OPTICAL TOMOGRAPHY OF A SUNSPOT - I - COMPARISON BETWEEN 2 INVERSION TECHNIQUES

A quantitative comparison between the Milne-Eddington (ME) inversion t echnique implemented by Skumanich & Lites and the SIR (Stokes Inversio n based on Response Functions) proposed by Ruiz Cobo & del Toro Iniest a is presented. Numerical experiments are carried out to explore the c apabilities and limitations of both diagnostic techniques. Such experi ments consist of inversions of Stokes profiles previously synthesized in ''realistic'' solar atmospheric models. The results show that the M E inversion provides accurate, line-of-sight (LOS) averaged values for the input stratification of the vector magnetic field. Its greater sp eed compared to SIR makes it useful for quick analysis of large quanti ties of data (such as those currently provided by modern spectropolari meters) if one is only interested in LOS-averaged quantities. However, the higher order description of the atmosphere used dy SIR (which ack nowledges variation of the thermal, dynamic, and magnetic parameters t hrough the photosphere) allows retrieval of the stratification of all these parameters to good accuracy. This is so even in the presence of discontinuities such as those foreseen in magnetic canopies of sunspot s. The trade-offs between thermodynamic and magnetic parameters observ ed in some ME inversions are reduced considerably in the case of SIR i nversions because of the more realistic treatment of the thermodynamic s in this analysis. Notably, both allow one to extract quantitative in ferences of fairly weak magnetic fields (below 500 G), even when they are applied to Zeeman-sensitive lines in the visible spectrum; i.e., w ell below the commonly accepted limit of 500 G. The thermodynamic para meters resulting from the ME inversion are understood theoretically in terms of the generalized response functions introduced by Ruiz Cobo & del Toro Iniesta and through the concept of height of formation for i nferred values proposed by Sanchez Almeida, Ruiz Cobo, & del Toro Inie sta. The present comparison and verification of the reliability of inv ersion methods is a natural first step toward the ongoing analysis of the three-dimensional magnetic structure of a sunspot. By using SIR (w ith ME results for initialization) on maps of a whole sunspot observed by the Advanced Stokes Polarimeter, we obtain maps at different optic al layers (i.e., an optical tomography) of the temperature, vector mag netic field, and LOS velocity. Such a tomography will appear in subseq uent papers of the present series. To illustrate fits to the observed Stokes profiles, we show here actual inversion results for three point s observed within a sunspot: one within the umbra, another from the ou termost parts of the penumbra, and a third from the magnetic canopy su rrounding the sunspot.