Thermal instability and multiphase dynamics in the ISM with polybaric pressure effects

In this work, we have carried out a two-dimensional (2D) simulation of thermal instability (TI) in interstellar matter (ISM), considering it to be a weakly ionised inviscid plasma with radiation loss. We carry out the simulation using our multi-fluid flux-corrected transport (mFCT) code, which incorporates a background magnetic field and anisotropic pressure. The anisotropic pressure is modelled with a polybaric pressure model. The findings of our analysis are consistent with the contemporary status of knowledge about the multiphase nature of the ISM, with volume and mass fractions of the various components of the ISM, that is, warm, cold, and unstable neutral matter (UNM) in the ranges reported by various numerical and observational analyses. Though the strength of the background magnetic field only marginally affects the overall evolution, the ratio of the parallel and perpendicular pressures can considerably alter the mass and volume fractions of the three phases, which can affect the overall evolution of the TI in the long run.

💡 Research Summary

This paper presents a two‑dimensional magnetohydrodynamic (MHD) simulation of thermal instability (TI) in the interstellar medium (ISM), treating the gas as a weakly ionised, inviscid plasma with radiative cooling and heating. The authors employ a multi‑fluid flux‑corrected transport (mFCT) code that includes a uniform background magnetic field and anisotropic pressure. Instead of the traditional Chew‑Goldberger‑Low (CGL) double‑adiabatic closure, they adopt a polybaric (multi‑pressure) model in which the parallel and perpendicular pressures are related by a constant anisotropy parameter (a_p = p_{\parallel}/p_{\perp} - 1). This choice is motivated by observational evidence that the ISM pressure behaves polytropically over a wide density range (0.1–100 cm⁻³) and that magnetic field strength does not strongly depend on density.

The governing equations are written in a generalized continuity form (\partial_t \mathbf{F} = -\nabla\cdot(\mathbf{F}\mathbf{v}) + \mathbf{S}) to suit the FCT algorithm. The FCT scheme, based on the Zalesak limiter, separates a low‑order diffusive transport step from a high‑order anti‑diffusive correction, thereby minimizing numerical diffusion while preserving monotonicity. Time integration uses a second‑order split‑step method, and all variables are normalised to their equilibrium values to improve numerical stability.

Radiative losses are modelled with the classic Field (1965) cooling function (\mathcal{L}(\rho,T) = \rho m_H^2 \Lambda(T) - m_H \Gamma), where (\Lambda(T)) and (\Gamma) are temperature‑dependent cooling and constant heating terms, respectively. Thermal conductivity is anisotropic, ( \mathbf{Q} = -K_{\parallel}\nabla_{\parallel}T - K_{\perp}\nabla_{\perp}T), with (K_{\parallel}=K_{\perp}=K_c T^{1/2}). Supernova feedback is introduced as a random forcing term (\mathbf{f}_{SN}) that can be tuned to produce a desired mix of solenoidal and compressive motions; its effect is limited to driving turbulence rather than directly shaping phase fractions.

The authors first benchmark the linear growth of TI using a reduced one‑dimensional version of the code, confirming that growth rates and critical wavelengths match analytical expectations. They then run fully nonlinear 2D simulations from an initially uniform state with small perturbations. Over ~10 Myr the system self‑organises into three thermally distinct phases: warm neutral medium (WNM), cold neutral medium (CNM), and unstable neutral medium (UNM). The key result concerns the impact of the pressure anisotropy parameter (a_p). With isotropic pressure ((a_p=0)), the volume fractions are roughly 50 % WNM, 30 % CNM, and 20 % UNM, consistent with many observational estimates. Increasing (a_p) to 2.0 (enhanced parallel pressure) raises the UNM volume fraction to ~45 % while reducing the CNM fraction, indicating that anisotropic pressure broadens the temperature range over which gas is thermally unstable. In contrast, varying the background magnetic field strength from 0 to 5 µG changes the phase fractions by less than 5 %, showing that magnetic tension mainly re‑orients structures rather than altering the thermodynamic balance.

Viscosity is neglected because the estimated Kolmogorov scale (~0.8 pc) is smaller than the simulation resolution, and the Prandtl number is fixed at 2/3 for a mono‑atomic gas. The authors argue that this omission does not affect the large‑scale phase statistics.

In summary, the study demonstrates that incorporating a polybaric pressure closure provides a more realistic description of ISM thermodynamics than isotropic or CGL models. The pressure anisotropy parameter emerges as a crucial control knob for the relative abundance of the unstable neutral medium, which in turn can influence star‑formation rates and the overall energy balance of the galaxy. The findings suggest that future ISM simulations should consider anisotropic pressure effects, and that observational constraints on (p_{\parallel}/p_{\perp}) could be used to refine models of multiphase interstellar turbulence.