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 perf
ormed in two consecutive stages. First, for each grain size, we constr
uct a relative spatial density distribution (i.e., a density distribut
ion normalized to an arbitrary factor), which depends almost entirely
on dust dynamics. We arrive at an extended set of data tables which qu
antitatively describe the asymmetric and season-dependent structure fo
rmed by different-sized grains. This step is done quite accurately usi
ng sophisticated dynamical models. Next, we model the dust production
and loss rates in two conceivable formation scenarios to estimate abso
lute spatial dust densities. These results are uncertain by one or two
orders of magnitude because the hypervelocity impact process is poorl
y characterized. We use the absolute spatial densities to estimate the
normal and edge-on optical depths of the Phobos and Deimos tori and o
btain values from 10(-8) to 10(-5). Spacecraft data are required to su
bstantially reduce these uncertainties. (C) 1997 Academic Press.