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Stokes profile inversion in Meso-Structured Magnetic Atmospheres
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Modern Solar Facilities – Advanced Solar Science, 297–302 F. Kneer, K. G. Puschmann, A. D. Wittmann (eds.) c Universitätsverlag Göttingen 2007 Stokes profile inversion in Meso-Structured Magnetic Atmospheres T. A. Carroll Astrophysikalisches Institut Potsdam, Germany Email: tcarroll@aip.de Abstract. Based on the Meso-Structured Magnetic Atmosphere (MESMA) approximation (Carroll & Kopf 2007) we present first results of an inversion of spectropolarimetric observations obtained from internetwork regions. To cope with the inherent complexity of the mostly unresolved magnetic field in the solar photosphere the MESMA approach provides a statistical description of the underlying atmosphere in terms of a random Markov field. This statistical model allows us to derive a stochastic transfer equation for polarized light. The stochastic transfer equation explicitly accounts for the spatial correlation – the characteristic length scale – of the underlying magnetic and non-magnetic structures. We use this new diagnostic parameter in an inversion approach to demonstrate that the magnetic flux structures in the solar internetwork possess a finite correlation length which is not compatible with the classical flux tube picture. 1 Introduction The entire solar photosphere exhibits a rich structure of large- and small-scale magnetic features like sunspots, pores faculae or plages. But except for sunspots and pores these magnetic fields cannot be spatially resolved with present telescopes, although these fields clearly manifest themselves in high resolution spectropolarimetric observations. With the improvement of spectropolarimetric sensitivity and spatial resolution over the last years it became clear that these unresolved magnetic fields are much more ubiquitous than previously thought. This raises the question of the significance of these elusive and complex magnetic fields for the solar magnetism in general (Schrijver & Title 2003; Sánchez Almeida 2004) and how these magnetic fields can be appropriately investigated by spectropolarimetric observations. The interpretation of Stokes profiles in the context of the thin flux tube model relies on the basic picture of an embedded cylindrical magnetic structure surrounded by a quasi field-free medium. Based on that assumption a so called 1.5-dimensional radiative transfer is applied where a number of rays piercing through the underlying 2- or 3-dimensional geometry of the model to obtain the spectral ’signature’ of the underlying magnetic structure (Solanki 1993). But if the underlying structures are much more dynamic, disrupted and intermittent, the conventional static flux tube model will allow only a poor representation of the real magnetic field structure. In this sense the flux tube modeling provides a rather macroscopic treatment of the problem – in the 1.5 dimensional sense – since the averaging process for all line-of-sights (LOS) is performed after the actual integration of the transfer equation. 298 T. A. Carroll: MESMA The other extreme, in contrast to the macroscopic view, is the MISMA approximation. The assumption here is that the atmospheric conditions along the line-of-sight are rapidly changing. The fluctuation of the atmospheric parameters occurs on very short scales, such that a micro-structured or micro-turbulent approach is justified. This allows an averaging over all atmospheric parameters at each spatial position before the actual transfer equation is integrated. Despite its appealing simplicity in the way this approach treats the radiative transfer , the idealized assumptions about the underlying atmosphere strongly limit the application of this approach. Structures in the solar photosphere whether magnetic or non-magnetic are in general not in a microturbulent state. Magneto-convective simulations suggest that neither predefined static macro-structures nor pure micro-structures are present in the solar photosphere , the possible structuring seems much more to comprise a broad range of different scales (Schaffenberger et al. 2005; Vögler et al. 2005; Stein & Nordlund 2006). This paper is organized as follows: In Sect. 2 I briefly summarize the basic concept of line formation in stochastic media and present the stochastic polarized transfer equation. In Sect. 3 I give an overlook of the first results of an inversion of spectropolarimetric observations obtained from internetwork regions. Sect. 4 concludes with a summary of the here presented analysis. 2 The stochastic transfer equation for polarized light The approach described here is based on a statistical model of the atmosphere in terms of a random Markov field, the MEso-Structured Magnetic Atmosphere (MESMA) which was introduced by Carroll & Kopf (2007). In this contribution I will just give a brief summary of the basic concept of the MESMA approach, for a more detailed presentation of the statistical model and derivation of the stochastic transfer equation the reader is referred to Carroll & Staude (2003, 2005a) and Carroll & Kopf (2007...