tokens: six ARs. Each time interval is limited to a duration when the corresponding AR is between −60° and +60° with respect to the central meridian to avoid extreme magnetic field projection effects (Bobra et al. 2014 ). Table 1 includes also the onset time and the associated GOES class of the flares occurred in each AR, based on the GOES solar flare catalog. 9 9 https://hesperia.gsfc.nasa.gov/ Furthermore, Table 1 gives information on the dominant evolutionary phases of the ARs, and on how long their δ -spots were observed. Table 1 Summary Table of the Properties of the Studied Six ARs: NOAA Number and the Study Period of AR, Information about the Investigated Flares, Dominant Evolution Phase of the ARs Note. The last coulomb shows the time interval when δ -spot(s) appeared in an AR. 3. Data Analysis The emergence and shearing components of the magnetic helicity of the six ARs are calculated using Equation ( 1 ). The total magnetic helicity flux for a given AR was generated by summing the emergence and shearing components. The three helicity injection rates for each AR were obtained by integrating the helicity flux over the entire area of the AR. The three helicity flux components are further normalized by their respective largest absolute value in order to facilitate comparison on similar scales. The normalized emergence, shearing, and total helicity fluxes are shown in the top panels of Figures 2 – 3 . In the upper panels of Figures 2 – 3 , the blue line is the emergence term, the red line the magnetic helicity flux associated with shearing motions at the photosphere, and the black line is the total magnetic flux. Figure 2. Time analysis of three flaring ARs, namely (a) AR 11166 (b) AR 12192, and (c) AR 11890. The top panels show time series of the normalized emergence (EM, blue), shearing (SH, red), and total (Total, black) helicity fluxes. The red vertical lines mark the onset time of flares. The second through fourth rows show the wavelet power spectrum (WPS) of the normalized emergence, shearing, and total helicity fluxes, respectively. Rather than plotting power directly, the color bars visualize the logarithm of the ratio of the power to the expected power for Gaussian-distributed white noise and significance compared to noise. The x -axis of each WPS is the observation time, and the y -axis is the period, both in hours. On the WPS plots, the black lines bound the cone-of-influence, i.e., the domain where edge effects become important. The plots to the right of each WPS are the corresponding global wavelet spectra (power averaged over time, similar to a Fourier power spectrum). The orange dashed lines mark the one σ confidence in global wavelet spectrum analyses. Figure 3. Same as Figure 2 , but for the three non-flaring ARs, namely (a) AR 12645, (b) AR 12470, and (c) AR 11785. By inspecting the top panels of Figures 2 – 3 (a)–(c), we can see that the normalized shearing and total helicity flux components show similar evolution trends in
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