The Relationship between Kinetic and Magnetic Helicity in Solar Active Regions

Using Helioseismic and Magnetic Imager/Solar Dynamics Observatory data, we search for a relationship between kinetic helicity and magnetic helicity in solar active regions (ARs) using a sample of 62 ARs from 2010 May to 2015 May. The sample includes 32 mature ARs and 30 emerging ARs. We calculate kinetic helicity in the interior in the depth range from 0.6 to 11.6 Mm, magnetic helicity in the corona, helicity flux across the photosphere, and the magnetic twist and magnetic writhe of the ARs at the photosphere. From these data, relationships are found between magnetic helicity, helicity flux, and magnetic twist. However, magnetic writhe appears not to be related to the other magnetic quantities. No relationship is found between the kinetic helicity and any magnetic quantity. In particular, no relationship is found between the kinetic helicity and any of the following: magnetic helicity, magnetic helicity flux, magnetic twist, or magnetic writhe. These results suggest that (1) the magnetic helicity in the corona above ARs is mainly derived from the magnetic twist, and (2) the flow dynamics in the region from 0.6 to 11.6 Mm below the photosphere is not the primary source for the generation of magnetic helicity in ARs.