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The turbulent small-scale dynamo (SSD) is likely to be responsible for the magnetization of the interstellar medium (ISM) that we observe in the Universe today. The SSD efficiently converts kinetic energy E kin into magnetic energy E mag and is often used to explain how an initially weak magnetic field with E mag ≪ E kin is amplified, and then maintained at a level E mag ≲ E kin. Usually, this process is studied by initializing 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 mag ∼ E kin or even if initially E mag ≫ E 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. [ABSTRACT FROM AUTHOR]

Cosmic rays (CRs) are a dynamically important component of the interstellar medium (ISM) of galaxies. The ∼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 Alfvén 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), Alfvén Mach number, |$\mathcal {M}_{\text{A0}}$| (strength of the large-scale field with respect to the turbulence), and ionization fraction by mass, χ – 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; |$\mathcal {M}_{\text{A0}}$| drives the level of anisotropy between parallel and perpendicular diffusion and χ modulates the magnitude of the diffusion coefficients, while in our choice of units, |$\mathcal {M}$| is unimportant except in the sub-Alfvénic (⁠|$\mathcal {M}_{\text{A0}}\lesssim 0.5$|⁠) 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 subgrid recipes for global ISM, galaxy, or cosmological simulations. [ABSTRACT FROM AUTHOR]

The interstellar medium (ISM) of star-forming galaxies is magnetized and turbulent. Cosmic rays (CRs) propagate through it, and those with energies from ~ GeV - TeV are likely subject to the streaming instability, whereby the wave damping processes balances excitation of resonant ionic Alfvén waves by the CRs, reaching an equilibrium in which the propagation speed of the CRs is very close to the local ion Alfvén velocity. The transport of streaming CRs is therefore sensitive to ionic Alfvén velocity fluctuations. In this paper we systematically study these fluctuations using a large ensemble of compressible MHD turbulence simulations. We show that for sub-Alfvénic turbulence, as applies for a strongly magnetized ISM, the ionic Alfvén 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 Alfvén velocity PDF up to second moments. For super-Alfvénic turbulence, magnetic and density fluctuations are correlated in complex ways, and these correlations as well as contributions from the magnetic fluctuations sets the ionic Alfvén 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-Alfvénic 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 Alfvén velocity structure from observations of the magnetized ISM. [ABSTRACT FROM AUTHOR]

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, |$\delta {\boldsymbol{B}}$| , and large-scale, |${\boldsymbol{B}}_0$|⁠ , fields, |${\left\langle (\delta \mathrm{{\boldsymbol {\mathit {B}}}}\cdot {\mathrm{{\boldsymbol {\mathit {B}}}}_0})^{2} \right\rangle ^{1/2}_{\mathcal {V}}}$|⁠. 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-Alfvénic 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 magnetohydrodynamic (MHD) turbulence. Furthermore, we explore the relation between the turbulent mean field and total Alfvén Mach numbers, and demonstrate that sub-Alfvénic turbulence can only be developed through a strong, large-scale magnetic field, which supports an extremely super-Alfvénic turbulent magnetic field. This means that the magnetic field fluctuations are significantly subdominant to the velocity fluctuations in the sub-Alfvénic large-scale field regime. Throughout our study, we broadly discuss the implications for observations of magnetic fields and understanding the dynamics in the magnetized ISM. [ABSTRACT FROM AUTHOR]

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 p, do magnetic fields become most concentrated? There has been some disagreement about whether k p is controlled by the viscous scale, k ν (where turbulent kinetic energy dissipates), or the resistive scale, k η (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 ≤ Re ≤ 3600, and magnetic Reynolds numbers of 270 ≤ Rm ≤ 4000, to explore the dependence of k p on k ν and k η. Using physically motivated models for the kinetic and magnetic energy spectra, we measure k ν, k η, and k p, making sure that the obtained scales are numerically converged. We determine the overall dissipation scale relations |$k_\nu = (0.025^{+0.005}_{-0.006})\, k_\text{turb}\, \mbox{Re}^{3/4}$| and |$k_\eta = (0.88^{+0.21}_{-0.23})\, k_\nu \, \mbox{Pm}^{1/2}$|⁠ , where k turb is the turbulence driving wavenumber and Pm = Rm/Re is the magnetic Prandtl number. We demonstrate that the principle dependence of k p is on k η. For plasmas, where Re ≳ 100, we find that |$k_p= (1.2_{-0.2}^{+0.2})\, k_\eta$|⁠ , 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 Re > 100, compared to Re < 100. We report a minimum critical hydrodynamic Reynolds number, Recrit = 100 for bonafide turbulent dynamo action. [ABSTRACT FROM AUTHOR]

