We have calculated the coherence and detectable lifetimes of synthetic near-Earth object (NEO) families created by catastrophic disruption of a progenitor as it suffers a very close Earth approach. The closest or slowest approaches yield the most vio
lent `s-class disruption events. We found that the average slope of the absolute magnitude (H) distribution, $N(H)propto10^{(0.55pm0.04),H}$, for the fragments in the s-class families is steeper than the slope of the NEO population citep{mainzer2011} in the same size range. The families remain coherent as statistically significant clusters of orbits within the NEO population for an average of $bartau_c = (14.7pm0.6)times10^3$ years after disruption. The s-class families are detectable with the techniques developed by citet{fu2005} and citet{Schunova2012} for an average duration ($bartau_{det}$) ranging from about 2,000 to about 12,000 years for progenitors in the absolute magnitude ($H_p$) range from 20 to 13 corresponding to diameters in the range from about 0.5 to 10$km$ respectively. The short detectability lifetime explains why zero NEO families have been discovered to-date. Nonetheless, every tidal disruption event of a progenitor with D$>0.5km$ is capable of producing several million fragments in the $1meter$ to $10meter$ diameter range that can contribute to temporary local density enhancements of small NEOs in Earths vicinity. We expect that there are about 1,200 objects in the steady state NEO population in this size range due to tidal disruption assuming that one $1km$ diameter NEO tidally disrupts at Earth every 2,500 years. These objects may be suitable targets for asteroid retrieval missions due to their Earth-like orbits with corresponding low $v_{infty}$. The fragments from the tidal disruptions at Earth have $sim5times$ the collision probability with Earth compared to the background NEO population.
We report on our search for genetically related asteroids amongst the near-Earth object (NEO) population - families of NEOs akin to the well known main belt asteroid families. We used the technique proposed by Fu et al. (2005) supplemented with a det
ailed analysis of the statistical significance of the detected clusters. Their significance was assessed by comparison to identical searches performed on 1,000 fuzzy-real NEO orbit distribution models that we developed for this purpose. The family-free fuzzy-real NEO models maintain both the micro and macro distribution of 5 orbital elements (ignoring the mean anomaly). Three clusters were identified that contain four or more NEOs but none of them are statistically significant at geq 3{sigma}. The most statistically significant cluster at the sim 2{sigma} level contains 4 objects with H < 20 and all members have long observational arcs and concomitant good orbital elements. Despite the low statistical significance we performed several other tests on the cluster to determine if it is likely a genetic family. The tests included examining the clusters taxonomy, size-frequency distribution, consistency with a family-forming event during tidal disruption in a close approach to Mars, and whether it is detectable in a proper element cluster search. None of these tests exclude the possibility that the cluster is a family but neither do they confirm the hypothesis. We conclude that we have not identified any NEO families.
