Numerical modeling of solar faculae close to the limb

F. Kneer,O. V. Okunev

doi:10.1051/0004-6361:20052879

Abstract

A numerical simulation was performed to interpret high-resolution spectropolarimetric observations of polar faculae on the Sun. A semi-empirical three-dimensional model of facula structures, controlled by several free parameters, was constructed. It consists of two components, the atmosphere within small-scale magnetic flux tubes and the exterior atmosphere. Multi-ray 1.5D radiative transfer calculations were performed along oblique rays passing through a highly inhomogeneous atmosphere of the simulation box. By the comparison of the properties of the calculated Stokes profiles from the synthetic faculae with the observed properties, a set of free parameters of the model (such as: size, number density of flux tubes, internal temperature stratification and magnetic field strength) was deduced, which satisfies the observational constraints. The hypothesis about solar faculae as a conglomerate of small-scale magnetic flux tubes is verified. The model reproduces all observed properties: the continuum contrast and its center-to-limb variation, the Stokes I and V profiles of Fe I and Fe II lines, the apparent magnetic field strengths, and the displacement towards the limb of the continuum intensity against the line-of-sight magnetograms.

Highlights

The polar areas of the Sun take part in the magnetic activity cycle, as do activity regions at low latitudes of the Sun
The latter depends on the merging height, which in turn depends on the number density of magnetic flux tubes (MFTs) on the surface, or number of tubes in the simulation box
We have introduced the filling factor of the model fmod defined as the ratio of the area occupied by the flux tubes at z = 0 km to the total area of the simulation box: fmod πR20NMFT · S box Distribution NMFT in the box fmod

Summary

Introduction

The polar areas of the Sun take part in the magnetic activity cycle, as do activity regions at low latitudes of the Sun. For the successful study of such small-scale magnetic structures close to the solar limb one has to combine high spectral and spatial resolution spectropolarimetric observations with efficient methods of data analysis and interpretation including numerical simulations. Kneer: Modeling of polar faculae on the Sun integration path) are used for adjustment of the guess model This peculiarity of the method makes it difficult to apply it to problems where the atmosphere along the LOS is very irregular and high coverage with grid points is mandatory. Keller et al (2004) have used the MURaM code of the Lindau-Chicago group (Vögler & Schüssler 2003; Vögler et al 2005), which solves numerically the complete set of the time-dependent magneto-hydrodynamic equations together with non-gray radiative transfer They obtained good agreement with the observations of solar faculae by Lites et al (2004).

Basic assumptions

Model of a single magnetic flux tube

Construction of the 3D box and multiple rays

Atmospheric parameters and radiative transfer in a magnetized atmosphere

Internal thermal model

Results of numerical modeling and comparison with observations

Spectropolarimetric profiles from synthetic faculae

Spatial distribution and fine structure

Center-to-limb variation of brightness contrast and of Stokes V amplitudes

Apparent magnetic field strength

Conclusions