Observational Completion Limit of Minor Planets from the Asteroid Belt to Jupiter Trojans. (arXiv:2010.07822v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Hendler_N/0/1/0/all/0/1">Nathanial P Hendler</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Malhotra_R/0/1/0/all/0/1">Renu Malhotra</a>

With the growing numbers of asteroids being discovered, identifying an
observationally complete sample is essential for statistical analyses and for
informing theoretical models of the dynamical evolution of the solar system. We
present an easily implemented method of estimating the empirical observational
completeness in absolute magnitude, H_lim, as a function of semi-major axis.
Our method requires fewer assumptions and decisions to be made in its
application, making results more transportable and reproducible amongst studies
that implement it, as well as scalable to much larger datasets of asteroids
expected in the next decade with the Vera C.~Rubin Observatory’s Legacy Survey
of Space and Time (LSST). Using the values of H_lim(a) determined at high
resolution in semimajor axis, a, we demonstrate that the observationally
complete sample size of the main belt asteroids is larger by more than a factor
of 2 compared to using a conservative single value of H_lim, an approach often
adopted in previous studies. Additionally, by fitting a simple, physically
motivated model of H_lim(a) to 7e5 objects in the Minor Planet Database, our
model reveals statistically significant deviations between the main belt and
the asteroid populations beyond the main belt (Hungarias, Hildas and Trojans),
suggesting potential demographic differences, such as in their size,
eccentricity or inclination distributions.

With the growing numbers of asteroids being discovered, identifying an
observationally complete sample is essential for statistical analyses and for
informing theoretical models of the dynamical evolution of the solar system. We
present an easily implemented method of estimating the empirical observational
completeness in absolute magnitude, H_lim, as a function of semi-major axis.
Our method requires fewer assumptions and decisions to be made in its
application, making results more transportable and reproducible amongst studies
that implement it, as well as scalable to much larger datasets of asteroids
expected in the next decade with the Vera C.~Rubin Observatory’s Legacy Survey
of Space and Time (LSST). Using the values of H_lim(a) determined at high
resolution in semimajor axis, a, we demonstrate that the observationally
complete sample size of the main belt asteroids is larger by more than a factor
of 2 compared to using a conservative single value of H_lim, an approach often
adopted in previous studies. Additionally, by fitting a simple, physically
motivated model of H_lim(a) to 7e5 objects in the Minor Planet Database, our
model reveals statistically significant deviations between the main belt and
the asteroid populations beyond the main belt (Hungarias, Hildas and Trojans),
suggesting potential demographic differences, such as in their size,
eccentricity or inclination distributions.

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