angular velocity, ω.

The same projection with respect to the fixed solar basis and the same rs as in Fig. 11.

Considered are the bilobed shape with model A, the shape 67P with model A, and the shape 67P with model α, and weighted activity fEAF in Fig. 13.

Sect. 2.3.

All values of the effective active fraction are bounded by fEAF ≤0.085.

In the regions A−1,−1,−1, A1,±1,1 ⊂ASH and A1,±1,−1, A−1,−1,1 ⊂ANH all setups agree to attribute nonzero activity.

The uncertainties for the weights fEAF,i, j,k suffer from sig-
A1,1,1 the torque direction has three positive components with respect to the solar basis.

In particular, this produces a positive b3 component for the torque, an increase in the angular frequency, |ω|, and a decrease in the rotation period at that time.

For the weights fEAF,i,j,k of all other regions with (i, j, k) �(1, 1, 1), the nonlinear fits hold high uncertainties.

In particular, this affects all regions of the northern hemisphere, ANH.

Low solar irradiation around the perihelion passage results in low dynamical activity and weak signals for these locations.

In addition, the discussion of uncertainties remains unchanged once the shape resolution of ∆x ≈150 m is moderately decreased or increased.

We consider two types of TPM, model A and model α.

The qualitative discussion does not differ for both model types and for the values α = 1.5 and α = 2.

In general, the temporal sampling and the uncertainties prescribed for the ω data affect the fit.

Our discussion does not change for a data set with modified sampling and uncertainty weights.

The same control for the rotation state is possible for each combination between the two shapes, the bilobed shape and the shape 67P, and the two TPMs, model A and model α.

This ability is a characteristic of the domain decomposition.

For lowestenergy states and sublimation following an instantaneous TPM, each region is related to torque formation pointing into one of the eight spatial quadrants with respect to the solar basis.

Each region collects one specific combination of (signs for) the vectorial torque efficiency.

Thus, the weights of the effective active fraction control all torque directions.

Eight is the minimum number for weights (and regions), and it is obtained by our approach.