On spectropolarimetric measurements with visible lines

TL;DR

This paper evaluates the effectiveness of visible spectral lines in spectropolarimetric measurements of solar magnetic fields, providing qualitative and quantitative evidence supporting their reliability for distinguishing weak and strong fields.

Contribution

It offers a detailed analysis of the sensitivity of visible Stokes profiles using response functions, and derives a formula to estimate uncertainties considering various observational and model parameters.

Findings

Visible lines can reliably distinguish weak and strong magnetic fields under certain conditions.

Response functions effectively quantify the sensitivity of Stokes profiles to physical parameters.

Weak magnetic fields are detectable with visible lines if the polarization signal exceeds noise by a factor of three or four.

Abstract

The ability of new instruments for providing accurate inferences of vector magnetic fields and line-of-sight velocities of the solar plasma depends a great deal on the sensitivity to these physical quantities of the spectral lines chosen to be measured. Recently, doubts have been raised about visible Stokes profiles to provide a clear distinction between weak fields and strong ones filling a small fraction of the observed area. The goal of this paper is to give qualitative and quantitative arguments that help in settling the debate since several instruments that employ visible lines are either operating or planned for the near future. The sensitivity of the Stokes profiles is calculated through the response functions (e.g. Ruiz Cobo & Del Toro Iniesta, 1994). Both theoretical and empirical evidences are gathered in favor of the reliability of visible Stokes profiles. The response functions are used as well for estimating the uncertainties in the physical quantities due to noise in the observations. A useful formula has been derived that takes into account the measurement technique (number of polarization measurements, polarimetric efficiencies, number of wavelength samples), the model assumptions (number of free parameters, the filling factor), and the radiative transfer (response functions). We conclude that a scenario with a weak magnetic field can reasonably be distinguished with visible lines from another with a strong field but a similar Stokes $V$ amplitude, provided that the Milne-Eddington approximation is good enough to describe the solar atmosphere and that the polarization signal is at least three or four times larger than the typical rms noise of $ 10^{-3} I_{\rm c}$ reached in the observations.