tokens: equation of state (EOS) has been studied for hydrodynamic turbulence and for a polytropic EOS (Federrath Banerjee 2015 ) or an adiabatic EOS (Nolan et al. 2015 ; Mohapatra Sharma 2019 ), indicating additional dependencies, on (for example) the adiabatic index γ , the relation between density fluctuations and . In the magnetized case the majority of studies focus on the isothermal case , finding an additional dependency on the ratio of thermal to magnetic pressure (e.g., Kowal et al. 2007 ; Padoan Nordlund 2011 ; Molina et al. 2012 ). Overall, a highly dynamic picture of turbulence has been found, challenging our ability to examine the general case. In this paper, we present adiabatic magnetohydrodynamic simulations of stationary turbulence in the subsonic ( to 0.6), super-Alfvénic (), and high (ratio of thermal to magnetic pressure with ) regime. This regime approximates the turbulent intracluster medium (ICM; Brunetti Lazarian 2007 ; Brüggen Vazza 2015 ) even though our magnetohydrodynamics (MHD) model neglects effects stemming from low collisionality (Schekochihin Cowley 2006 ; Schekochihin et al. 2008 ). However, studies including effects from low collisionality, e.g., through the Chew–Goldberger–Low MHD model, found that they generally introduce only small differences compared to the MHD model, e.g., a small increase in density fluctuations (Kowal et al. 2011 ; Santos-Lima et al. 2017 ), but leave imprints on Faraday rotation maps (Nakwacki et al. 2016 ). Here, we specifically focus on the effects of departure from an isothermal equation of state by varying the adiabatic index γ and the cooling function between simulations. The rest of this paper is organized as follows. In Section 2 , we introduce the numerical setup and the simulations conducted. In Section 3 , we present results from analyzing the simulations starting with a high-level overview of the energy spectra, to correlations in the stationary regime, to statistics of distribution functions that can potentially be used to break degeneracies between the thermodynamics and sonic Mach number. The results are discussed in Section 4 , and we conclude with a brief outlook in Section 5 on how our findings point the way to future measurements that can be used to better diagnose the properties of turbulence in astrophysical plasmas. 2. Numerical Details In this work we utilize the equations of compressible, ideal MHD equations that are closed by an ideal equation of state , with γ as the ratio of specific heats. The symbols have their usual meaning, i.e., density ρ , velocity , total pressure consisting of thermal pressure and magnetic pressure , and magnetic field , which includes a factor . Cooling is included via and is the total energy density with specific internal energy e . Vector quantities that are not in boldface refer to the L 2 norm of the vector and ⨂ denotes the outer product. The details of the acceleration field that we use to mechanically drive our simulations are
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