At least 20% of nearby main sequence stars are known to be surrounded by disks of dusty material resulting from the collisional erosion of planetesimals, similar to asteroids and comets in our own Solar System. The material in these 'debris disks' is directly linked to the larger bodies, like planets, in the system through collisions and gravitational perturbations. Observations at millimeter wavelengths are especially critical to our understanding of these systems, since the large grains that dominate emission at these long wavelengths reliably trace the underlying planetesimal distribution. In this thesis, I have used state-of-the-art observations at millimeter wavelengths to address three related questions concerning debris disks and planetary system evolution: 1) How are wide-separation, substellar companions formed? 2) What is the physical nature of the collisional process in debris disks? And, 3) Can the structure and morphology of debris disks provide probes of planet formation and subsequent dynamical evolution? Using ALMA observations of GQ Lup, a pre-main sequence system with a wide-separation, substellar companion, I have placed constraints on the mass of a circumplanetary disk around the companion, informing formation scenarios for this and other similar systems (Chapter 2). I obtained observations of a sample of fifteen debris disks with both the VLA and ATCA at centimeter wavelengths, and robustly determined the millimeter spectral index of each disk and thus the slope of the grain size distribution, providing the first observational test of collision models of debris disks (Chapter 3). By applying an MCMC modeling framework to resolved millimeter observations with ALMA and SMA, I have placed the first constraints on the position, width, surface density gradient, and any asymmetric structure of the AU Mic, HD 15115, Epsilon Eridani, Tau Ceti, and Fomalhaut debris disks (Chapters 4-8). These observations of individual systems hint at trends in disk structure and dynamics, which can be explored further with a comparative study of a sample of the eight brightest debris disks around Sun-like stars within 20 pc (Chapter 9). This body of work has yielded the first resolved images of notable debris disks at millimeter wavelengths, and complements other ground- and space-based observations by providing constraints on these systems with uniquely high angular resolution and wavelength coverage. Together these results provide a foundation to investigate the dynamical evolution of planetary systems through multi-wavelength observations of debris disks.

debris disks; circumstellar matter; submillimeter observations; planetary systems

Astronomy