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Philipp Grete

Publications and source records attributed to Philipp Grete.

At least 19 recordsLinked to original sources
arXiv2026

Supersonic Motion in the Driving Region of M82

The prototypical starburst galaxy M82 is host to an expansive, multiphase outflow whose driving mechanism is not fully understood. Longstanding models suggest that energy and mass injection from supernova into the hottest phase of the galactic wind could drive the cooler phases, but validating these models has been difficult due to the lack of constraints on the hot wind energetics. The high-resolution spectral capabilities of XRISM have generated the tightest constraints to date on the temperatures of the hot wind, as well as the first direct measurement of its velocity dispersion. In this work, we use these new observational constraints to test a model of a supernova-driven free wind. We generate a suite of highly idealized hydrodynamic simulations varying the energy and mass loading of the starburst and construct mock spectra to compare against the XRISM results. We find that the observed velocity dispersion is impossible to replicate using our free-wind model alone, and extra broadening is required to fit the spectrum. We interpret this broadening to be due not to bulk outflow, but rather to smaller scale non-thermal motions in the driving region of the starburst. This implies supersonic motion (Mach 1.71-3.14) of the hot gas in the central region of the galaxy. As supersonic motions are unexpected, it is possible that a significant amount of the energy that should go into heating the gas is instead going towards other sources such as amplifying magnetic fields and driving cosmic rays.

astro-ph.GA↗
arXiv2026

Inverse energy transfer in decaying MHD turbulence: A shell-to-shell analysis

In decaying magnetohydrodynamic turbulence, energy can be transported from small to large scales, known as inverse transfer. We explore the mechanism behind this phenomenon using shell-to-shell transfer functions. Independent of magnetic net-helicity, large magnetic scales receive energy directly from the integral scale in both the magnetic and kinetic reservoirs, leading to increasingly non-local transfer for larger receiving scales. The resulting rate of energy increase in each receiving scale is proportional to its energy, resulting in self-similar, multiplicative growth. Even though the system is magnetically dominated, contributions from kinetic-magnetic and magnetic-magnetic energy-exchange are similar in magnitude. In the case of vanishing net-helicity, transfer functions between the positively and negatively helical parts of the field are computed. We find that inverse transfer only occurs within each helical sector, not across them. Our findings are consistent with the theory underlying the conservation of the Hosking integral, which explains inverse transfer as merging of local magnetic islands with equal-signed helicity.

physics.plasm-ph↗
arXiv2025

The Launching of Galactic Winds from a Multiphase ISM

Galactic outflows are a key agent of galaxy evolution, yet their observed multiphase nature remains difficult to reconcile with theoretical models, which often fail to explain how cold gas survives interactions with hot, fast winds. We present high-resolution 3D hydrodynamic simulations of hot outflows interacting with a multiphase interstellar medium (ISM), parameterised by its cold-gas volume filling fraction $f_v$, depth $L_{\rm ISM}$, and clump size $r_{\rm cl}$. We identify a universal survival criterion $f_v L_{\rm ISM} \gtrsim r_{\rm crit}$ that generalises the classical single-cloud condition ($r_{\rm cl} > r_{\rm crit}$) and correctly predicts cold-gas survival across diverse ISM configurations - including scale-free - down to $r_{\rm cl}/r_{\rm crit} \sim 10^{-2}$. The surviving cold phase rapidly loses memory of the initial ISM structure and evolves toward a self-similar clump mass spectrum following Zipf's law ($\mathrm{d}N/\mathrm{d}m \propto m^{-2}$), implying that turbulent mixing and radiative condensation universally shape multiphase outflows. Cold gas assembles into plumes or confined shells of size $\sim \chi r_{\mathrm{cl,min}}$, growing as mass is accreted from the hot phase. The interaction of a laminar wind with a clumpy ISM drives turbulence in both phases, with first-order velocity structure functions following a Kolmogorov scaling and an injection scale set by $L_{\rm ISM}$, while velocity dispersions reach $\sigma \sim c_{\rm s,cold}$. The areal covering fraction of cold gas approaches unity even for $f_v \sim 10^{-3}$, though its volume filling fraction stays low, explaining the "misty" appearance of observed outflows. Together, these results link small-scale cloud-wind interactions to galaxy-scale feedback, and we discuss their implications for interpreting observations and for modelling multiphase galactic winds in larger-scale simulations.

