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 drive turbulence and maintain 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 (ℓf) of turbulence in isothermal, incompressible, and subsonic media, we study the relation between different morphological measures and their connection to fractional polarization (pf). We find that Faraday depolarization at low frequencies gives rise to small-scale polarized structures that have higher filamentarity as compared to the intrinsic structures that are comparable to ℓf. Above ∼3 GHz, the number of connected polarized structures per unit area (NCC,peak) is related to the mean pf (〈pf〉) of the emitting region as , provided the scale of the detectable emitting region is larger than ℓf. This implies that NCC,peak represents the number of turbulent cells projected on the plane of the sky and can be directly used to infer ℓf via the relation . An estimate of ℓf 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.