Krivov, A.V. and D.P. Hamilton. Martian Dust Belts: Waiting for Discovery. Icarus 128, 335-353.

In this paper, we present modeling results of the presumed dust belts of Mars. We combine recently obtained theoretical results in dynamics of circumplanetary dust grains with up-to-date impact models and use a new numerical code to construct a three-dimensional, time-dependent, and size-dependent distribution of dust material. Our modeling is performed in two consecutive stages. First, for each grain size, we construct a relative spatial density distribution (\ie a density distribution normalized to an arbitrary factor), which depends almost entirely on dust dynamics. We arrive at an extended set of data tables which quantitatively describe the asymmetric and season-dependent structure formed by different-sized grains. This step is done quite accurately using sophisticated dynamical models. Next, we model the dust production and loss rates in two conceivable formation scenarios to estimate absolute spatial dust densities. These results are uncertain by one or two orders of magnitude because the hypervelocity impact process is poorly characterized. We use the absolute spatial densities to estimate the normal and edge-on optical depths of the Phobos and Deimos tori and obtain values from $10^{-8}$ to $10^{-5}$. Spacecraft data are required to substantially reduce these uncertainties.
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