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Dust grains migrating under Poynting-Robertson drag may be trapped inmean-motion resonances with planets. Such resonantly trapped grains areobserved in the solar system. In extrasolar systems, the exozodiacal lightproduced by dust grains is expected to be a major obstacle to future missionsattempting to directly image terrestrial planets. The patterns made byresonantly trapped dust, however, can be used to infer the presence of planets,and the properties of those planets, if the capture and evolution of the grainscan be modelled. This has been done with N-body methods, but such methods arecomputationally expensive, limiting their usefulness when considering large,slowly evolving grains, and for extrasolar systems with unknown planets andparent bodies, where the possible parameter space for investigation is large.In this work, we present a semi-analytic method for calculating the capture andevolution of dust grains in resonance, which can be orders of magnitude fasterthan N-body methods. We calibrate the model against N-body simulations, findingexcellent agreement for Earth to Neptune mass planets, for a variety of grainsizes, initial eccentricities, and initial semimajor axes. We then apply themodel to observations of dust resonantly trapped by the Earth. We find thatresonantly trapped, asteroidally produced grains naturally produce the`trailing blob' structure in the zodiacal cloud, while to match the intensityof the blob, most of the cloud must be composed of cometary grains, which owingto their high eccentricity are not captured, but produce a smooth disk.

Capture and evolution of dust in planetary mean-motion resonances: a fast, semi-analytic method for generating resonantly trapped disk images