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Understanding the nature of compressible fluctuations in a broad range of turbulent plasmas, from the intracluster medium to the solar wind, has been an active field of research in the past decades. Theoretical frameworks for weakly compressible MHD turbulence in an inhomogeneous background magnetic field predict a linear scaling of the normalized mass density fluctuation ($\delta \rho / \rho_0$), as a function of the turbulent Mach number ($\mathcal{M}_t$), $\delta \rho / \rho_0 \propto \mathcal{M}_t$. However, so far the scaling relation has been tested only using moderate to low plasma beta ($\beta \lesssim 1$) solar wind observational data where the compressibility is weak $\delta \rho / \rho_0 \sim 0.1$. Here, we combine NASA's Magnetospheric Multiscale Mission data in Earth's magnetosheath, where $\beta \sim 10$ is high, and $\beta \sim 1$ highly-compressible magnetohydrodynamic turbulence simulations at unprecedented resolutions. Both show that $\delta \rho / \rho_0 \propto \mathcal{M}_t$ holds across a broad range of $\delta \rho / \rho_0$, $\mathcal{M}_t$ and $\beta$, demonstrating that $\delta \rho / \rho_0 \propto \mathcal{M}_t$ is a robust compressible turbulence relation, going beyond the asymptotics of the weakly compressible theory. We discuss the findings in the context of understanding the nature of strongly compressible turbulent fluctuations and the driving parameter in astrophysical and space plasmas., Comment: Submitted to ApJ

The interstellar medium (ISM) of disk galaxies is turbulent, and yet the fundamental nature of ISM turbulence, the energy cascade, is not understood in detail. In this study, we use high-resolution simulations of a hydrodynamical, gravitationally stratified, supernova (SNe)-driven, multiphase ISM to probe the nature of a galactic turbulence cascade. Through the use of kinetic energy flux transfer functions split into interactions between compressible $\mathbf{u}_c$ and incompressible $\mathbf{u}_s$ modes, we show that there exists a large-to-small-scale cascade in both $\mathbf{u}_c$ and $\mathbf{u}_s$ when mediated by an additional $\mathbf{u}_s$ mode. But the $\mathbf{u}_s$ cascade is highly non-local. Moreover, there is a $\mathbf{u}_c$ mediated component of the $\mathbf{u}_s$ cascade that proceeds in the opposite direction -- an inverse cascade from small-to-large scales. The cascade feeds flux into scales well beyond the scale height, energizing the winds and fueling the direct cascades. Both the strongly non-local and the inverse $\mathbf{u}_s$ cascades happen on scales that have a power law $\mathbf{u}_s$ energy spectrum, highlighting how degenerate the spectrum is to the true underlying physical processes. We directly show that the inverse cascade comes from $\mathbf{u}_s$ modes interacting with expanding SNe remnants (SNRs) and that $\mathbf{u}_s$ modes are generated to leading order via baroclinic, highly corrugated cooling layers between warm $(T\lesssim 10^4\,\rm{K})$ and hot $(T\gg10^4\,\rm{K})$ gas in these SNRs. Finally, we outline a complete phenomenology for SNe-driven turbulence in a galactic disk, estimate a $10^{-16}\,\rm{G}$ Biermann field generated from SNR cooling layers, and highlight the strong deviations that SNe-driven turbulence has from the conventional Kolmogorov model., Comment: Main text 24 pages, 13 figures. Appendix, 6 pages, 7 figures. Submitted to ApJ. Comments welcome

