Title: Debiased Orbital and Absolute Magnitude Distribution of the Near-Earth Objects

Authors: William F. Bottke, Jr., Alessandro Morbidelli, Robert Jedicke, Jean-Marc Petit, Harold F. Levison, Patrick Michel, & Travis S. Metcalfe

Status: To appear in Icarus.

Abstract: The orbital and absolute magnitude distribution of the Near-Earth Objects (NEOs) is difficult to compute, partly because only a modest fraction of the entire NEO population has been discovered so far, but also because the known NEOs are biased by complicated observational selection effects. To circumvent these problems, we created a model NEO population which was fit to known NEOs discovered or accidentally rediscovered by Spacewatch. Our method was to numerically integrate thousands of test particles from five source regions which we believe provide most NEOs to the inner solar system. Four of these source regions are in or adjacent to the main asteroid belt, while the fifth one is associated with the Transneptunian disk. The nearly-isotropic comets, which include the Halley-type comets and the long-period comets, were not included in our model. Test bodies from our source regions which passed into the NEO region (perihelia q < 1.3 AU and aphelia Q > 0.983 AU) were tracked until they were eliminated by striking the Sun, a planet, or were ejected out of the inner solar system. These integrations were used to create five residence time probability distributions in semimajor axis, eccentricity, and inclination space (one for each source). These distributions show where NEOs from a given source are statistically most likely to be located. Combining these five residence time probability distributions with an NEO absolute magnitude distribution computed from previous work and a probability function representing the observational biases associated with the Spacewatch NEO survey, we produced a NEO model population which could be fit to 138 NEOs discovered or accidentally rediscovered by Spacewatch. By testing a range of possible source combinations, a "best-fit" NEO model was computed which (i) provided the debiased orbital and absolute magnitude distributions for the NEO population and (ii) indicated the relative importance of each NEO source region.

Our best-fit model is consistent with 960 +/- 120 NEOs having H < 18 and a < 7.4 AU. Approximately 44% (as of December 2000) have been found so far. The limits on this estimate are conditional, since our model does not include nearly-isotropic comets. Nearly-isotropic comets, however, are generally restricted to a Tisserand parameter (with respect to Jupiter) of T < 2, such that few are believed to have a < 7.4 AU. Our computed NEO orbital distribution, which is valid for bodies as faint as H < 22, indicates that the Amor, Apollo, and Aten populations contain 32 +/- 1%, 62 +/- 1%, and 6 +/- 1% of the NEO population, respectively. We estimate that the population of objects completely inside Earth's orbit (IEOs) arising from our source regions is 2% the size of the NEO population. This value does not include the putative Vulcanoid population located inside Mercury's orbit. Overall, our model predicts that ~ 61% of the NEO population comes from the inner main belt (a < 2.5 AU), ~24% comes from the central main belt (2.5 < a < 2.8 AU, ~8% comes from the outer main belt (a > 2.8 AU), and ~6% comes from the Jupiter-family comet region (2 < T < 3). The steady-state population in each NEO source region, as well as the influx rates needed to replenish each region, were calculated as a by-product of our method. The population of extinct comets in the Jupiter-family comet region was also computed.

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