Properties and evolution of NEO families created by tidal disruption at Earth

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 violent `s-class' disruption events. We found that the average slope of the absolute magnitude (H) distribution, $N(H)\propto10^{(0.55\pm0.04)\,H}$, 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 $\barτ_c = (14.7\pm0.6)\times10^3$ years after disruption. The s-class families are detectable with the techniques developed by \citet{fu2005} and \citet{Schunova2012} for an average duration ($\barτ_{det}$) 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$>0.5\km$ is capable of producing several million fragments in the $1\meter$ to $10\meter$ diameter range that can contribute to temporary local density enhancements of small NEOs in Earth's 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 $1\km$ 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 $\sim5\times$ the collision probability with Earth compared to the background NEO population.