Power-law Indices of EUV Intensity Power Spectrum in Flaring Coronal Active Regions

Abstract

Solar intensity power spectra are usually characterised by coloured noise, with the spectral energy following a segmented power-law function of frequency, $S(f)\propto f^{-α}$, over different frequency ranges. Typically, the power-law index exceeds 1 in the low-frequency part ($α_\mathrm{lf}$) and is around 0 at high frequencies ($α_\mathrm{hf}$). This work investigates the spatial and temporal evolution of the power-law indices of coronal EUV intensity power spectra in flare-hosting active regions. The spatial distribution of the power-law index in the low-frequency domain ($α_\mathrm{lf}$) closely mirrors EUV intensity images, indicating that $α_\mathrm{lf}$ can reveal the dynamics of coronal plasma structures. Temporally, $α_\mathrm{lf}$ remains stable in quiescent active regions, but it exhibits significant variability before the flare onset. Motivated by this behaviour, we analysed 14 flare events, quantifying the temporal variation of the indices $α_\mathrm{lf}$ and $α_\mathrm{hf}$ as potential flare precursors. In all flare events considered, notable deviations of $α_\mathrm{lf}$ beyond a defined threshold consistently occurred at the flare site within a few minutes before the flare. In some cases, the change in the value of $α_\mathrm{lf} - α_\mathrm{hf}$ was detected within 30--90\, minutes before the flare. This proof-of-concept study suggests that the temporal variation of the power-law indices in coronal EUV intensity power spectra could potentially serve as short-term precursors of solar flares, which needs to be validated on a larger flare sample.

Figures (9)

• Figure 1: Demonstration of power-law index estimation in Fourier power spectra of time series of coronal EUV intensity. (a) An AIA 171Å image showing an example of a region of interest. The blue box indicates the macropixel where the signals shown in panels b--d are extracted from. (b): Fourier power spectra of detrended signals in each pixel of the macropixel (blue dots). The red plus symbols represent the mean spectrum (see the red plus) and are then fitted by a broken power-law function (Eq. \ref{['eq:break']}) with the power-law indices ($\alpha_\mathrm{lf}$ and $\alpha_\mathrm{hf}$) indicated in the panel. (c): Time variation of $\alpha_\mathrm{lf}$ and $\alpha_\mathrm{hf}$ from 11:30 to 13:00 UT. All times shown in this figure start from 11:00 UT.
• Figure 2: Power-law index map for a full-disk image sequence from 08:00 UT to 16:10 UT on 29th March 2023. (a) full-disk AIA 171 Å image with 6 regions of interest (ROIs, labelled 1--6) overplotted. (b--c): The map of $\alpha_\mathrm{lf}$ with different spatial resolution (64/32 pixels per macropixel in b/c). (d--e): Time evolution of intensity (green) and $\alpha_\mathrm{lf}$ (blue) in 6 selected ROIs. The grey region indicates the time interval of an M1.3 flare.
• Figure 3: Time evolution of $\alpha_\mathrm{lf}$ and $\alpha_\mathrm{hf}$ in AR 12158 during 11:50 to 17:58 UT on 10th September 2014. (a): AIA 171 Å image showing the studied AR. The blue boxes labelled 1, 2 and 3 (ROI$_1$, ROI$_2$ and ROI$_3$) are three macropixels of interest, the first two that have the reversal of $\alpha_\mathrm{hf}$ and $\alpha_\mathrm{lf}$, i.e., $\alpha_\mathrm{hf}>1$ and $\alpha_\mathrm{lf}<1$, while ROI$_3$ sees the increase in $\alpha_\mathrm{hf}$ before flares. (b--c): Maps of $\alpha_\mathrm{lf}$ (b) and $\alpha_\mathrm{hf}$ (c) correspond to the image sequence. The grid size is $10\times10$ pixels. The three blue boxes are the same as in (a). (d): abnormal Fourier spectra in ROI$_2$ with $\alpha_\mathrm{hf}>\alpha_\mathrm{lf}$. (e): time-varying averaged 171 Å intensity of AR 12158. The grey areas denote time intervals of C1.5 and X1.6 flares, respectively. (f--h): time series of power-law indexes in ROI$_1$, ROI$_2$ and ROI$_3$, respectively. The purple dotted curves are smoothed temporal signals of $\alpha_\mathrm{lf}$, which are used to calculate the actual difference and growth rate of $\alpha_\mathrm{lf}$. The black boxes mark the reversal of $\alpha_\mathrm{lf}$ and $\alpha_\mathrm{hf}$ before the flares. The vertical dotted lines denote the time of minimum/maximum smoothed $\alpha_\mathrm{lf}$ for two flares. The value and time difference between the minimum and maximum $\alpha_\mathrm{lf}$ are marked by $\Delta\alpha_\mathrm{lf}$ and $\Delta t$, respectively. An animation of panels (e) and (a--c) showing the temporal evolution of average intensity over the targeted active region, AIA 171 Å images, maps of the two power-law indices, and the three corresponding proxy maps derived from the power-law indices maps is available. The animation covers the period from 12:20 UT to 17:19 UT, with a real-time duration of 11 seconds.
• Figure 4: The 2D density distribution of $\alpha_\mathrm{lf}$ vs. $\alpha_\mathrm{hf}$ in relative frequency for all analysed cases. The dotted lines indicate $\alpha_\mathrm{hf}=1+\alpha_\mathrm{lf}$. The 2D density plots are normalised by their maxima. The location of the salmon horizontal/vertical lines indicates the mean of $\alpha_{lf}/\alpha_{hf}$, and the lengths indicate their standard deviations. Note that the number of the reverse varies from hundreds to thousands across cases, and the total number of samples is around $10^6$, therefore, in some cases, the portion of $\alpha_\mathrm{lf}-\alpha_\mathrm{hf}\leq1$ takes less than 0.1%, appearing as white in the contour plot. To make these minor portions visible, we overplotted them as red dots.
• Figure 5: The multi-scale structural similarity measure (MS-SSIM) between the AIA image (left in each pair) and $\Delta\alpha_\mathrm{lf}$ map (right in each pair) for selected cases. The AIA images are degraded to the same resolution as the proxy maps.