Gradients of Synchrotron Polarization: Tracing 3D Distribution of Magnetic Fields

We describe a new technique for probing galactic and extragalactic 2D and 3D magnetic field distribution using gradients of polarized synchrotron emission. The fluctuations of magnetic field are elongated along the ambient magnetic field. Therefore, the field variations are maximal perpendicular to the B-field. This allows tracing the B-field with synchrotron polarization gradients. We demonstrate that the Faraday depolarization allows us to map 3D B-field structure. The depolarization ensures that the polarization gradients sample the regions close to the observer with the sampling depth controlled by the frequency of radiation. We also analyze the B-field properties along the line of sight (LOS) by applying the gradient technique to the wavelength derivative of synchrotron polarization. This Synchrotron Derivative Polarization Gradients technique can recover the 3D vectors of the underlying B-fields. The new techniques are different from the Faraday tomography, as they provide a way to map the 3D distribution of B-field components perpendicular to the LOS. In addition, we find that the alignment of gradients of polarization with the synchrotron polarization can be used to separate the contribution of the foreground from the polarization of cosmological origin. We notice that the same alignment is also present for the dust polarization.