The usefulness of analytic response functions^*

Instituto de Astrofísica de Andalucía, Consejo Superior de Investigaciones Científicas, Apdo. de Correos 3004, 18080 Granada, Spain e-mail: orozco@iaa.es;jti@iaa.es

Received: 7 August 2006
Accepted: 8 October 2006

Abstract

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.