A 4200-hour HyperFlash and 'ECLAT campaign on the hyperactive FRB 20240114A: constraining energetics with the most brilliant bursts

Hyperactive repeaters provide a unique window into the evolving environments and energy budgets of fast radio burst (FRB) sources, though they may not be representative of the FRB population in general. High-cadence observations are key to capturing the rarest and most energetic bursts, which occur only once per hundreds to thousands of hours. Here we present an unprecedented 4, 200-hour observing campaign targeting FRB 20240114A as part of the HyperFlash and ÉCLAT FRB monitoring programs. Over 806 days, we detected 178 high-energy (about 10 40-42 erg) bursts with HyperFlash, which together amount to 4.4 times 10 42 erg of released radio energy (assuming isotropic emission and 1-GHz emission bandwidth). The cumulative energy of the HyperFlash bursts is about twice that of about 11, 000 lower-energy bursts detected with FAST, emphasising the significant role that the highest-energy bursts play in depleting the central engine's stored energy. In fact, the single most brilliant burst from our sample, which we term the STROOP, contributes roughly 1/3 of all the energy we measure, and is at the maximum energy seen in studies of both repeating and apparently one-off FRBs alike. We also find a break in the burst energy distribution at about 2 times10 40 erg and a linear dispersion measure (DM) increase of +0.96 plus or minus 0.06 pc cm-3 over a period of 318 days. We discuss these findings in the context of a magnetar source model and highlight comparisons with the energetics of intermediate and giant X-ray/ γ-ray flares from Galactic sources.