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Magnetic fields are an energetically important component of star formation galaxies, but it is often difficult to measure their properties from observations. One of the complexities stems from the fact that the magnetic fields, especially in spiral galaxies, have a two-scale nature: a large-scale field, coherent over kpc scales, and a small-scale random field, with a scale of |${\lesssim} 100 \, {\rm pc}$|⁠. Moreover, it is known that the strength of small- and large-scale fields is comparable and this makes it even harder to find their imprints in radio polarization observations such as the Faraday rotation measure (RM), which is the integral over the path-length of the product of the thermal electron density and the parallel component of the magnetic field to the line of sight. Here, we propose and demonstrate the use of second-order structure functions of RM computed with multiple higher-order stencils as a powerful analysis to separate the small- and large-scale magnetic field components. In particular, we provide new methods and calibrations to compute the scale and the strength of the large-scale magnetic field in the presence of small-scale magnetic fluctuations. We then apply the method to find the scale of large-scale magnetic fields in the nearby galaxies M51 and NGC 6946, using archival data, and further discuss the need for computing the RM structure functions with higher-order stencils. With multiple modern radio polarization observatories and eventually the Square Kilometre Array, RM observations will significantly improve in quantity and quality, and the higher-order stencil structure function techniques developed here can be used to extract information about multiscale magnetic fields in galaxies. [ABSTRACT FROM AUTHOR]

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]

Magnetic fields and turbulence are important components of the interstellar medium (ISM) of star-forming galaxies. It is challenging to measure the properties of the small-scale ISM magnetic fields (magnetic fields at scales smaller than the turbulence driving scale). Using numerical simulations, we demonstrate how the second-order rotation measure (RM, which depends on thermal electron density, n e, and magnetic field, b) structure function can probe the properties of small-scale b. We then apply our results to observations of the Small and Large Magellanic Clouds (SMC and LMC). First, using Gaussian random b , we show that the characteristic scale, where the RM structure function flattens is approximately equal to the correlation length of b. We also show that computing the RM structure function with a higher-order stencil (more than the commonly-used two-point stencil) is necessary to accurately estimate the slope of the structure function. Then, using Gaussian random b and lognormal n e with known power spectra, we derive an empirical relationship between the slope of the power spectrum of b, n e, and RM. We apply these results to the SMC and LMC and estimate the following properties of small-scale b : correlation length (160  ± 21 pc for the SMC and 87  ±  17 pc for the LMC), strength (14  ± 2  |$\mu {\rm G}$| for the SMC and 15  ± 3  |$\mu {\rm G}$| for the LMC), and slope of the magnetic power spectrum (−1.3  ±  0.4 for the SMC and −1.6  ±  0.1 for the LMC). We also find that n e is practically constant over the estimated b correlation scales. [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]

Magnetic fields are a dynamically important component of the turbulent interstellar medium (ISM) of star-forming galaxies. These magnetic fields are due to a dynamo action, which is a process of converting turbulent kinetic energy to magnetic energy. A dynamo that acts at scales less than the turbulent driving scale is known as the turbulent dynamo. The ISM is a multiphase medium and observations suggest that the properties of magnetic fields differ with the phase. Here, we aim to study how the properties of the turbulent dynamo depend on the phase. We simulate the non-isothermal turbulent dynamo in a two-phase medium (most previous work assumes an isothermal gas). We show that the warm phase (T ≥ 103 K) is transsonic and the cold phase (T < 103 K) is supersonic. We find that the growth rate of magnetic fields in the exponentially growing stage is similar in both phases. We compute the terms responsible for amplification and destruction of vorticity and show that in both phases vorticity is amplified due to turbulent motions, further amplified by the baroclinic term in the warm phase, and destroyed by the term for viscous interactions in the presence of logarithmic density gradients in the cold phase. We find that the final ratio of magnetic to turbulent kinetic energy is lower in the cold phase due to a stronger Lorentz force. We show that the non-isothermal turbulent dynamo is significantly different from its isothermal counterpart and this demonstrates the need for studying the turbulent dynamo in a multiphase medium. [ABSTRACT FROM AUTHOR]

Pulsars can act as an excellent probe of the Milky Way magnetic field. The average strength of the Galactic magnetic field component parallel to the line of sight can be estimated as |$\langle B_\parallel \rangle = 1.232 \, \text{RM}/\text{DM}$|⁠ , where RM and DM are the rotation and dispersion measure of the pulsar. However, this assumes that the thermal electron density and magnetic field of the interstellar medium are uncorrelated. Using numerical simulations and observations, we test the validity of this assumption. Based on magnetohydrodynamical simulations of driven turbulence, we show that the correlation between the thermal electron density and the small-scale magnetic field increases with increasing Mach number of the turbulence. We find that the assumption of uncorrelated thermal electron density and magnetic fields is valid only for subsonic and trans-sonic flows, but for supersonic turbulence, the field strength can be severely overestimated by using |$1.232 \, \text{RM}/\text{DM}$|⁠. We then correlate existing pulsar observations from the Australia Telescope National Facility with regions of enhanced thermal electron density and magnetic fields probed by 12CO data of molecular clouds, magnetic fields from the Zeeman splitting of the 21 cm line, neutral hydrogen column density, and H α observations. Using these observational data, we show that the thermal electron density and magnetic fields are largely uncorrelated over kpc scales. Thus, we conclude that the relation |$\langle B_\parallel \rangle = 1.232 \, \text{RM}/\text{DM}$| provides a good estimate of the magnetic field on Galactic scales, but might break down on sub-kpc scales. [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]