Completeness of Impact Monitoring

Abstract The completeness limit is a key quantity to measure the reliability of an impact monitoring system. It provides the impact probability threshold for which every virtual impactor (VI) with impact probability above this value has to be detected. The completeness limit depends on the confidence region sampling: a goal of this paper is to increase the completeness without increasing the computational load, thus we propose a new method to sample the Line Of Variations (LOV) with respect to the previously one used in NEODyS. The step-size of the sampling is not uniform in the LOV parameter, since the probability of each LOV segment between consecutive points is kept constant. Moreover, the sampling interval has been extended to the larger interval [ − 5 , 5 ] in the LOV parameter and a new decomposition scheme in sub-showers and sub-returns is provided to deal with the problem of duplicated LOV points appearing in the same return. The impact monitoring system clomon -2 has been upgraded with all these new features, resulting in a decrease of the impact probability IP * corresponding to the generic completeness limit by a factor  ≃ 4 and in an increase of the computational load by a factor  ≃ 2. Moreover, since the generic completeness limit is an analytic approximation, we statistically investigate the completeness actually reached by the system. For this we used two different methods: a direct comparison with the results of the independent system Sentry at JPL and an empirical power-law to model the number of virtual impactors as a function of the impact probability. We found empirically that the number of detected virtual impactors with IP  >  IP * appears to grow according to a power-law, proportional to I P − 2 / 3 . An analytical model explaining this power-law is currently an open problem, but we think it is related to the way the number of virtual impactors within a time t rel from the first observed close approach accumulates. We give an analytical model and we prove that this cumulative number grows with a power-law proportional to t r e l 3 . The power-law allows us to detect a loss of efficiency in the virtual impactors search for impact probabilities near the generic completeness limit. The outcome of the comparison with Sentry shows that the two histograms of the number of VIs as a function of IP are very consistent for IP  >  IP *, which supports the confidence in the reliability of both systems.