The Ly <i>α</i> Emission in Solar Flares. II. A Statistical Study on Its Relationship with the White-light plus Soft X-Ray Emission

Abstract The hydrogen Ly α 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 WL flares (WLFs) to investigate the relationships among the Ly α , 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 Ly α contrast in these WLFs is in the range of 0.8%–28.5% with a mean value of 7.0%. Positive power-law relationships exist among peak enhancements in SXR, Ly α , and WL. For most events, the Ly α peak is nearly cotemporal with the peak of the SXR time derivative, whereas the WL peak is either cotemporal with or lags those of Ly α and SXR derivative. The Ly α and WL rise times are similar (∼3–4 minutes) and correlated. We also find that the radiated energy in Ly α and HMI narrowband WL has a positive power-law relationship with duration. In particular, the power-law index for the narrowband WL is very close to one-third, as predicted by magnetic reconnection theory. On average, the radiated energies in the GOES Ly α and SXR bands are approximately 3 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 modeling and interpreting the flares on solar-type stars.