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Sensitivity of spectral lines to temperature, velocity, and magnetic field

Abstract
We present an analytical and numerical study of the sensitivity of weak solar photospheric lines to temperature, velocity, and magnetic fields. Our investigation is based on the concept of response functions (Landi degl'Innocenti & Landi degl'Innocenti 1977; Ruiz Cobo & del Toro Iniesta 1994). Lines commonly used in solar spectropolarimetry, like  630.25 nm in the visible and 1564.85 nm in the infrared, are examined in detail as emerging from reference quiet Sun and sunspot models. We develop a simple phenomenological model capable of describing the response of any given line to these atmospheric parameters. We find that: (a) the sensitivity of the lines to velocity and magnetic fields increases with the sharpness of the intensity and circular polarization profiles; (b) the sensitivity to temperature is determined mainly by the variation of the source function with temperature, which is smaller at longer wavelengths; and (c) lines quoted to be insensitive to temperature, like 1564.85 nm and 557.61 nm, exhibit larger changes in equivalent width than lines presumed to have higher sensitivities to T, such as 630.25 nm. The relations provided by our model are universal and can be used to decide which line is better suited to measuring a given atmospheric parameter. The results of this study are of practical interest for the design of new instruments and for better exploitation of existing ones.