Narrowly-Banded Spectra with Peak Frequency Around 1 GHz of FRB 20201124A: Implications for Energy Function and Radiation Physics

The radiation physics of fast radio bursts (FRBs) remains an open question. Current observations have discovered that narrowly-banded bursts of FRB 20201124A are active in 0.4-2 GHz and their spectral peak frequency ($ν^{\rm obs}_{p}$) are mostly toward $\sim 1$ GHz. Utilizing a sample of 1268 bursts of FRB 20201124A detected with the FAST telescope, we show that the $1σ$ spectral regime of 71.4\% events (in-band bursts) is within the FAST bandpass. Their intrinsic burst energies ($E^{\rm obs}_{\rm BWe}$) and spectral widths ($σ_s^{\rm obs}$) are well measured by fitting the spectral profile with a Gaussian function. The derived $E^{\rm obs}_{\rm BWe}$ and $σ_s^{\rm obs}$ distributions are log-normal and centering at $\log E^{\rm obs}_{\rm BWe}/{\rm erg}=37.2~ (σ=0.76)$ and $\log σ_s^{\rm obs}/{\rm GHz}=-1.16~ (σ=0.17)$. Our Monte Carlo simulation analysis infers its intrinsic $ν_p$ distribution as a normal function centered at $ν_{p,c}=1.16$ GHz ($σ=0.22$) and its intrinsic energy function as $Φ(E)\propto E^{-0.60}e^{-E/E_c}$ with $E_c=9.49 \times 10^{37}$ erg. We compare these results with that of typical repeating FRBs 20121102A and 20190520B that are active over a broad frequency range at several specific frequencies and discuss possible observational biases on the estimation of the event rate and energy function. Based on these results, we argue that FRB 20201124A likely occurs in a fine-tuned plasma for maser radiations at a narrow frequency range, while FRB 20121102A and FRB 20190520B could involve clumpy plasma conditions that make maser emission around several specific frequencies in a broad range.