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

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4. Conclusions

We have tested a number of diagnostics of solar magnetic elements off disc centre. To this end we have calculated the centre-to-limb variation of Stokes profiles of three spectral lines in 2-D magnetohydrostatic models of flux tubes. Of the diagnostics considered here only the ratio of the amplitudes of Stokes V to the root mean square of Q and U, i.e., [FORMULA], continues to give reliable results near the limb (in this case the inclination angle of the field). The rest of the diagnostics based on visible lines: the Stokes V amplitude, the centre-of-gravity technique and the Stokes V magnetic line ratio break down to a greater or lesser degree.

Probably the most important reason for this breakdown is that for near-limb observations, lines of sight pass through a sizeable amount of field free (or weak field) plasma in which absorption in the core of sufficiently strong lines (e.g. 5250.2 Å) may significantly influence their Stokes profiles. It affects profile shapes, Stokes amplitudes, line ratios, etc. Its influence on the profiles calculated here is particularly large, since we have used a relatively cool atmospheric model for the field-free atmosphere between flux tubes, in which the visible lines are significantly saturated.

We find that simple, plane-parallel models are quite adequate to determine the inclination angles of small magnetic flux tubes. Consequently, the analyses of Solanki et al. (1987), Sánchez Almeida & Martínez Pillet (1994), Bernasconi et al. (1995), Lites et al. (1993) and Bernasconi (1997) cannot be criticized in this respect. Caution is indicated if the magnetic field configuration has a sheet-like structure or if sunspot magnetic canopies are also present in the spatial resolution element (Solanki et al. 1996a).

The Stokes V amplitude decreases more rapidly for a flux tube with a finite diameter than for a plane-parallel model. For the atmospheres considered here, however, the 2-D models often lie closer to a simple [FORMULA] scaling than the 1-D calculations. In 2-D models (again, for the atmospheric models used here) the magnetic line ratio (MLR) can attain values exceeding unity.

The CLV of Stokes V amplitude, area and [FORMULA] centre-of-gravity wavelengths provides an indication of the CLV of the magnetograph signal expected for vertical flux tubes. Our calculations suggest that at smaller µ the magnetic flux is underestimated relative to [FORMULA]. The centre-of-gravity method provides a somewhat better estimate than parameters like the Stokes V amplitude or the V value at a fixed wavelength.

There is another important point regarding the MLR. Since the value of the MLR depends sensitively on the angle between the flux-tube axis and the line of sight, an inclined thin flux tube near the centre of the solar disc should also give MLR values near unity (or possibly exceeding unity) even if it consists of a kG field. Such a line ratio would, using a simpler model, be suggestive of an intrinsically weak field. Observations at 15648 Å are, however, rather insensitive to this effect and should give unambiguous results. 3

Finally, the current investigation reveals that the superiority of the Fe I 15648 Å line over Fe I 5250.2 Å as a probe of the magnetic field also extends to observations off solar disc centre. This underlines once more the need for a full-disc magnetometer operating on a daily basis in the Fe I 15648 Å line.

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© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998