2026ApJ...997..286O

Recent Sun-as-a-star studies have shown that postflare loops can manifest as a secondary peak in the Hα light curve, suggesting that stellar postflare loops are detectable. To understand what determines the timing of such a secondary peak in the Hα light curve associated with postflare loops, we must quantitatively identify the key physical processes controlling the appearance of Hα postflare loops. Previous case studies have indicated that the timing of the appearance of Hα postflare loops is likely governed by radiative cooling. However, the statistical characteristics of the timing of Hα postflare loops' appearance remain insufficiently investigated. In this study, we statistically investigated the timing of the appearance of Hα postflare loops to quantify their cooling processes. As a result, we found a negative correlation between the time difference between the soft X-ray peak and the appearance of the Hα postflare loops (Δt) and the soft X-ray peak flux (F_X). This relationship is consistent with the theoretical scaling between radiative cooling timescale (τ_rad) and F_X, where ${\tau }_{{\rm{rad}}}\propto \,{F}_{{\rm{X}}}^{-1/2}$. This statistical result indicates that the timing of the appearance of Hα postflare loops relative to the soft X-ray peak is primarily controlled by radiative cooling. Furthermore, we examined the dependence of the scaling law on flare spatial scales (L). Consequently, we demonstrated that the spatial scale of unresolved stellar flares can be estimated using the following scaling law: $L\propto {F}_{{\rm{X}}}^{1/3}{\rm{\Delta }}{t}^{2/3}$. Our results are useful for interpreting secondary peaks in the Hα data of stellar flares and provide a new method to estimate the spatial scale of unresolved stellar flares.