The Study Of Torus Instability And Magnetic Topology Of Solar Active Region

Magnetic flux rope plays an important role in eruptions,and the torus instability of a current channel can account for the initiation and the main acceleration of a flux rope.Accompaning the rising of a flux rope,magnetic reconnection happens simultaneously and releases the magnetic energy,which results in a solar flare.We present a parametric study of torus instability threshold and discuss the characteristics and the cause of the extreme ultraviolet late phase;we also analyse the role of magnetic topology in these studies.A parametric numerical study of the torus instability threshold for the force-free Titov-Demoulin(tokamak)equilibrium of a line-tied toroidal current channel and flux rope is presented.This addresses the scatter about the nominal critical value of ncr=3/2 for the decay index,which characterizes the equilibrium external poloidal field(the so-called strapping field)at the position of the current channel.Values scattering in the range ncr? 1-2 are typically found in numerical and observational studies of flux rope eruptions on the Sun.Basing on the result of parametric study,we have following conclusions:1.For a thick flux rope,the critical decay index measured at the magnetic axis is relatively high,one should regards the current weighted decay index to present the threshold.For vanishing external toroidal(guide,or shear)field,we find the threshold to lie in the theoretically expected range of[1,2],albeit with a reversed dependence on the minor radius.2.The value of decay index depends on the measurement of height,The zero level of height is photosphere for observational study,while it is the center of ring current for theoretical study.The reversed dependence on the minor radius is coming from the measurement basing on the photosphere but not the center of ring current.3.An external toroidal field introduces a strong stabilizing effect on the instability,raising the threshold up to and even somewhat above 2,which explains observational and numerical results in this range.4.Self-similar expansion is a good approximation for the eruption onset of a flux rope,especially for a flux rope shaped as a semicircle.A second peak in extreme ultraviolet sometimes appears during the gradual phase of solar flares,which is known as EUV late phase(ELP).A stereotypical ELP flare is associated with two separated sets of flaring loops with distinct sizes,and it has been debated whether the ELP is caused by additional heating or extended plasma cooling in the longer loop system.Here we carry out a survey of 55 M-and-above GOES-class flares with ELP during 2010-2014.Based on the flare-ribbon morphology observed in the chromosphere,these flares are categorized as circular-ribbon(19 events),two-ribbon(23 events),and complex-ribbon(13 events)flares.Among them,22 events(40%)are associated with coronal mass ejections,while the rest are confined.An extreme ELP,with the late-phase peak exceeding the main-phase peak,is found in 52%of two-ribbon flares,42%of circular-ribbon flares,and 31%of complex-ribbon flares,suggesting that additional heating is more likely present during ELP in two-ribbon flares than in circular-ribbon flares.Overall,we found cooling is the dominant factor causing the delay of the ELP peak relative to the main-phase peak,mainly because the loop system responsible for the ELP emission is larger than that responsible for the main-phase emission.In addition,all of the circular-ribbon flares can be well explained by a composite "dome-plate" quasi-separatrix layer(QSL).In about half of the circular-ribbon flares,the dome-plate QSL embeds the fan-spine structure of a magnetic null point;but no null point is found in the remaining half,which suggests the dome-plate QSL as a general and robust structure to characterize circular-ribbon flares.