On the FRB luminosity function – – II. Event rate density

Abstract

The luminosity function of Fast Radio Bursts (FRBs), defined as the event rate per unit cosmic co-moving volume per unit luminosity, may help to reveal the possible origins of FRBs and design the optimal searching strategy. With the Bayesian modelling, we measure the FRB luminosity function using 46 known FRBs. Our Bayesian framework self-consistently models the selection effects, including the survey sensitivity, the telescope beam response, and the electron distributions from Milky Way / the host galaxy / local environment of FRBs. Different from the previous companion paper, we pay attention to the FRB event rate density and model the event counts of FRB surveys based on the Poisson statistics. Assuming a Schechter luminosity function form, we infer (at the 95% confidence level) that the characteristic FRB event rate density at the upper cut-off luminosity L * = 2.9 +11.9 −1.7 × 10 44 erg s −1 is φ * = 339 +1074 −313 Gpc −3 yr −1 , the power-law index is α = −1.79 +0.31 −0.35 , and the lower cut-off luminosity is L 0 ≤ 9.1 × 10 41 erg s −1 . The event rate density of FRBs is found to be 3.5 +5.7 −2.4 × 10 4 Gpc −3 yr −1 above 10 42 erg s −1 , 5.0 +3.2 −2.3 × 10 3 Gpc −3 yr −1 above 10 43 erg s −1 , and 3.7 +3.5 −2.0 × 10 2 Gpc −3 yr −1 above 10 44 erg s −1 . As a result, we find that, for searches conducted at 1.4 GHz, the optimal diameter of single-dish radio telescopes to detect FRBs is 30-40 m. The possible astrophysical implications of the measured event rate density are also discussed in the current paper.

A Bimodal Burst Energy Distribution of a Repeating Fast Radio Burst Source

“…where N 1 is normalization constant, and N ev is the total number of bursts included. For 3 × 10 38 ≤ E ≤ 8 × 10 39 erg, the energy function is consistent with a power law with α E = 1.37 ± 0.18, consistent with the results obtained from the ASKAP sample and all the bursts from the FRB catalog 8,11,[36][37][38] . A bimodal distribution is clearly needed to properly cover the full energy range.…”

“…where E = 0 for E < 10 38 erg and E = 1 for E > 10 38 . The characteristic energy E 0 is determined The grey shaded bars denote days without observations of the source.…”

A Fast Radio Burst Discovered in FAST Drift Scan Survey

“…FAST's sensitivity makes it one of the most effective telescope at detecting FRBs from high redshift, therefore its FRB detection rate is an important observable. Li et al (2017) predicted that the FRB detection rate for the FAST 19-beam would be 5±2 detections per 1000 hr, based on an all-sky event rate of 3×10 4 day −1 that crosses an energy threshold of 0.03 Jy ms. From a different approach, by measuring the event rate density of the luminosity function presented in Luo et al (2018Luo et al ( , 2020 predicted an all-sky event rate of 10 4 -10 5 day −1 for events with flux higher than 5 mJy, which correspond to 1.5-15 events per 1000 hr given the field of view of the FAST 19-beam. With one detection of FRB 181123, we can place a lower bound of 0.034 event per 1000 hour, which can be translated to an all-sky rate of >9×10 2 day −1 .…”

“…More detections may be made in the same data set we used and the true event rate density may be better constrained to a (much) higher value than our limit. This could lead to better constraints on the event rate density of energetic events (Luo et al 2020), giving tighter constraints on the consistency with the compact star merger models (see also Wang et al 2020). FAST is a very sensitive telescope.…”

“…Considering that our search system does not have a 100% recall rate, no upper bound can be set. Due to small number statistics, the lower limit of k>0.034 event per 1000 hr is not yet constraining to most theoretical predictions (Li et al 2017;Luo et al 2018Luo et al , 2020.…”