A Model for Dynamic Evolution of Emerging Magnetic Fields in the Sun

Abstract

In this paper we study the dynamic evolution of emerging magnetic fields in the solar atmosphere by deriving a model based on a three-dimensional MHD simulation. The simulation shows that magnetic field lines initially forming a twisted flux tube below the solar surface emerge into the atmosphere by magnetic buoyancy. Outer field lines of the flux tube are almost free to expand in a wide fan shape without strong confinement by surrounding field lines. On the other hand, inner field lines are subject to strong confinement by adjacent twisted field lines that prevent the lateral expansion of inner field lines. By examining the result of the simulation, we derive a model of emerging field lines to demonstrate that the height of an emerging field line increases at the average rate of (g(0)k) (1/2) H/2, where g(0), k, and H are the gravitational acceleration, curvature of the emerging field line, and a scale height of magnetic field strength. Applying this model to the outer and inner field lines, we show that inner field lines are less dynamical than outer field lines and inner field lines are likely to form quasi-static structure in the corona such as prominences and sigmoids. We also discuss that the shape of inner field lines is reflected in the chirality of a modeled sigmoid.