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.

arXiv comment27 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

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