Astron. Astrophys. 329, 785-791 (1998)

4. Comparison with the dust production rate by mutual collisions of EKOs

Stern (1996) predicted a time-averaged production rate of debris between and g s^-1 due to the mutual collisions of EKOs, depending on the parameters used in his collisional simulations. In this section, we shall estimate the production rate of dust grains due to mutual collisions of EKOs, based on the prediction by Stern (1996), in the equivalent mass range used in our estimation.

From laboratory measurements of impact ejection, Gault et al.(1963 ) showed that the mass of the largest fragment is about 10% of the total ejected mass for ranging from g to g. We extrapolated this relation to the crater produced by the impact of an interstellar dust grain. Namely, the impact of an interstellar dust grain excavates a small amount of target material and produces only ejecta with small sizes. For hard icy surfaces, we obtained a crater mass g from Eq.(3). Such a crater mass suggests that the mass of the largest fragment is about g, corresponding to a spherical dust grain with radius . Therefore we assume that the maximum radius of dust grains produced by impacts of interstellar dust is 10 . As noted before, in the case of a particles surface, the radius of the ejecta is smaller than that of the incident interstellar dust grains, i.e. .

On the other hand, the size of the collisional debris predicted by Stern (1996) ranges from multi-kilometer blocks to fine dust. In order to compare our results with his, it is necessary to estimate the fraction of dust grains with radii smaller than amongst the debris produced by mutual EKO collisions, as predicted by Stern (1996).

The size distribution of collisional debris was assumed by Stern (1996) to be in the range of radius a from 0.1 m to 1 km. In this case, the total mass production rate of collisional debris is given by

where is g s^-1 in Stern (1996). We found that the constant is . Using this result, the production rate of dust grains with radii between 0.1 m and 10 m can be given by

The value of ranges from g s^-1 to g s^-1, and is of about the same magnitude as that by impacts of interstellar dust given in Table 1.

We test the sensitivity of our result to the choice of . Application of =1 decreases the range of in Eq.(40) to the range g s^-1 g s^-1, about 24% that for =10 . These production rates are still of the same order of magnitude as those we derived earlier. Furthermore, we tested the sensitivity of the results to the minimum dust radius of 0.1 , and found that the minimum radius does not have a significant influence on the production rate .

We note that the mutual collisions of debris made by the collisions between EKOs may play a significant role in the production of small dust grains. Since this scenario is rather complex and its examination is beyond the scope of this work, it will be studied at a later date.

© European Southern Observatory (ESO) 1998

Online publication: December 8, 1997
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