Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconstructing the size distribution of the primordial Main Belt   In this work we aim to constrain the slope of the size distribution of
main-belt asteroids, at their primordial state. To do so we turn out attention
to the part of the main asteroid belt between 2.82 and 2.96~AU, the so-called
"pristine zone", which has a low number density of asteroids and few, well
separated asteroid families. Exploiting these unique characteristics, and using
a modified version of the hierarchical clustering method we are able to remove
the majority of asteroid family members from the region. The remaining,
background asteroids should be of primordial origin, as the strong 5/2 and 7/3
mean-motion resonances with Jupiter inhibit transfer of asteroids to and from
the neighboring regions. The size-frequency distribution of asteroids in the
size range $17<D(\rm{km})<70$ has a slope $q\simeq-1$. Using Monte-Carlo
methods, we are able to simulate, and compensate for the collisional and
dynamical evolution of the asteroid population, and get an upper bound for its
size distribution slope $q=-1.43$. In addition, applying the same 'family
extraction' method to the neighboring regions, i.e. the middle and outer belts,
and comparing the size distributions of the respective background populations,
we find statistical evidence that no large asteroid families of primordial
origin had formed in the middle or pristine zones.

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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: math
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol