Radiative properties of complex magnetic elements in the solar photosphere

In this thesis I investigate the photometric and geometric properties of bright magnetic features in the lower solar atmosphere. The contribution of these fea- tures to Total Solar Irradiance (TSI here after) variations observed at different temporal scales has been broadly showed during the last years. Nevertheless, measurements and theoretical investigations of their properties, on which recon- structions of TSI variations are based, have produced discrepant results. In order to interpret discrepancies presented in the literature and to improve our understanding of physical properties of magnetic elements, both experimen- tal and theoretical aspects have been investigated. In the first part of the thesis I show results obtained by the analysis of full disk PSPT broad band images from Rome and Hawaii. Geometric properties and the possible connection with photometric properties have been investigated through the measurement of fractal dimension of features observed in chromo- sphere. Results I obtain agree very well with the ones presented in the literature carried out on similar data and with the same fractal dimension estimator. The fractal dimension increases in fact with features area and reaches a plateau at areas larger than about 1000-2000 Mm2. Nevertheless, by the analyses of im- ages of fractals whose dimension is known by the theory, I show that fractal dimension estimation is critically effected by pixelization, technique employed to select magnetic structures on images and resolution. In particular the in- crease of fractal dimension with object size is an effect of pixelization and thus some conclusions previously drawn in the literature should be revisited. Photometric properties are investigated by the analyses of contrast of identi- fied features in two photospheric bands and in the chromosphere. In particular the variation of the contrast with position on the solar disk and with object size is investigated. I show that the contrast in the chromosphere is not depen- dent on disk position and that in the photosphere monotonically increases from the center toward the limb. A comparison with previously published results shows a better agreement with authors that employed an identification meth- ods similar to the ones I employed to select magnetic features on images. The contrast, especially at the limb, is also critically affected by seeing. Comparison of the scaling of average and maximum contrast with object size suggests that the smaller magnetic elements, whose clustering forms the features analyzed, are characterized by different photometric properties. The increase of average contrast with object size, very similar to the increase observed for the fractal dimension, is instead an effect of filling factor. In order to investigate the physical origin of the results and validate some of the conclusions drawn, 2D numerical codes based on the magnetic flux tube model have been developed. Plane parallel gray atmosphere in LTE is supposed and radiative and convective energy transport mechanisms have been taken into account. In particular two classes of models are investigated. In the first one convection is modelled by the Mixing length theory and radiation by the radiative diffusion approximation. In the second one only radiation is taken into account, but radiative diffusion approximation is dropped and radiative equilibrium is imposed by an iterative scheme. The presence of the magnetic field is mimicked by imposing a lower pressure and density in the magnetic region. In order to evaluate the radiation field a numerical code, based on the short characteristic technique, was developed. A detailed description of the code, as well as results obtained by tests aimed to investigate and compare different numerical techniques and spurious effects, are presented. The radiative flux is finally evaluated by a quadrature scheme. At this aim two schemes have been developed and compared. The software developed has allowed to investigate radiation field through the flux tube models studied. I show that the presence of a magnetic structure generates areas of different shapes and contrast around it. These features vary with the position of the structures on the solar disk (the sight angle) and have spatial scales smaller than the typical scale of a flux tube (about 100 km), so resolution better than 0.1 arcsec is required to observe them. The contrast of magnetic features varies also in function of the optical depth, so that for the same model different center to limb variations of the contrast can be observed. This indicates that contrast is strongly dependent on observation wavelength, thus partially explaining the discrepant results obtained in the literature. Investigation of the results also shows that the center to limb variation of the contrast reflects the temperature stratification inside and outside the tube. Measurements carried out at different wavelengths are thus fundamental for the determination of temperature of magnetic structures and for the investigation of their physical properties.