Gradient measurement of synchrotron polarization diagnostic: Application
  to spatially separated emission and Faraday rotation regions
  Considering the spatially separated polarization radiation and Faraday
rotation regions to simulate complex interstellar media, we study synchrotron
polarization gradient techniques' measurement capabilities. We explore how to
trace the direction of projected magnetic field of emitting-source region at
the multi-frequency bands, using the gradient technique compared with the
traditional polarization vector method. Furthermore, we study how Faraday
rotation density in the foreground region, i.e., a product of electron number
density and parallel component of magnetic fields along the line of sight,
affects the measurement of projected magnetic field. Numerical results show
that synchrotron polarization gradient technique could successfully trace
projected magnetic field within emitting-source region independent of radio
frequency. Accordingly, the gradient technique can measure the magnetic field
properties for a complex astrophysical environment.
