From Magnitudes to Diameters: The Albedo Distribution of Near Earth Objects and the Earth Collision Hazard

A recently published model of the Near Earth Object (NEO) orbital-magnitude distribution (Bottke et al., 2002, Icarus156, 399-433.) relies on five intermediate sources for the NEO population: the ν₆ resonance, the 3:1 resonance, the outer portion of the main belt (i.e., 2.8-3.5 AU), the Mars-crossing population adjacent to the main belt, and the Jupiter family comet population. The model establishes the relative contribution of these sources to the NEO population. By computing the albedo distribution of the bodies in and/or near each of the five sources, we can deduce the albedo distribution of the NEO population as a function of semimajor axis, eccentricity, and inclination. A problem with this strategy, however, is that we do not know a priori the albedo distribution of main belt asteroids over the same size range as observed NEOs (diameter D<10 km). To overcome this problem, we determined the albedo distribution of large asteroids in and/or near each NEO source region and used these results to deduce the albedo distribution of smaller asteroids in the same regions. This method requires that we make some assumptions about the absolute magnitude distributions of both asteroid families and background asteroids. Our solution was to extrapolate the observed absolute magnitude distributions of the families up to some threshold value H_thr, beyond which we assumed that the families' absolute magnitude distributions were background-like.We found that H_thr=14.5 provides the best match to the color vs heliocentric distance distribution observed by the Sloan Digital Sky Survey. With this value of H_thr our model predicts that the debiased ratio between dark and bright (albedo smaller or larger than 0.089) objects in any absolute-magnitude-limited sample of the NEO population is 0.25±0.02. Once the observational biases are properly taken into account, this agrees very well with the observed C/S ratio (0.165 for H<20). The dark/bright ratio of NEOs increases to 0.87±0.05 if a size-limited sample is considered. We estimate that the total number of NEOs larger than a kilometer is 855±110, which, compared to the total number of NEOs with H<18 (963±120), shows that the usually assumed conversion H=18?D=1 km slightly overestimates the number of kilometer-size objects.Combining our orbital distribution model with the new albedo distribution model, and assuming that the density of bright and dark bodies is 2.7 and 1.3 g/cm³, respectively, we estimate that the Earth should undergo a 1000 megaton collision every 63,000±8000 years. On average, the bodies capable of producing 1000 megaton of impact energy are those with H<20.6. The NEOs discovered so far carry only 18±2% of this collision probability.