Supersonic magnetohydrodynamic (MHD) turbulence is a ubiquitous state for many astrophysical plasmas. However, even the basic statistics for this type of turbulence remains uncertain. We present results from supersonic MHD turbulence simulations at unparalleled resolutions, with plasma Reynolds numbers of over a million. In the kinetic energy spectrum we find a break between the scales that are dominated by kinetic energy, with spectral index $-2$, and those that become strongly magnetized, with spectral index $-3/2$. By analyzing the Helmholtz decomposed kinetic energy spectrum, we find that the compressible modes are not passively mixed through the cascade of the incompressible modes. At high magnetic Reynolds number, above $10^5$, we find a power law in the magnetic energy spectrum with spectral index $-9/5$. On the strongly magnetized, subsonic scales the plasma tends to self-organize into locally relaxed regions, where there is strong alignment between the current density, magnetic field, velocity field and vorticity field, depleting both the nonlinearities and magnetic terms in the MHD equations, which we attribute to plasma relaxation on scales where the magnetic fluctuations evolve on shorter timescales than the velocity fluctuations. This process constrains the cascade to inhomogenous, volume-poor, fractal surfaces between relaxed regions, which has significant repercussions for understanding the nature of magnetized turbulence in astrophysical plasmas and the saturation of the fluctuation dynamo., Comment: 22 pages. 10 figures. Currently the world's largest MHD turbulence simulation on a grid of 10,080^3 (Re and Rm over a million). Comments welcome, email james.beattie@princeton.edu

Many polyatomic astrophysical plasmas are compressible and out of chemical and thermal equilibrium, and yet, due to Stokes' hypothesis, a means to carefully control the decay of compressible modes in these systems has largely been neglected. This is especially important for small-scale, turbulent dynamo processes, which are known to be sensitive to the effects of compression. To control the viscous properties of the compressible modes, we perform supersonic, visco-resistive dynamo simulations with additional bulk viscosity $\nu_{\rm bulk}$, deriving a new $\nu_{\rm bulk}$ Reynolds number $\rm{Re}_{\rm bulk}$, and viscous Prandtl number $\rm{P}\nu \equiv \rm{Re}_{\rm bulk} / \rm{Re}_{\rm shear}$, where $\rm{Re}_{\rm shear}$ is the shear viscosity Reynolds number. For $10^{-3} \leq \rm{P}\nu \leq \infty$, we explore a broad range of statistics critical to the dynamo problem, including the integral and spectral energy ratios, growth rates, and the magnetic $E_{\rm mag}(k)$ and kinetic $E_{\rm kin}(k)$ energy spectrum. We derive a general framework for decomposing $E_{\rm mag}$ growth rates into incompressible and compressible terms via orthogonal tensor decompositions of $\nabla\otimes\mathbf{v}$, where $\mathbf{v}$ is the fluid velocity. We find that compressible modes play a dual role, growing and decaying $E_{\rm mag}$, and that field-line stretching is the main driver of growth, even in supersonic dynamos. In the absence of $\nu_{\rm bulk}$, compressible modes pile up on small-scales, creating an apparent spectral bottleneck, which disappears for $\rm{P}\nu \approx 1$. As $\rm{P}\nu$ decreases, compressible modes are dissipated at increasingly larger scales, in turn suppressing incompressible modes through a coupling between viscosity operators. We emphasise the importance of further understanding the role of $\nu_{\rm bulk}$ in compressible astrophysical plasmas., Comment: 28 pages, 18 figures, submitted to MNRAS. Comments welcome. Re-uploaded on 11 Dec with compressed large figures to reduce file size

