Implications from ASKAP Fast Radio Burst Statistics

Abstract

Although there has recently been tremendous progress in studies of fast radio bursts (FRBs), the nature of their progenitors remains a mystery. We study the fluence and dispersion measure (DM) distributions of the ASKAP sample to better understand their energetics and statistics. We first consider a simplified model of a power-law volumetric rate per unit isotropic energy dN/dE ∝ E −γ with a maximum energy E max in a uniform Euclidean Universe. This provides analytic insights for what can be learnt from these distributions. We find that the observed cumulative DM distribution scales as N (> DM) ∝ DM 5−2γ (for γ > 1) until a maximum DM max above which bursts near E max fall below the fluence threshold of a given telescope. Comparing this model with the observed fluence and DM distributions, we find a reasonable fit for γ ∼ 1.7 and E max ∼ 10 33 erg Hz −1 . We then carry out a full Bayesian analysis based on a Schechter rate function with cosmological factor. We find roughly consistent results with our analytical approach, although with large errors on the inferred parameters due to the small sample size. The power-law index and the maximum energy are constrained to be γ 1.6 ± 0.3 and logE max [erg Hz −1 ] 34.1 +1.1 −0.7 (68% confidence), respectively. From the survey exposure time, we further infer a cumulative local volumetric rate of logN (E > 10 32 erg Hz −1 ) [Gpc −3 yr −1 ] 2.6 ± 0.4 (68% confidence). The methods presented here will be useful for the much larger FRB samples expected in the near future to study their distributions, energetics, and rates.

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

“…For the other threshold luminosities, such as 10 43 and 10 44 erg s −1 , our measurements give the event rate densities as 5.0 +3.2 −2.3 × 10 3 and 3.7 +3.5 −2.0 × 10 2 Gpc −3 yr −1 , respectively. In particular, our measured volumetric rate distribution is identical with the energy function derived by Lu & Piro (2019) from 10 31 to 10 32 erg Hz −1 based on 20 ASKAP FRBs.…”

STARE2: Detecting Fast Radio Bursts in the Milky Way

“…It is, however, difficult to make a prediction for the rate of Galactic FRBs given the considerable amount of uncertainty in the FRB luminosity function. Lu & Piro (2019) analyzed a sample of FRBs and found that the number of FRBs above a given energy, N FRB (> E), follows a power law distribution of index −0.7, with a cutoff above ∼ 10 34 ergs Hz −1 . Lu & Piro (2019) also constrained the volumetric rate of FRBs to > 1.1 × 10 3 Gpc −3 yr −1 above 10 32 ergs Hz −1 .…”

“…Lu & Piro (2019) analyzed a sample of FRBs and found that the number of FRBs above a given energy, N FRB (> E), follows a power law distribution of index −0.7, with a cutoff above ∼ 10 34 ergs Hz −1 . Lu & Piro (2019) also constrained the volumetric rate of FRBs to > 1.1 × 10 3 Gpc −3 yr −1 above 10 32 ergs Hz −1 . We note this rate is a lower limit due to incompleteness of the ASKAP sample and contributions to the DM from the host galaxy and circumgalactic medium of the Milky Way that were not taken into account.…”

“…Using equations 1 and 2, assuming a volumetric rate of FRBs of 10 3 Gpc −3 yr −1 above 10 35 erg s −1 Hz −1 , and assuming the luminosity function given by Lu & Piro (2019), we can infer how far down the luminosity function we must extrapolate such that the rate of FRBs in the Milky Way is ∼ 1 yr −1 . We find that regardless of whether FRBs track stellar mass or star formation, the FRB rate in the Milky Way should be above ∼ 1 yr −1 for FRBs with energy greater than ∼ 10 29 Φ 1.4 3 erg s −1 Hz −1 , where Φ 3 is ΦFRB(>10 35 ergs s −1 Hz − 1) 10 4 Gpc −3 yr −1 .…”

Radiation forces constrain the FRB mechanism

“…The maser model yields no solution for FRB luminosity > ∼ 10 44 erg s −1 when the acceleration of upstream particles by IC scatterings shuts off the maser mechanism in less than 1 ms unless we consider the luminosity of the relativistic jet Lj > ∼ 10 51 erg s −1 ; Lj scales linearly with the FRB radio luminosity. We note that the analysis of ASKAP sample of bursts shows that there are FRBs with luminosity as high as ∼ 10 46 erg s −1 (Lu & Piro, 2019).…”