The Lyman-alpha Emission in Solar Flares. II. A Statistical Study on Its Relationship with the White-light plus Soft X-ray Emission

Abstract

The hydrogen \lya\ line and the white-light (WL) continuum are two key diagnostics of energy transport in the lower atmosphere during solar flares, yet their relationship remains poorly understood. Here we present a statistical analysis of 69 white-light flares (WLFs) to investigate the relationships among the \lya, soft X-ray (SXR), and WL continuum emissions using the data from GOES and the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory. We find that the \lya\ contrast in these WLFs ranges 0.8--28.5\% with a mean value of 7.0\%. Positive power-law relationships exist among peak enhancements in SXR, \lya, and WL. For most events, the \lya\ peak is nearly co-temporal with the peak of SXR time derivative, whereas the WL peak is either co-temporal with or lags those of \lya\ and SXR derivative. The \lya\ and WL rise times are similar ($\sim$3--4 min) and correlated. We also find that the radiated energy in \lya\ and HMI narrow-band WL has a positive power-law relationship with duration. In particular, the power-law index for the narrow-band WL is very close to 1/3 as predicted by magnetic reconnection theory. On average, the radiated energies in GOES \lya\ and SXR bands are approximately three orders of magnitude greater than the energy emitted in the continuum near 6173 Å with a bandwidth of 1 Å. Our findings provide new constraints on lower-atmosphere energy transport in solar flares and can serve as valuable references for modelling and interpreting the flares on solar-type stars.

Figures (8)

• Figure 1: Spatial distribution of the 69 WLFs. Magenta, cyan, and gray circles represent X-, M-, and C-class flares, respectively.
• Figure 2: Example of a WLF (# 42 in Table \ref{['flarelist']}) and a comparison of the SXR duration based on different pre-flare backgrounds ($F_{\text{bkg}}$). (a) and (b) The original HMI continuum image and the base-difference image, respectively, of the X3.3 flare on 2013 November 5. The cyan box indicates the spatial integration region for the WL emission curve (black line in panel (c)). Red arrows point to the two bright flare ribbons in WL images. (c) Light curves of WL (black), Ly$\alpha$ (magenta), SXR (blue), and SXR time derivative (green). Note that the time profiles of WL, Ly$\alpha$, and the SXR time derivative are plotted in an arbitrary scale. The four-minute $F_{\text{bkg}}$ interval used in this study is marked by the gray bar in the bottom-left corner. (d) Comparison of the SXR duration estimated using our pre-flare background selection (y-axis) versus the officially recorded GOES duration (x-axis). Their linear Kendall's Tau correlation coefficient (KCC) is noted in the bottom-right corner. The black dashed line is the 1:1 reference line. Note that both SXR durations are computed using a half-maximum threshold, which is solely to validate the background selection.
• Figure 3: Distribution of the Ly$\alpha$ contrast. Magenta, cyan, and gray bars represent X-, M-, and C-class flares, respectively. The range, median, and mean of the Ly$\alpha$ contrast are annotated in the figure.
• Figure 4: Relationships between peak enhancements ($F_{\text{enhancement}}$) in Ly$\alpha$, WL, and SXR bands. Here the WL enhancement represents the emission increase in the HMI continuum near 6173 Å with an assumed bandpass of $\Delta\lambda=1$ Å. The gray dashed line and the orange solid line in each panel represent the 1:1 reference and the power-law best fit, respectively. The corresponding Kendall's Tau correlation coefficient (KCC) and power-law fitting result are annotated in the top-left and bottom-right corners, respectively.
• Figure 5: Distributions of the peak time ($t_{\text{p}}$) differences among Ly$\alpha$, WL, and the SXR time derivative. Magenta, cyan, and gray bars represent X-, M-, and C-class flares, respectively. To clearly show the distribution, the x-axis range in all panels is limited to $\pm$200 s, which covers the vast majority of the flares ($>$94%), and the few events outside this range do not affect the overall statistical results. The black vertical line in each panel marks $\Delta t_{\text{p}} = 0$, and the green shaded region represents the maximum temporal uncertainty. The uncertainties for $t_{\text{p1}}$, $t_{\text{p2}}$, and $t_{\text{p3}}$ are 55 s, 12 s, and 47 s, respectively.