Magnetic Helicity Injection and Sigmoidal Coronal Loops

We studied the relationship between magnetic helicity injection and the formation of sigmoidal loops. We analyzed seven active regions: three regions showed coronal loops similar to the potential field, and four regions showed the sigmoidal loops. The magnetic helicity injection rate was evaluated using the method proposed by Kusano et al. In order to compare the helicity of regions of various sizes, we defined the normalized helicity injection rate as the magnetic helicity injection rate divided by the magnetic flux squared. We found that the sigmoidal regions and nonsigmoidal regions have comparable normalized helicity injection rates. Next, we calculated the magnetic helicity content of the sigmoidal loops by using the magnetic flux tube model (Longcope & Welsch) and compared it with the magnetic helicity injected from around the footpoints of three sigmoidal loops. For two sigmoidal loops, it is found that these values are comparable. Another loop showed significant disagreement between helicity injection rate and its magnetic helicity content. Excluding this region on the basis of its complexity (perhaps multiple loops forming a sigmoidal loop), we can conclude that geometric twist of the sigmoidal loops is consistent with the magnetic helicity injected from around the footpoints of the sigmoidal loops.

我们研究了磁螺度注入与S形环形成之间的关系。我们分析了七个活动区：其中三个区域显示出与势场相似的日冕环，四个区域显示出S形环。磁螺度注入率是使用Kusano等人提出的方法进行评估的。为了比较不同大小区域的螺度，我们将归一化螺度注入率定义为磁螺度注入率除以磁通量的平方。我们发现S形区域和非S形区域具有相当的归一化螺度注入率。接下来，我们使用磁通管模型（Longcope和Welsch）计算了S形环的磁螺度含量，并将其与从三个S形环的足点周围注入的磁螺度进行了比较。对于两个S形环，发现这些值是相当的。另一个环在螺度注入率与其磁螺度含量之间显示出显著差异。基于其复杂性（也许是多个环形成一个S形环）排除这个区域，我们可以得出结论：S形环的几何扭转与从S形环足点周围注入的磁螺度是一致的。