# As A Matter of State: The role of thermodynamics in magnetohydrodynamic turbulence

## TL;DR

This study investigates how thermodynamics influence magnetohydrodynamic turbulence by varying the adiabatic index and cooling functions, revealing degeneracies in observable relations that can be broken with higher-order statistical analysis.

## Contribution

The paper presents a comprehensive suite of MHD simulations exploring the effects of thermodynamics on turbulence, highlighting how different equations of state alter key plasma correlations.

## Key findings

- Thermal and magnetic pressures are strongly anticorrelated regardless of thermodynamics.
- Density-magnetic field anticorrelation weakens with increasing adiabatic index.
- Relations between density, thermal pressure, and Mach number depend on thermodynamics, affecting observational inferences.

## Abstract

Turbulence simulations play a key role in advancing the general understanding of the physical properties turbulence and in interpreting astrophysical observations of turbulent plasmas. For the sake of simplicity, however, turbulence simulations are often conducted in the isothermal limit. Given that the majority of astrophysical systems are not governed by isothermal dynamics, we aim to quantify the impact of thermodynamics on the physics of turbulence, through varying adiabatic index, $\gamma$, combined with a range of optically thin cooling functions. In this paper, we present a suite of ideal magnetohydrodynamics simulations of thermally balanced stationary turbulence in the subsonic, super-Alfv\'enic, high beta (ratio of thermal to magnetic pressure) regime, where turbulent dissipation is balanced by two idealized cooling functions (approximating linear cooling and free-free emission) and examine the impact of the equation of state by considering cases that correspond to isothermal, monatomic and diatomic gases. We find a strong anticorrelation between thermal and magnetic pressure independent of thermodynamics, whereas the strong anticorrelation between density and magnetic field found in the isothermal case weakens with increasing $\gamma$. Similarly, with the linear relation between variations in density and thermal pressure with sonic Mach number becomes steeper with increasing $\gamma$. This suggests that there exists a degeneracy in these relations with respect to thermodynamics and Mach number in this regime, which is dominated by slow magnetosonic modes. These results have implications for attempts to infer (e.g.) Mach numbers from (e.g.) Faraday rotation measurements, without additional information regarding the thermodynamics of the plasma. However, our results suggest that this degeneracy can be broken by utilizing higher-order moments of observable distribution functions.