  In circumstellar discs, collisional grinding of planetesimals produces
second-generation dust. While it remains unclear whether this ever becomes a
major component of the total dust content, the presence of such dust, and
potentially the substructure within, it can be used to explore a disc's
physical conditions. A perturbing planet produces nonaxisymmetric structures
and gaps in the dust, regardless of its origin. The dynamics of planetesimals,
however, will be very different than that of small dust grains due to weaker
gas interactions. Therefore, planetesimal collisions could create dusty disc
structures that would not exist otherwise. In this work, we use N-body
simulations to investigate the collision rate profile of planetesimals near
mean-motion resonances. We find that a distinct bump or dip feature is produced
in the collision profile, the presence of which depends on the libration width
of the resonance and the separation between the peri- and apocenter distances
of the edges of the resonance. The presence of one of these two features
depends on the mass and eccentricity of the planet. Assuming that the radial
dust emission traces the planetesimal collision profile, the presence of a bump
or dip feature in the dust emission at the 2:1 mean-motion resonance can
constrain the orbital properties of the perturbing planet. This assumption is
valid, so long as radial drift does not play a significant role during the
collisional cascade process. Under this assumption, these features in the dust
emission should be marginally observable in nearby protoplanetary disks with
ALMA.
