Luminosity distribution of fast radio bursts from CHIME/FRB Catalog 1 by means of the updated Macquart relation

Abstract

Fast radio bursts (FRBs) are extremely strong radio flares lasting several micro- to milliseconds and come from unidentified objects at cosmological distances, most of which are only seen once. Based on recently published data in the CHIME/FRB Catalog 1 in the frequency bands 400–800 MHz, we analyze 125 apparently singular FRBs with low dispersion measure (DM) and find that the distribution of their luminosity follows a lognormal form according to statistical tests. In our luminosity measurement, the FRB distance is estimated by using the Macquart relation that was obtained for 8 localized FRBs, and we find it still applicable for 18 sources after adding the latest 10 new localized FRBs. In addition, we test the validity of the luminosity distribution up to the Macquart relation and find that the lognormal-form feature decreases as the uncertainty increases. Moreover, we compare the luminosity of these apparent nonrepeaters with that of the previously observed 10 repeating FRBs also at low DM, noting that they belong to different lognormal distributions with the mean luminosity of nonrepeaters being two times greater than that of repeaters. Therefore, from the two different lognormal distributions, different mechanisms for FRBs can be implied.

Appendices

Appendix A: Verification of the Macquart relation with updated 18 localized FRBs

When the Macquart relation was given, only 8 localized FRBs were considered. Now, we add the newly localized 10 FRBs, and a total of 18 data points are taken into account to verify the Macquart relation. Since the M81 is too close to us (Bhardwaj et al. 2021), FRB 20200120E is not listed in the above 18 data. The fitted line of 18 data is given, with the goodness of fit as 0.75. As shown in Fig. 5, our fitted line (solid) is almost parallel to that of the Macqurat relation (dashed), and the deviation of two slopes is less than 6%. This indicates that the DM-z relation is still valid, at least for the case that z is less than 0.7. While the obvious difference between the two lines is reflected as a fact that our fitting has an intercept value of 84.43 pc cm⁻³ with the vertical axis. A possible reason for this gap is that the different DM data have been used. Our $\mathrm{DM}_{\mathrm{excess}}$ contains the $\mathrm{DM_{host}}$ and $\mathrm{DM}_{\mathrm{sur}}$, but the $\mathrm{DM}_{\mathrm{cosmic}}$ in the Macquart relation does not. Meanwhile, the contribution of the Milk Way galaxy halo is not considered in our analysis either. Therefore, the gap value of $84.43~\text{pc} \, \mbox{cm}^{-3}$ may infer the DM in the host galaxy, surrounding medium, halo, or both of them.

Appendix B: Analysis of full DM data

Under our data selection, we only analyze the repeaters and nonrepeaters at low DM in the main text, so we discuss the full data here, including FRBs at both high and low DM. Same as the above, we test lognormal feature for these data under K–S, Lilliefors, and A–D tests in Table 4. The results are consistent with the low DM data. Meanwhile, the goodness of fit, K–S, and M–W–W tests are also applied on the fitted curves, and the results are shown in Table 5 that further support the lognormal distribution of luminosity for nonrepeaters.

Table 4 Statistical test results of lognormal distribution for repeaters and nonrepeaters for full DM

Table 5 Statistical test results of different luminosity distribution for all nonrepeaters

Besides that, we plot full DM data in Fig. 6 to compare whether repeaters and nonrepeaters have the same distribution with mean values of the two samples (repeaters: $1.23\times 10^{44}~\mbox{erg}\,\mbox{s}^{-1}$, nonrepeater: $5.48\times 10^{44}~\mbox{erg}\,\mbox{s}^{-1}$). Although the repeaters and nonrepeaters still show the different distributions ($p_{ks}=6.17\times 10^{-4}$ and $p_{mww}=5.70\times 10^{-5}$) as in the case of low DM selection, the mean values of all data are inconsistent with the data at low DM, indicating that the high and low DM may be different. Furthermore, the maximum and minimum luminosity of nonrepeaters is $8.00\times 10^{45}~\text{erg}\, \mbox{s}^{-1}$ and $6.83\times 10^{42}~\text{erg}\, \mbox{s}^{-1}$, respectively, which has a wider distribution range than the sample at low DM. Therefore, these imply that the reasons for these differences are possibly the observational effects, data-processing methods, or even their intrinsic physical properties, and we need further study to answer these puzzles.

Fig. 6

The distinction for all repeaters and nonrepeaters (both low- and high-dispersion measure (DM)) in the aspect of luminosity. The top panel (subfigure a) is the CDF of repeaters and nonrepeaters for luminosity. The dashed (solid) line is for repeaters (nonrepeaters). The bottom panel (subfigure b) is the histogram of luminosity for two samples. The crosshatched (empty) histogram means the repeaters (nonrepeaters). The dashed (solid) line represents the mean value of repeaters (nonrepeaters)

Overall, no matter whether we use the low DM or full DM data, it does not impact our main conclusions on the luminosity distribution form of nonrepeaters, which is that the lognormal type is better for describing them.