STATISTICAL DESCRIPTION OF SYNCHROTRON INTENSITY FLUCTUATIONS: STUDIES OF ASTROPHYSICAL MAGNETIC TURBULENCE

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 to the correlations arising from a particular gamma = 2 index that provides synchrotron emissivity proportional to the squared intensity of perpendicular to the line-of-sight component of magnetic field. We provide a detailed study of the statistics in the latter case assuming that the underlying magnetic turbulence is axisymmetric. We obtain general relations valid for an arbitrary model of magnetic axisymmetric turbulence and analyze the relations for the 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 cosmic microwave background or highly redshifted H I emission. We also provide the expressions for the synchrotron polarization (Stokes parameters and their combinations) for the model of axisymmetric magnetic turbulence.