The Field Condition: A New Constraint on Spatial Resolution in Simulations of the Nonlinear Development of Thermal Instability

We present the dynamics of a thermally bistable medium using one-dimensionalnumerical calculations, including cooling, heating, thermal conduction, andphysical viscosity.We set up a two-phase medium from a thermally unstableone-phase medium and follow its long-term evolution. To clarify the role ofthermal conduction, we compare the results of the two models, with and withoutthermal conduction. The calculations show that the thermal conduction helps togenerate the kinetic energy of translational motions of the clouds. Next, wefocus on spatial resolution because we have to resolve the Field length$\lambda_{\rm F}$, which is the characteristic length scale of the thermalconduction. The results show convergence only when thermal conduction isincluded and a large enough cell number is used. We find it necessary tomaintain a cell size of less than $\lambda_{\rm F}/3$ to achieve a convergedmotion in the two-phase medium. We refer to the constraint that $\lambda_{\rmF}/3$ be resolved as the ``Field condition''. The inclusion of thermalconduction to satisfy the Field condition is crucial to numerical studies ofthermal instability (TI) and may be important for studies of the turbulentinterstellar two-phase medium: the calculations of TI without thermalconduction may be susceptible to contamination by artificial phenomena that donot converge with increasing resolutions.Comment: 12 pages, 3 figures, Accepted to ApJ