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Astron. Astrophys. 333, 721-731 (1998)

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1. Introduction

A number of spectropolarimetric diagnostics have been developed specifically to study the structure and dynamics of small magnetic flux tubes that are observed in the photospheric layers of the solar atmosphere (see Solanki 1993 for a detailed review). Most of these diagnostics have been developed and tested for vertically incident lines of sight only, corresponding to observations at the centre of the solar disc. The present paper is intended to study the utility of some of these diagnostics for observations outside disc centre.

One reason why most Stokes diagnostics have been tested only under conditions pertaining to the centre of the solar disc is that away from disc centre the geometry of the magnetic feature plays a significant role. At the centre of the solar disc (i.e. at [FORMULA], where [FORMULA] is the heliocentric angle), the geometry of a vertical flux tube, i.e. its finite width, cross-sectional shape and area as a function of height, usually does not affect observations (see, e.g., Steiner & Pizzo 1989; Solanki 1989; Keller et al. 1990). Exceptions are any Stokes V asymmetry produced by flows outside the flux tubes (Grossmann-Doerth et al. 1988; Solanki 1989), strongly split lines in the infrared (Zayer et al. 1989; Solanki et al. 1992; Bruls & Solanki 1994) and investigations aiming at the study of magnetic canopies or the upper photosphere / lower chromosphere in general (Solanki et al. 1991; Faurobert-Scholl 1992, 1994; Briand & Solanki 1995).

The reason for the unimportance of the flux-tube geometry at [FORMULA] is the alignment of the flux tube axis with the line of sight. At [FORMULA] the dominant fraction of the polarized radiation comes from rays that stay completely within the flux tube in the visible layers, while only a minor portion pierces the flux tube boundary (Solanki 1989).

The situation changes completely when moving away from [FORMULA]. Every ray then passes through both strong flux-tube magnetic field and intermediate field-free plasma, so that the size and shape of the flux tube cannot be ignored any longer. Of the few investigations that take the geometry into account when calculating spectral lines produced by flux tubes viewed at an angle, most have restricted the rays to the central plane, i.e. the plane formed by the flux tube axis and a sightline ray passing through that axis (e.g. Walton 1987; Zayer et al 1989; Grossmann-Doerth et al. 1989; Steiner et al. 1996, Ploner & Solanki 1997). This plane divides a cylindrical flux tube into two equal halves, as seen by the observer. So far only Bünte et al. (1993) and Audic (1991) have considered Stokes transfer along rays passing through the full, axially symmetric flux tube, including regions outside the central plane. 1 These two investigations differ in their aims. Bünte et al. (1993) were specifically interested in the centre-to-limb variation (CLV) of the Stokes V asymmetry, while Audic (1991) considered idealized spectral lines resulting from a single model flux tube for a simulated high resolution observation.

The present work is complementary to both of these. We investigate various diagnostics of solar magnetic field strength and inclination, temperature, magnetic filling factor and flux-tube diameter. We lay particular emphasis on the dependence of these diagnostics on the flux-tube diameter. We restrict ourselves to the currently typical situation of observations that cannot resolve the flux tubes.

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© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998