A Simple Model for the Distribution of Quiet‐Sun Magnetic Field Strengths

We derive a first order linear differential equation describing the shape ofthe probability density function of magnetic field strengths in the quiet Sun(PDF). The modeling is very schematic. It considers convective motions whichcontinuously supply and withdraw magnetic structures. In addition, a magneticamplification mechanism increases the field strength up to a threshold thatcannot be exceeded. These three basic ingredients provide PDFs in goodagreement with the PDFs produced by realistic numerical simulations of magnetoconvection, as well as with quiet Sun PDFs inferred from observations. Inparticular, the distribution is approximately lognormal, and it produces anexcess of magnetic fields (i.e., a 'hump' in the distribution) right before themaximum field strength. The success of this simple model may indicate that onlya few basic ingredients shape the quiet Sun PDF. Our approach provides aconcise parametric representation of the PDF, as required to develop automaticmethods of diagnostics.Comment: Accepted for publication in ApJ. 7 pages and 3 fig