We employ an analytical model that incorporates both wavelength-dependent and wavelength-independent depolarization to describe radio polarimetric observations of polarization at $lambda lambda lambda , 3.5, 6.2, 20.5$ cm in M51 (NGC 5194). The aim i
s to constrain both the regular and turbulent magnetic field strengths in the disk and halo, modeled as a two- or three-layer magneto-ionic medium, via differential Faraday rotation and internal Faraday dispersion, along with wavelength-independent depolarization arising from turbulent magnetic fields. A reduced chi-squared analysis is used for the statistical comparison of predicted to observed polarization maps to determine the best-fit magnetic field configuration at each of four radial rings spanning $2.4 - 7.2$ kpc in $1.2$ kpc increments. We find that a two-layer modeling approach provides a better fit to the observations than a three-layer model, where the near and far sides of the halo are taken to be identical, although the resulting best-fit magnetic field strengths are comparable. This implies that all of the signal from the far halo is depolarized at these wavelengths. We find a total magnetic field in the disk of approximately $18~mu$G and a total magnetic field strength in the halo of $sim 4-6~mu$G. Both turbulent and regular magnetic field strengths in the disk exceed those in the halo by a factor of a few. About half of the turbulent magnetic field in the disk is anisotropic, but in the halo all turbulence is only isotropic.
Depolarization of diffuse radio synchrotron emission is classified in terms of wavelength-independent and wavelength-dependent depolarization in the context of regular magnetic fields and of both isotropic and anisotropic turbulent magnetic fields. P
revious analytical formulas for depolarization due to differential Faraday rotation are extended to include internal Faraday dispersion concomitantly, for a multilayer synchrotron emitting and Faraday rotating magneto-ionic medium. In particular, depolarization equations for a two- and three-layer system (disk-halo, halo-disk-halo) are explicitly derived. To both serve as a `users guide to the theoretical machinery and as an approach for disentangling line-of-sight depolarization contributions in face-on galaxies, the analytical framework is applied to data from a small region in the face-on grand-design spiral galaxy M51. The effectiveness of the multiwavelength observations in constraining the pool of physical depolarization scenarios is illustrated for a two- and three-layer model along with a Faraday screen system for an observationally motivated magnetic field configuration.
