Solar active regions contain electric currents. Information on the distribution of currents is important for understanding the processes of energy release on the surface of the Sun and in the overlying layers. The paper presents an analysis of the probability density function (PDF) of the absolute value of the photospheric vertical electric current density ($|j_z|$) in 48 active regions before and after flares in 2010--2017. Calculation of $|j_z|$ is performed by applying the differential form of Ampere's circuital law to photospheric vector magnetograms obtained from observations of the Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO). It has been established that for the studied active regions PDF($|j_z|$) is described by the Gauss function in the low-$|j_z|$ region ($|j_z| < 10110 \pm 1321$ statampere/cm$^2$) and the decaying power-law function in the region of higher $|j_z|$ values. Also, for some active regions PDF($|j_z|$) can be described by the special kappa-function. The distributions of the parameters of the approximating functions are obtained using the least squares method. The average absolute value of the power-law function index is $3.69 \pm 0.51$, and $3.99 \pm 0.51$ of the kappa-function. No systematic changes in parameters during the flares are detected. An explicit connection between the parameters and the flare X-ray class, as well as with the Hale magnetic class of the active regions, is not found. Arguments are presented in favor of the suggestion that the Gaussian distribution in the low-value region of PDF($|j_z|$) represents noise in the data, while the power-law "tail" reflects the nature of electric currents in the solar active regions.

中文翻译：

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太阳耀斑活跃区域中光球垂直电流的密度分布

太阳能活动区包含电流。有关电流分布的信息对于理解太阳表面和上覆层的能量释放过程很重要。论文对2010--2017年耀斑前后48个活动区光球垂直电流密度绝对值($|j_z|$)的概率密度函数(PDF)进行了分析。$|j_z|$ 的计算是通过将安培电路定律的微分形式应用于从太阳动力学天文台 (SDO) 上的日震和磁成像仪 (HMI) 仪器的观测中获得的光球矢量磁图来执行的。已经确定，对于研究的活动区域，PDF($|j_z|$) 由低 $|j_z|$ 区域中的高斯函数描述 ($|j_z| < 10110 \pm 1321$ statampere/cm$^2$) 和 $|j_z|$ 值较高区域的衰减幂律函数。此外，对于某些活动区域，PDF($|j_z|$) 可以通过特殊的 kappa 函数来描述。使用最小二乘法获得逼近函数的参数分布。幂律函数指数的平均绝对值为 $3.69 \pm 0.51$，kappa 函数的平均绝对值为 $3.99 \pm 0.51$。没有检测到耀斑期间参数的系统变化。没有发现参数与耀斑 X 射线类别以及活动区域的 Hale 磁类别之间的明确联系。提出的论点支持 PDF($|j_z|$) 低值区域中的高斯分布代表数据中的噪声，而幂律“尾”