A Field-length based refinement criterion for adaptive mesh simulations of the interstellar medium

Adequate modelling of the multiphase interstellar medium requires optically thin radiative cooling, comprising an inherent thermal instability. The size of the occurring condensation and evaporation interfaces is determined by the so-called Field-length, which gives the dimension at which the instability is significantly damped by thermal conduction. Our aim is to study the relevance of conduction scale effects in the numerical modelling of a bistable medium and check the applicability of conventional and alternative adaptive mesh techniques. The low physical value of the thermal conduction within the ISM defines a multiscale problem, hence promoting the use of adaptive meshes. We here introduce a new refinement strategy that applies the Field condition by Koyama & Inutsuka as a refinement criterion. The described method is very similar to the Jeans criterion for gravitational instability by Truelove and efficiently allows to trace the unstable gas situated at the thermal interfaces. We present test computations that demonstrate the greater accuracy of the newly proposed refinement criterion in comparison to refinement based on the local density gradient. Apart from its usefulness as a refinement trigger, we do not find evidence in favour of the Field criterion as a prerequisite for numerical stability.

💡 Research Summary

The interstellar medium (ISM) is intrinsically multiphase and its dynamics are strongly influenced by optically thin radiative cooling. Cooling gives rise to the classical thermal instability, which in the presence of thermal conduction is suppressed on scales smaller than the so‑called Field length (λ_F). Because λ_F in realistic ISM conditions is extremely short—often orders of magnitude below the typical grid spacing—any numerical study that wishes to resolve the condensation and evaporation fronts must treat this problem as multiscale. Adaptive mesh refinement (AMR) is therefore the natural tool, but the choice of refinement criterion is critical.

In most existing AMR implementations the refinement trigger is based on gradients of density, pressure, or temperature. While such criteria reliably capture shocks and strong compressions, they are blind to the comparatively gentle variations that characterize the conductive transition layers produced by thermal instability. Consequently, the interface thickness can be under‑resolved, leading to artificial diffusion, spurious oscillations, and an inaccurate representation of the balance between heating, cooling, and conduction.

The authors propose to adopt the “Field condition” originally introduced by Koyama & Inutsuka (2004) as a direct refinement criterion. The idea is simple: the local grid spacing Δx should be smaller than a prescribed multiple N of the local Field length, i.e. Δx ≤ N · λ_F, with N typically chosen between 4 and 8. This mirrors the well‑known Truelove criterion for gravitational collapse (Δx ≤ λ_J/4) and guarantees that the physically relevant unstable scale is always resolved. The Field length itself is computed from the local thermodynamic state using

λ_F = √