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.