Title: Polarization properties of turbulent synchrotron bubbles: an approach based on Chandrasekhar-Kendall functions,
Abstract: Synchrotron emitting bubbles arise when the outflow from a compact
relativistic engine, either a Black Hole or a Neutron Star, impacts on the
environment. The emission properties of synchrotron radiation are widely used
to infer the dynamical properties of these bubbles, and from them the injection
conditions of the engine. Radio polarization offers an important tool to
investigate the level and spectrum of turbulence, the magnetic field
configuration, and possibly the degree of mixing. Here we introduce a formalism
based on Chandrasekhar-Kendall functions that allows us to properly take into
account the geometry of the bubble, going beyond standard analysis based on
periodic cartesian domains. We investigate how different turbulent spectra,
magnetic helicity and particle distribution function, impact on global
properties that are easily accessible to observations, even at low resolution,
and we provide fitting formulae to relate observed quantities to the underlying
magnetic field structure.