Observing the polar magnetic fields from the Earth viewpoint: the limitations of common modeling assumptions

The magnetic nature of the solar poles has profound implications for the solar cycle, space weather, and space climate. Virtually every measurement of the magnetic field in the polar regions has been carried out from the ecliptic plane, which subjects observations to severe foreshortening effects. Additionally, the typical spatial resolution of space-based solar observations is not high enough to fully resolve the weak-to-moderate magnetic structures predicted by numerical simulations of the Sun’s photosphere.A common modeling technique used to account for the existence of unresolved magnetic structures when interpreting solar spectropolarimetric observations is the introduction of a so-called “magnetic filling factor”. This model assumes that the magnetic field only occupies a fraction of the area of the resolution element, and thus allows for an unmagnetized contribution to the emergent Stokes spectra.We test the effectiveness of this modeling technique on synthetic photospheric spectra emerging from a realistic radiative magnetohydrodynamic simulation emulating real polar observations. The data are interpreted using a Milne-Eddington inversion model with a variable magnetic filling factor, and the retrieved magnetic field is then compared to the ground truth of the simulation. We find that the strength of the field is typically overestimated and its orientation is moderately skewed with respect to the real distribution, rendering the calculation of the polar magnetic flux fraught with systematic biases.Our results show that a simple Milne-Eddington inversion with a variable filling factor is not an adequate modeling technique for characterizing the solar magnetic fields that exist at much smaller spatial scales than our ability to resolve them.