  It is expected since the early 1970s that tenuous dust rings are formed by
grains ejected from the Martian moons Phobos and Deimos by impacts of
hypervelocity interplanetary projectiles. In this paper, we perform direct
numerical integrations of a large number of dust particles originating from
Phobos and Deimos. In the numerical simulations, the most relevant forces
acting on dust are included: Martian gravity with spherical harmonics up to 5th
degree and 5th order, gravitational perturbations from the Sun, Phobos, and
Deimos, solar radiation pressure, as well as the Poynting-Robertson drag. In
order to obtain the ring configuration, simulation results of various grain
sizes ranging from submicron to 100 microns are averaged over a specified
initial mass distribution of ejecta. We find that for the Phobos ring grains
smaller than about 2 microns are dominant; while the Deimos ring is dominated
by dust in the size range of about 5-20 microns. The asymmetries, number
densities and geometrical optical depths of the rings are quantified from
simulations. The results are compared with the upper limits of the optical
depth inferred from Hubble observations. We compare to previous work and
discuss the uncertainties of the models.
