The Jeans Condition: A New Constraint on Spatial Resolution in Simulations of Isothermal Self-gravitational Hydrodynamics

Abstract

We demonstrate with a new three-dimensional adaptive mesh refinement code that perturbations arising from discretization of the equations of self-gravitational hydrodynamics can grow into fragments in multiple-grid simulations, a process we term "artificial fragmentation." We present star formation calculations of isothermal collapse of dense molecular cloud cores. In simulation of a Gaussian-profile cloud free of applied perturbations, we find artificial fragmentation can be avoided across the isothermal density regime by ensuring the ratio of cell size to Jeans length, which we call the Jeans number, J= Delta x/ lambda _{{J}} , is kept below 0.25. We refer to the constraint that lambda _{{J}} be resolved as the Jeans condition. When an m=2 perturbation is included, we again find it necessary to keep J