Rotation measure structure functions with higher-order stencils as a probe of small-scale magnetic fluctuations and its application to the Small and Large Magellanic Clouds

Abstract

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, $n_{\mathrm{e}}$, 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 $n_{\mathrm{e}}$ with known power spectra, we derive an empirical relationship between the slope of the power spectrum of $b$, $n_{\mathrm{e}}$, and RM. We apply these results to the SMC and LMC and estimate the following properties of small-scale $b$: correlation length ($160\pm 21\mathrm{pc}$ for the SMC and $87\pm 17\mathrm{pc}$ for the LMC), strength ($14\pm 2\mu \mathrm{G}$ for the SMC and $15\pm 3\mu \mathrm{G}$ for the LMC), and slope of the magnetic power spectrum ($-1.3\pm 0.4$ for the SMC and $-1.6\pm 0.1$ for the LMC). We also find that $n_{\mathrm{e}}$ is practically constant over the estimated $b$ correlation scales.

27 pages (including 6 appendices), 29 figures (16 in the main text and 13 in the appendices), and 4 tables (2 in the main text and 2 in the appendices); MNRAS accepted

References in corpus (30)

• A New Electron Density Model for Estimation of Pulsar and FRB Distances
• The Statistics of Supersonic Isothermal Turbulence
• The Density Probability Distribution in Compressible Isothermal Turbulence: Solenoidal versus Compressive Forcing
• On the Star Formation Efficiency of Turbulent Magnetized Clouds
• The Vertical Structure of Warm Ionised Gas in the Milky Way
• Inefficient star formation through turbulence, magnetic fields and feedback
• The outer scale of turbulence in the magneto-ionized Galactic interstellar medium
• Estimating extragalactic Faraday rotation
• Magnetic field amplification in turbulent astrophysical plasmas
• The sonic scale revealed by the world's largest supersonic turbulence simulation
• The density structure and star formation rate of non-isothermal polytropic turbulence
• The effect of magnetic fields on properties of the circumgalactic medium
• A Radio and Optical Polarization Study of the Magnetic Field in the Small Magellanic Cloud
• Magnetic Fields in the Milky Way
• Studying Turbulence from Doppler-broadened Absorption Lines: Statistics of Logarithms of Intensity
• The distribution of polarized radio sources $>$15$\mu$Jy in GOODS-N
• Galactic interstellar turbulence in the southern sky seen through spatial gradients of the polarization vector
• Densities and filling factors of the DIG in the Solar neighbourhood
• Seed magnetic fields in turbulent small-scale dynamos
• Relative distribution of cosmic rays and magnetic fields
• Magnetic fields in the Milky Way from pulsar observations: effect of the correlation between thermal electrons and magnetic fields
• Detection of a Coherent Magnetic Field in the Magellanic Bridge through Faraday Rotation
• The distribution of mean and fluctuating magnetic fields in the multi-phase ISM
• Heightened Faraday Complexity in the inner 1 kpc of the Galactic Centre
• A Radio Polarisation Study of Magnetic Fields in the Small Magellanic Cloud
• A Unified Model for the Fan Region and the North Polar Spur: A bundle of filaments in the Local Galaxy
• Magnetic fields in elliptical galaxies: Using the Laing-Garrington effect in radio galaxies and polarized emission from background radio sources
• The Diffuse Ionized Gas Halo of the Small Magellanic Cloud
• Turbulent magnetic field in the HII region Sh 2-27
• Polarization Gradient Study of Interstellar Medium Turbulence Using The Canadian Galactic Plane Survey

Cited by in corpus (13)

• Electron-Ion Temperature Ratio in Astrophysical Shocks
• The spectrum of magnetized turbulence in the interstellar medium
• Measuring the hot ICM velocity structure function using XMM-Newton observations
• Diagnosis of 3D magnetic field and modes composition in MHD turbulence with Y-parameter
• Batchelor, Saffman, and Kazantsev spectra in galactic small-scale dynamos
• Measuring the ICM velocity structure within the A3266 galaxy cluster
• A new window into the sub-parsec scale magnetic field in the Milky Way? Unveiling small-scale magneto-ionic structures with Faraday complexity
• Interpolation techniques for reconstructing Galactic Faraday rotation
• Probing the Morphology of Polarized Emission Induced by Fluctuation Dynamo using Minkowski Functionals
• Diagnosing Interstellar Magnetic Turbulence with TeV Pulsar Halos
• De-Biasing Structure Function Estimates From Sparse Time Series of the Solar Wind: A Data-Driven Approach
• Non-Gaussian Magnetic Structures in the Small-Scale Turbulent Dynamo
• Probing the magneto-ionic medium of the Milky Way using pulsars