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

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