A Nan\c{c}ay Radio Telescope study of the hyperactive repeating FRB 20220912A

The repeating fast radio burst source FRB 20220912A was remarkably active in the weeks after its discovery. Here we report 696 bursts detected with the Nan\c{c}ay Radio Telescope (NRT) as part of the Extragalactic Coherent Light from Astrophysical Transients (\'ECLAT) monitoring campaign. We present 68 observations, conducted from October 2022 to April 2023, with a total duration of 61 hours and an event rate peaking at $75^{+10}_{-9}$ bursts per hour above a fluence threshold of 0.59 Jy ms in the $1.2-1.7$-GHz band. Most bursts in the sample occur towards the bottom of the observing band. They follow a bimodal wait-time distribution, with peaks at 33.4 ms and 67.0 s. We find a roughly constant dispersion measure (DM) over time ($\delta$DM $\lesssim$ 2 pc cm$^{-3}$) when taking into account `sad-trombone' drift, with a mean drift rate of $-8.8$MHz ms$^{-1}$. Nonetheless, we confirm small $\sim0.3$ pc cm$^{-3}$ DM variations using microshot structure, while finding that microstructure is rare in our sample -- despite the 16 $\mu$s time resolution of the data. The cumulative spectral energy distribution shows more high-energy bursts ($E_\nu \gtrsim 10^{31}$ erg/Hz) than would be expected from a simple power-law distribution. The burst rate per observation appears Poissonian, but the full set of observations is better modelled by a Weibull distribution, showing clustering. We discuss the various observational similarities that FRB 20220912A shares with other (hyper)active repeaters, which as a group are beginning to show a common set of phenomenological traits that provide multiple useful dimensions for their quantitative comparison and modelling.