Refining the Magnetic Field Estimate for the Solar Polar Region

The Astrophysical Journal:  The magnetic fields in the solar polar region are important to our understanding of the internal dynamo process, the global coronal structure, and the origin of the solar wind. The inference of polar fields based on spectropolarimetric observation is highly model-dependent and can suffer from various systematic effects. Here we analyze a raster map of the southern polar region taken by the Hinode Spectro-Polarimeter, utilizing the Stokes Inversion based on Response functions code. The inversions provide height-dependent vector magnetic field maps between optical depths log(tau) = -2 and 0. We examine the impact on the total magnetic flux estimate from adopting (1) 1- vs 2-component atmospheric models via a ``filling factor'' parameter and (2) different initial guess atmospheric models. At log(tau) = -1.5, the polar magnetic flux is estimated to be (1.84+/- 0.03)x 10^{21} Mx and (1.38+/- 0.02) x 10^{21} Mx under the 1- and 2-component atmosphere assumption, respectively. The magnetic flux is approximately constant or increases slightly with height, respectively. We find that the 2-component (1-component) configuration is preferred for 58.3% (32.3\%) of the pixels and that different initial guess models often converge to quite different solutions. Our work highlights the importance of including unresolved magnetic structures or stray light into consideration. Model degeneracy and the convergence to local minima limit the precision of the polar magnetic flux inference (no better than several tens of percent in this case). Trends with respect to height are additionally influenced by inversion configurations and polarization signal criteria. Higher-resolution observations and advanced inversion algorithms may alleviate these limitations.