On the structure and evolution of complexity in sigmoids: a flux emergence model

Sigmoids are structures with a forward or inverse S-shape, generally observed in the solar corona in soft X-ray emission. It is believed that the appearance of a sigmoid in an active region is an important factor in eruptive activity. The association of sigmoids with dynamic phenomena such as flares and coronal mass ejections (CMEs) make the study of sigmoids important. Recent observations of a coronal sigmoid, obtained with the X-Ray Telescope (XRT) on board Hinode, showed the formation and eruption phase with high spatial resolution. These observations revealed that the topological structure of the sigmoid is complex: it consists of many differently oriented loops that all together form two opposite J-like bundles or an overall S-shaped structure. A series of theoretical and numerical models have been proposed, over the past years, to explain the nature of sigmoids but there is no explanation on how the aforementioned complexity in sigmoids is built up. In this paper, we present a flux emergence model that leads to the formation of a sigmoid, whose structure and evolution of complexity are in good qualitative agreement with the recent observations. For the initial state of the experiment a twisted flux tube is placed below the photosphere. A density deficit along the axis of the tube makes the system buoyant in the middle and it adopts an O-shape as it rises toward the outer atmosphere. During the evolution of the system, expanding field lines that touch the photosphere at bald-patches (BPs) form two seperatrix surfaces where dissipation is enhanced and current sheets are formed. Originally, each of the BP seperatrix surfaces has a J-like shape. Each one of the J's consist of reconnected field lines with different shapes and different relative orientation. The further dynamical evolution of the emerging flux tube results in the occurrence of many sites that resemble rotational discontinuities. Thus, additional current layers are formed inside the rising magnetized volume increasing the complexity of the system. The reconnected field lines along these layers form an overall S-shaped structure. The reconnection process continues to occur leading to the formation of another current concentration in the middle of the sigmoid where a flaring episode occurs. This central brightening is accompanied by the eruption of a flux rope from the central area of the sigmoid and the appearance of "post-flare" loops underneath the current structure.