Studying the local magnetic field and anisotropy of magnetic turbulence by synchrotron polarization derivative

Due to the inevitable accumulation of the observed information in the direction of the line of sight, it is difficult to measure the local magnetic field of MHD turbulence. However, the correct understanding of the local magnetic field is a prerequisite for reconstructing the Galactic 3D magnetic field. We study how to reveal the local magnetic field direction and the eddy anisotropy on the basis of the statistics of synchrotron polarization derivative with respect to the squared wavelength $dP\mathrm{/}d{\lambda }^2$. In the low frequency and strong Faraday rotation regime, we implement numerical simulations in the combination of multiple statistic techniques, such as structure function, quadrupole ratio modulus, spectral correlation function, correlation function anisotropy and spatial gradient techniques. We find that (1) statistic analysis of $dP\mathrm{/}d{\lambda }^2$ indeed reveals the anisotropy of underlying MHD turbulence, the degree of which increases with the increase of the radiation frequency; (2) the synergy of both correlation function anisotropy and gradient calculation of $dP\mathrm{/}d{\lambda }^2$ enables the measurement of the local magnetic field direction.