Study On The Relationship Between The Event Rate Of Gamma-ray Bursts And The Star Formation Rat

It is generally agreed that long-duration Gamma-Ray Bursts(l GRBs)originate from the collapse of massive stars,while short-duration GRBs(s GRBs)originate from the merger of two compact stars.The l GRBs are usually applied as a good tracer of star formation.Many researches have used different methods to study the event rate of different l GRB samples and the relationship between them and the star formation rate(SFR)from multiple aspects.The results are different and controversial,especially at low redshift.This paper mainly focuses on how to use of two completely different methods to calculate the event rate of l GRBs with different redshift completeness and compare with the SFR.At the same time,we want to verify whether the low-redshift excess of GRB rate is caused by the sample size,the sample completeness or the detection threshold.The most important thing is to explore if the excess of GRB rate compared with the SFR at low redshift is caused by low-luminosity bursts(LL-GRBs).We firstly use the non-parametric methods to calculate the luminosity function and event rates for different GRB samples and checkout the dependence on the criteria of sample selection and detection threshold.Using the evolution relationship of luminosity with redshift L(?)(1+z)~kwith a diverse k,we found that the cumulative distributions of non-evolving luminosities either or redshifts are determined by the sample selection rather than the instrumental sensitivity.Importantly,all event rates show excess of Gaussian profile instead of monotonous decline no matter whether the sample is complete.Therefore,we predict that two types of l GRBs are favored.Second,we choose three Swift long burst samples and classify them into low-and high-luminosity bursts(HL-GRBs).We still adopt the non-parametric method to study the event rate of the two types of l GRBs in each sample and found that the HL-GRBs event rates are consistent with the SFR within the whole redshift range while the event rates of LL-GRBs exceed the SFR at low redshift of z(27)1.Therefore,we believe that the excess at low redshift is caused by LL-GRBs regardless of the sample size and the redshift completeness and its origin may be unrelated to the formation of massive stars.At the same time,we use traditional methods to recalculate the event rates of l GRBs.The results still show that the event rate of LL-GRBs at the low redshift exceed the SFR but that of HL-GRBs are consistent with the whole redshift range of SFR.It is again verified that the excess of event rate at low redshift is caused by the LL-GRBs,which indicates that the HL-and the LL-GRBs have different physical origins and provide new clues for the study of the progenitor of GRBs and their central engines.