Slowly-growing Spiral Mode Instabilities in Protostellar Disks
Over the past several decades, computational fluid dynamics has advanced rapidly, and the range of available numerical algorithms and computationally feasible physical problems has expanded. Modern numerical solvers provide a compelling opportunity to probe for as-yet undiscovered effects that emerge with longer integrations and higher numerical precision. In this study, we first derive a range of linear modal instabilities in self-gravitating disks. Improved resolution permits identification of slowly-growing instabilities, which may have a close connection to structures observed by ALMA. We use our linear solutions to the hydrodynamic governing equations to assess the fidelity of meshless and conventional grid-based hydrodynamic solvers. We then study the weakly nonlinear long-term development of endogenously developed spiral modes. We also explore how modern fluid codes maintain recently discovered eccentric disk mode solutions that display unperturbed structure at the inner and outer disk radii. By comparing modern simulations with prior results, we hope to provide a stronger understanding of the impact of fluid mechanics upon the evolution of protostellar disks.