Spectral resolution effects on the information content in solar spectra

Context. When interpreting spectropolarimetric observations of the solar atmosphere, wavelength variations in the emergent intensity and polarization translate into information on the depth stratification of physical parameters such as the temperature, velocity, and magnetic field. Resolving the fine details in the shapes of the spectral lines and their polarization gives us the capability to resolve small-scale depth variations in these physical parameters. With the advent of large-aperture solar telescopes and the development of state-of-the-art instrumentation, the requirements on spectral resolution have become a prominent question. Aims. We aim to quantify how the information content contained in a representative set of polarized spectra of photospheric spectral lines depends on the spectral resolution and spectral sampling of that spectrum. Methods. We used a state-of-the-art numerical simulation of a sunspot and the neighboring quiet Sun photosphere to synthesize polarized spectra of magnetically sensitive neutral iron lines. We then applied various degrees of spectral degradation to the synthetic spectra and analyzed the impact on its dimensionality using principal component analysis and the wavelength power spectrum using wavelet decomposition. Finally, we applied the Stokes Inversion based on Response functions (SIR) code to the degraded synthetic data to assess the effect of spectral resolution on the inferred parameters. Results. We find that the dimensionality of the Stokes spectra and the power contained in the small spectral scales significantly change with the spectral resolution. We find that regions with strong magnetic fields where convection is suppressed have more homogeneous atmospheres and produce less complex Stokes profiles. On the other hand, regions with strong gradients in the physical quantities give rise to more complex Stokes profiles that are more affected by spectral degradation. The degradation also makes the inversion problem more ill-defined, so inversion models with a larger number of free parameters overfit and give wrong estimates. Conclusions. The impact of spectral degradation in the interpretation of solar spectropolarimetric observations depends on multiple factors, including the spectral resolution, noise level, line spread function (LSF) shape, complexity of the solar atmosphere, and degrees of freedom in our inversion methods. To mitigate this impact, incorporating a good estimation of the LSF into the inversion process is recommended. Having a finely sampled spectrum may be more beneficial than achieving a higher signal-to-noise ratio per wavelength bin. Considering the inclusion of different spectral lines that can counter these effects, and calibrating the effective degrees of freedom in modeling strategies, are also important considerations. These strategies are crucial for the accurate interpretation of such observations and have the potential to offer more cost-effective solutions.