Many astrophysical small-scale dynamos (SSDs) amplify weak magnetic fields via highly compressible, supersonic turbulence, but established SSD theories have overlooked these compressible effects. To address this, we perform visco-resistive SSD simulations across a range of sonic Mach numbers ($\mathcal{M}$), hydrodynamic Reynolds numbers ($\mathrm{Re}$), and magnetic Prandtl numbers ($\mathrm{Pm}$). We develop robust methods to measure kinetic and magnetic energy dissipation scales ($\ell_\nu$ and $\ell_\eta$) and the scale of strongest magnetic fields ($\ell_\mathrm{p}$) during the kinematic phase. We demonstrate that $\ell_\nu/\ell_\eta \sim \mathrm{Pm}^{1/2}$ is a universal feature for $\mathrm{Pm} \geq 1$ SSDs, regardless of $\mathcal{M}$ or $\mathrm{Re}$. Incompressible SSDs (either $\mathcal{M} \leq 1$ or $\mathrm{Re} < \mathrm{Re}\mathrm{crit} \approx 100$) concentrate magnetic energy at $\ell_\mathrm{p} \sim \ell_\eta$ with inversely correlated field strength and curvature. However, for compressible SSDs ($\mathcal{M} > 1$ and $\mathrm{Re} > \mathrm{Re}\mathrm{crit}$), shocks concentrate magnetic energy in large structures with $\ell_\mathrm{p} \sim (\ell_\mathrm{turb} / \ell_\mathrm{shock})^{1/3} \ell_\eta \gg \ell_\eta$, where $\ell_\mathrm{shock}$ is the characteristic shock width, and $\ell_\mathrm{turb}$ is the outer scale of the turbulent field. In this regime, magnetic field-line curvature becomes nearly independent of field strength. These results have implications for galaxy mergers and cosmic ray transport models in the interstellar medium., Comment: 30 pages, 15 figures, dataset available from MNRAS

Network capacity and reliability for free space optical communication (FSOC) is strongly driven by ground station availability, dominated by local cloud cover causing an outage, and how availability relations between stations produce network diversity. We combine remote sensing data and novel methods to provide a generalised framework for assessing and optimising optical ground station networks. This work is guided by an example network of eight Australian and New Zealand optical communication ground stations which would span approximately $60^\circ$ in longitude and $20^\circ$ in latitude. Utilising time-dependent cloud cover data from five satellites, we present a detailed analysis determining the availability and diversity of the network, finding the Australasian region is well-suited for an optical network with a 69% average site availability and low spatial cloud cover correlations. Employing methods from computational neuroscience, we provide a Monte Carlo method for sampling the joint probability distribution of site availabilities for an arbitrarily sized and point-wise correlated network of ground stations. Furthermore, we develop a general heuristic for site selection under availability and correlation optimisations, and combine this with orbital propagation simulations to compare the data capacity between optimised networks and the example network. We show that the example network may be capable of providing tens of terabits per day to a LEO satellite, and up to 99.97% reliability to GEO satellites. We therefore use the Australasian region to demonstrate novel, generalised tools for assessing and optimising FSOC ground station networks, and additionally, the suitability of the region for hosting such a network., Comment: Accepted in Journal of Optical Communications and Networking. 16 pages, 16 figures

The turbulent small-scale dynamo (SSD) is likely to be responsible for the magnetisation of the interstellar medium (ISM) that we observe in the Universe today. The SSD efficiently converts kinetic energy $E_{\rm kin}$ into magnetic energy $E_{\rm mag} $, and is often used to explain how an initially weak magnetic field with $E_{\rm mag} \ll E_{\rm kin}$ is amplified, and then maintained at a level $E_{\rm mag} \lesssim E_{\rm kin}$. Usually, this process is studied by initialising a weak seed magnetic field and letting the turbulence grow it to saturation. However, in this Part I of the Growth or Decay series, using three-dimensional, visco-resistive magnetohydrodynamical turbulence simulations up to magnetic Reynolds numbers of 2000, we show that the same final state in the integral quantities, energy spectra, and characteristic scales of the magnetic field can also be achieved if initially $E_{\rm mag} \sim E_{\rm kin}$ or even if initially $E_{\rm mag} \gg E_{\rm kin}$. This suggests that the final saturated state of the turbulent dynamo is set by the turbulence and the material properties of the plasma, independent of the initial structure or amplitude of the magnetic field. We discuss the implications this has for the maintenance of magnetic fields in turbulent plasmas and future studies exploring the dynamo saturation., Comment: 16 pages. 11 figures. Accepted to MNRAS. Part I focuses on the journey towards saturation. Part II focuses on the decay into saturation

