FAST Observations of an Extremely Active Episode of FRB 20201124A. II. Energy Distribution

We report the properties of more than 800 bursts detected from the repeating fast radio burst (FRB) source FRB 20201124A with the Five-hundred-meter Aperture Spherical radio Telescope (FAST) during an extremely active episode on UTC 2021 September 25-28 in a series of four papers. In this second paper of the series, we study the energy distribution of 881 bursts (defined as significant signals separated by dips down to the noise level) detected in the first four days of our 19 hr observational campaign spanning 17 days. The event rate initially increased exponentially but the source activity stopped within 24 hr after the 4th day. The detection of 542 bursts in one hour during the fourth day marked the highest event rate detected from one single FRB source so far. The bursts have complex structures in the time-frequency space. We find a double-peak distribution of the waiting time, which can be modeled with two log-normal functions peaking at 51.22 ms and 10.05 s, respectively. Compared with the emission from a previous active episode of the source detected with FAST, the second distribution peak time is smaller, suggesting that this peak is defined by the activity level of the source. We calculate the isotropic energy of the bursts using both a partial bandwidth and a full bandwidth and find that the energy distribution is not significantly changed. We find that an exponentially connected broken-power law function can fit the cumulative burst energy distribution well, with the lower and higher-energy indices being -1.22 ± 0.01 and -4.27 ± 0.23, respectively. Assuming a radio radiative efficiency of η _r = 10^-4, the total isotropic energy of the bursts released during the four days when the source was active is already 3.9 × 10⁴⁶ erg, exceeding ~23% of the available magnetar dipolar magnetic energy. This challenges the magnetar models which invoke an inefficient radio emission (e.g., synchrotron maser models).