A Statistical Analysis of Fluence and Energy Distributions of Non-repeating Fast Radio Bursts Detected by CHIME

TL;DR

This study analyzes 415 non-repeating FRBs detected by CHIME after careful sample completeness filtering. The authors model the fluence distribution with a three-segment power-law, and they fit smoothly broken power-laws to the DM and DM$_{\mathrm{exc}}$ distributions, deriving redshifts via the Macquart relation. Isotropic energies are inferred and revealed to be bimodal, dominated by a narrowly clustered component around $E_{\text{iso}} \sim 2.3\times10^{40}$ erg, with a secondary, broader low-energy population near $\sim 1.6\times10^{39}$ erg. The results imply a near-uniform energy reservoir for the main non-repeating FRB population and hint at multiple origins or emission regimes for the lower-energy component, with implications for progenitor models and FRB cosmology; caveats include redshift uncertainties and selection biases, motivating larger, well-localized samples in the future.

Abstract

Fast Radio Bursts (FRBs) are energetic radio bursts that typically last for milliseconds. They are mostly of extragalactic origin, but the progenitors, trigger mechanisms and radiation processes are still largely unknown. Here we present a comprehensive analysis on 415 non-repeating FRBs detected by CHIME, applying manual filtering to ensure sample completeness. It is found that the distribution of fluence can be approximated by a three-segment power-law function, with the power-law indices being $-3.76 \pm 1.61$, $0.20 \pm 0.68$ and $2.06 \pm 0.90$ in the low, middle, and high fluence segments, respectively. Both the total dispersion measure (\text{DM}) and the extragalactic \text{DM} follow a smoothly broken power-law distribution, with characteristic break DM values of $\sim 703$ pc $\rm cm^{-3}$ and $\sim 639$ pc $\rm cm^{-3}$, respectively. The redshifts are estimated from the extragalactic \text{DM} by using the Macquart relation, which are found to peak at $ z \sim 0.6$. The isotropic energy release ($E_{\text{iso}}$) is also derived for each burst. Two-Gaussian components are revealed in the distribution of $E_{\text{iso}}$, with the major population narrowly clustered at $\sim 2.3 \times 10^{40} {\rm erg}$. The minor population have a characteristic energy of $\sim 1.6 \times 10^{39}$ erg and span approximately one order of magnitude. The distribution hints a near-uniform energy release mechanism for the dominant population as expected from some catastrophic channels, whereas the lower-energy component (potentially including repeat-capable sources) may reflect a broader diversity in FRB origins, emission mechanisms and evolutionary stages.

Figures (6)

• Figure 1: The fluence distribution of non-repeating FRBs (filtered data with $\rm N = 415$ events). The left panel shows the the histogram of the observational data, with a bin ratio of 1.3. The best MCMC fitting result engaging a three-segment power-law function is also illustrated. The right panel illustrates the variation of $\alpha_1$, $\alpha_2$, and $\alpha_3$ with respect to the bin ratio.
• Figure 2: The distribution of dispersion measure for non-repeating FRBs in the filtered sample. The left panel shows the total $\mathrm{DM}$ distribution, while the right panel displays the distribution of $\mathrm{DM}_{\text{exc}}$, which is obtained by subtracting the Galactic contribution from $\mathrm{DM}$. Note that the Galactic contribution is calculated by referencing to the NE2001 and YT20 models. Error bars indicate 1$\sigma$ statistical uncertainty in each bin. A smoothly broken power-law function (the solid curve) is used to fit the histogram in each panel. The vertical dashed line marks the $\mathrm{DM}_{\mathrm{c}}$ parameter of this model, which roughly corresponds to the break point of the best fit curve.
• Figure 3: Redshift distribution of non-repeating FRBs in the filtered sample. Error bars indicate 1$\sigma$ statistical uncertainty in each bin. The solid curve shows the best-fit result by using a smoothly broken power-law function. The vertical dashed line marks the peak of the fit curve, which corresponds to a redshift of $z = 0.564$.
• Figure 4: The distribution of isotropic energy release of non-repeating FRBs in the filtered sample. The solid curve shows the best-fit result by engaging two Gaussian components, with each component shown by the dashed curve separately. The green dashed curve corresponds to the minor Gaussian component centered at $\mu_1 = 39.21 \pm 0.96$, with a dispersion of $\sigma_1 = 1.29 \pm 0.37$. The orange dashed curve corresponds to the major Gaussian component centered at $\mu_2 = 40.35 \pm 0.07$, with a dispersion of $\sigma_2 = 0.69 \pm 0.13$ .
• Figure 5: Left panel: the fluence distribution of non-repeating FRBs with a bin ratio of 1.3. Blue dots correspond to original unfiltered full sample with $\mathrm {N} = 461$ events, and red dots correspond to filtered sample with $\mathrm {N}=415$ bursts. A best-fit curve engaging a three-segment power-law function is also plotted for the histogram correspondingly. Right panel: variation of $\alpha_1$,$\alpha_2$, and $\alpha_3$ with respect to the bin ratio.