Cosmic rays (CRs) are a dynamically important component of the interstellar medium (ISM) of galaxies. The $\sim$GeV CRs that carry most CR energy and pressure are likely confined by self-generated turbulence, leading them to stream along magnetic field lines at the ion Alfv\'en speed. However, the consequences of self-confinement for CR propagation on galaxy scales remain highly uncertain. In this paper, we use a large ensemble of magnetohydrodynamical turbulence simulations to quantify how the basic parameters describing ISM turbulence -- the sonic Mach number, $\mathcal{M}$ (plasma compressibility), Alfv\'en Mach number, $\mathcal{M}_{A0}$ (strength of the large-scale field with respect to the turbulence), and ionisation fraction by mass, $\chi$ -- affect the transport of streaming CRs. We show that the large-scale transport of CRs whose small-scale motion consists of streaming along field lines is well described as a combination of streaming along the mean field and superdiffusion both along (parallel to) and across (perpendicular to) it; $\mathcal{M}_{A0}$ drives the level of anisotropy between parallel and perpendicular diffusion and $\chi$ modulates the magnitude of the diffusion coefficients, while in our choice of units, $\mathcal{M}$ is unimportant except in the sub-Alfv\'enic ($\mathcal{M}_{A0} \lesssim 0.5$) regime. Our finding that superdiffusion is ubiquitous potentially explains the apparent discrepancy between CR diffusion coefficients inferred from measurements close to individual sources compared to those measured on larger, Galactic scales. Finally, we present empirical fits for the diffusion coefficients as a function of plasma parameters that may be used as sub-grid recipes for global interstellar medium, galaxy or cosmological simulations., Comment: Accepted in MNRAS

The turbulent dynamo is a powerful mechanism that converts turbulent kinetic energy to magnetic energy. A key question regarding the magnetic field amplification by turbulence, is, on what scale, $k_{\rm p}$, do magnetic fields become most concentrated? There has been some disagreement about whether $k_{\rm p}$ is controlled by the viscous scale, $k_\nu$ (where turbulent kinetic energy dissipates), or the resistive scale, $k_\eta$ (where magnetic fields dissipate). Here we use direct numerical simulations of magnetohydrodynamic turbulence to measure characteristic scales in the kinematic phase of the turbulent dynamo. We run $104$-simulations with hydrodynamic Reynolds numbers of $10 \leq {\rm Re} \leq 3600$, and magnetic Reynolds numbers of $270 \leq {\rm Rm} \leq 4000$, to explore the dependence of $k_{\rm p}$ on $k_\nu$ and $k_\eta$. Using physically motivated models for the kinetic and magnetic energy spectra, we measure $k_\nu$, $k_\eta$ and $k_{\rm p}$, making sure that the obtained scales are numerically converged. We determine the overall dissipation scale relations $k_\nu = (0.025^{+0.005}_{-0.006})\, k_{\rm turb}\, {\rm Re}^{3/4}$ and $k_\eta = (0.88^{+0.21}_{-0.23})\, k_\nu\, {\rm Pm}^{1/2}$, where $k_{\rm turb}$ is the turbulence driving wavenumber and ${\rm Pm}={\rm Rm}/{\rm Re}$ is the magnetic Prandtl number. We demonstrate that the principle dependence of $k_{\rm p}$ is on $k_\eta$. For plasmas where ${\rm Re} \gtrsim 100$, we find that $k_{\rm p} = (1.2_{-0.2}^{+0.2})\, k_\eta$, with the proportionality constant related to the power-law `Kazantsev' exponent of the magnetic power spectrum. Throughout this study, we find a dichotomy in the fundamental properties of the dynamo where ${\rm Re} > 100$, compared to ${\rm Re} < 100$. We report a minimum critical hydrodynamic Reynolds number, ${\rm Re}_{\rm crit} = 100$ for bonafide turbulent dynamo action., Comment: 15 pages, 10 figures; accepted for publication in MNRAS, 2022 April 4

