The Calculation of Line-of-sight Electric Current Density Associated with An X2.2 Flare in Active Region AR11158

The explosion of energic solar activity is closely related to the current structure in the active region, Ampere's law j_z=1/μ(▽×B)_z is the theoretical basis for measuring the current density in the active region. Due to the inevitable existence of random noise in the measured vector magnetic field, the current density calculated by using the different form of Ampere's law is significantly different. In order to compare the differences between the calculated results of different form and explore one of the most practical current calculation methods, this article is based on the vector magnetogram in activity region AR11158 measured by SDO (Solar Dynamic Observatory)/HMI (Helioseismic and Magnetic Imager) on February 15, 2011. The distribution of the line-of-sight electric current density in the active region is calculated using differential algorithm and integral algorithm of Ampere's law. The results demonstrate that the distribution of line-of-sight electric current density j_z obtained by the differential algorithm is more severely affected by random noise than the result obtained by the integral algorithm, the current structures in the current distribution diagram obtained by the integral algorithm is much clearer than the former. In addition, the noise signal of the calculated current distribution map will decrease sharply, as enlarging the radius of the integral loop, the current structure in the obtained current distribution map will become clear. However, when the radius of the integral loop continues to expand, part of the fine structures of the current distribution map will also be distorted when obtaining a clear current distribution diagram. The result of this study demonstrates that the map of current distribution which is calculated by expanding the integral loop properly can reduce the effect on calculation results from random noise, and obtaining a clear and true line-of-sight electric current distribution map. Though the noise is eliminated if the radius of the integral path is too large, some fine structures in the current distribution will be lost. Therefore, during the course of actual calculating electric current. It is suggested to use high-resolution vector magnetogram and use the integral algorithm of Ampere's law to calculate the line-of-sight electric current in the active region by selecting an appropriate integration path, which can help us to explore the relationship between the eruptive flares and the structures of current in the active region.