astro-ph.GA↗
arXiv2025

An Improved Fit to the Density Distribution in Supersonic Isothermal Turbulence

The density distribution of supersonic isothermal turbulence plays a critical role in many astrophysical systems. It is commonly approximated by a lognormal distribution with a variance of $\sigma_{s,{\rm V}}^2 \approx \ln(1 + b^2 M_{\rm V}^2),$ where $s \equiv \ln \rho/\rho_0,$ $M_{\rm V}$ is the rms volume-weighted Mach number, and $b$ is a parameter that depends on the driving mechanism, which can be solenoidal (divergence-free), compressive (curl-free), or a mix of both. However, this fit neglects the driving correlation time, $\tau_{\rm a}$, which plays a key role when compressive driving is significant. Here we conduct turbulence simulations spanning a wide range of Mach numbers, driving mechanisms, and $\tau_{\rm a}$ values. In the compressive case, $\sigma_{s,{\rm V}}^2$ is not well fit by the standard expression. Instead, it scales approximately linearly with $M_{\rm V},$ and its dependence on $\tau_{\rm a}$ is $\sigma_{s,{\rm V}}^2 \approx M_{\rm V} [1 + \frac{2}{3}(1 + \lambda_{\rm a})\Theta(1 + \lambda_{\rm a})]$, where $\lambda_{\rm a} \equiv \ln(\tau_{\rm a}/\tau_{\rm e})$, $\tau_{\rm e}$ is the eddy turnover time, and $\Theta$ is the Heaviside step function. Mixed-driven turbulence shows a weak dependence on $\tau_{\rm a},$ and for solenoidally-driven turbulence, $\sigma_{s,{\rm V}}^2 \approx \frac{1}{3}M_{\rm V}$, which is consistent with the standard expression when $M_{\rm V} \lesssim 8.$ The volume-weighted mean and skewness also show systematic trends with $M_{\rm V}$ and $\tau_{\rm a}$, deviating from lognormal expectations. The mass-weighted density distribution displays significant broadening and skewness in compressively-driven cases, especially at large $\tau_{\rm a}/\tau_{\rm e}$. These results provide a refined framework for modeling astrophysical turbulence.

astro-ph.GA↗
arXiv2025

XMAGNET : Kinetic, Thermal and Magnetic AGN Feedback in Massive Galaxies at Halo Masses $\sim 10^{13.5}$ M$_\odot$

The interplay between radiative cooling of the circumgalactic medium (CGM) and feedback heating governs the evolution of the universe's most massive galaxies. This paper presents simulations of feedback processes in massive galaxies showing how kinetic, thermal, and magnetic active galactic nuclei (AGN) feedback interacts with the CGM under different environmental conditions. We find that in massive galaxies with shallower central gravitational potential and higher CGM pressure (multiphase galaxy; MPG) pure kinetic AGN feedback is most efficient in preventing CGM cooling from becoming catastrophic while maintaining the CGM entropy within the observed range. For the same galaxy, partitioning AGN energy injection into kinetic ($75\%$) and thermal ($25\%$) energy results in an entropy bump within $r\lesssim15$ kpc while also having a larger amount of cold gas extending out to $r\sim80$ kpc. A magnetohydrodynamic MPG run with seed magnetic field in the CGM (1~$\mu$G) and partial magnetised AGN feedback ($1\%$ of total AGN power) also shows a higher entropy (within $r<15$ kpc) and cold gas mass, albeit the cold gas remains constrained within $r\lesssim30$ kpc. For a similarly massive galaxy with deeper potential well and low CGM pressure (single phase galaxy; SPG) our simulations show that for both hydro and MHD runs with partial thermal AGN energy, the feedback mechanism remains tightly self-regulating with centrally concentrated cooling (within $r<1$ kpc). Our simulations of a similar mass galaxy with a deeper potential well and higher CGM pressure (SPG-Cool) show that our AGN feedback mechanism cannot get rid of the high CGM density and pressure and its long term evolution is similar to the multiphase galaxy.

