Landslides on Comet 67P/Churyumov–Gerasimenko: Stability of Ejecta in Places of their Depositions

Introduction: The phenomenon of landslide is a form of the gravity movement. Comets have weak gravity field, so it is believed that probability of landslides is very low. However observations from space missions to comets 9P/Tempe 1 and 67P/Churyumov – Gerasimenko revealed existence of these mass motion.

The causes of landslides are usually related to instabilities of slopes. It is often possible to indicate a few causes of the landslide but usually only one factor is considered to be a trigger. Causes are the factors responsible for making the slope unstable in respect to small disturbances. Some causes could also trigger landslides [1].

In the present paper we consider comet 67P/Churyumov–Gerasimenko. Investigation of its nucleus indicated existence of deposits typical for landslides. In previous works we consider ejecta from some places of the comets. In presen paper we investigate stability of ejecta in the place of landing.  

 

Slopes of the surface:

On the small bodies of spherical shape the area with large slope (in respect to the local gravity) is rather limited. The different situation could be observed on highly asymmetric bodies [2].

The gravitational field of 67P/Churyumov–Gerasimenko comet is very complicated. There are several regions of different slopes of the physical surface in respect to the gravity. The most of the surface (~74%) has the slope in the range 0< α<40^o. The slope in the range 40^o < α<70^o is found on ~17% of the surface.

Fig. 1.  Assumed mass distribution in the comet (green volume) and the surface of the constant value of the gravitational potential (red surface) for -0.45 m² s^-2. The green surface contains mass used for the modelling the gravity of the comet and it is close (but not identical) to the physical surface of the comet.

Mechanism of ejection

We followour previous works, we use a simple model of processes leading to the formation of slow ejecta – Fig. 2. The phase transition heats a certain underground volume [3, 4]. It leads to vaporization of volatiles. Eventually a cavity is formed. If the pressure in the cavity exceeds some critical value then the crust could be crushed and its fragments will be ejected in space.

Fig. 2. A simple model of processes leading to the formation of slow ejecta.

 

The trajectories of test particles ejected with the velocity 0.7 m s^-1 from different parts of Imhoteb are given in Fig. 3. Note that ejecta are deposited mainly in two different regions, one in the large lobe and another in the small lobe. 

 

Fig. 3 The trajectories of motion of the matter ejected from Imhotep (on the large lobe) with the velocity 0.7 m s^-1.

 

 

Results and conclusions

Ejecta landing on the highly inclined surface could trigger another landslide. It depend on angles of landing and the properties of the material of the comet.Let consider the fate of a dry single grain. If comet material could be treated as dirty snow then non-elastic behaviour seems to be most probable. We have performed several calculations of motion of test particles after landing assuming fully non-elastic collision, therefore test particles have only tangential component of velocity after impact (see Fig. 4 upper part). Under this assumption a friction coefficient of grains and surface seems to be the only unknown parameter of motion. The angle of repose for many loose materials is in the range ~35^o, (e.g. for dry quartz sand it is 34^o) – e.g. Nichols and Franklin (1898). This corresponds to value for coefficient of friction of ~0.7. Unfortunately this approach is rather unrealistic. Note that the slope of face of tetrahedrons represent only average slope of the physical surface.             

 

 Fig. 4. Upper part  – an ‘ideal’ situation: on smooth surface of comet (given by a face of the shape model) the fate of ejecta after landing depends on: friction coefficient, inclination of the place of landing in respect to the local gravity g, angle between the vector of velocity v (or vector of momentum p) and the normal to the surface. Large angles could lead to developing a new landslide (regular or ballistic). However the true motion is determined by small scale details of the comet's surface as well as shape and amount of grains – lower part.   

 

 

The motion of grains is not determined by this average slope and average coefficient of friction. The small-scale effects are decisive. The grain can slide over the entire face if it overcome the worst obstacle on the face. For grains of the shape and size shown in lower part of Figure 4, the worst obstacle is the vertical obstacle B. To break it, the sliding grain must have enough kinetic energy to crush the obstacle. Obstacle A could be overcome but it requires more energy than sliding along an ‘ideal’ smooth face. Note that we do not have data about these critical small scale obstacles. Moreover, the size and shapes of grains are also important as well as the thickness of the deposited layer. Eventually, in realistic calculation we cannot assume ~0.7 as an effective value of coefficient of friction. We must assume significantly higher value. For values from the range 1-1.5 only a few particles move from their landing face to another face. Most of them are stopped later. For thick deposit layer different approach is necessary – the thick layer could make the face more smooth. In such a case futher motion is possible. Therefore for landslides of large volume one cannot treat the landslide as a motion of single test particle. 

 

Acknowledgements: The research is partly supported by Poland's National Science Center (Narodowe Centrrum Nauki) [decision No. 2018/31/B/ST 10/00169].

 

References

[1] Czechowski L., (2016)  LPSC 2016, 2781 pdf.

[2] Czechowski L., (2017)  EGU 2017 April, 26, 2017

[3] Kossacki K., Czechowski L., 2018,  Icarus vol. 305, pp. 1-14, doi: 10.1016/j.icarus.2017.12.027

[4] Kossacki, K.J., Szutowicz, S., 2010, Icarus 207, 320- 340.

[5] Czechowski L. and Kossacki K.J. 2019. Dynamics of material ejected from depression Hatmehit. Submitted.