De-Chao Song¹, Ying Li^1,2, Qiao Li¹, and Xiaofeng Liu^1,2
1 Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, CAS, Nanjing 210023, China
2 School of Astronomy and Space Science, University of Science and Technology of China, Hefei 230026, China

Introduction: Solar flares are among the most energetic eruptive phenomena in the solar system, producing enhanced radiation across nearly the entire electromagnetic spectrum. Among flare emissions, white-light (WL) continuum and hydrogen Lyα emission at 1216 Å provide particularly important diagnostics of energy deposition in the lower solar atmosphere. White-light flares (WLFs) are intense brightening in the WL continuum, indicating substantial energy deposition in the lower chromosphere and possibly even deeper layers. Lyα, the strongest line in the solar vacuum ultraviolet spectrum, traces the chromospheric and transition-region response. Although WL and Lyα emissions are thought to share a common flare-energy driver, their relationship remains poorly understood. In this Nugget, we present a statistical study of 69 WLFs observed during 2010–2015 (Figure 1), combining WL continuum intensity near 6173 Å from SDO/HMI with GOES Lyα and SXR irradiance.

Figure 1. Spatial distribution of the 69 WLFs on the solar disk. The sample includes 22 X-class (magenta), 44 M-class (cyan), and 3 C-class (gray) flares.

Stronger Lyα Enhancement in WLFs: We define the Lyα contrast as . For our 69 WLFs, this contrast ranges from 0.8% to 28.5% (mean 7.0%), with a 95th percentile (P95) of ~20%. In comparison, Milligan et al.^[1] reported a P95 of only ~10% for 477 M- and X-class flares not restricted to WLFs, indicating that WLFs produce a notably stronger Lyα response.

Peak-time Ordering: A Nonthermal Imprint: For most WLFs, the Lyα peak is nearly cotemporal with the SXR time-derivative peak — a hallmark of the Neupert effect — underscoring the nonthermal origin of flare Lyα emission (Figure 2 (b)). The WL peak is cotemporal with or slightly lags the Lyα and SXR derivative peaks by a median of ~30–40 s (Figures 2a and 2c), likely due to hydrogen recombination and/or radiative backwarming processes.

Figure 2. Distributions of the peak-time differences among Lyα, WL, and the SXR time derivative, highlighting the temporal ordering of impulsive-phase emissions. The green background is the uncertainty introduced by the different temporal resolutions of the observations.

Correlated Rise Phases and Timescale Comparisons: The Lyα and WL emissions exhibit positive power-law correlations in rise time (Kendall’s tau correlation coefficient, KCC = 0.41) and in the peak-enhancement growth rate , KCC = 0.49), with remarkably similar rise times of ~3–4 minutes, suggesting a common impulsive driver. However, their decay times (e-folding) and durations (rise plus decay times) show only low-to-medium correlations (KCCs ≤ 0.34), indicating distinct post-peak cooling mechanisms. Compared with previous studies, the Lyα rise times of these WLFs (median ~2.7 min) are shorter than those of ordinary solar flares (~5.6 min)^[2], and their WL rise times (also median ~2.7 min) are shorter than those reported for WL stellar flares on solar-type stars (~5.9 min)^[3], further indicating the inherently impulsive nature of WLFs.

Radiated Energy: What Shapes It? For the Lyα band, all four parameters — peak enhancement, rise time, decay time, and duration — exhibit positive power-law correlations with E_Lyα (KCCs ≥ 0.40), with the strongest dependencies on the decay time and duration (KCCs ≥ 0.53), implying that the Lyα energy budget accumulates significantly during the gradual phase.

Figure 3. Relationships of the radiated energy with the peak enhancement, rise time, decay time, and duration for the Lyα (top) and WL (bottom) bands.

In contrast, E_WL shows the strongest correlation with its peak enhancement (KCC = 0.67), whereas its correlations with the rise time, decay time, and duration are all weaker. This indicates that E_WL are more closely associated with the magnitude of the impulsive peak enhancement than with flare timescales. The WL energy–duration relation closely matches the theoretical one-third predicted by simplified magnetic reconnection models and is comparable to values found for solar WLFs (index = 0.38 ± 0.06)^[4] and stellar superflares (index = 0.39 ± 0.03)^[5], consistent with a common reconnection-driven scaling across solar and stellar flare energy ranges.

Conclusions and Outlook: We establish quantitative power-law scaling relationships between Lyα and WL emissions for 69 solar WLFs. These empirical solar scaling laws provide a useful bridge for estimating the Lyα emission properties of solar-like stellar flares from routinely observed WL emissions. We also note that HMI’s narrowband pseudocontinuum near 6173 Å differs from broadband stellar photometry, which introduces some limitations.

For details of this work, please refer to our recent publication:
Song, D.-C., Li, Y., Li, Q., & Liu, X. 2026, ApJ, 1001, 195, doi:10.3847/1538-4357/ae5797

References:

[1] Milligan, R. O., Hudson, H. S., Chamberlin, P. C., et al. 2020, Space Weather, 18, e02331
[2] Lu, L., Feng, L., Li, D., et al. 2021, ApJS, 253, 29
[3] Yan, Y., He, H., Li, C., et al. 2021, MNRAS, 505, L79
[4] Namekata, K., Sakaue, T., Watanabe, K., et al. 2017, ApJ, 851, 91
[5] Maehara, H., Shibayama, T., Notsu, Y., et al. 2015, EP&S, 67, 59