Flat tails in FRB and pulsar energy distributions: implications for optimizing nearby FRB surveys

Fast radio bursts (FRBs) are energetic, short-duration radio pulses of unclear origin. To explore effective survey strategies for detecting FRBs from nearby globular clusters (GCs), we investigate the burst energy distribution, which has a strong influence on the detection rate. We re-analyze FRBs and pulsars exhibiting broad energy distributions by fitting their high-energy tails with power-law models. Two cosmological repeating FRBs (FRB 20201124A and FRB 20220912A), one nearby FRB (FRB 20200120E), and two pulsars (RRATs J1846$-$0257 and J1854+0306), exhibit power-law indices of $α\gtrsim -1$, suggesting that their bright pulses contribute significantly to the total radio pulse energy. The brightest bursts from these sources can be fitted with a power-law model ($α_{\rm Bri} = -0.26 \pm 0.05$), suggesting that an extremely flat index is required to naturally derive high-luminosity FRBs from low-luminosity sources. We present detailed survey strategies for FAST, MeerKAT and Parkes cryoPAF in the search for FRBs in nearby GCs using different power-law indices, recommending targets for observation. We suggest that combining observations with FAST ($\sim3$ hours) and Parkes cryoPAF (10$-$20 hours) is practicable for discovering new FRBs in nearby GCs.