Inferring the Intrinsic Energy Function of FRB 20220912A

TL;DR

This study addresses whether the bimodal energy distribution observed in FRB 20220912A is intrinsic or a byproduct of band-limited observing bands. By modeling FRB spectra as Gaussians in frequency, applying a band-limited selection function, and performing large-scale Monte Carlo simulations, the authors show that band-limited selection alone cannot convert a unimodal intrinsic energy distribution into bimodal; bimodality can arise if the central frequency distribution is itself bimodal. An in-depth analysis of FAST data for FRB 20220912A reveals that the intrinsic energy distribution comprises a high-energy log-normal component with $E_{ m c}\approx8.13\times10^{37}$ erg and a low-energy power-law component with index $-1.011\pm0.028$, with the low-energy peak largely explained by selection effects; after correcting for these effects the bimodality persists, indicating an intrinsic origin linked to the emission mechanism. The work discusses morphology-related challenges, compares with other FAST repeaters, and argues that the bimodal energy function likely reflects the underlying radiation physics of magnetar-driven FRBs, rather than being solely a consequence of observational biases. These findings have implications for understanding FRB engines and guiding future sub-band and morphology-aware analyses.

Abstract

The statistical analysis of fast radio burst (FRB) samples from repeaters may suffer from a band-limited selection effect, which can bias the observed distribution. We investigated the impact of this selection bias on the energy function through simulations and then applied our analysis to the particular case of FRB 20220912A. Our simulations show that, in the sample of bursts observed by the Five hundred meter Aperture Spherical Telescope (FAST), assuming a unimodal intrinsic energy distribution, the band selection effect alone is insufficient to produce a bimodal energy distribution; only the bimodal central frequency distribution can achieve this. The bursts' energy of FRB 20220912A that primarily fell within the observing band showed no significant correlation with the central frequency. In contrast, bursts with higher central frequency tend to exhibit narrower bandwidth and longer duration. The distribution of the intrinsic energy can be modeled as a log-normal distribution with a characteristic energy of $8.13 \times 10^{37}$ erg, and a power-law function with the index of $1.011 \pm 0.028$. In contrast to the initial energy function reported by \cite{2023ApJ...955..142Z}, the low-energy peak vanishes, and the high-energy decline becomes steeper, which implies the low-energy peak is an observational effect. The bimodality of the energy distribution seems to originate from the intrinsic radiation mechanism.

Figures (6)

• Figure 1: Completeness function for different values of $\nu_{0}$, which shows the fraction of bursts that can be detected in the simulation. The black bold line is the scenario where $\nu_{0}$ aligns with the band edge ($1 \mathrm{GHz}$), resulting in only half of the spectrum being received. The red dotted line represents the 90% completeness threshold.
• Figure 2: The observed energy distributions $p_{\mathrm{obs}}(E_{\mathrm{obs}})$ for different values of $\nu_{0}$. The black bold line is the scenario where $\nu_{0}$ aligns with the band edge ($1 \mathrm{GHz}$), resulting in only half of the spectrum being received.
• Figure 3: The PDFs of the observed energy distribution $p_{\mathrm{obs}}(E_{\mathrm{obs}})$ are depicted for different unimodal $\nu_{0}$ distributions. Each panel corresponds to a specific unimodal distribution, with the intrinsic energy function following a lognormal distribution.
• Figure 4: The PDFs of observed energy distributions $p_{\mathrm{obs}}(E_{\mathrm{obs}})$ in the case of two-Gaussian $\nu_{0}$ distribution ($\sigma_1 = \sigma_2 = 0.1$). Each subplot displays a series of $p_{\mathrm{obs}}(E_{\mathrm{obs}})$ for a fixed $\nu_1$. In each panel, these curves are plotted for different values of $\alpha$ ranging from 0.7 to 1 at intervals of 0.08. The special cases $\alpha = 0$, $0.5$, and $1$, which are also shown in the sub-figures.
• Figure 5: The linear fits of $k_{\log_{10}(E_{\mathrm{int}})}$, $k_{\log_{10}(\mathrm{W}_{\mathrm{eq}})}$ and $k_{\log_{10}(\mathrm{BW}_{50})}$ for bursts with different ranges of $\nu_0$. $\Delta f$ means that the linear fit is made using the bursts with $\nu_0$ ranging from $1.25 - \Delta f$ GHz to $1.25 + \Delta f$ GHz. The violin plots represent the posterior distribution and the blue bar is the mean value of the posterior. The red dotted line represents the edge of the observing band, corresponding to the band edge $\Delta f = 0.25$.