Magnetic field distribution in the quiet Sun: a reduced model approach

Context. The quiet Sun presents magnetized plasma whose field strengths vary from zero to about 2 kG. The probability density function of the magnetic field strength B efficaciously describes the statistical properties of the quiet Sun magnetic field. Aims. We simulate the dynamics and the evolution of quiet Sun magnetic elements to produce a probability density function of the field strengths associated with such elements. Methods. The dynamics of the magnetic field are simulated through a numerical model in which magnetic elements are passively driven by an advection field presenting spatio-temporal correlations which mimicks the granulation and the mesogranulation scales observed on the solar surface. The field strength can increase due to an amplification process which takes place where the magnetic elements converge. Starting from a δ-like probability density function centered on B = 30 G, we obtain magnetic field strengths up to 2 kG (in absolute value). To derive the statistical properties of the magnetic elements several simulation runs are performed. Results. The model is able to produce kG magnetic fields in a time interval of the order of the granulation time scale. The mean unsigned flux density and the mean magnetic energy density of the synthetic quiet Sun reach respectively 〈B〉sat ≃ 100 G and 〈B2〉 sat ≃ 350 G in the stationary regime. The derived probability density function of the magnetic field strength decreases rapidly from B = 30 G to B ∼ 100 G and presents a secondary maximum for B = 2 kG. From this result it follows that magnetic fields ≥ 700 G dominate the unsigned flux density and magnetic energy density although the probability density function of the field strength presents a maximum for B ∼ 10 G. Conclusions. A photospheric advection field with spatio-temporal correlations, driving the magnetic elements, and reduced rules magnetic amplification are able to create a realistic probability density function of the quiet Sun magnetic field. More in detail, as found in recently published works, they naturally produce an excess of magnetic fields around 2 kG if an upper limit is imposed on the field strength.