  Irregular satellites are the minor bodies found orbiting all four Solar
System giant planets, with large semi-major axes, eccentricities, and
inclinations. Previous studies have determined that the Solar System's
irregular satellites are extremely collisionally evolved populations today,
having lost $\sim$99 per cent of their initial mass over the course of hundreds
of Myr. Such an evolution implies that the irregular satellites must have
produced a population of dusty collisional debris in the past, which is
potentially observable due to the resulting reprocessing of stellar light. In
this paper we examine the signatures of the debris discs produced by extrasolar
analogues of this process. Radiation pressure, quantified by the parameter
$\beta$, is the driving force behind the liberation of dust grains from the
planetary Hill sphere, and results in the formation of circumstellar dust
rings, even in the absence of an underlying belt of asteroids in the system.
Our simulated discs reproduce many of the same features seen in some classes of
observed debris discs, such as thin ring morphology, a large blowout size, and
azimuthal symmetry. We compare our simulated discs' radial profiles to those of
the narrow dust rings observed around Fomalhaut and HR 4796A, and show that
they can broadly reproduce the observed radial distribution of dust.