The interstellar medium (ISM) of star-forming galaxies is magnetized and turbulent. Cosmic rays (CRs) propagate through it, and those with energies from $\sim\,\rm{GeV} - \rm{TeV}$ are likely subject to the streaming instability, whereby the wave damping processes balances excitation of resonant ionic Alfv\'en waves by the CRs, reaching an equilibrium in which the propagation speed of the CRs is very close to the local ion Alfv\'en velocity. The transport of streaming CRs is therefore sensitive to ionic Alfv\'en velocity fluctuations. In this paper we systematically study these fluctuations using a large ensemble of compressible MHD turbulence simulations. We show that for sub-Alfv\'enic turbulence, as applies for a strongly magnetized ISM, the ionic Alfv\'en velocity probability density function (PDF) is determined solely by the density fluctuations from shocked gas forming parallel to the magnetic field, and we develop analytical models for the ionic Alfv\'en velocity PDF up to second moments. For super-Alfv\'enic turbulence, magnetic and density fluctuations are correlated in complex ways, and these correlations as well as contributions from the magnetic fluctuations sets the ionic Alfv\'en velocity PDF. We discuss the implications of these findings for underlying "macroscopic" diffusion mechanisms in CRs undergoing the streaming instability, including modeling the macroscopic diffusion coefficient for the parallel transport in sub-Alfv\'enic plasmas. We also describe how, for highly-magnetized turbulent gas, the gas density PDF, and hence column density PDF, can be used to access information about ionic Alfv\'en velocity structure from observations of the magnetized ISM., Comment: Invited submission accepted for publication in Frontiers in Astronomy and Space Sciences: Multi-scale Magnetic Field Measurements in the Multi-Phase Interstellar Medium; 46 pages; 12 Figures, 2 tables

Energy equipartition is a powerful theoretical tool for understanding astrophysical plasmas. It is invoked, for example, to measure magnetic fields in the interstellar medium (ISM), as evidence for small-scale turbulent dynamo action, and, in general, to estimate the energy budget of star-forming molecular clouds. In this study we motivate and explore the role of the volume-averaged root-mean-squared (rms) magnetic coupling term between the turbulent, $\delta\mathbf{B}$ and large-scale, $\mathbf{B}_0$ fields, $\left< (\delta\mathbf{B}\cdot\mathbf{B}_0)^{2} \right>^{1/2}_{\mathcal{V}}$. By considering the second moments of the energy balance equations we show that the rms coupling term is in energy equipartition with the volume-averaged turbulent kinetic energy for turbulence with a sub-Alfv\'enic large-scale field. Under the assumption of exact energy equipartition between these terms, we derive relations for the magnetic and coupling term fluctuations, which provide excellent, parameter-free agreement with time-averaged data from 280 numerical simulations of compressible MHD turbulence. Furthermore, we explore the relation between the turbulent, mean-field and total Alfv\'en Mach numbers, and demonstrate that sub-Alfv\'enic turbulence can only be developed through a strong, large-scale magnetic field, which supports an extremely super-Alfv\'enic turbulent magnetic field. This means that the magnetic field fluctuations are significantly subdominant to the velocity fluctuations in the sub-Alfv\'enic large-scale field regime. Throughout our study, we broadly discuss the implications for observations of magnetic fields and understanding the dynamics in the magnetised ISM., Comment: Accepted in MNRAS. 20 pages. 16 figures. 1 table

All stars produce explosive surface events such as flares and coronal mass ejections. These events are driven by the release of energy stored in coronal magnetic fields, generated by the stellar dynamo. However, it remains unclear if the energy deposition in the magnetic fields is driven by direct or alternating currents. Recently, we presented observational measurements of the flare intensity distributions for a sample of $\sim10^5$ stars across the main sequence observed by $\textit{TESS}$, all of which exhibited power-law distributions similar to those observed in the Sun, albeit with varying slopes. Here we investigate the mechanisms required to produce such a distribution of flaring events via direct current energy deposition, in which coronal magnetic fields braid, reconnect, and produce flares. We adopt a topological model for this process which produces a power-law distribution of energetic flaring events. We expand this model to include the Coriolis effect, which we demonstrate produces a shallower distribution of flare energies in stars that rotate more rapidly (corresponding to a weaker decline in occurrence rates toward increasing flare energies). We present tentative evidence for the predicted rotation-power-law index correlation in the observations. We advocate for future observations of stellar flares that would improve our measurements of the power-law exponents, and yield key insights into the underlying dynamo mechanisms that underpin the self-similar flare intensity distributions., Comment: 19 pages, 11 figures, accepted for publication in ApJ

