  Structures in circumstellar disks such as gaps and rings are often attributed
to planets. This connection has been difficult to show unequivocally, as other
processes may also produce these features. Particularly, a photoelectric
instability (PEI) has been proposed, operating in gas-rich optically thin
disks, that generates structures predicted by planet--disk interactions. We
examine the question of how to disentangle planetary effects on disk structure
from the effects of the PEI. We use the Pencil Code to perform 2D global
hydrodynamical models of the dynamics of gas and dust in a thin disk, with and
without planetary perturbers. Photoelectric heating is modeled with an equation
of state where pressure is proportional to dust surface density. The drag force
on grains and its backreaction on the gas are included. Analyzing the situation
without PEI, we find that gas--dust interactions alter the shape of the
planetary gap from the dust-free case when the local dust-to-gas ratio
$\varepsilon$ approaches unity. This result applies also to primordial disks,
because dust drifting inwards accumulates at the edge of the planetary gap, and
any initial dust-to-gas ratio eventually achieves $\varepsilon=1$ if the dust
reservoir is sufficient. We find a result particular to high dust-to-gas ratio
disks as well: as dust drifts inwards, the dust front becomes a sharp
transition, and the backreaction triggers the Rossby wave instability. When PEI
is included, we find that it obscures structures induced by planets unless the
planet's mass is sufficiently large to carve a noticeable gap. Specifically,
the instability generates arcs and rings of regular spacing: a planet is
discernible when it carves a dust gap wider than the wavelength of the PEI.
