Probing the morphology of polarized emission induced by fluctuation dynamo using Minkowski functionals

The morphology and the characteristic scale of polarized structures provide crucial insights into the mechanisms that drives turbulence and maintains magnetic fields in magneto-ionic plasma. We aim to establish the efficacy of Minkowski functionals as quantitative statistical probes of filamentary morphology of polarized synchrotron emission resulting from fluctuation dynamo action. Using synthetic observations generated from magnetohydrodynamic simulations of fluctuation dynamos with varying driving scales ($\ell_{\rm f}$) of turbulence in isothermal, incompressible, and subsonic media, we study the relation between different morphological measures, and their connection to fractional polarization ($p_{\rm f}$). We find that Faraday depolarization at low frequencies give rise to small-scale polarized structures that have higher filamentarity as compared to the intrinsic structures that are comparable to $\ell_{\rm f}$. Above $\sim3\,{\rm GHz}$, the number of connected polarized structures per unit area ($N_{\rm CC, peak}$) is related to the mean $p_{\rm f}$ ($\langle p_{\rm f} \rangle$) of the emitting region as $\langle p_{\rm f} \rangle \propto N_{\rm CC, peak}^{-1/4}$, provided the scale of the detectable emitting region is larger than $\ell_{\rm f}$. This implies that $N_{\rm CC,peak}$ represents the number of turbulent cells projected on the plane of the sky and can be directly used to infer $\ell_{\rm f}$ via the relation $\ell_{\rm f} \propto N_{\rm CC,peak}^{-1/2}$. An estimate on $\ell_{\rm f}$ thus directly allows for pinning down the turbulence driving mechanism in astrophysical systems. While the simulated conditions are mostly prevalent in the intracluster medium of galaxy clusters, the qualitative morphological features are also applicable in the context of interstellar medium in galaxies.