Magnetic field distribution in the quiet sun

Modern observations of the solar surface performed with high polarimetric sensitivity and high spatial resolution reveal how magnetic fields are present almost everywhere on the solar photosphere. These fields fill more than 90% of the solar surface causing weak polarization signals to emerge from those regions where old magnetometers could not reveal any magnetic field: the quiet Sun. Nowadays, thanks to remarkable improvements in theory, observations and diagnostic techniques, it is well known that quiet Sun magnetic fields vary between zero and about 2000 G and are continuously moved and shuffled by photospheric plasma motions acting over timescales of few minutes. In this scenario, the weak polarization signals covering the solar photosphere can be interpreted as the result of the linear combination of the polarization emerging from discrete magnetic flux tubes; these flux tubes are smaller than the angular resolution of observations and fill the solar photosphere with a complex topology imposed by the photospheric plasma dynamics. In spite of the recent improvements much work remains to be done to completely understand the solar surface magnetism. In this thesis we investigate the quiet Sun magnetism through the development and integration of dynamical models, synthesis and inversion of lines sensible to magnetic fields via Zeeman effect and MHD simulations. The work done can be organized in four main topics: We simulated the dynamics and the evolution of quiet Sun magnetic elements to study the statistical properties of the field strengths associated with such elements. The dynamics of the magnetic field is simulated by means of a numerical model in which magnetic elements are passively driven by an advection field characterized by spatio-temporal correlations that mimick the granulation and mesogranulation scales observed on the solar surface. The field strength can increase due to an amplification process that occurs where magnetic elements converge. Our model is able to produce kG magnetic fields in a time interval of the order of the granulation timescale. The mean unsigned flux density and the mean magnetic energy density of the synthetic quiet Sun reach values of about 100 G and about 350 G, respectively. The probability density function of the magnetic field strength derived from this simulation shows how B > 700 G fields dominate both the unsigned flux density and magnetic energy density, although the probability density function of the field strength presents a maximum at B = 10 G. We performed the first syntheses of manganese lines in realistic quiet Sun model atmospheres. Plasmas varying in magnetic field strength, magnetic field direction, and velocity, contribute to the synthetic polarization signals. The syntheses show how the manganese lines weaken with increasing field strength. In particular, kG magnetic concentrations produce MnI 5538 circular polarization signals (Stokes V) which can be up to two orders of magnitude smaller than what the Weak Field Approximation predicts. Therefore, the polarization emerging from an atmosphere having weak and strong fields is biased towards the weak fields, and hyperfine structure features characteristic of weak fields show up even when the magnetic flux and energy are dominated by kG fields. Moreover, atmospheres with unresolved velocities produce very asymmetric line profiles, which cannot be reproduced by simple one-component model atmospheres. Inversion techniques accounting for complex magnetic atmospheres must be implemented for a proper diagnosis. We analyzed Stokes I and V signals observed by the HINODE SOT/SP instrument by adopting the MIcro Structured Magnetic Atmosphere hypothesis. The analysis has as a final goal the definition of a probability density function for the statistical description of quiet Sun magnetic fields for a direct comparison with recently published results. Here we present preliminary results obtained from the inversion of about 15000 spectropolarimetric profiles. We analyzed the properties of the MnI 5395 photospheric line in relation to its larger activity, than most other photospheric lines, related to the solar cycle. We performed classical one-dimensional modelling as a starting point to understand the properties of the line and then we used recent three-dimensional MHD simulations for verification and analysis. The MnI 5395 sensitivity to solar activity derives from its hyperfine structure. This overrides the thermal and granular Doppler smearing through which other photospheric lines lose such sensitivity. We take the nearby FeI 5395 line as example of the latter and analyze the formation of both lines indetail to demonstrate granular Doppler brightening.