The probability density function (PDF) of the logarithmic density contrast, $s=\ln (\rho/\rho_0)$, with gas density $\rho$ and mean density $\rho_0$, for hydrodynamical supersonic turbulence is well-known to have significant non-Gaussian (intermittent) features that monotonically increase with the turbulent Mach number, $\mathcal{M}$. By studying the mass- and volume-weighted $s$-PDF for an ensemble of 36 sub-to-trans-Alf\'venic mean-field, supersonic, isothermal turbulence simulations with different modes of driving, relevant to molecular gas in the cool interstellar medium, we show that a more intricate picture emerges for the non-Gaussian nature of $s$. Using four independent measures of the non-Gaussian components, we find hydrodynamical-like structure in the highly magnetised plasma for $\mathcal{M} \lesssim 4$. However, for $\mathcal{M} \gtrsim 4$, the non-Gaussian signatures disappear, leaving approximately Gaussian $s$-statistics -- exactly the opposite of hydrodynamical turbulence in the high-$\mathcal{M}$ limit. We also find that the non-Gaussian components of the PDF increase monotonically with more compressive driving modes. To understand the $\mathcal{M} \lesssim 4$ non-Gaussian features we use one-dimensional (1D) pencil beams to explore the dynamics along and across the large-scale magnetic field, $\mathbf{B}_0$. We discuss kinetic, density and magnetic field fluctuations from the pencil beams, and identify physical sources of non-Gaussian components to the PDF as single, strong shocks coupled to fast magnetosonic compressions that form along $\mathbf{B}_0$. We discuss the Gaussianisation of the $\mathcal{M} \gtrsim 4$ $s$-fields through the lens of two phenomenologies: the self-similarity of the $s$-field and homogenisation of the dynamical timescales between the over- and under-dense regions in the compressible gas., Comment: 32 pages, 24 figures (6 in Appendix). Accepted in MNRAS

Studying the driving modes of turbulence is important for characterizing the impact of turbulence in various astrophysical environments. The driving mode of turbulence is parameterized by $b$, which relates the width of the gas density PDF to the turbulent Mach number; $b\approx 1/3$, $1$, and $0.4$ correspond to driving that is solenoidal, compressive, and a natural mixture of the two, respectively. In this work, we use high-resolution (sub-pc) ALMA $^{12}$CO ($J$ = $2-1$), $^{13}$CO ($J$ = $2-1$), and C$^{18}$O ($J$ = $2-1$) observations of filamentary molecular clouds in the star-forming region N159E (the Papillon Nebula) in the Large Magellanic Cloud (LMC) to provide the first measurement of turbulence driving parameter in an extragalactic region. We use a non-local thermodynamic equilibrium (NLTE) analysis of the CO isotopologues to construct a gas density PDF, which we find to be largely log-normal in shape with some intermittent features indicating deviations from lognormality. We find that the width of the log-normal part of the density PDF is comparable to the supersonic turbulent Mach number, resulting in $b \approx 0.9$. This implies that the driving mode of turbulence in N159E is primarily compressive. We speculate that the compressive turbulence could have been powered by gravo-turbulent fragmentation of the molecular gas, or due to compression powered by H I flows that led to the development of the molecular filaments observed by ALMA in the region. Our analysis can be easily applied to study the nature of turbulence driving in resolved star-forming regions in the local as well as the high-redshift Universe., Comment: 14 pages, 7 figures. MNRAS in press