The usefulness of analytic response functions

Aims. We introduce analytical response functions and their main properties as an important diagnostic tool that help understand Stokes profile formation physics and the meaning of well-known behaviors of standard inversion codes of the radiative transfer equation often used to measure solar magnetic fields. Methods. A Milne-Eddington model atmosphere is used as an example where response functions are analytical. A sample spectral line has been chosen to show the main qualitative properties. Results. We show that analytic response functions readily provide explanations for various well-known behaviors of spectral lines, such as the sensitivity of visible lines to weak magnetic fields or the trade-offs often detected in inversion codes between the Milne-Eddington thermodynamic parameters. We also show that response functions are helpful in selecting sample wavelengths optimized for specific parameter diagnostics.