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 ≡ Δx/λJ, is kept below 0.25. We refer to the constraint that λJ be resolved as the Jeans condition. When an m = 2 perturbation is included, we again find it necessary to keep J ≤ 0.25 to achieve a converged morphology. Collapse to a filamentary singularity occurs without fragmentation of the filament, in agreement with the predictions of Inutsuka & Miyama. Simulation beyond the time of this singularity requires an arresting agent to slow the runaway density growth. Physically, the breakdown of isothermality due to the buildup of opacity acts as this agent, but many published calculations have instead used artificial viscosity for this purpose. Because artificial viscosity is resolution dependent, such calculations produce resolution-dependent results. In the context of the perturbed Gaussian cloud, we show that use of artificial viscosity to arrest collapse results in significant violation of the Jeans condition. We also show that if the applied perturbation is removed from such a calculation, numerical fluctuations grow to produce substantial fragments not unlike those found when the perturbation is included. These findings indicate that calculations that employ artificial viscosity to halt collapse are susceptible to contamination by artificial fragmentation. The Jeans condition has important implications for numerical studies of isothermal self-gravitational hydrodynamics problems insofar as it is a necessary but not, in general, sufficient condition for convergence.
Original language | English |
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Pages (from-to) | L179-L183 |
Journal | Astrophysical Journal |
Volume | 489 |
Issue number | 2 PART II |
DOIs | |
State | Published - 1997 |
Externally published | Yes |
Funding
The authors wish to thank Tod Woods for critical code assistance and Shu-ichiro Inutsuka and Christopher Matzner for insightful discussions. Conversations with Peter Bodenheimer, Andi Burkert, and Matthew Bate about their work were illuminating. This research was supported by the Institute of Geophysics and Planetary Physics through the University Collaborative Research Program. Research on star formation by R. I. K. and C. F. M. is supported in part by a grant from NASA’s Astrophysics Theory Program to the Center for Star Formation Studies. R. I. K. was additionally supported under the auspices of the US Department of Energy at the Lawrence Livermore National Laboratory under contract W-7405-Eng-48. The research of C. F. M. is also supported in part by NSF grant AST95-30480. The authors wish to thank the Pittsburgh Supercomputing Center for provision of Cray C90 resources through grant AST940011P.
Keywords
- Gravitation
- Hydrodynamics
- ISM: clouds
- Methods: numerical
- Stars: formation