Confining Burst Energy Function and Spectral Fringe Pattern of FRB 20121102A with Multifrequency Observations

The observed spectral shapes variation and tentative bimodal burst energy distribution (E-distribution) of fast radio burst (FRB) 20121102A with the FAST telescope are great puzzles. Adopting the published multifrequency data observed with the FAST and Arecibo telescopes at L band and the Green Bank Telescope (GBT) at C band, we investigate these puzzles through Monte Carlo simulations. The intrinsic energy function (E-function) is modeled as dp dE E E, and mu -a the spectral profile is described as a Gaussian function. A fringe pattern of its spectral peak frequency (nu p) in 0.5-8 GHz is inferred from the nu p distribution of the GBT sample. We estimate the likelihood of alpha E and the standard deviation of the spectral profile (sigma s) by utilizing the Kolmogorov-Smirnov test probability for the observed and simulated specific E-distributions. Our simulations yield a = -E 1.82 0.30 +0.10, and s = -s 0.18 0.06 +0.28 (3 sigma confidence level) with the FAST sample. These results suggest that a single power-law function is adequate to model the E-function of FRB 20121102A. The variations of its observed spectral indices and E-distributions with telescopes in different frequency ranges are due to both physical and observational reasons, i.e., narrow spectral width for a single burst and discrete nu p fringe pattern in a broad frequency range among bursts, and the selection effects of the telescope bandpass and sensitivity. The putative nu p fringe pattern cannot be explained with the current radiation physics models of FRBs. Some caveats of possible artificial effects that may introduce such a feature are discussed.