astro-ph.GA↗
arXiv2025

Self-Similar Cosmic-Ray Transport in High-Resolution Magnetohydrodynamic Turbulence

We study the propagation of cosmic rays (CRs) through a simulation of magnetohydrodynamic (MHD) turbulence at unprecedented resolution of $10{,}240^3$. We drive turbulence that is subsonic and super-Alfv\'enic, characterized by $\delta B_{\rm rms}/B_0=2$. The high resolution enables an extended inertial range such that the Alfv\'en scale $l_A$, where $\delta B (l_A)\approx B_0$, is well resolved. This allows us to properly capture how the cascade transitions from large amplitudes on large scales to small amplitudes on small scales. We find that sharp bends in the magnetic field are key mediators of particle transport even on small scales via resonant curvature scattering. We further find that particle scattering in the turbulence shows strong hints of self-similarity: (1) the diffusion has weak energy dependence over almost two decades in particle energy and (2) the particles' random walk exhibits a broad power-law distribution of collision times such that the diffusion is dominated by the rarest, long-distance excursions. Our results suggest that large-amplitude MHD turbulence can provide efficient scattering over a wide range of CR energies and may help explain many CR observations above a $\sim$TeV: the flattening of the B/C spectrum, the hardening of CR primary spectra and the weak dependence of arrival anisotropy on CR energy.

astro-ph.HE↗
arXiv2025

The Density Distribution of Compressively-Forced Supersonic Turbulence Depends on the Driving Correlation Time

Supersonic turbulence plays a critical role in shaping astrophysical systems, from molecular clouds to the circumgalactic medium. Key properties of this turbulence include the Mach number, driving scale, and nature of the driving mechanism, which can be solenoidal (divergence-free), compressive (curl-free), or a mix of the two. A less studied property is the correlation time of the driving accelerations, $\tau_{\rm a}.$ While this timescale has a minimal impact on solenoidally-driven turbulence, we show that it has a strong impact on compressively-driven turbulence. Using high-resolution simulations with tracer particles, we analyze the evolution of density fluctuations, focusing on the PDF of the logarithmic density, $s$, and its rate of change, $\frac{ds}{dt},$ and the conditional statistics of $\frac{ds}{dt}$ and $\frac{d^2s}{dt^2}$. When the driving correlation time is comparable to the eddy turnover time, $\tau_{\rm a} \approx \tau_{\rm e},$ compressive driving leads to the formation of large, low-density voids in which the variance of $\frac{ds}{dt}$ is large. These are directly linked to sustained accelerated expansions, which results in a strong correlation between density and the divergence of the driving acceleration field. In contrast, when $\tau_{\rm a} \approx 0.1 \, \tau_{\rm e}$, compressive driving does not produce such voids, resulting in a narrower, less skewed distribution. We show using analytical estimates that $\tau_{\rm a}$ is may be significantly less than $\tau_{\rm e}$ in supernova-driven turbulence, highlighting the need to better understand the role of the driving correlation time in shaping the density structure of turbulent astrophysical systems.

astro-ph.GA↗
arXiv2025

The XMAGNET exascale MHD simulations of SMBH feedback in galaxy groups and clusters: Overview and preliminary cluster results

We present initial results from extremely well-resolved 3D magnetohydrodynamical simulations of idealized galaxy clusters, conducted using the AthenaPK code on the Frontier exascale supercomputer. These simulations explore the self-regulation of galaxy groups and cool-core clusters by cold gas-triggered active galactic nucleus (AGN) feedback incorporating magnetized kinetic jets. Our simulation campaign includes simulations of galaxy groups and clusters with a range of masses and intragroup and intracluster medium properties. In this paper we present results that focus on a Perseus-like cluster. We find that the simulated clusters are self-regulating, with the cluster cores staying at a roughly constant thermodynamic state and AGN jet power staying at physically reasonable values ($\simeq 10^{44}-10^{45}$~erg/s) for billions of years without a discernible duty cycle. These simulations also produce significant amounts of cold gas, with calculations having strong magnetic fields generally both promoting cold gas formation and allowing cold gas out to much larger clustercentric radii ($\simeq 100$~kpc) than simulations with weak or no fields ($\simeq 10$~kpc), and also having more filamentary cold gas morphology. We find that AGN feedback significantly increases the strength of magnetic fields at the center of the cluster. We also find that the magnetized turbulence generated by the AGN results in turbulence where the velocity power spectra are tied to AGN activity whereas the magnetic energy spectra are much less impacted after reaching a stationary state.