The rich structure that we observe in molecular clouds is due to the interplay between strong magnetic fields and supersonic (turbulent) velocity fluctuations. The velocity fluctuations interact with the magnetic field, causing it too to fluctuate. Using numerical simulations, we explore the nature of such magnetic field fluctuations, |$\delta \mathrm{{\boldsymbol {\mathit {B}}}}$|⁠ , over a wide range of turbulent Mach numbers, |$\operatorname{\mathcal {M}}= 2\!-\!20$| (i.e. from weak to strong compressibility), and Alfvén Mach numbers, |$\operatorname{\mathcal {M}_{\text{A0}}}= 0.1\!-\!100$| (i.e. from strong to weak magnetic mean fields, B 0). We derive a compressible quasi-static fluctuation model from the magnetohydrodynamical (MHD) equations and show that velocity gradients parallel to the mean magnetic field give rise to compressible modes in sub-Alfvénic flows, which prevents the flow from becoming two dimensional, as is the case in incompressible MHD turbulence. We then generalize an analytical model for the magnitude of the magnetic fluctuations to include |$\operatorname{\mathcal {M}}$|⁠ , and find |$|\delta \mathrm{{\boldsymbol {\mathit {B}}}}| = \delta B = c_{\rm s}\sqrt{\pi \rho _0}\operatorname{\mathcal {M}}\operatorname{\mathcal {M}_{\text{A0}}}$|⁠ , where c s is the sound speed and ρ 0 is the mean density of gas. This new relation fits well in the strong B -field regime. We go on to study the anisotropy between the perpendicular (B ⊥) and parallel (B ∥) fluctuations and the mean-normalized fluctuations, which we find follow universal scaling relations, invariant of |$\operatorname{\mathcal {M}}$|⁠. We provide a detailed analysis of the morphology for the δB ⊥ and δB ∥ probability density functions and find that eddies aligned with B 0 cause parallel fluctuations that reduce B ∥ in the most anisotropic simulations. We discuss broadly the implications of our fluctuation models for magnetized gases in the interstellar medium. [ABSTRACT FROM AUTHOR]

Stars form in highly magnetized, supersonic turbulent molecular clouds. Many of the tools and models that we use to carry out star formation studies rely upon the assumption of cloud isotropy. However, structures like high-density filaments in the presence of magnetic fields and magnetosonic striations introduce anisotropies into the cloud. In this study, we use the two-dimensional power spectrum to perform a systematic analysis of the anisotropies in the column density for a range of Alfvén Mach numbers (⁠|$\operatorname{\mathcal {M}_{\text{A}}}=0.1{\!-\!10}$|⁠) and turbulent Mach numbers (⁠|$\operatorname{\mathcal {M}}=2{\!-\!20}$|⁠), with 20 high-resolution, three-dimensional turbulent magnetohydrodynamic simulations. We find that for cases with a strong magnetic guide field, corresponding to |$\operatorname{\mathcal {M}_{\text{A}}}\lt 1$|⁠ , and |$\operatorname{\mathcal {M}}\lesssim 4$|⁠ , the anisotropy in the column density is dominated by thin striations aligned with the magnetic field, while for |$\operatorname{\mathcal {M}}\gtrsim 4$| the anisotropy is significantly changed by high-density filaments that form perpendicular to the magnetic guide field. Indeed, the strength of the magnetic field controls the degree of anisotropy and whether or not any anisotropy is present, but it is the turbulent motions controlled by |$\operatorname{\mathcal {M}}$| that determine which kind of anisotropy dominates the morphology of a cloud. [ABSTRACT FROM AUTHOR]

This document is a correction to a paper titled "Fundamental scales in the kinematic phase of the turbulent dynamo" published in the Monthly Notices of the Royal Astronomical Society. The correction addresses a typo in section 2.1 of the paper, specifically in the description of the traceless rate of strain tensor. The correct tensor is provided, and it is stated that the error only affected the reporting in the paper, not the results or conclusions of the study. [Extracted from the article]