## 2. Hydromagnetic model and line transfer## 2.1. Magnetohydrostatic modelWe describe the magnetic structure of the network or an active region plage by a periodic array of rotationally symmetric, vertical flux tubes in magnetohydrostatic (MHS) equilibrium. They are embedded in a static field-free gas. The magnetic structure is obtained as a numerical solution of the MHS equations for prescribed internal and external stratification of the gas pressure. The procedure is described in detail by Steiner et al. (1986). The radius of the flux tube at (i.e. unit continuum optical depth at 5000 Å in the embedding atmosphere), the filling factor (i.e. the area occupied by the flux-tube magnetic field at divided by the total area) and the pressure stratification may be prescribed freely. The vertical component of the magnetic field is kept constant across the flux tube radius at the bottom of the computational box, which then is still true to within a few percent at . We have determined the value of the internal gas pressure at , by prescribing , the field strength on the flux tube axis at that level. Here we keep fixed at the typically observed value of 1600 G (e.g., Rüedi et al. 1992). The internal gas pressure stratification is given by the temperature of the plage flux-tube model PLA of Solanki (1986) and the condition of hydrostatic equilibrium, while the external atmosphere is described by HSCOOL, which is similar to the HSRA (Gingerich et al. 1971), except that it is cooler by approximately 250 K at all heights. This choice of demonstrates the influence of the non-magnetic atmosphere between the flux tubes on the Stokes profiles particularly clearly. The flux-tube models calculated and analyzed during the present investigation are listed in Table 1. For comparison we often use a 1-D plane-parallel atmosphere with data from PLA and with a homogeneous, vertical magnetic field equal to the values along the flux-tube axis of the other models. It turns out that model C gives results very similar to model B for almost all parameters, except the magnetic line ratio (Sect. 3.5) and is not discussed separately except in that section.
## 2.2. Radiative transfer along multiple raysThe procedure employed to diagnose the hydromagnetic models
described in Sect. 2.1 is basically the same as that described by
Bünte et al. (1993). To summarize, we first determine the
atmospheric quantities required for the radiative transfer of Zeeman
split lines along a set of parallel rays inclined to the vertical by a
prescribed angle . The rays pass through a
periodic two-dimensional array of identical model flux tubes and are
distributed such that the whole set samples a full period of the
flux-tube array at a given height. This is appropriate for simulating
low spatial resolution observations. Fig. 1 shows outlines of two
arrays of flux tubes of different and the bundle
of rays passing through them in the central plane at two different
We use rays in all of the following
calculations. We also consider Stokes We use an adaptive step size grid along each ray. It ensures that
the number of grid points along any ray section that pierces a flux
tube is larger than some minimum value (recall that the Stokes
parameters Once the atmosphere has been computed along each ray, the Stokes parameters are calculated using the radiative transfer code described by Solanki (1987), which, for the solution of the Unno-Rachkovsky equations, now incorporates the Diagonal Element Lambda Operator (DELO) routines of Rees et al. (1989). We have calculated three spectral lines for each model, Fe I 5250.2 Å, Fe I 5247.1 Å and Fe I 15648 Å, all of which have in the past been extensively used to study solar magnetism. For the two visible lines we use the same atomic data as Solanki et al. (1987), while for the infrared line we follow Solanki et al. (1992). © European Southern Observatory (ESO) 1998 Online publication: April 20, 1998 |