astro-ph.GA↗
arXiv2024

AthenaK: A Performance-Portable Version of the Athena++ AMR Framework

We describe AthenaK: a new implementation of the Athena++ block-based adaptive mesh refinement (AMR) framework using the Kokkos programming model. Finite volume methods for Newtonian, special relativistic (SR), and general relativistic (GR) hydrodynamics and magnetohydrodynamics (MHD), and GR-radiation hydrodynamics and MHD, as well as a module for evolving Lagrangian tracer or charged test particles (e.g., cosmic rays) are implemented using the framework. In two companion papers we describe (1) a new solver for the Einstein equations based on the Z4c formalism and (2) a GRMHD solver in dynamical spacetimes also implemented using the framework, enabling new applications in numerical relativity. By adopting Kokkos, the code can be run on virtually any hardware, including CPUs, GPUs from multiple vendors, and emerging ARM processors. AthenaK shows excellent performance and weak scaling, achieving over one billion cell updates per second for hydrodynamics in three-dimensions on a single NVIDIA Grace Hopper processor and with a typical parallel efficiency of 80% on 65536 AMD GPUs on the OLCF Frontier system. Such performance portability enables AthenaK to leverage modern exascale computing systems for challenging applications in astrophysical fluid dynamics, numerical relativity, and multimessenger astrophysics.

astro-ph.IM↗
arXiv2024

The properties of magnetised cold filaments in a cool-core galaxy cluster

Filaments of cold gas ($T\leq 10^{4}$ K) are found in the inner regions of many cool-core clusters. These structures are thought to play a major role in the regulation of feedback from active galactic nuclei (AGN). We study the morphology of the filaments, their formation, and their impact on the propagation of the outflowing AGN jets. We present a set of GPU-accelerated 3D (magneto)hydrodynamical simulations of an idealized Perseus-like cluster using the performance portable code AthenaPK. We include radiative cooling, and a self-regulated AGN feedback model that redistributes accreted material through kinetic, thermal and magnetic feedback. We confirm that magnetic fields play an important role in both the formation and evolution of the cold material. These suppress the formation of massive cold discs and favour magnetically supported filaments over clumpy structures. Achieving resolutions of $25-50$ pc, we find that filaments are not monolithic as they contain numerous and complex magnetically supported sub-structures. We find that the mass distribution of these clumps follows a $\mathrm{d}N/\mathrm{d}M \propto M^{-1.6}$ power-law for all investigated filaments. Studying the evolution of individual filaments, we find that their formation pathways can be diverse. We find examples of filaments forming through a combination of gas uplifting and condensation, as well as systems of purely infalling clumps condensing out of the intracluster medium. The density contrast between the cold gas and the outflowing hot material leads to recurring deflections of the jets, favouring inflation of bubbles.

astro-ph.GA↗
arXiv2023

A morphological analysis of the substructures in radio relics

Recent observations of radio relics - diffuse radio emission in galaxy clusters - have revealed that these sources are not smooth but consist of structures in the form of threads and filaments. We investigate the origin of these filamentary structures and the role of projection effects. To this end, we have developed a tool that extracts the filamentary structures from background emission. Moreover, it is capable of studying both two-dimensional and three-dimensional objects. We apply our structure extractor to, both, observations and cosmological simulations of radio relics. Using Minkowski functionals, we determine the shape of the identified structures. In our 2D analysis, we find that the brightest structures in the observed and simulated maps are filaments. Our analysis of the 3D simulation data shows that radio relics do not consist of sheets but only of filaments and ribbons. Furthermore, we did not find any measurable projection effects that could hide any sheet-like structures in projection. We find that, both, the magnetic field and the shock front consist of filaments and ribbons that cause filamentary radio emission.

