Luminosity Function Of Fast Radio Bursts And The Problem Of Their Physical Origi

Fast Radio bursts(FRBs)are exceptionally luminous transient radio pulses of unexplained physical origin with short durations.There have been hundreds of FRBs reported,among which most are one-off events and only 25 are identified as repeaters,and according to the observations.Therefore,the FRBs can be divided into non-repeating FRBs and repeating FRBs(an FRB is recognized as a repeating FRBs if a second burst has been detected in the same position of the sky).In this paper,we collect a sample of 21 repeating FRBs and 571 non-repeating FRBs detected by different radio instruments before September 2021.Using the Anderson-Darling test,we compare the distributions of extra-Galactic dispersion measure(DME)of repeating,non-repeating and all FRBs.It is found that the DME values of two sub-samples are lognormally distributed and we notice that the distribution of DME for non-repeating samples is not lognormally distributed.The DME of repeaters and non-repeaters are drawn from the different distribution on basis of the Mann-Whitney-Wilcoxon test.In addition,assuming the repeating FRBs to be universal and representative,one can utilize the averaged fluence of repeating FRBs as an indication to derive an apparent Intensity Distribution Function(IDF)with a power-law index of α=1.10±0.14,which is good in agreement with the previous IDF of 16 non-repeating FRBs found by Li et al.(2017)[1].According to the intensity distribution function,we predict that the Five-hundred-meter Aperture Spherical radio Telescope(FAST)as the largest single dish will detect about 3±1 repeating FRBs within a duty circle of 1000 hours.Based on the above statistics of repeating and nonrepeating FRBs,we propose that both types of FRBs may have different cosmological origin,spatial distribution and circum-burst environments.Interestingly,the differential luminosity distributions of repeating and non-repeating FRBs can also be well described by a broken power-law function with the same power-law index of-1.4.The physical origin of FRBs remains unknown.The research on the intrinsic redshift distribution and energy function might help us to reveal the potential origins of FRBs.Using large samples of FRBs from the first CHIME/FRB catalog,we apply LyndenBell’s C-method to study the redshif’t distribution,formation rate and energy function of FRBs.We parametrise the strongly redshift evolution of the FRB energy as E(z)=E0(1+z)k,where z is the burst redshift,and we derive k=5.23 using the nonparametricτ statistics method.After removing redshift evolution,the local energy function being given by Ψ(E0)∝ E0-0.38±0.01 for dim segment and Ψ(E0)∝ E0-2.01±0.12 for bright segment.For CHIME sample,we find that the formation rate evolves is p(z)=(1+z)-4.62±1.00 for z<0.84 and ρ(z)=(1+z)-3.74±0.67 for z≥0.84,the local formation rate of FRBs is about 8.56 × 103 Gpc-1yr-1.We also found the formation rate evolves much faster than the star formation rate up to z～0.43,and the formation rate declines rapidly at all redshift ranges,which is dramatically different from the star formation rate.As a result,we suggest that FRBs are most probably originated from the old populations(such as old neutron stars and black holes).