Statistical Description of Synchrotron Intensity Fluctuations: Studies of Astrophysical Magnetic Turbulence

Abstract

We provide a theoretical description of synchrotron fluctuations arising from magnetic turbulence. We derive an expression that relates the correlation of synchrotron fluctuations for an arbitrary index of relativistic electrons with the correlations of squared fluctuations of magnetic field component perpendicular to the line of sight. The latter correlations we study assuming that the turbulence is axisymmetric. We obtain general relations valid for an arbitrary model of magnetic turbulence and analyse the relations for particular example of magnetic turbulence that is supported by numerical simulations. We predict that the synchrotron intensity fluctuations are anisotropic with larger correlation present along the direction of magnetic field. This anisotropy is dominated by the quadrupole component with the ratio between quadrupole and monopole parts being sensitive to the compressibility of underlying turbulence. Our work opens avenues for quantitative studies of magnetic turbulence in our galaxy and beyond using synchrotron emission. It also outlines the directions of how synchrotron foreground emission can be separated from cosmological signal, i.e. from CMB or highly redshifted HI emission. For the sake of completeness we also provide the expressions for the synchrotron polarization (Stocks parameters and their combinations) for the model of axisymmetric magnetic turbulence.