Signatures of Planets in the Observable Structure of Circumstellar Debris Disks

Recent advances in astronomical instrumentation mean that we are now able to image the thermal emission from the disks of dust around main sequence stars that may be the fossil remnants of planetary formation. These observations imply that the distribution of dust in the debris disks is neither smooth nor symmetrical; e.g., mid-infrared images of the disk of dust around the young A0V star HR 4796A show two lobes of emission, one of which may be ~5% brighter than the other. The observed structure of the debris disk in the solar system, i.e., the zodiacal cloud, also contains asymmetries: it has an offset center of symmetry, it is warped, and there is an asymmetric ring of dust co-orbiting with the Earth. Since the zodiacal cloud's asymmetries have been shown to be signatures of the gravitational perturbations of the solar system's planets, it is hoped that it may be possible to indirectly detect extrasolar planetary systems by their signatures in debris disk observations. This dissertation uses the physical processes that affect the evolution of debris material in the solar system to create a generalized model for the evolution of circumstellar debris material. It then shows how planetary perturbations affect that evolution, thereby causing the signatures of planets seen in the structure of the zodiacal cloud. This model can be used to provide a quantitative interpretation of debris disk observations, and the necessary modeling techniques are demonstrated by their application to observations of the HR 4796 disk. As well as determining the large scale structure of the HR 4796 disk, the modeling shows how a small body (>10 Earth mass) in the HR 4796 system that is on an orbit with an eccentricity larger than 0.02 could be the cause of the observed brightness asymmetry.