On the degeneracy of solutions from stellar spectropolarimetric data

Abstract In this work we investigate the inversion accuracy of stellar magnetic fields through the analysis of spectropolarimetric data. We performed several noise-free tests to untangle the impact among the atmospheric and magnetic parameters in the data analysis. Using a single spectral line, we found that under ideal scenario, without noise, the magnetic parameters can be recovered with very high accuracy, while some of the atmospheric ones show a considerable incertitude. If multi-line profiles are considered instead, then the accuracy of the recovered atmospheric parameters increases significantly. Nonetheless, it is quite common that for the inversion of stellar spectropolarimetric data, the atmospheric parameters and the stellar inclination angle of the star are fixed; we show that this procedure could induce very high errors in the inference of the magnetic properties, specially in what concerns to fix the inclination angle. We show that even small deviations from the true inclination angles could have as consequence that the recovery of the magnetic properties of the star are no longer reliable. This is because we demonstrate that given a set of Stokes profiles observed along the rotational phase, they can be satisfactorily fitted regardless of the assumed stellar inclination angle, thereby revealing a degeneracy in the solution. Although this work validates the solution generation solely for a de-centered dipolar geometry, a comparable degeneracy is anticipated when modeling the magnetic field with higher-order spherical harmonics–an effect that remains to be formally characterized.