Detection and Characterization of Extrasolar Planets through Mean-Motion Resonances. II. The Effect of the Planet's Orbital Eccentricity on Debris Disk Structures

Structures observed in debris disks may be caused by gravitational interaction with planetary or stellar companions. These perturbed disks are often thought to indicate the presence of planets and offer insights into the properties of both the disk and the perturbing planets. Gaps in debris disks may indicate a planet physically present within the gap, but such gaps can also occur away from the planet's orbit at mean-motion resonances (MMRs), and this is the focus of our interest here. We extend our study of planet-disk interaction through MMRs, presented in an earlier paper, to systems in which the perturbing planet has moderate orbital eccentricity, a common occurrence in exoplanetary systems. In particular, a new result is that the 3:1 MMR becomes distinct at higher eccentricity, while its effects are absent for circular planetary orbits. We also only consider gravitational interaction with a planetary body of at least 1 Jupiter mass. Our earlier work shows that even a 1 Earth mass planet can theoretically open an MMR gap; however, given the narrow gap that can be opened by a low-mass planet, its observability would be questionable. We find that the widths, locations, and shapes of two prominent structures, the 2:1 and 3:1 MMRs, could be used to determine the mass, semimajor axis, and eccentricity of the planetary perturber and present an algorithm for doing so. These MMR structures can be used to narrow the position and even determine the planetary properties (such as mass) of any inferred but as-yet-unseen planets within a debris disk. We also briefly discuss the implications of eccentric disks on brightness asymmetries and their dependence on the wavelengths with which these disks are observed.