astro-ph.CO↗
arXiv2022

Parthenon -- a performance portable block-structured adaptive mesh refinement framework

On the path to exascale the landscape of computer device architectures and corresponding programming models has become much more diverse. While various low-level performance portable programming models are available, support at the application level lacks behind. To address this issue, we present the performance portable block-structured adaptive mesh refinement (AMR) framework Parthenon, derived from the well-tested and widely used Athena++ astrophysical magnetohydrodynamics code, but generalized to serve as the foundation for a variety of downstream multi-physics codes. Parthenon adopts the Kokkos programming model, and provides various levels of abstractions from multi-dimensional variables, to packages defining and separating components, to launching of parallel compute kernels. Parthenon allocates all data in device memory to reduce data movement, supports the logical packing of variables and mesh blocks to reduce kernel launch overhead, and employs one-sided, asynchronous MPI calls to reduce communication overhead in multi-node simulations. Using a hydrodynamics miniapp, we demonstrate weak and strong scaling on various architectures including AMD and NVIDIA GPUs, Intel and AMD x86 CPUs, IBM Power9 CPUs, as well as Fujitsu A64FX CPUs. At the largest scale on Frontier (the first TOP500 exascale machine), the miniapp reaches a total of $1.7\times10^{13}$ zone-cycles/s on 9,216 nodes (73,728 logical GPUs) at ~92% weak scaling parallel efficiency (starting from a single node). In combination with being an open, collaborative project, this makes Parthenon an ideal framework to target exascale simulations in which the downstream developers can focus on their specific application rather than on the complexity of handling massively-parallel, device-accelerated AMR.

cs.DC↗
arXiv2022

As a matter of dynamical range -- scale dependent energy dynamics in MHD turbulence

Magnetized turbulence is ubiquitous in many astrophysical and terrestrial plasmas but no universal theory exists. Even the detailed energy dynamics in magnetohydrodynamic (MHD) turbulence are still not well understood. We present a suite of subsonic, super-Alfvénic, high plasma-beta MHD turbulence simulations that only vary in their dynamical range, i.e., in their separation between the large-scale forcing and dissipation scales, and their dissipation mechanism (implicit large eddy simulation, ILES, versus and direct numerical simulation, DNS). Using an energy transfer analysis framework we calculate the effective, numerical viscosities and resistivities and demonstrate and that all ILES calculations of MHD turbulence are resolved and correspond to an equivalent visco-resistive MHD turbulence calculation. Increasing the number of grid points used in an ILES corresponds to lowering the dissipation coefficients, i.e., larger (kinetic and magnetic) Reynolds numbers for a constant forcing scale. Independently, we use this same framework to demonstrate that -- contrary to hydrodynamic turbulence -- the cross-scale energy fluxes are not constant in MHD turbulence. This applies both to different mediators (such as cascade processes or magnetic tension) for a given dynamical range as well as to a dependence on the dynamical range itself, which determines the physical properties of the flow. We do not observe any indication of convergence even at the highest resolution (largest Reynolds numbers) simulation at $2{,}048^3$ cells, calling into question whether an asymptotic regime in MHD turbulence exists, and, if so, what it looks like.

astro-ph.GA↗
arXiv2021

Magnetized Decaying Turbulence in the Weakly Compressible Taylor-Green Vortex

Magnetohydrodynamic turbulence affects both terrestrial and astrophysical plasmas. The properties of magnetized turbulence must be better understood to more accurately characterize these systems. This work presents ideal MHD simulations of the compressible Taylor-Green vortex under a range of initial sub-sonic Mach numbers and magnetic field strengths. We find that regardless of the initial field strength, the magnetic energy becomes dominant over the kinetic energy on all scales after at most several dynamical times. The spectral indices of the kinetic and magnetic energy spectra become shallower than $k^{-5/3}$ over time and generally fluctuate. Using a shell-to-shell energy transfer analysis framework, we find that the magnetic fields facilitate a significant amount of the energy flux and that the kinetic energy cascade is suppressed. Moreover, we observe nonlocal energy transfer from the large scale kinetic energy to intermediate and small scale magnetic energy via magnetic tension. We conclude that even in intermittently or singularly driven weakly magnetized systems, the dynamical effects of magnetic fields cannot be neglected.

