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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