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Magnetic fields and turbulence are important components of the interstellarmedium (ISM) of star-forming galaxies. It is challenging to measure theproperties of the small-scale ISM magnetic fields (magnetic fields at scalessmaller than the turbulence driving scale). Using numerical simulations, wedemonstrate how the second-order rotation measure (RM, which depends on thermalelectron density, $n_{\rm e}$, and magnetic field, $b$) structure function canprobe the properties of small-scale $b$. We then apply our results toobservations of the Small and Large Magellanic Clouds (SMC and LMC). First,using Gaussian random $b$, we show that the characteristic scale where the RMstructure function flattens is approximately equal to the correlation length of$b$. We also show that computing the RM structure function with a higher-orderstencil (more than the commonly-used two-point stencil) is necessary toaccurately estimate the slope of the structure function. Then, using Gaussianrandom $b$ and lognormal $n_{\rm e}$ with known power spectra, we derive anempirical relationship between the slope of the power spectrum of $b$, $n_{\rme}$, and RM. We apply these results to the SMC and LMC and estimate thefollowing properties of small-scale $b$: correlation length ($160~\pm 21~{\rmpc}$ for the SMC and $87~\pm~17~{\rm pc}$ for the LMC), strength ($14~\pm2~\mu{\rm G}$ for the SMC and $15~\pm 3~\mu{\rm G}$ for the LMC), and slope ofthe magnetic power spectrum ($-1.3~\pm~0.4$ for the SMC and $-1.6~\pm~0.1$ forthe LMC). We also find that $n_{\rm e}$ is practically constant over theestimated $b$ correlation scales.

monthly notices of the royal astronomical society

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