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Modern Solar Facilities – Advanced Solar Science, 303–306 F. Kneer, K. G. Puschmann, A. D. Wittmann (eds.) c  Universitätsverlag Göttingen 2007 Line ratio method applied to inter-network magnetic fields E. Khomenko1,2,* and M. Collados1 1 Instituto de Astrofı́sica de Canarias, Tenerife, Spain 2 Main Astronomical Observatory, NAS, Kyiv,Ukraine * Email: khomenko@iac.es Abstract. We investigate the validity of the Stokes V amplitude ratio as an indicator of the magnetic field strength in solar inter-network regions with the help of MHD simulations. We show that the Stokes V amplitude ratio of the Fe I 15652-15648 Å lines and Fe I 5247-5250 Å lines show a good correlation with the magnetic field strength even for magnetic fields with a complex internal structure like those in MHD simulations. However, in the latter case, the amplitude ratio sub-estimates the magnetic field strength, always revealing sub-kG values. The Stokes V amplitude ratio of the Fe I 6301-6302 Å lines shows no correlation with the magnetic field strength. The reasons of this behaviour are explained. 1 Introduction It is an open question whether the characteristic field strength in solar inter-network regions lies in the kG or sub-kG range (see, e.g., Lin 1995; Socas-Navarro & Sánchez Almeida 2002; Khomenko et al. 2003; Domı́nguez Cerdeña et al. 2006; López Ariste et al. 2006). Since Stenflo (1973), the Stokes V amplitude ratio of the the Fe I 5257, 5250 Å pair of lines was used as an indicator of the intrinsic field strength of the unresolved network elements. A common assumption used a priory in many observational works about inter-network fields is that the ratio of the Stokes V amplitudes of the Fe I 6301, 6302 and Fe I 15648, 15652 lines is directly related to the field strength contained in the resolution element, i.e. the same as for the Fe I 5257, 5250 Å pair. However, this approach is valid if the pair of spectral lines used for the analysis have exactly the same sensitivity to all atmospheric parameters, except for the magnetic field, and form at the same height. The purpose of this paper is to check the validity of the Stokes V line ratio method for the Fe I 5247-5250 Å, 6301-6302 Å and 15652-15648 Å pairs of lines, as applied to the complex fields obtained via MHD simulations, assuming that these fields provide an adequate representation of the fields in solar inter-network regions. 2 MHD simulations, Stokes spectra synthesis and calibration of the line ratio We have used a snapshot of realistic 3D simulations of solar magneto-convection with a bipolar structure of the magnetic field and = 30 G (see Vögler et al. 2005, for details). The horizontal spatial resolution is 20 km. The Stokes spectra of the Fe I 5247, 5250, 6301, 6302, 15648, and 15652 Å lines formed at solar disc centre (μ = 1) were calculated for 304 E. Khomenko and M. Collados: Line ratio method applied to inter-network Figure 1. Left: Calibration curves for the line ratio. Thin lines: Vmic = 0 and Vmac = 0 (applied to the profiles with original resolution); Thick lines: Vmic = 0.3 km s−1 , Vmac = 0.7 km s−1 (applied to the profiles with reduced resolution). Solid lines: Fe I 6301, 6302; dashed lines: Fe I 5247, 5250; dotted lines: Fe I 15648, 15652 lines. Right: The map of the longitudinal magnetic field component at logτ5 = −1 in the 30 G flux snapshot from the simulations of Vögler et al. (2005). Figure 2. Magnetic field strength obtained from the line ratio of the Fe I 6301 and 6302 Å lines (left), Fe I 5247 and 5250 Å lines (middle) and Fe I 15652 and 15648 Å lines (left). Top panels: Spatial resolution of 20 km. Bottom panels: Spatial resolution of 0.6–0.7 arcsec. Only profiles with amplitudes above a threshold of 5 × 10−3 in units of Ic were used. every vertical column of the selected snapshot. In order to make realistic the comparison of the synthetic spectra with observations, we performed a convolution of the two-dimensional snapshot with an adequate point-spread function decreasing the spatial resolution to about 0.6–0.7 arcsec (Khomenko et al. 2005). The line ratio is defined as the amplitude of the blue lobe of Stokes V of the line with the smaller Landé factor divided by the amplitude of the line with the larger one. The calibration curves for the...

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