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

Abstract

We present the dynamics of a thermally bistable medium using one-dimensional numerical calculations, including cooling, heating, thermal conduction, and physical viscosity.We set up a two-phase medium from a thermally unstable one-phase medium and follow its long-term evolution. To clarify the role of thermal conduction, we compare the results of the two models, with and without thermal conduction. The calculations show that the thermal conduction helps to generate the kinetic energy of translational motions of the clouds. Next, we focus on spatial resolution because we have to resolve the Field length $\lambda_{\rm F}$, which is the characteristic length scale of the thermal conduction. The results show convergence only when thermal conduction is included and a large enough cell number is used. We find it necessary to maintain a cell size of less than $\lambda_{\rm F}/3$ to achieve a converged motion in the two-phase medium. We refer to the constraint that $\lambda_{\rm F}/3$ be resolved as the ``Field condition''. The inclusion of thermal conduction to satisfy the Field condition is crucial to numerical studies of thermal instability (TI) and may be important for studies of the turbulent interstellar two-phase medium: the calculations of TI without thermal conduction may be susceptible to contamination by artificial phenomena that do not converge with increasing resolutions.