Which orbital elements for asteroids impact statistics? Robustness tests in impact probability computation

A classic (and fundamental) problem in the study of the collisional evolution of asteroids is the evaluation of the rate of close encounters among the members of the small bodies population of interest. Besides the frequency of impact, that in the framework of the asteroids studies is expressed in terms of "intrinsic probability of collision" (Wetherill 1967), the distribution of the impact velocity is of paramount importance too.

The intensity of the collisional environment created by a dominant group of asteroids depends on the joint distribution of the sizes and the orbits of the population. A common approach is to assume that the diameters and orbital distributions are independent. Indeed, the mean intrinsic probability of collision is a pure geometrical quantity depending only on the distribution of the impactor orbits. In this way, the frequency of impacts from the projectiles population hitting a given target is proportional to the product between size frequency of the projectiles and the mean intrinsic probability of collision. In other words, we assume that the mean intrinsic probability of collision is the same for different intervals of impactor sizes.

Even in this idealized situation, both the sizes and orbital distributions are sources of considerable uncertainty. Here we will focus on the role of the orbital distributions.

In order to compute the intrinsic probability of collision, different approaches have been developed over the last half century, which differ from each other in terms of the degree of approximation and the underlying dynamical hypotheses. All such methods require as input a list or a distribution of orbits, from which the statistics of collision are derived. The input orbital distribution must be as realistic as possible in order to obtain a reliable and really useful result. However, the uncertainties about the real distribution of orbits often introduce errors in the computation of probabilities that may be larger than the errors due to approximations implemented in the computational methods about the dynamical behavior of the bodies.

The orbital distribution of asteroids is affected by several observational biases. In such situation the choice of the set of orbits mapping the "real" orbital distribution of the projectiles is a critical problem. In some cases the computation of the impact statistics relies on a model of the orbital structure of the population (Dell'Oro et al. 2013). As a consequence, the computed probability of impact results to be a model dependent quantity the reliability of which depends on the validity of the assumed dynamical model. Other approaches consist in computing impact probability taking into account the orbits of the largest projectiles in the assumption that this sample is bias free (Farinella & Davis 1992, Bottke et al. 1994). On the other hand the contribution to the overall collisional environment produced by the smaller impactors (responsible for surface evolution mechanisms like craterization) is simply ignored.

We are carrying on a project that aims to explore in a systematic way how impact statistics parameters depend on the distribution of the orbits of the impactors. The main goal is to provide an assessment of the impact probabilities and the impact velocity distributions as realistic as possible, along with the corresponding regions of confidence. The latest results will be shown and discussed.

References

• Bottke W.F., Nolan M.C., Greenberg R., Kolvoord R.A., 1994. Icarus, 107, 255-268.
• Dell'Oro A., Campo Bagatin A., Benavidez P.G., Alemañ R.A., 2013. Astronomy and Astrophysics, 558, A95.
• Farinella P., Davis D.R., 1992. Icarus, 97, 111-123.
• Wetherill G.W., 1967. Journal of Geophysical Research, 72, 2429-2444.