physics.flu-dyn↗
arXiv2020

As a matter of tension -- kinetic energy spectra in MHD turbulence

Magnetized turbulence is ubiquitous in many astrophysical and terrestrial systems but no complete, uncontested theory even in the simplest form, magnetohydrodynamics (MHD), exists. Many theories and phenomenologies focus on the joint (kinetic and magnetic) energy fluxes and spectra. We highlight the importance of treating kinetic and magnetic energies separately to shed light on MHD turbulence dynamics. We conduct an implicit large eddy simulation of subsonic, super-Alfvénic MHD turbulence and analyze the scale-wise energy transfer over time. Our key finding is that the kinetic energy spectrum develops a scaling of approximately $k^{-4/3}$ in the stationary regime as the kinetic energy cascade is suppressed by magnetic tension. This motivates a reevaluation of existing MHD turbulence theories with respect to a more differentiated modeling of the energy fluxes.

physics.plasm-ph↗
arXiv2020

K-Athena: a performance portable structured grid finite volume magnetohydrodynamics code

Large scale simulations are a key pillar of modern research and require ever-increasing computational resources. Different novel manycore architectures have emerged in recent years on the way towards the exascale era. Performance portability is required to prevent repeated non-trivial refactoring of a code for different architectures. We combine Athena++, an existing magnetohydrodynamics (MHD) CPU code, with Kokkos, a performance portable on-node parallel programming paradigm, into K-Athena to allow efficient simulations on multiple architectures using a single codebase. We present profiling and scaling results for different platforms including Intel Skylake CPUs, Intel Xeon Phis, and NVIDIA GPUs. K-Athena achieves $>10^8$ cell-updates/s on a single V100 GPU for second-order double precision MHD calculations, and a speedup of 30 on up to 24,576 GPUs on Summit (compared to 172,032 CPU cores), reaching $1.94\times10^{12}$ total cell-updates/s at 76% parallel efficiency. Using a roofline analysis we demonstrate that the overall performance is currently limited by DRAM bandwidth and calculate a performance portability metric of 62.8%. Finally, we present the implementation strategies used and the challenges encountered in maximizing performance. This will provide other research groups with a straightforward approach to prepare their own codes for the exascale era. K-Athena is available at https://gitlab.com/pgrete/kathena .

cs.DC↗
arXiv2019

Kinetic and internal energy transfer in implicit large eddy simulations of forced compressible turbulence

We revisit the problem of how energy transfer through the turbulent cascade operates in compressible hydrodynamic turbulence. In general, there is no conservative compressible cascade since the kinetic and internal energy reservoirs can exchange energy through pressure dilatation. Moreover, statistically stationary turbulence at high Mach number can only be maintained in nearly isothermal gas, i.e., if excess heat produced by shock compression and kinetic energy dissipation is continuously removed from the system. We mimic this process by a linear cooling term in numerical simulations of turbulence driven by stochastic forcing. This allows us to investigate turbulence statistics for a broad range of Mach numbers. We compute the rate of change of kinetic and internal energy in wavenumber shells caused by advective, compressive, and pressure dilatation effects and constrain power-law fits to compressible turbulence energy spectra to a range of wavenumbers in which the total energy transfer is close to zero. The resulting scaling exponents are significantly affected by the forcing. Depending on the root mean square Mach number, we find a nearly constant advective component of the cross-scale flux of kinetic energy at intermediate wavenumbers for particular mixtures of solenoidal and compressive modes in the forcing. This suggests the existence of a natural, Mach number dependent mixture of forcing modes. Our findings also support an advection-dominated regime at high Mach numbers with specific scaling exponents (Burgers scaling for the pure velocity fluctuation $u$ and Kolmogorov scaling for the mass-weighted variable $v=ρ^{1/3}u$).

physics.flu-dyn↗
arXiv2019

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

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, $γ$, 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-Alfvénic, 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 $γ$. Similarly, with the linear relation between variations in density and thermal pressure with sonic Mach number becomes steeper with increasing $γ$. 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.

astro-ph.GA↗