| Solar magnetic fields, produced in the interor and extending all the way into the interplanetary space, connect the Sun with the terrestrial environment. They manifest themselves on the solar surface over a wide range of scales, from ubiquitous ephemeral regions as small as 1016 Maxwells, to active regions as large as 1023 Maxwells. The appearance of kilo-Gauss magnetic flux bundles on the photosphere is observationally well studied. However the physical processes that produce observed magnetic structures are yet to be well-understood, due to the lack of information below the solar surface. To illustrate the physics of sub-surface magnetic fields, we carry out numerical simulations of the emergence of magnetic flux ropes from the convection zone through the photosphere and into the corona. The spatial scale of our simulations varies from ephemeral regions to active regions. This study of the formation of magnetic structures shows the importance of the interaction of rising magnetic fields and turbulent convective motions:;The first simulation addresses the emergence of a flux rope with a total axial flux of 3 x 1019 Mx. From a shallow convection zone, it self-consistently forms an ephemeral region at the photosphere and disrupts the near-surface convection pattern, with magnetic flux quickly becoming concentrated in the downflow regions. In another simulation, a flux rope with a total axial flux of 1 x 1021 Mx, buoyantly rises from 10 Mm below the photosphere, interacts with convective cells of varying scales and forms a small active region with a pair of sunspots by the coalescence of small-scale flux and the subsequent intensification from convective collapse.;At the beginning of the emergence, vertical motion dominates the energy transport into the corona when the flux first passes through the photosphere. After that, horizontal motions, i.e., shearing, separating motion of magnetic dipoles, and rotation of magnetic polarities take over the energy transport, while vertical motion transports energy back into the convection zone due to the concentration of magnetic flux in downflow regions.;In our simulations, we find strong shearing motions draw the magnetic field parallel to the polarity inversion line. Tether-cutting reconnection then transfers the magnetic shear into the corona. Together, with the rotation of sunspots, these processes produce and transport free magnetic energy into the corona during times of the flux emergence and cancellation. The free energy in the corona increases to 8 x 1030 erg within 3 hours, which may provide the energy necessary for solar eruptive events, such as coronal mass ejections, flares, and filament eruptions.;A comparison of our simulation with observations of active region 11158 finds the same physical processes at work over longer time scales and larger spatial scales. Strong shear flows, enhanced horizontal field strength, and converging flows at the polarity inversion line are found to precede a fast coronal mass ejection accompanied by an X-class flare. The close match between the simulation and observations support the conclusion that shearing motion builds up the necessary magnetic energy to drive eruptive events. |
