Energy-Dependent Hard X-Ray QPP Modulation in M- and X-Class Solar Flares Observed by Aditya-L1/HEL1OS

Quasi-periodic pulsations (QPPs) in solar-flare hard X-ray (HXR) emission provide observational constraints on the temporal variability of flare energy release and energetic-electron production. In our previous study, we established a systematic catalogue of HXR QPPs in HEL1OS observations of X-class solar flares, identifying statistically significant pulsations in 25 of 34 events with sufficient data quality (S. Rajkapoor Kanaujiya et al. 2026). Here, we extend this investigation by comparing the energy dependence of the modulation depth of QPPs in M- and X-class flares across four HEL1OS energy channels spanning 8-20 keV. The comparison comprises 18 M-class events and the X-class sample from our previous study, with the number of available measurements varying between energy channels. In both flare populations, the modulation depth increases with photon energy. For M-class flares, it rises from approximately 2.3% at 8-11 keV to 13.2% at 17-20 keV, whereas for X-class flares increase from approximately 1.0% to 3.1%. The stronger increase towards higher energies in the M-class sample constitutes the principal observational contrast. These results demonstrate an energy-dependent increase in the relative amplitude of HXR QPPs in both populations and motivate a systematic statistical assessment of whether their energy-dependent modulation-depth distributions differ. The comparison provides a basis for constraining models of QPP generation and the modulation of energetic-electron emission during solar flares.